The primary purpose of this research article is to study the famous K$\ddot{o}$the's Conjecture for the special cases - when a ring $\mathfrak{R}$ is commutative, and when $\mathfrak{R}$ is an Algebra over a field. Furthermore, some open problems involving tensor product of Algebras over a field has also been discussed extensively along with their proofs. Subsequently, an equivelent statement of K$\ddot{o}$the's problem in terms of algebra of matrices has been established.

Build a special identical equation, use its calculation characters to prove and search for solution of any odd converging to 1 equation through (*3+1)/2^k operation, change the operation to (*3+2^m-1)/2^k, and get a solution for this equation, give a specific example to verify. Thus prove the Collatz Conjecture is true. Furthermore, analysis the sequences produced by iteration calculation during the procedure of searching for solution, build a weight function model, prove it decrease progressively to 0, build a complement weight function model, prove it increase to its convergence state. Build a (*3+2^m-1)/2^k odd tree, prove if odd in (*3+2^m-1)/2^k long huge odd sequence can not converge, the sequence must outstep the boundary of the tree after infinite steps of (*3+2^m-1)/2^k operation.

It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

This article is a study on the (k,s)-Riemann-Liouville fractional integral, a generalization of the Riemann-Liouville fractional integral. Firstly, we introduce several properties of the extended integral of continuous functions. Furthermore, we make the estimation of the Box dimension of the graph of continuous functions after the extended integral. It presents that the upper Box dimension of the (k,s)-Riemann-Liouville fractional integral for any continuous functions is no more than the upper Box dimension of the functions on the unit interval I=[0,1], which indicates that the upper Box dimension of the integrand f(x) will not be increased by the σ-order (k,s)-Riemann-Liouville fractional integral ksD−σf(x) where σ>0 on I. Additionally, we prove that the fractal dimension of ksD−σf(x) of one-dimensional continuous functions f(x) is still one.

In this paper we study a conjecture proposed by P.Duxbury , C.laror , L.Leduino de Salles Neto in 2021\cite{conjecture} on the Golumb Ruler Problem which is a classical optimization model in discrete case . In \cite{conjecture} the authors constucted a continuous model for the Golumb Ruler Problem associated to the discrete case and conjectured that the optimal value of both cases are equal . We deal with this conjecture via algebraic geometrical methods .

For the solution existence condition of the Navier-Stokes equation, we propose a conjecture as follows: "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

A simple protocol for preparation of O-acylated enol form - (R/S)-ethyl-2-acetoxy-4-phenyl-4H-chromene-3-carboxylate 5 was presented. The compound was characterized by 1H-, 13C-and DEPT135 NMR spectra, including {1H,1H} COSY, {1H,13C} HSQC, {1H,13C} HMBC and 2D-NOESY spectra. The preferred regioselectivity for O-acylation of 3,4-dihydrocoumarin 5 in the presence of substituent in 4-th position in the chroman ring and accounting the steric hindrance of the ester group in 3-th place was confirmed.

The question of what generates conscious experience has mesmerized thinkers since the dawn of humanity, yet its origins remain a mystery. The topic of consciousness has gained traction in recent years, thanks to the development of large language models that now arguably pass the Turing test, an operational test for intelligence. However, intelligence and consciousness are not related in obvious ways, as anyone who suffers from a bad toothache can attest - pain generates intense feelings and absorbs all our conscious awareness yet nothing particularly intelligent is going on. Still, in the hard sciences, this topic is frequently met with skepticism because to date no protocol to measure the content or intensity of conscious experiences in an observer-independent manner has been agreed upon. Here we present a novel proposal: Conscious experience arises whenever a quantum mechanical superposition forms. Our proposal has several implications: First, it suggests that the structure of the superposition determines the qualia of the experience. Second, quantum entanglement naturally solves the binding problem, ensuring the unity of phenomenal experience. Finally, a moment of agency may coincide with the formation of a superposition state. We outline a research program to experimentally test our conjecture via a sequence of quantum biology experiments. Applying these ideas opens up the possibility of expanding human experience through brain-quantum computer interfaces.

(1) Background: Plasmodium vivax causes the largest malaria burden in Brazil, and chloroquine resistance poses a challenge to eliminating malaria by 2035. Illegal mining in the Roraima Yanomami indigenous territory can lead to the introduction of resistant parasites. This study aimed to investigate mutations in the pvcrt-o and pvmdr-1 genes to determine their potential as predictors of P. vivax chloroquine-resistant phenotypes. (2) Methods: Samples were collected in two health centers of Boa Vista. A questionnaire was completed, and blood was drawn from each patient. Then, DNA extraction, PCR, amplicon purification, and DNA sequencing were performed. After alignment with the Sal-1, the amplified fragment was analyzed. Patients infected with the mutant parasites were queried in the Surveillance Information System. (3) Results: 98% (157/164) of participants were from illegal mining areas. The pvcrt-o was sequenced in 151 samples, and the K10 insertion was identified in 13% of them. The pvmdr1 was sequenced in 80 samples: the MYF haplotype (958M) was detected in 92% of them, the TYF in 8%, while MYL was absent. No cases of recrudescence, hospitalization, or death were found. (4) Conclusions: Mutations in the pvcrt-o and pvmdr-1 genes have no potential to predict chloroquine resistance in P. vivax.

We use binary string to represent a natural number and show the composite procedure of odd-number and even-number functions, thus we propose full binary directed tree to represent the set of natural numbers and give another partition the natural number set to three sets: pure odd, pure even and mixed number. For the Collatz conjecture we make use of the parity of a natural number to analyse the sequence of iteration (or composite) of Collatz function and reduced Collatz function analog to the inverse function. We give tabular and binary strings to the algebra expression to state the sequence of Collatz, this is the key topic to proof the conjecture: the discrete powers of 2 can be changed to ultimately continuous powers of 2, finally get to pure even number and to the smallest number 1. The sequence created by the infinite iterations of the Collatz function becomes the ultimately periodic sequence if any natural number is the beginning value, proving the conjecture that has been held for 87 years.

Here we analyze three well-known conjectures: (i) the existence of infinitely-many twin primes, (ii) Goldbach’s strong conjecture, and (iii) Polignac’s conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of the Goldbach’s strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac’s conjecture. Our first step is an analysis of the existence of infinitely-many twin primes numbers. For this, using the formula 4((n−1)!+1) ≡ −n (mod n(n + 2)) – satisfied if and only if (n, n + 2) are twin primes –, together with Wilson’s theorem, we obtain conditions that must be met for two numbers to be twin primes. Our results, obtained from an analytic and functional study, lead us to conclude that there may exist infinitely-many twin primes. Next, we consider the validity of the Goldbach’s strong conjecture. After showing that the conjecture is true for the first even numbers, we notice a pattern that we analyze for any even number, reducing it to three cases: (i) when the even number 2n is two times a prime number n; (ii) when the even number 2n is such that n = 2m, with 2m − 1 and 2m + 1 twin primes; (iii) all other cases, i.e., for any 2n even number ∀n ∈ N with n > 1, n prime or not, with independence of n = 2m being 2m−1 and 2m+1 twin primes or not. In this last case we show that one can always find a certain r ∈ N such that 1 < r < n satisfying that n−r and n+r are primes, so that their sum is 2n. In this case we use the reduction to absurd method, and our results lead us to conclude that Goldbach’s strong conjecture is true to the best of our calculations, as well as the Polignac’s conjecture.

The Shimensi super-large tungsten polymetallic deposit is located in Late Jurassic- Early Cretaceous Porphyry-Skarn tungsten ore belt in the south Yangtze metallogenic belt. There are 3 types of mineralization: veinlet-disseminated type, thick quartze vein type and hydrothermal crypto-explosive breccia type. Based on geological studies, this paper presents new petrographic, microthermometric, laser Raman spectroscopic and hydrogen and oxygen isotope research of the fluid inclusions from the deposit. The results show that there are five different types of fluid inclusions: liquid-rich inclusions, vapor-rich inclusions, pure liquid inclusions, pure vapor inclusions, and fluid inclusions containing a solid crystal. The homogenization temperatures of the fluid inclusion range from 140℃-270℃, the salinities are 3%-5% NaCleq and the densities of ore-forming fluid range from 0.64 g/cm3 to 0.99 g/cm3. For the analyses of Laser Raman spectroscopic, the ore-forming fluids can be approximated by a Ca2+-Na+-SO42--Cl- fluid system with small amount of CO2, CH4 and N2. Otherwise, the datas of the pressure, pH and Eh show a fluid metallogenic environment of low pressure, weak acid and weak reduction. The values of the homogenization temperature in 3 types of orebodies suggest that the mineralization is characterized by the decrease of the temperature under the condition of the fluid immiscibility. The H-O isotope values are interpreted to indicate that the ore-forming fluids are mainly composed of magmatic water, and also the meteoric water was added with the process of the magma rising.

In this paper, a short survey of the existed results concerning the Jacobian Conjecture is first given. Then the 3-fold linear type polynomial map will be analyzed in detail. The expansion of the Jacobian condition is deduced to obtain its equivalent algebraic equations, and the Jacobian condition will be analyzed to derive two coordinate transformations that can maintain the invariance of the Jacobian condition. Finally, it is proved by mathematical induction method that one general chain expression presented in this paper is just the inverse polynomial map of 3-fold linear type polynomial map, i.e. LJC(n,[3]) holds such that the Jacobian Conjecture holds.

The α-synucleinopathies are a group of neurodegenerative diseases characterized by the deposition of α-synuclein aggregates (α-syn) in the brain. Currently, there is no suitable tracer to enable a definitive early diagnosis of these diseases. We reported candidates based on 4,4'-disarylbisthiazole (DABTA) scaffold with a high affinity towards α-syn and excellent selectivity over Aβ and tau fibrils. Based on prior in silico studies a focused library of 23 halide-containing and O-methylated DABTAs was prepared. The DABTAs were synthesized via a modified two-step Hantzsch thiazole synthesis, characterized, and used in competitive binding assays against [3H]PiB, and [3H]DCVJ. The DABTAs gave an overall chemical yield of 15 – 71%, with a calculated lipophilicity of 2.5 – 5.7. The ligands demonstrated an excellent affinity to α-syn with both [3H]PiB and [3H]DCVJ: Ki 0.1 – 4.9 nM and up to 20 – 3900-fold selectivity over Aβ and tau fibrils. It could be concluded that in-silico simulation is useful for the rational design of a new generation of DABTAs. Further investigation of the leads in the next step is encouraged: radiolabeling of the ligands with radioisotopes such as fluorine-18 or carbon-11 for in vivo, ex vivo and translational research and for further in vitro experiments on human-derived protein aggregates.

In this article, we present solutions for one of the oldest mathematical problems, the Collatz Conjecture, and provide a proof for the Riemann Hypothesis, utilizing a new number theory based on newly discovered number properties, which will also be presented in this paper. This is made possible through the Sophy-Peter mathematical framework, built upon this new number theory. The Collatz Conjecture will be disproven, but as an alternative, the Oscillating Theorem will be introduced, with its correctness proven within this article. Furthermore, we present the general version of the Riemann zeta function, developed based on the new number theory. The correctness of this function is verified by comparing it with existing results of the zeta function. Using this approach and the Sophy-Peter framework, we have successfully proven the Riemann Hypothesis, long considered a millennium problem. Moreover, since the general zeta function is proven, this implies the correctness of the new number theory and the Sophy-Peter framework.

Geographic Information Systems (GIS) played an important role in understanding the dynamics of the territorial spread of COVID-19 during the pandemic. Even today, it is important to understand such dynamics in view of the imminent risk of new epidemics and pandemics. This study aimed to identify space-time clusters of incidence and mortality due to COVID-19 during the pandemic, analyzing socioeconomic and demographic characteristics in order to highlight the priority areas for control and surveillance actions. This study was conducted in the Metropolitan Region of São Paulo (MRSP) from March 2020 to February 2022. To detect the clusters, a multidimensional punctual process was created to perform multiple tests for every geographic point using the SaTScan™ software. Socioeconomic and demographic differences were analyzed using nonparametric Mann-Whitney and Kruskal-Wallis tests. High-risk clusters of incidences were observed in May 2020 (RR=2; p-value <0.001) and March to June 2021 (RR=2.6; p-value <0.001) in the capital of São Paulo and neighboring municipalities, with statistically significant differences between the socioeconomic variables analyzed. No low-risk cluster of COVID-19 incidence was found, but low-risk clusters of mortality from COVID-19 were found in the period from July to December 2020 in the central region of the capital (RR=0.33; p-value <0.001), which concentrates the highest incomes and the lowest percentages of Black, Brown (Mixed-race), and Indigenous people in the MRSP.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

The effects of shade netting on the morphological and chemical composition (organic acids, sugars, total polyphenols, total and certain anthocyanins, proanthocyanidins) and in vitro antioxidant activity of raspberries and blackberries was conducted in the southeastern region of the Republic of North Macedonia. HPLC analysis confirmed a significant effect of shading nets on the amount of the most dominant anthocyanin in blackberries and raspberries. The amount of cyanidin-3-O-glucoside in blackberries covered with shading nets was significantly higher in comparison to the amount of the same anthocyanins in uncovered blackberries. The same tendency was observed for cyanidin-3-O-sophoroside for covered and uncovered raspberries from 2023. However, an opposite relationship was noticed for total anthocyanin content in favor of uncovered blackberry and raspberry from 2023. From all examined organic acids, the amount of acetic acid was the most affected in covered raspberries. The shade netting had a significant influence on polyphenolic content (such as high molecular proanthocyanidins, total and particular anthocyanins), the amounts of sugars (glucose and fructose), and organic acids as well as the intensity of color in blackberry and raspberry. Although net shading significantly influenced particular phenolic compounds presented in examined berry fruits, antioxidant activity was weakly correlated to this environmental change.

Mangrove plant seedling cultivation is crucial for the protection, management and restoration of mangrove ecosystem. In this study, we focused on Kandelia obovata, a typical mangrove, and evaluated nursery cultivation with different combinations of three salinity levels (S1: 0 ppt, S2: 10 ppt, and S3: 20 ppt), three genealogies (EZD, JX, and YZ), and five growth media (M1: 100% loess, M2: 100% sandy, M3: 50% loess + 50% sandy, M4: 40% loess + 40% sandy + 20% peat, and M5: 40% loess + 40% sandy + 20% coir), by measuring the growth parameters such as mortality rate, seedling height, diameter, and biomass partition. These growth indexes were significantly affected by salinity and medium, and genealogies also had significant effects on mortality rate and biomass accumulation. S2 or S3 both had lower mortality and higher growth indexes than S1. M1 was the medium that increased seedlings height, diameter and biomass the most and had the lowest death rate. EZD and JX were also higher levels than YZ in these indicators, but the difference between them was not obvious. S3, M1, and EZD consistently performed well in fuzzy evaluation and quality assessment. Furthermore, combinations involving these treatments also produced highly favorable results. These results furnish both a theoretical and practical foundation for advancing nursery cultivation techniques and germplasm breeding of K. obovata in mangroves.

This paper presents a biologically inspired flocking-based aggregation behaviour of a swarm of mobile robots. Aggregation behaviour is essential to many swarm systems, such as swarm robotics systems, in order to accomplish complex tasks that are impossible for a single agent. We developed a robot controller using Reynolds’ flocking rules to coordinate the movements of multiple e-puck robots during the aggregation process. To improve aggregation behaviour among these robots and address the scalability issues in current flocking-based aggregation approaches, we used a K-means algorithm to identify clusters of agents. Using the developed controller, we simulated the aggregation behaviour among the swarm of robots. Five experiments were conducted using Webots simulation software. The performance of the developed system was evaluated under a variety of environments and conditions, such as various obstacles, agent failure, different numbers of robots and arena sizes. The results of the experiments demonstrated that the proposed algorithm is robust and scalable. Moreover, we compared our proposed algorithm with another implementation of the flocking-based self-organizing aggregation behaviour based on Reynolds’ rules in a swarm of e-puck robots. Our algorithms outperformed this method in terms of cohesion performance and aggregation completion time.

This paper presents an analysis of the number of zeros in the binary representation of natural numbers. The primary method of analysis involves the use of the concept of the fractional part of a number, which naturally emerges in the determination of binary representation. This idea is grounded in the fundamental property of the Riemann zeta function, constructed using the fractional part of a number. Understanding that the ratio between the fractional and integer parts of a number, analogous to the Riemann zeta function, reflects the profound laws of numbers becomes the key insight of this work. The findings suggest a new perspective on the interrelation between elementary properties of numbers and more complex mathematical concepts, potentially opening new directions in number theory and analysis.

Carotid atherosclerotic lesions are a major cause of cerebrovascular disease (CVD). Identification and quantification of carotid plaques are important for categorizing the vulnerability of plaques for rupture and assessing the impact of treatments. The irregularity of plaque surface is associated with previous plaque rupture and plays an important role in the risk of stroke. Thus, the aim of this study is to develop and validate novel vulnerability biomarkers from three-dimensional ultrasound (3DUS) images by analyzing the surface morphological characterization of carotid plaque using fractal geometry features. 3D box-counting and 3D blanket are the two types of 3D fractal dimension that were employed to describe the smoothness of plaques. This fractal dimension analysis tool was used to evaluate the effect of atorvastatin using 3DUS carotid images, which were acquired from 6 patients treated with atorvastatin with 80 mg daily and 5 patients with placebo. The Student's T Test results showed that those two fractal features were effective for detecting the statin-related changes in carotid atherosclerosis with p<0.0068 and p<0.015 respectively, suggesting that 3D fractal dimension measurements can be used effectively to analyze the surface characteristics of carotid plaques, especially for evaluating the impact of the treatment.

Background and objectives: Chronic Kidney Disease and Mineral Bone Disorders (CKD-MBD) are frequently associated with an increased risk of both Vascular Calcifications (VCs) and bone fractures (BFs). The complex pathogenesis of VCs and BFs involves various factors such as calcium overload, phosphate imbalance, and secondary hyperparathyroidism. Key players, such as the vitamin K-dependent proteins (VKDPs) matrix Gla protein (MGP) and osteocalcin (BGP), have pivotal roles both for VCs and BFs. The Vitamin K Italian (VIKI) dialysis study, highlighted that hemodialysis patients treated with calcimimetics had higher levels of total BGP and MGP as compared to those untreated, suggesting a potential protective effect of these drugs on BFs and VCs, beyond the beneficial effect to reduce PTH levels. Methods: ETERNITY-ITA is a multi-center, comparative effectiveness, observational, longitudinal study that will enroll 160 hemodialysis patients (80 patients treated with Etelcalcetide and 80 age and sex-matched patients treated with Calcitriol or vitamin D analogs). Nephrologists will tailor the target dose of Etelcalcetide on individual level to achieve the KDIGO PTH target. In the Etelcalcetide-treated group, the addition of calcitriol will be allowed when required by clinical practice (for correction of hypocalcemia). Conclusion: The study will evaluate the real-world effect of Etelcalcetide on VKDP levels, such as BGP and MGP, at 3, 9, and 18 months from baseline. The resulting preservation of vascular and bone health will be assessed for the first time by examining aortic and iliac artery calcifications and vertebral fractures, respectively. Keywords: bone fractures; etecalcetide; hemodialysis; vascular calcification; vitamin K

Predicting the outcome of a future game between two National Basketball Association (NBA) teams poses a challenging problem of interest to statistical scientists as well as the general public. In this article, we formalize the problem of predicting the game results as a classification problem and apply the principle of maximum entropy to construct NBA maximum entropy (NBAME) model that fits to discrete statistics for NBA games, and then predict the outcomes of NBA playoffs by the NBAME model. The best NBAME model is able to correctly predict the winning team 74.4 percent of the time as compared to some other machine learning algorithms which is correct 69.3 percent of the time.

The combination of several therapeutic strategies is often seen as a good way to decrease the resistance rates, since bacteria overcome better single-drug treatments than multi-drug ones. This strategy is especially attractive when several targets and subpopulations are affected, as it is the case of Klebsiella pneumoniae persister cells, a subpopulation of bacteria able to transiently survive antibiotic exposures. This work aims to evaluate the potential of a repurposed anticancer drug, mitomycin C, combined with the K. pneumoniae lytic phage vB_KpnM-VAC13 in vitro and the safety in an in vivo murine model against two clinical isolates of this pathogen, one of them exhibiting an imipenem-persister phenotype. At the same time, we verified the absence of toxicity of mitomycin C at the concentration using the human chondrocyte cell line T/C28a2. The viability of these human cells was checked both by cytotoxicity assays and flow cytometry.

In Indonesia, types of meat are still identified manually due to increasing prices for beef and buf-falo ahead of Idul Fitri. Traders mix beef with pork to thwart the beef scam. Haar wavelet and GLCM, GLCM with angles of 0°, 45°, 90°, and 135°, as well as matrices using contrast, correlation, energy, homogeneity, and entropy, are used in feature extraction. The following are the results of meat image classification testing using k-NN, Haar wavelet, and GLCM: The k-NN algorithm shows superiority in identifying fresh (99%), frozen (99%), and rotten (96%) meat texture images with the most fantastic accuracy results in every situation. Meanwhile, GLCM routinely provides good results, especially regarding the texture image of fresh meat (183.21) and rotten meat (115.79). However, despite delivering less throughput than k-NN and GLCM, Haar wavelets are still helpful, especially when dealing with fresh meat texture images (89,96).

Let a,b,c be positive integers such that a²+b²=c², 2|b,gcd(a,b)=1. In 1956, Jesmanowicz conjectured that for any positive integer w, the only solution of (aw)^x+(bw)^y=(cw)^z in positive integers is (x, y, z) = (2, 2, 2). In this paper, based on Gaussian integer ring, we show that Je$\acute{s}$manowicz' conjecture is true for any positive integer

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

In this paper we present two ways to solve the Jacobian conjecture. The first way is an equivalent statement to the Jacobian conjecture using idempotent ideals. The second way is to use an equivalent thesis to the thesis of the Jacobian conjecture. In both cases we will show that the Jacobian conjecture is true.

This paper asserts that the falsity of Goldbach Conjecture results in the breakdown of Trichotomy Law. Assuming that Goldbach Conjecture breaks down at an even integer 2n, where n ≥ 3, we note that the differences of 2n with the odd primes in the interval (1, n) are composite integers. We form a product δ of the collection of the least prime factors of these composite integers. We show that for a base case this product breaks Trichotomy Law. With the inductive hypothesis that such is the case with 2n, we prove that for all even integers the breakdown of Goldbach Conjecture entails the breakdown of Trichotomy Law.

The Marun-Keu complex plays a significant role in understanding the geological evolution of the Ural orogen; however, it remains poorly understood. This study aims to provide insights into the complex's age, protolith composition, rock formation conditions, and its position in the region's history. The zircons from the host granitic gneisses are characterized by magmatic cores with an age of 470 Ma and metamorphic rims with an age of approximately 370 Ma. We suggest that the metamorphic rims were formed during eclogite metamorphism and that the metagranitoids hosting the eclogites experienced eclogite metamorphism simultaneously with the basic and ultrabasic rocks that are common in this area. Heterogeneous zircons were also isolated from the selvage of a pegmatite vein, in which four domains are distinguished, two to three of which can be identified within single grains, as follows: 1) igneous cores with an age of approximately 470 Ma and the geochemical characteristics of zircon crystallized in basic rocks; 2) zircons recrystallized during eclogite metamorphism with geochemical characteristics intermediate between those of the magmatic cores and true eclogitic zircon; 3) pegmatitic zircon, exhibiting the most sharply differentiated REE spectra of all four domains, characterized by a prominent positive Ce anomaly and a weakly expressed negative Eu anomaly; and 4) eclogitic zircon, observed in the form of veins and rims, superimposed in relation to the other three domains. The age of the latter three domains is within the error range and is estimated to be approximately 370 Ma. This indicates that the processes of eclogite metamorphism and the formation of pegmatites occurred at approximately the same time in the studied area.

In this article, we describe a simple procedure for evaluating the sterility of nutrient media using a shear-horizontal surface acoustic wave (SH-SAW) biosensor. We used the SH-SAW biosensor platform to monitor the time-dependent phase responses of the material for the media that binds to a monolayer of 3-mercaptopropanyl-N-hydroxy succinimide on the biosensor surface. Increases in the phase shift less than 50% of the starting phase shift recorded 180 minutes after the sterilization indicate a successful sterility test of the media. Our devices were then applied to sterility testing using a viable Escherichia coli (E. coli) K-12 solution to confirm our hypothesis. Filtered LB Broth was the negative control, and a 24-hour culture of E. coli was the positive control. Before testing, the cell solution was pelleted, the media decanted, and then replaced with a 1x phosphate-buffered saline solution (1x PBS). Since we know that the N-hydroxysuccinimide residues will bind to amine groups, only in cases where microbial species are present will the surface binding increase greater than 50%. We confirmed our hypothesis using SH-SAW biosensors and overnight E. coli cultures. The sensitivity for our 250 MHz quartz SH-SAW sensors was calculated based on the response from the E. coli K-12 solution over the linear dynamic range, which appears to be 2x10^4 – 2x10^7 CFU per ml and has a sensitivity of S = 1.655x10^5 o m2 Kg-1. The limit of detection (LOD) for these sensors was calculated to be approximately 2x10^-9 grams (g), which is estimated to be approximately 2,000 Escherichia coli (E. coli) K-12 cells. However, the sensitivity and insertion loss remained approximately unchanged before and after coating the sensor with 3,3'-Dithiobis(succinimidyl) Propionate (DSP).

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Histones display a wide variety of post-translational modifications, including acetylation, methylation, and phosphorylation. These epigenetic modifications can influence chromatin structure and function without altering the DNA sequence. Histones can also undergo post-translational O-GlcNAcylation, a rather understudied modification that plays critical roles in almost all biological processes and is added and removed by O-linked N-acetylglucosamine transferase and O-GlcNAcase, respectively. This review provides a current overview of our knowledge of how O-GlcNAcylation impacts the histone code both directly and by regulating other chromatin modifying enzymes. This highlights the pivotal emerging role of O-GlcNAcylation as an essential epigenetic marker.

Finding sustainable renewable energy sources for energy conversion and management is still an obscure topic. This paper presents a model-based simulation for an energy conversion system using piezoelectric energy harvester (PEH) technology. A dynamic mathematical model of a PEH device consists of a piezoelectric transducer, a controlled PWM rectifier, and a closed-loop buck boost converter is developed. A piezoelectric transducer converts mechanical vibrations from a wind force into an oscillating train of electrical charges. The sinewave peak-to-peak level relationship describes the changeable values of these charges, which depend on the severity of the wind vibration. The controlled PWM rectifier, in conjunction with a closed-loop buck-boost converter, converts this train of sinewave cycles into DC voltages. The control blocks of the closed-loop buck-boost converter use the perturbation and observation (P&amp;O) algorithm based on maximum power point tracking (MPPT), which adapts the operational voltage of the piezoelectric source to deliver the maximum power to load and improves the PEHS output voltage stability. A simulation program is employed to perform mathematical analysis on various wind vibration scenarios, piezoelectric sources without PWM converters, and piezoelectric vibration sources connected to a closed-loop P&amp;O converter. The crucial results of this paper demonstrate that the proposed dynamic PEHS model effectively feeds low-power electronic loads by directly adjusting the output voltage level to the set voltage, even under different vibration severity levels. As a result, the proposed PEHS dynamic model serves as a guideline for researchers in the development of self-powered sensors, which contributes to understanding sustainable energy alternatives.

Abstract: (1) Background: Surgery is the best curative option for Gastric Cancer (GC). However, morbimortality associated with surgery still a significant problem. Thus, it is essential to determine the preoperative surgical risk, to optimize outcomes in higher risk patients. (2) Methods: Patients who underwent curative gastrectomy between January 2010 and December 2013 were included, obtaining a sample of 131 patients, and the acuity of the scales understudy was evaluated. The predictive power of the scales was evaluated through calibration and discrimination. (3) Results and Conclusions: Regarding mortality, the scales demonstrated good calibration, with POSSUM and P-POSSUM obtaining the best O:E ratio. The scales presented good discrimination, with POSSUM showing the best result. Considering morbidity, the scales showed good calibration and discrimination. POSSUM and P-POSSUM seem to have potential in predicting morbidity and mortality when applied to the studied population, but there is a need for further studies in this area.

Increased nutrient withdrawal by rapidly expanding intensive cropping systems, in combination with imbalanced fertilization, is leading to potassium (K) depletion from agricultural soils in Asia. There is an urgent need to better understand the soil K-supplying capacity and K-use efficiency of crops to address this issue. Maize is increasingly being grown in rice-based systems in South Asia, particularly in Bangladesh and North East India. The high nutrient extraction, especially K, however, causes concerns for the sustainability of maize production systems in the region. The present study was designed to estimate, through a plant-based method, the magnitude, and variation in K-supplying capacity of a range of soils from the maize-growing areas and the K-use efficiency of maize in Bangladesh. Eighteen diverse soils were collected from several upazillas (or sub-districts) under 11 agro-ecological zones to examine their K-supplying capacity from the soil reserves and from K fertilization (@ 100 mg K kg-1 soil) for successive seven maize crops grown up to V10-V12 in pots inside a net house. A validation field experiment was conducted with five levels of K (0, 40, 80, 120 and 160 kg ha-1) and two fertilizer recommendations based on “Nutrient Expert for Maize-NEM” and “Maize Crop Manager-MCM” decision support tools (DSSs) in 12 farmers’ fields in Rangpur, Rajshahi and Comilla districts in Bangladesh. Grain yield and yield attributes of maize responded significantly (P < 0.001) to K fertilizer, with grain yield increase from 18 to 79% over control in all locations. Total K uptake by plants not receiving K fertilizer, considered as potential K-supplying capacity of the soil in the pot experiment, followed the order: Modhukhali >Mithapukur >Rangpur Sadar >Dinajpur Sadar >Jhinaidah Sadar >Gangachara >Binerpota >Tarash >Gopalpur >Daudkandi >Paba >Modhupur >Nawabganj Sadar >Shibganj >Birganj >Godagari >Barura >Durgapur. Likewise in the validation field experiment, the K-supplying capacity of soils was 83.5, 60.5 and 57.2 kg ha-1 in Rangpur, Rajshahi, and Comilla, respectively. Further, the order of K-supplying capacity for three sites was similar to the results from pot study confirming the applicability of results to other soils and maize-growing areas in Bangladesh and similar soils and areas across South Asia. Based on the results from pot and field experiments, we conclude that the site-specific K management using the fertilizer DSSs can be the better and more efficient K management strategy for maize.

The Source Region of the Yellow River (SRYR), renowned as the "Water Tower of the Yellow River", serves as an important water conservation domain in the upper reaches of the Yellow River, significantly influencing water resources within the basin. Based on the Weather Research and Forecasting (WRF) Model Hydrological modeling system (WRF-Hydro) model, the key variables of the atmosphere-land-hydrology coupling processes over the SRYR during the 2013 rainy season are analyzed. The investigation involves a comparative analysis between the coupled WRF-Hydro and the standalone WRF simulations, focusing on the hydrological response to the atmosphere. The results reveal that the WRF-Hydro model's proficiency in depicting streamflow variations over the SRYR, yielding a Nash Efficiency Coefficient (NSE) of 0.44 and of  0.61 during the calibration and validation periods, respectively. Compared to the standalone WRF simulations, the coupled WRF-Hydro model demonstrates enhanced performance in soil heat fluxes simulations, reducing the mean Root Mean Square Error (RMSE) of surface soil temperature by 0.96 K and soil moisture by 0.01 m\textsuperscript{\textsuperscript{3}}/m\textsuperscript{\textsuperscript{3}}. Furthermore, the coupled model adeptly captures the streamflow variation characteristics with the NSE of 0.33. This underscores the significant potential of the coupled WRF-Hydro model for delineating coupled atmosphere-land-hydrology processes in regions characterized by cold climates and intricate topography.

The blue sepal color of hydrangea is due to a metal complex anthocyanin composed of 3-O-glucosyldelphinidin (1) and an aluminum ion with the co-pigments 5-O-caffeoylquinic acid (2) and/or 5-O-p-coumaroylquinic acid (3). The three components, namely, anthocyanin, Al³⁺ and 5-O-acylquinic acids, are essential for blue color development, but the complex is unstable and only exists in aqueous solution. Furthermore, the complex did not give analyzable NMR spectra or crystals. Therefore, many trials to determine the detailed chemical structure of the hydrangea-blue complex have failed to date. Instead, via experiments mixing 1, Al³⁺ and 2 or 3 in a buffered solution at pH 4.0, we obtained the same blue solution derived from the sepals. However, the ratio was not stoichiometric but fluctuated. To determine the composition of the complex, we tried direct observation of the molecular ion of the complex using electrospray-ionization mass spectrometry. In a very low-concentration buffer solution (2.0 mM) at pH 4.0, we reproduced the hydrangea-blue color by mixing 1, 2 and Al³⁺ in ratios of 1:1:1, 1:2:1 and 1:3:1. All solution gave the same molecular ion peak at m/z = 843, indicating that the blue solution has a ratio of 1:1:1 for the complex. By using 3, the observed mass number was m/z = 827 and the ratio of 1, 3 and Al³⁺ was also 1:1:1. A mixture of 1, 3-O-caffeoylquinic acid (4) and Al³⁺ did not give any blue color but instead was purple, and the intensity of the molecular ion peak at m/z = 843 was very low. These results strongly indicate that the hydrangea blue-complex is composed of a ratio of 1:1:1 for 1, Al³⁺ and 2 or 3.

Purpose: The purpose of this study is to apply the Composite Radiographic Index modified (CRIm) in CBCT scans of patients with Medication related osteonecrosis of the jaws (MRONJ) in order to detect its validity, and corelate the radiologic findings with the clinical staging of the disease. Methods: This study included 43 patients with MRONJ diagnosis and CBCT scans performed in the School of Dentistry and approved by the Research Ethics Committee. Clinical staging for every patient (0-3) was provided according to AAOMS 2022 guidelines. In cases of patients with both jaws affected, each jaw was evaluated independently resulting to 52 CBCT scans. The 52 CBCT scans were assessed under standardized viewing conditions by 2 observers who evaluated independently the following 8 radiologic features: lytic changes, sclerosis, periosteal reaction, sequestration, non-healing extraction sockets and other findings (sinus implication, inferior alveolar canal involvement, jaw fracture). The CRIm index was constructed to assess the extent of osseous changes. The radiologic features were scored as absent (0), localized/single (1), extensive/multiple (2), yielding a theoretical range of 0–12. For statistical analysis Fisher’s exact test and Spearman’s correlation coefficient were performed. Results: A statistically significant association of clinical stage with lytic changes, sequestration and inferior alveolar canal involvement was found. Also, a statistically significant correlation of clinical stage with CRIm index classification was obtained. Conclusions: The CRIm index tends to increase as the clinical stages of MRONJ advance, suggesting a correlation between the clinical stage of MRONJ and the CRIm index.

The ability to detect the presence as well as classify the activities of individuals behind visually obscuring structures is of significant benefit to police, security and emergency services in many situations. This paper presents the analysis from a series of experimental results generated using a through-the-wall (TTW) Frequency Modulated Continuous Wave (FMCW) C-Band radar system named Soprano. The objective of this analysis was to classify whether an individual was carrying an item in both hands or not using micro-Doppler information from a FMCW sensor. The radar was deployed at a standoff distance, of approximately 0.5 m, outside a residential building and used to detect multiple people walking within a room. Through the application of digital filtering, it was shown that significant suppression of the primary wall reflection is possible, significantly enhancing the target signal to clutter ratio. Singular Value Decomposition (SVD) signal processing techniques were then applied to the micro-Doppler signatures from different individuals. Features from the SVD information have been used to classify whether the person was carrying an item or walking free handed. Excellent performance of the classifier was achieved in this challenging scenario with accuracies up to 94%, suggesting that future through wall radar sensors may have the ability to reliably recognize many different types of activities in TTW scenarios using these techniques.

We develop a primality test for Mersenne numbers and investigate the primality of the sequence of Catalan-Mersenne numbers. We use induction as a proof to show that the 5th Catalan-Mersenne number is a prime number, thus demonstrating the infinitude of Mersenne primes.

Let $(\Omega, \mu)$, $(\Delta, \nu)$ be measure spaces and $\{\tau_\alpha\}_{\alpha\in \Omega}$, $\{\omega_\beta\}_{\beta \in \Delta}$ be 1-bounded continuous Parseval frames for a Hilbert space $\mathcal{H}$. Then we show that \begin{align}\label{UE} \log (\mu(\Omega)\nu(\Delta))\geq S_\tau(h)+S_\omega (h)\geq -2 \log \left(\frac{1+\displaystyle \sup_{\alpha \in \Omega, \beta \in \Delta}|\langle\tau_\alpha , \omega_\beta\rangle|}{2}\right) , \quad \forall h \in \mathcal{H}_\tau \cap \mathcal{H}_\omega, \end{align} where \begin{align*} &\mathcal{H}_\tau := \{h_1 \in \mathcal{H}: \langle h_1 , \tau_\alpha \rangle \neq 0, \alpha \in \Omega\}, \quad \mathcal{H}_\omega := \{h_2 \in \mathcal{H}: \langle h_2, \omega_\beta \rangle \neq 0, \beta \in \Delta\},\\ &S_\tau(h):= -\displaystyle\int\limits_{\Omega}\left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \tau_\alpha\right\rangle \right|^2\,d\mu(\alpha), \quad \forall h \in \mathcal{H}_\tau, \\ & S_\omega (h):= -\displaystyle\int\limits_{\Delta}\left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\log \left|\left \langle \frac{h}{\|h\|}, \omega_\beta\right\rangle \right|^2\,d\nu(\beta), \quad \forall h \in \mathcal{H}_\omega. \end{align*} We call Inequality (\ref{UE}) as \textbf{Continuous Deutsch Uncertainty Principle}. Inequality (\ref{UE}) improves the uncertainty principle obtained by Deutsch \textit{[Phys. Rev. Lett., 1983]}. We formulate Kraus conjecture for 1-bounded continuous Parseval frames. We also derive continuous Deutsch uncertainty principles for Banach spaces.

The purpose of this paper is to study the sliding mode control as a Ricci flow process in the context of a three-story building structure subjected to seismic waves. The stability conditions result from two Lyapunov- functions, the first associated with slipping in a finite period of time, and the second with convergence of trajectories to the desired state. Simulation results show that the Ricci flow control leads to the minimization of the displacements of the floors. 3D Ricci solitons projection via a semi-conformal mapping to a surface is also studied.

A prime gap is the difference between consecutive prime numbers. The $n^{\text{th}}$ prime gap, denoted $g_{n}$, is calculated by subtracting the $n^{\text{th}}$ prime from the $(n+1)^{\text{th}}$ prime: $g_{n}=p_{n+1}-p_{n}$. Oppermann's conjecture is a prominent unsolved problem in pure mathematics concerning prime gaps. Despite verification for numerous primes, a general proof remains elusive. If true, the conjecture implies that prime gaps grow at a rate bounded by $g_{n}<{\sqrt {p_{n}}}$. We examine the ratio of Chebyshev functions for consecutive primes, $\frac{\theta(p_{n+1})}{\theta(p_{n})}$, and compare it to the square root of their ratio, $\sqrt {\frac{p_{n+1}}{p_{n}}}$. Assuming this inequality holds for primes larger than $10^{8}$, we demonstrate the truth of Oppermann's conjecture. For sufficiently large $n$, this inequality guarantees that $g_{n}<{\sqrt {p_{n}}}$ for all primes beyond a certain point. Our proof also validates Andrica's, Legendre's, and Brocard's conjectures for primes exceeding a specific threshold.

We can analyze the properties of the Collatz Conjecture by using Terras’ Theorem, and computational graphical calculations. To do this, we introduce the concept of “tree" which shows the relationship between the input and output positive integers of the Collatz process. This approach offers a novel way for determining the non-existence of loops and diverge trees through computer simulations.

In 1937,German mathematician L.Collatz proposed the following conjeture:for any positive integer,if it is even,divide it by 2,if it is odd,multiply it by 3 and add 1 to get an even number.Continuing with the above rule, the final result will be 1.This paper gives a proof of this conjecture.

The Collatz conjecture (or 3n+1 problem) has been explored for about 86 years. In this article, we prove the Collatz conjecture. We will show that this conjecture holds for all positive integers by applying the Collatz inverse operation to the numbers that satisfy the rules of the Collatz conjecture. Finally, we will prove that there are no positive integers that do not satisfy this conjecture.

Collatz conjecture (3x+1 problem) is a natural phenomenon in set theory that may be reconstructed using known combinatorics and order theory. Construction begins by selecting a specific order isomorphism with a bijectional order-embedding. Mapping by 3x+1 induces a unique property to only members of the mapped embedding. Under selective congruence from recursive division by two, that complex controls sequence behavior. This demonstration uses an order isomorphism consisting of two linear orders: the (1) odd positive integers and the always odd (2) Rule 50 Jacobsthal numbers, as the embedding. The argument proceeds by cardinality. When the order isomorphism is mapped under 3x+1, all Rule 50 Jacobsthal numbers are mapped to all the powers of four. This one-to-one correspondence guarantees that every odd integer is assigned to a Rule 50 Jacobsthal number, and subsequently, to a power of four. To align this construction with the conjecture, expand the set to all positive integers by showing that: (1) the powers of four embed the powers of two, in a natural way, and (2) the unique factorization of any positive even integer, not congruent to a power of two, is simply an odd integer, once the factorized power of two is divided out. In other words, if the initial choice for a positive integer is not congruent to a power of two, then recursion continues until a Rule 50 Jacobsthal number (guaranteed by cardinality) is attained. Since this value mapped by 3x+1 is always a power of four, repeated division by two will always send the sequence to one. Because this same process occurs for any choice of positive integer, Collatz conjecture is true.

Since 1742, the year in which the Prussian Christian Goldbach wrote a letter to Leonhard Euler with his Conjecture in the weak version, mathematicians have been working on the problem. The tools in number theory become the most sophisticated thanks to the resolution solutions. Euler himself said he was unable to prove it. The weak guess in the modern version states the following: any odd number greater than 5 can be written as the sum of 3 primes. In response to Goldbach's letter, Euler reminded him of a conversation in which he proposed what is now known as Goldbach's strong conjecture: any even number greater than 2 can be written as a sum of 2 prime numbers. The most interesting result came in 2013, with proof of weak version by the Peruvian Mathematician Harald Helfgott, however the strong version remained without a definitive proof. The weak version can be demonstrated without major difficulties and will not be described in this article, as it becomes a corollary of the strong version. Despite the enormous intellectual baggage that great mathematicians have had over the centuries, the Conjecture in question has not been validated or refuted until today.

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

Seedling emergence is crucial for the establishment and growth of crops and is influenced by topsoil temperature and moisture. Mulching has been widely used to promote seedling emergence in areas with a cold spring. This study was conducted to determine and simulate the effects of transparent plastic film mulch on surface soil moisture, temperature, and seedling emergence of spring maize in Northwest China. Four treatments were used: no mulching (CK), full plastic film mulch (PMF), and partial plastic film mulch, 60 cm in width (PM60, 40 cm uncovered between rows of mulch) or 30 cm in width (PM30, 20 cm uncovered between rows of mulch). The effects of soil water conservation and temperature enhancement gradually decreased as the plastic film width decreased, but there was little difference between PMF and PM60 treatments. Soil-water-modified growing degree days (WGDD) described the beneficial effects of soil moisture and temperature with respect to seedling emergence under mulching conditions. Plastic film mulching markedly accelerated seedling emergence and increased final seedling emergence rate because mulching can shorten the autotrophy duration and maintain surface soil moisture, which leads to increased germination. The effects of seedling emergence improvement decreased as the plastic film width decreased. The relationship between WGDD and cumulative relative seedling emergence (CRE) was adequately described by a Gompertz function.

The association between human and cat (F. catus) is well known. This domestic animal is also known for its malodorous urine and feces. The complexity of the odorous urine and feces impacts human life by triggering the human sensory organ in a negative way. The objective of this research was to identify the volatile organic chemicals (VOCs) and associated odors in cat urine and feces using gas chromatography-mass spectrometry and simultaneous sensory analysis of fresh and aged samples. The solid-phase microextraction (SPME) technique was used to pre-concentrate the VOCs emitted from urine or feces samples. Twenty-one compounds were identified as emitted from fresh urine, whereas 64 compounds were emitted from fresh feces. A contrasting temporal impact was observed on the emission of VOCs for urine and feces. On aging, the emission increased to 36 detected chemicals for stale urine, whereas only 17 chemicals were detected in stale feces. Not all compounds were malodorous; some compounds had a pleasant hedonic smell to the human nose. Although trimethylamine, low molecular weight organic acids, and ketones were contributors to the odor to some extent, phenolic compounds and aromatic heterocyclic organic N compounds generated the most intense odors and substantially contributed to the overall malodor, as observed by this study. This work might be useful to formulate cat urine and feces odor remediation approaches to reduce odor impacts.

This article utilized electrodeposition technology to fabricate Zn and Zn-Y₂O₃-Al₂O₃ composite coatings on Q235 steel plates. The composite coatings were obtained by adding Y₂O₃/Al₂O₃ nanoparticles (0, 5, 10, and 15 g/L) to acidic chloride solutions. This study then examined the impact of these nanoparticles on the microstructure, morphology, microhardness, hydrophobicity, and corrosion resistance of the composite coatings. The results indicate that the addition of the nanoparticles increased the nucleation sites on the surface of the coating, thereby refining the grain size and reducing the roughness of the coating surface. When 10g/L of Y₂O₃ and 10g/L of Al₂O₃ nanoparticles were added, the hardness of the composite coating (369 Hv) was 2.49 times higher than that of the pure Zn coating (148 Hv), which was attributed to the dispersion strengthening and grain refinement effects of the nanoparticles. The corrosion resistance of the Zn and Zn-Y₂O₃-Al₂O₃ composite coatings was studied using linear sweep voltammetry and AC impedance spectroscopy. The addition of the nanoparticles improved the corrosion resistance of the composite coating, and the composite coating prepared in an electrolyte containing 10 g/L of Y₂O₃ and 10 g/L of Al₂O₃ nanoparticles exhibited the best corrosion resistance. Meanwhile, the composite coating exhibited good hydrophobicity, with a contact angle of 120.9°, 1.94 times that of the pure Zn coating (62.2°). The Zn-Y₂O₃-Al₂O₃ nanocomposite coating material has significant potential advantages in the field of steel corrosion.

Let $\mathbb{K}$ be a non-Archimedean (complete) valued field satisfying \begin{align*} \left|\sum_{j=1}^{n}\lambda_j^2\right|=\max_{1\leq j \leq n}|\lambda_j|^2, \quad \forall \lambda_j \in \mathbb{K}, 1\leq j \leq n, \forall n \in \mathbb{N}. \end{align*} For $d\in \mathbb{N}$, let $\mathbb{K}^d$ be the standard $d$-dimensional non-Archimedean Hilbert space. Let $m \in \mathbb{N}$ and $\text{Sym}^m(\mathbb{K}^d)$ be the non-Archimedean Hilbert space of symmetric m-tensors. We prove the following result. If $\{\tau_j\}_{j=1}^n$ is a collection in $\mathbb{K}^d$ satisfying $\langle \tau_j, \tau_j\rangle =1$ for all $1\leq j \leq n$ and the operator $\text{Sym}^m(\mathbb{K}^d)\ni x \mapsto \sum_{j=1}^n\langle x, \tau_j^{\otimes m}\rangle \tau_j^{\otimes m} \in \text{Sym}^m(\mathbb{K}^d)$ is diagonalizable, then \begin{align}\label{WELCHNONABSTRACT} \max_{1\leq j,k \leq n, j \neq k}\{|n|, |\langle \tau_j, \tau_k\rangle|^{2m} \}\geq \frac{|n|^2}{\left|{d+m-1 \choose m}\right| }. \end{align} We call Inequality (\ref{WELCHNONABSTRACT}) as the non-Archimedean version of Welch bounds obtained by Welch [\textit{IEEE Transactions on Information Theory, 1974}]. We formulate non-Archimedean Zauner conjecture.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

Klebsiella pneumoniae complex is one of the most commonly isolated bacteria within human infections. These microorganisms are opportunistic pathogens that pose a serious threat to public health due to possibility of transmission in the human population. Resistance to carbapenems is one of the most important antimicrobials resistance mechanisms amongst them. In this situation therapeutic options are limited. Therefore, the aim of this study was to evaluate fosfomycin, colistin, ceftazidime-avibactam and meropenem-vaborbactam in vitro activity against multidrug-resistant K. pneumoniae complex strains. The study involved 160 strains of Gram-negative rods: K. pneumoniae – 138 and K. variicola - 22. Minimal inhibitory concentration of fosfomycin was estimated by agar dilution method and for colistin by microdilution method. The susceptibility to ceftazidime-avibactam and meropenem-vaborbactam was determined by gradient strip method. All of the analysed K. pneumoniae complex isolates produced extended-spectrum beta-lactamases and 60.0% carbapenemases. The most of the analysed strains were susceptible to fosfomycin and colistin (62.5%). Among pandrug-resistant K. pneumoniae complex isolates the most were susceptible to colistin (43.9%). Fosfomycin has good activity against ESBL- and VIM-positive isolates from this complex. In turn, colistin has satisfactory in vitro activity against KPC- and VIM-positive isolates from K. pneumoniae complex. Ceftazidime-avibactam has good activity against K. pneumoniae complex strains producing ESBL, KPC and OXA enzymes. In turn, meropenem-vaborbactam has satisfactory in vitro activity against ESBL- and KPC-positive isolates from this complex.

In this study, I examined the Beals conjecture on the basis of formulas that produce composite numbers, and I developed some other conjectures that, if answered, would be an answer to the Beals conjecture. Apart from this, I have examined the Beals conjecture from another perspective and posed The Germany Problem.

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

The Goldbach Conjecture, which is frequently termed as “1 + 1”, has been a fascinating goal for many mathematicians over centuries. A Chinese mathematician, Dr. Jingrun Chen, proved 1 + 2, which is a great success and the best result so far achieved. Although there were several attempts proving the conjecture, these attempts are either tediously long, complicated, or logically imperfect, thus not widely accepted. Taking advantage of the periodicity of primes, here the author provides a straight forward rigorous proof for the Conjecture.

A geometric Planck-scale model of quantum electrodynamics is tested against observations. Based on Dirac’s proposal to describe spin 1/2 particles as tethered objects, elementary fermions are conjectured to be fluctuating rational tangles with unobservable tethers. As Battey-Pratt and Racey showed, when such tangles propagate, they obey the free Dirac equation. Classifying rational tangles yields the observed spectrum of elementary fermions. Classifying deformations of tangle cores yields exactly three types of gauge interactions. They exchange three types of elementary gauge bosons and have the symmetry groups U(1), broken SU(2) and SU(3). The possible rational tangles for fermions, Higgs and gauge bosons allow only the observed Feynman diagrams. The complete Lagrangian of the standard model arises, including the Lagrangian of quantum electrodynamics. Over 50 tests of the tangle model are deduced. They include details on the perturbation expansion of the g-factor and the existence of limit values for electric and magnetic fields. Measurements agree with most tests, though this could change in the future. Some tests are genuine predictions that still need to be checked. In particular, the geometry of the process occurring at QED interaction vertices suggests an ab-initio estimate for the fine structure constant. In addition, the average geometric shapes of the elementary particle tangles suggest ab-initio lower and upper limits for the mass values of the electron and the other leptons.

Komlos conjecture is about the existing of a constant upper bound over the dimension n of the function $K(n)$ defined by $$K(n)=max_{ \{ \overrightarrow{V_1},...,\overrightarrow{V_n} \} \in \{ \overrightarrow{V_i} \in { R}^n \| \overrightarrow{V_i} \| \leq 1 \} ^n } min_{ \{\epsilon_1,...\epsilon_n\} \in \{-1,+1\}^n } \|\sum_{i=0}^{n} \epsilon_i \overrightarrow{V_i}\}\|_{\infty} $$ In this paper, the function $K(n)$ is evaluated first for lower dimensions, $n\leq 5$, where it found that $K(2)=\sqrt{2}$. For higher dimension, the function $f(n)=\sqrt{ n-\lceil\log_2(2^{n-1}/n) \rceil}$ is found to be a lower bound for the function $K(n)$, from where it is concluded that the Komlos conjecture is false i.e., the universal constant $k=max_{n \in N} K(n) $ does not exist because of $$\lim_{n \rightarrow \infty } K(n) \geq \lim_{n \rightarrow \infty } \sqrt{ \log_2(n)-1 }=+\infty$$

Pancreatic cancer is a fatal disease with mortality rate of 5% and a with a limited survival rate of 5 years. Despite of the extensive efforts that has been made to cure the disease it still has been considered as ‘undruggable’. It is characterized by epithelial to dense stromal tumor formation however due to lack of diagnosis options and treatment test available to detect the disease to the point at which resection of the tumor is possible, it makes it the fourth leading cause of cancer related death. The unavailable information regarding the early detection of biological markers along with the increased invasive tumor, the inherit chemoresistance against medication radiation and chemotherapy stubbornly fail the therapeutic options available. These associated problems made the scientists to reevaluate the approaches that are currently in practice and take a step back to fully understand the basic biological pathways that are involved in the pancreatic cancer, the heterogeneity of the tumor itself along with expression and a number of mutations that are observed at different locations. Clinical trial along with new approaches are nowadays focus of research to treat this tumor. The review paper describes the basic cellular pathways involved in pancreatic cancer, the gene mutations and their expression having effect on the pathology of the diseases along with treatment options that are available to treat the tumor. These efforts will help with the expansion of our knowledge to undergo the clinical trial and the synthesis of novel medicines for the prognosis of the disease.

Traditional photodynamic therapy (PDT) is often limited in its efficacy by insufficient light penetration, inefficient photosensitizer energy transfer, and inadequate target tissue oxygenation. X-ray activated PDT (XPDT), using nanoparticle (NPs) photosensitizers comprised of europium-doped yttrium oxide cores encased within silica shells (Y₂O₃:Eu@SiO₂), offers the potential of overcoming most of these limitations. Aimed at maximizing the generation of reactive oxygen species (ROS), this study reports methodologies for investigation of the effects of synthesis conditions on the characteristics of Y₂O₃:Eu@SiO₂ NP. Transmission electronic microscope (TEM) revealed that the NP core diameter was linearly, positively correlated with condensation time (R2 = 0.7357, p < 0.05) and linearly, negatively correlated with urea concentration (R2 = 0.958, p < 0.05). The addition of cetyltrimethylammonium bromide (CTAB) during core synthesis demonstrated enhanced particle dispersion. Silica coating via APTES-1 and TEOS-3 conditions resulted in Y₂O₃:Eu@SiO₂ NPs that generated the highest ROS, with 8.7-fold and 8.9-fold increase respectively in relative fluorescence intensity at 8 Gy irradiation compared to a 5.2-fold increase in PBS under the same condition. In vivo evaluation using 18F-fluorothymidine positron emission tomography (18F-FLT PET) of mouse xenografts of a human prototypical cancer (ovarian) revealed a 55% reduction in tumor proliferation of radiation-sensitive CAOV3 tumors treated with Y₂O₃:Eu@SiO₂ NPs compared to a 19% reduction in tumor proliferation of radiation-resistant SKOV3 tumors on the fourth day post-treatment. Taken together, these findings suggest Y₂O₃:Eu@SiO₂ NPs can serve as effective photosensitizers for XPDT and their performance characteristics can be optimized by selecting synthesis conditions and parameters to deliver the desirable therapeutic effects, offering novel approaches to circumventing many of the limitations of conventional PDT in the treatment of cancer.

In this paper, some convexity properties and some inequalities for the (p,k)-analogue of the Gamma function, Г_p,k(x) are given. In particular, a (p,k)-analogue of the celebrated Bohr-Mollerup theorem is given. Furthermore, a (p,k)-analogue of the Riemann zeta function, ζ_p,k(x) is introduced and some associated inequalities are derived. The established results provide the (p,k)-generalizations of some known results concerning the classical Gamma function.

Studies carried out have revealed that every day around three thousand and twelve people lose their lives in the world due to traffic accidents and poor air quality. Large cities, with their millions of inhabitants and vehicles, face many problems relating to vehicular traffic. In 2015 the speed limit was modified on several roads in the city of São Paulo-Brazil. However, in 2017 the speed limits were increased again, but not on all previous routes. This study analyzed the impact of this change on the number of accidents and pollutant concentrations, over a period of ten years, comparing the periods before and after the implementation of the measure, using real data collected and provided by the authorities of the city and the state transit and environmental companies, on more than forty routes and two nearby air quality stations. The results show a clear reduction in the number of accidents without victims on the roads of the city of São Paulo starting in 2010. However, the restrictive measures imposed by government officials may have contributed to the decrease in the number of accidents, but the number of fatalities has not changed much. Air pollution has not improved substantially with speed changes, as new speed increases have been linked to new episodes of congestion. The average number of fatalities due to accidents has been increasing since 2010 and accidents are becoming more serious. The application of a general linear statistical model (GLM) estimated the impact of the speed reduction policy in terms of the number of injuries avoided per month: 43.4 and 14.1 on other roads and on Pinheiros marginal, respectively. The results highlight the need for a constant data collection by the authorities in cities with high vehicle traffic. The important temporal time trend in terms of reduction of injuries but not in terms of fatalities and air quality, shows the need to apply joint public policies, not only speed reduction, but also the use of new technologies and raising drivers’ awareness of the problem.

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.

ESG (Environmental, Social, and Governance) responsibility fulfillment increasingly affects enterprise valuation. Although researchers debate about the precise effects, the prevailing view suggests a linear relationship between ESG performance and enterprise value. This study introduces a novel ESG responsibility performance metric through the Regulated Intermediary Model to delve into this relationship within the Chinese context. Our findings reveal an inverted U-shaped relationship between ESG performance and enterprise value, with financing constraints having a significant moderating effect. These findings remain robust after employing instrumental variables to mitigate potential endogeneity. Heterogeneity analysis demonstrates that this inverted U-shaped relationship is particularly pronounced in non-polluting and non-state-owned enterprises. Moreover, a comparison between equity and debt financing mechanisms underscores that improved ESG performance is associated with lower cost of equity financing, thereby enhancing enterprise value. Financial institutions are encouraged to leverage innovative financial instruments to diversify enterprise financing channels and alleviate financing constraints of enterprises that fulfill their ESG responsibilities.

The concept of economic self-reliance, widely known by Thai people as the philosophy of sufficiency economy, has been widely promoted in rural Thai societies. By practicing this philosophy, it is expected that the citizens’ quality of life and local environments could be sustainably improved. This study aims to explore the contribution of the community practices of the sufficiency economy philosophy to rural villagers’ quality of life improvement, and to investigate potential factors that determine the trust of villagers in the philosophy. With the purpose to propose strategies which could enhance trust and promote villagers’ practices of the philosophy, the study investigated influences of three relevant factors on trust towards the philosophy. Those factors included factors related to cognitive-based trust, factors related to emotional-based trust, and factors related to demographic characteristics. Questionnaire surveys and in-depth interviews with community leaders and local villagers were conducted in the Ban Jamrung community, in Thailand’s Rayong province. The results of the statistical analysis revealed that the residents who applied the sufficiency economy philosophy in their daily lives experienced a relatively better quality of life. Additionally, it was found that trust in the philosophy could be predicted more by rational factors than by emotional factors. These findings could be utilized to develop strategies to maintain and enhance the trust of the people in the philosophy of sufficiency economy.

A hydrothermal pretreatment of the microalga Nannochloropsis gaditana at mild temperatures has been studied in order to reduce N and O content in the biocrude obtained by hydrothermal liquefaction (HTL). The work is focused on the evaluation of temperature, reactor loading and time (factors) to maximize the yield of the pretreated biomass and the heteroatom contents transferred from the microalga biomass to the aqueous phase (responses). The study followed the factorial design and response surface methodology. An equation for every response has been obtained, which leads to the accurate calculation of the operating conditions required to obtain a given value of these responses. Temperature and time are critical factors with a negative effect on the pretreated biomass yield, but a positive one on the N and O recovery in the aqueous phase. The slurry concentration has to be low to increase heteroatom recovery and high to maximize the pretreated microalga yields

Urbanization is considered as a main indicator of regional economic development due to its positive effect on promoting industrial development; however, many regions, especially developing countries, are troubled by its negative effect — the aggravating environmental pollution. Many researchers have indicated that rapid urbanization stimulated the expansion of industrial production scale and increased industrial pollutant emissions. However, this judgement contains a grave deficiency in that urbanization not only expands industrial production scales but can also increase industrial labour productivity and change the industrial structure. To modify this deficiency, we first decompose the influence which urbanization impacts on industrial pollutant emissions into the scale effect, the intensive effect and the structure effect by using the Kaya Identity and the LMDI Method; second, we perform an empirical study of the three effects’ impacts by applying the spatial panel model with data from 282 Chinese cities between 2003 and 2013. Our results indicate that (1) there are significant reverse U-shapes between Chinese urbanization rate and its industrial pollutant emissions; (2) the scale effect and the structure effect have aggravated Chinese industrial waste water discharge, sulphur dioxide emissions and soot (dust) emissions, while the intensive effect has generated a decreasing and ameliorative impact on that aggravated trend. The definite relationship between urbanization and industrial pollutant emissions depends on the combined influence of the scale effect, the intensive effect and the structure effect; (3) there are significant spatial autocorrelations of industrial pollutant emissions between Chinese cities, but the spatial spillover effect from other cities does not aggravate local urban industrial pollutant emissions, we offer an explanation to this contradiction that the vast rural areas surrounding Chinese cities have served as sponge belts and have absorbed the spatial spillover of cities’ industrial pollutant emissions. According to the results, we argue that this type of decomposition of the influence into three effects is necessary and meaningful, it establishes a solid foundation for understanding the relationship between urbanization and industrial pollutant emissions, and effectively helps to meet relative policy making.

Historic sites are important components of every city's cultural history because they preserve rich historical knowledge and distinctive values passed down from previous generations to the present. Due to the progress of urbanization and modernization, many historic sites face pressure from damage and transformation. In this paper, a method for assessing cultural heritage damage was developed to measure the extent of spatial damage in historic sites. Using sample data obtained in Xiyang, Qixian, and Xiaoyi, all historic cities in Shanxi Province, Mainland China, and combined weights were estimated using the Delphi technique and the CRITIC weight method. Following this, the Spatial Damage Degree Model (SDDM) based on K-means cluster analysis and K-nearest neighbor (KNN) classification was developed. The findings show that the model efficiently solves the problem of assessing spatial damage levels in historic sites. Through multiple linear regression analysis, it was shown that the damage to historic sites was predominantly caused by three factors: natural erosion, construction damage, and planning and policy. SDDM was used to calculate the spatial damage levels of historic sites, allowing conservators to fully comprehend the features and concerns related to historic sites. As a result, more scientific and rational preservation approaches may be developed, improving the efficiency of historic site restoration and conservation and encouraging the sustainable development of urban and rural heritage.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

Despite prophylaxis and attempts to select a therapy, the frequency of preeclampsia does not decrease, and it still takes the leading position in the structure of maternal mortality and morbidity worldwide. In this review, we present a new theory of the etiology and pathogenesis of preeclampsia which is based on the interaction of Na/K-ATPase and its endogenous ligands including marinobufagenin. The signaling pathway of marinobufagenin involves an inhibition of transcriptional factor Fli1, a negative regulator of collagen synthesis, followed by deposition of collagen in the vascular tissues and altered vascular functions. Moreover, in vitro and in vivo neutralization of marinobufagenin is associated with restoration of Fli1. The inverse relationship between marinobufagenin and Fli1 opens new possibilities in the treatment of cancer: since Fli1 is a proto-oncogene, a hypothesis on suppression of Fli1 by cardiotonic steroids as potential anti-tumor therapeutic strategy is discussed as well. We propose a novel therapy of preeclampsia which is based on immunoneutralization of the marinobufagenin by monoclonal antibodies, which is capable to impair marinobufagenin-Na/K-ATPase interactions.

Design process can be divided into stages of analysis and synthesis. This paper presents the application of the object-oriented technique to the synthesis as well as theoretical considerations concerning to design of gear size ranges. The synthesis consists in composition (aggregation) of single details into units – according to the rule: “from details up to general view”. The basics of the object-oriented synthesis were formulated. Furthermore, the consecutive stages of synthesis were formulated. The interactions between these stages were discussed. Some aspects were described in details e.g.: creation of interfaces for performance of the embodiment phase the designed artefact via CAD system drawing with specification (dimensions are still parametrically set). The final step of the procedure is creation of so called substantial (concrete) form of artifacts i.e. final assignment of dimensions which stored in the special data base. The final stage of the design process is issuing of technical documentation (technical drawings) created automatically via CAD system. The considerations are terminated by the list of advantages connected with the object-oriented approach to design (in comparison to the traditional way).

The Collatz conjecture, a longstanding mathematical puzzle, posits that, regardless of the starting integer, iteratively applying a specific formula will eventually lead to the value 1. This paper introduces a novel approach to validate the Collatz conjecture by leveraging the binary representation of generated numbers. Each transition in the sequence is predetermined using the Collatz conjecture formula, yet the path of transitions is revealed to be intricate, involving alternating increases and decreases for each initial value. The study delves into the global flow of the sequence, investigating the behavior of the generated numbers as they progress toward the termination value of 1. The analysis utilizes the concept of probability to shed light on the complex dynamics of the Collatz conjecture. By incorporating probabilistic methods, this research aims to unravel the underlying patterns and tendencies that govern the convergence of the sequence. The findings contribute to a deeper understanding of the Collatz conjecture, offering insights into the inherent complexities of its trajectories. This work not only validates the conjecture through binary representation but also provides a probabilistic framework to elucidate the global flow of the sequence, enriching our comprehension of this enduring mathematical mystery.

Reptilians or reptoids are staple characters of Hollywood cinema, science fiction literature, ufology and conspiracy theories. Despite its popularity, the reptoid has been dismissed by the scientific community as a figment of the imagination; born out of a speculation, paranoia and wanton anthropocentricism. In this paper, however, the Life Sequence Conjecture is advanced as a supportive framework for the notion of reptilian extraterrestrials. This paper is not an argument in support of the existence of extraterrestrials. Rather, it proposes that if extraterrestrials do exist, then a reptilian morphology is not untenable.

Protein O-GlcNAcylation has been associated with neurodegenerative diseases such as Alzheimer´s disease (AD). O-GlcNAcylation of Amyloid Precursor Protein (APP) regulates both the trafficking and the processing of the APP through the amyloidogenic pathway, resulting in the release and aggregation of the Aβ1-42 peptide. Microglia clear Aβ aggregates and dead cells to maintain brain homeostasis. Here, using LC-MS/MS we reveal that the Aβ1-42 peptide modifies the microglia O-GlcNAcome. We have identified 55 proteins, focusing our research on Galectin-1 protein, since it is a very versatile protein from a functional point of view. Combining biochemical with genetic approaches we demonstrate that Aβ1-42 peptide specifically targets Galectin-1S8 O-GlcNAcylation via OGT. In addition, this Gal-1-O-GlcNAcylated form, in turn, controls human microglia migration. Given the importance of microglia migration in the progression of AD, this study reports the relationship between Aβ1-42 peptide and Serine 8- O-GlcNAcylation of Galectin to drive microglial migration

Salinity, resulting from climate change and excessive mineral fertilization, burdens farmers and negatively impacts soil and water ecosystems in the Northeastern Nile Delta. Organic and biological approaches are crucial for addressing these issues. This study examined the effects of individual and combined inoculations with cyanobacteria, yeast, and Arbuscular Mycorrhizal Fungi (AMF), with or without K-humate, on enhancing salinity tolerance, increasing yield, and improving crop quality of wheat and faba bean. The aim was to reduce NPK mineral fertilizer application rates to 25% of recommended doses. An economic evaluation was also conducted. In a preliminary laboratory experiment, the interactive effects of these microbiomes on the production of plant antioxidant enzymes and soil enzymes were investigated under salinity stress. Results showed that co-inoculation, especially with K-humate, yielded superior outcomes compared to individual inoculations. The laboratory experiment findings were confirmed by a field trial conducted in saline-alkaline soil in the Northeastern Nile Delta region. The study found that the integrated inoculation of cyanobacteria, yeast, and mycorrhizae with K-humate, along with 25% mineral NPK fertilization enhanced microbial activity, including AMF colonization, spore density, and total bacteria, cyanobacteria, and yeast counts in the plant rhizosphere. It also increased soil enzyme activity, improving soil fertility compared to individual or mineral control treatments. This integration resulted in wheat yields of 2.77 tons/ha and faba bean yields of 4.75 tons/ha. Crop quality improved, with higher levels of nitrogen, potassium, phosphorus, and protein in wheat grains and faba bean seeds. Microbiomes inoculation increased potassium uptake over sodium, enhancing the potassium/sodium ratio and salt stress tolerance. This approach reduces reliance on costly mineral fertilizers by up to 75%, enabling economically viable cultivation in marginal lands. These sustainable practices optimize resource utilization, maximize economic efficiency, and preserve natural resources.

Piezoelectric c-axis oriented zinc oxide (ZnO) thin films, from 1.8 up to 6.6 µm thick, have been grown by radio frequency magnetron sputtering technique onto fused silica substrates. A delay line consisting in two interdigital transducers (IDTs) with wavelength λ = 80 µm was photolith-ographically implemented onto the surface of the ZnO layers. Due to the IDTs split finger con-figuration and metallization ratio (0.5), the propagation of both the fundamental, third and nineth harmonic Rayleigh waves is excited; also, three leaky surface acoustic waves (SAWs) were detected travelling at velocity close to that of the longitudinal bulk wave in SiO2. The acoustic waves propagation in ZnO/fused silica was simulated by using 2D finite-element method (FEM) tech-nique to identify the nature of the experimentally detected waves. It turned out that, in addition to the fundamental and harmonic Rayleigh waves, also high-frequency leaky surface waves are ex-cited by the harmonic wavelengths; such modes are identified as leaky-Sezawa (LS) waves under cut-off. The velocity of all the modes was found in good agreement with the theoretically calcu-lated values. The existence of a low-loss region for the Sezawa wave below the cut off was theo-retically predicted and experimentally assessed.

This study aimed to identify whether gyrate atrophy of the choroid and retina (GACR) heterozygous individuals have possible clinical manifestations and to explore the potential pathogenic mechanism. In this retrospective study, we surveyed a two-generation pedigree of an individual diagnosed with GACR. Two family members underwent ophthalmological, hematologic, and genetic tests. An arginine-restricted diet with vitamin B6 supplementation was implemented; clinical assessments were repeated every 3 months during follow-up. Relative OAT mRNA expression was determined using real-time quantitative polymerase chain reaction. The 19-year-old compound heterozygous daughter (OAT: c.1186C&gt;T; c.748C&gt;T), had bilateral high myopia, posterior staphyloma, chorioretinal atrophy, macular abnormalities, and elevated hematologic ornithine. The 54-year-old heterozygous mother (OAT: c.1186C&gt;T), presented with bilateral severe myopia, asymmetric posterior staphyloma, retina and choroidal capillary layer atrophy, retinal pigment epithelium abnormalities, and mildly elevated hematologic ornithine. Compared to normal individuals, the daughter and mother had 29% and 46% relative OAT mRNA expression, respectively (P&lt;0.001). We believe that this is the first report of a carrier of one OAT variant allele with mild phenotypes, suggesting that family members should be aware of the possible involvement of autosomal recessive conditions. Additional data suggests nonsense mediated decay-initiated mRNA degradation may cause GACR.

The Collatz conjecture is a well-known number theory puzzle that states that every positive integer would eventually converge to the trivial cycle of 1, 2, 1, 2,... when repeatedly exposed to a particular transformation. In this transformation, even numbers are divided in half, odd numbers are tripled, and one is added. In this study, we present a new method for creating a directed graph and using it to display and analyze Collatz sequences. Our technique creates what we call a Collatz directed graph by joining an endless number of simple directed graphs, each of which corresponds to a natural number. We show by careful mathematical analysis that all positive integers are included in this Collatz directed graph. Moreover, we give an evidence that verifies the Collatz conjecture by showing that the sole cycle in this graph is the trivial cycle of 1, 2, 1, 2,... We also prove that there is no sequence that diverges to infinity in this graph. Our results provide insights into the fundamental structure of Collatz sequences and further our knowledge of the Collatz conjecture .

The following is the Collatz Conjecture: Suppose we begin with a positive number, multiply it by 3 and add 1 if it is odd, and divide it by 2 if it is even. Then continue doing this as long as you can. Will it matter where you start, whether you end up at the number 1? The Collatz conjecture has been studied for around 85 years. We transform the Collatz function from decimal to binary, then use the binary string's character to prove the Collatz conjecture. In addition, we use mathematics to give another interpretation to chaos, which is the ultimately periodic positive integer sequence.

In this paper, we examine the weak abc conjecture and the strong abc conjecture using some functions. we attempt to discuss the possibilty that the negative consequence of the weak abc conjecture. Namely, we derive that the weak abc conjecture is not true. Additionally, we show that the strong abc conjecture is not true.

This work reports the isolation, purification, and anti-inflammatory evaluation of compounds from the plant species Ageratina pichinchesis. Using open-column chromatography, 11 known compounds were purified, whose chemical structures were elucidated by nuclear magnetic resonance techniques (1D and 2D). All compounds were evaluated in the in vitro model of RAW 264.7 mouse macrophage cells measuring nitric oxide inhibition as a determination of the anti-inflammatory effect. Outstandingly, the compound betuletol 3-O-β-glucoside (11) exhibited inhibition of nitric oxide with an IC50 of 75.08 ± 3.07% at 75 µM, additionally, it inhibited the secretion of interleukin 6 (IL-6) and activation of nuclear factor (NF-kβ). These results show that compound 11 could be considered as a potential anti-inflammatory agent in suppressing the expression of NF-kβ target genes such as the proinflammatory pathway and inducible nitric oxide synthase (iNOS). Consequently, the medicinal use attributed in traditional medicine to the A. pichinchensis species is due to the diversity of compounds that the plant biosynthesizes, demonstrating that its effect relates to anti-inflammatory effects associated with compound 11.

Kim-Kim ([9]) studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace Transformation and investigate some properties and formulas related to them.

We consider the financial planning problem of a retiree wishing to enter a retirement village at a future uncertain date. The date of entry is determined by the retiree's utility and bequest maximisation problem within the context of uncertain future health states. In addition, the retiree must choose optimal consumption, investment, bequest and purchase of insurance products prior to her full annuitisation on entry to the retirement village. A hyperbolic absolute risk-aversion (HARA) utility function is used to allow necessary consumption for basic living and medical costs. The retirement village will typically require an initial deposit upon entry. This threshold wealth requirement leads to exercising the replication of an American put option at the uncertain stopping time. From our numerical results, active insurance and annuity markets are shown to be a critical aspect in retirement planning.

We are in the era where various processes need to be online. However, data from digital learning platforms are still underutilised in higher education, yet, they contain student learning patterns, whose awareness would contribute to educational development. This limits development of adaptive teaching and learning mechanisms. In this paper, a model for data exploitation to dynamically study students progress is proposed. Variables to determine current students progress are defined and are used to group students into different clusters. K-means clustering is performed on real data consisting of students from a South African tertiary institution. Cluster migration is analysed and the corresponding learning patterns are revealed.

Cardiovascular diseases are a broadly understood concept focusing on vascular and heart dys-function. Lack of physical exercise, type 2 diabetes, obesity, hypertension, dyslipidemia, throm-boembolism, kidney, and lung diseases all contribute to the development of heart and blood vessel dysfunction. Although effective and important, traditional treatment with diuretics, statins, beta–blockers, calcium inhibitors, ACE inhibitors, and anti–platelet drugs remain a second–line treatment after dietary intervention and lifestyle changes. Scientists worldwide are still looking for an herbal product that would be quite effective and free from side effects, either taken together or before the standard pharmacological intervention. Such herbal–originated medication therapy may include Morus alba L. (white mulberry), Elaeagnus rhamnoides (L.) A. Nelson (sea–buckthorn), Allium sativum L. (garlic), Convallaria majalis L. (lily of the valley), Leonurus cardiaca L. (mother-wort), and Crataegus spp. (hawthorn). Valuable herbal raw materials include leaves, fruits, seeds, and even thorns. This short review focuses on six herbs that can constitute an interesting and po-tential therapeutic option in the management of cardiovascular disorders.

In previous papers we have derived equations of motion with radiation terms and proved the existence-uniqueness of periodic solution of the 3-body problem of classical electrodynamics. The number of equations of motion – 12 is more than the number of unknown functions – 9. It turns out that 9 equations are independent and the rest 3 ones are consequences of them. These three equations have a solution and they give the expressions for the energy of the moving particles. The main goal of the present paper is to estimate the energy of rounding about the nuclei particles and compare it with the values given by quantum mechanics.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

Snow cover products are primarily derived from the Moderate-resolution Imaging Spectrometer (MODIS) and Advanced Very High-Resolution Radiometer (AVHRR) datasets. MODIS achieves both snow/non-snow discrimination and snow cover fractional retrieval, while early AVHRR-based snow cover products only focused on snow/non-snow discrimination. The AVHRR Climate Data Record (AVHRR -CDR) provides a nearly 40-year global dataset that has a potential to fill a gap in long term snow cover fractional monitoring. Our study selects the Qinghai-Tibet Plateau as the experimental area, utilizing AVHRR-CDR surface reflectance data (AVH09C1) and calibrating with MODIS snow product MOD10A1. The snow cover percentage retrieval from the AVHRR dataset is performed using Surface reflectance at 0.64μm (SR1) and Surface reflectance at 0.86μm (SR2), along with a simulated Normalized Difference Snow Index (NDSI) model. Also, in order to detect the effects of land cover type and topography on snow inversion, we tested the accuracy of the algorithm with and without these influences, respectively (vanilla algorithm & improved algorithm). The accuracy of the AVHRR snow cover percentage data product is evaluated using MOD10A1、 ground snow-depth measurements and ERA5. Results indicate that the logic model based on NDSI has the best fitting effect, with R-square and RMSE values of 0.83 and 0.10, respectively. Meanwhile, the accuracy was improved after taking into account the effects of land cover type and topography. The model is validated using MOD10A1 snow-covered areas, showing snow cover area differences of less than 4% across 6 temporal phases. Improved algorithm results in better consistency with MOD10A1 than vanilla algorithm. Moreover, the RMSE reaches greater levels when the elevation is below 2,000 meters or above 6,000 meters, and is lower when the slope is between 16° and 20°. Using ground snow-depth measurements as ground truth, the multi-year recall rates are mostly above 0.7, with an average recall rate of 0.81. Results also show a high degree of consistency with ERA5. The validation results demonstrate that the AVHRR snow cover percentage remote sensing product proposed in this study exhibits high accuracy in the Tibetan Plateau region, also demonstrating that land cover type and topographic factors are important to the algorithm. Our study lays the foundation for the global snow cover percentage product based on AVHRR-CDR，furthermore lays a basic work for generating a long-term AVHRR-MODIS fractional snow cover dataset.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

The effect of proteolytic enzymes including Cathepsin K, a cysteine cathepsin, in onset and progression of cancers in human has been research intensive. Cathepsin K involves in many aspects and stages of cancers including apoptosis, cell proliferation, cancer immunology, inflammatory cell recruitment to tumors and aiding in the process of mobilization of normal healthy cells from their tissue compartments assisting in metastasis and angiogenesis. The objective of this review is to collect together and summarize and analyze the biochemical and physiological pathways of how cathepsin K is involved in onset and progression of cancers with more emphasis on breast and prostate cancers and cathepsin K regulated mechanisms underlying metastasis of such cancers to bones. Information for the review was gathered through published literature from global databases such as Google Scholar, PUBMED and NCBI on different studies on physiological interactions between enzymatic activity of cathepsin K with cancers and metastasis to bones. Analysis of published studies reveal that immunohistochemical studies of breast cancer cells indicate that they overexpress cathepsin K resulting in induction of aberrant mechanisms of cell signaling in breast cancers, creating a higher tendency for their metastasis to bones. Immunohistochemical, immunoprecipitation and fluorgenic assays of several studies done on the association of the same enzymatic activity on prostate cancers shows elevated levels of cathepsin K. Lesions derived from prostate cancer cell masses were observed to undergo increased bone formation and resorption levels. Such resorption levels cause secretion of biological factors promoting tumor expansion. In addition, studies indicate that Cathepsin K was observed to be a key component promoting higher bone resorption levels in patients suffering from cancer. Authors suggest that, to completely understand the association of cathepsin K on cancerous cells and their mechanism in metastasis, distributary patterns of cathepsin K in healthy human tissues needs to be extensively studied initially. It is also suggested that metastasis of breast and prostate cancers to bone could be terminated and overcome by successful production of efficient and precise inhibitory therapeutics targeting the enzymatic activity of Cathepsin K with minimum unintended adverse health effects.

Based on the perspective of complex directed weighted network analysis, this paper constructs a static resilience evaluation framework for trade networks from two dimensions: structural resilience and node resilience. It studies the evolution of static resilience in the upstream, midstream, downstream, and recycling trade networks of global wood forest products from 2002 to 2021. The study finds that the total trade volume of global wood forest products has increased by 58.0%, 77.3%, 71.2%, and 77.2% in the upstream, midstream, downstream, and recycling sectors, respectively. The downstream trade network exhibits efficient information transmission and resource mobility capabilities. All four types of trade networks exhibit scale-free characteristics, with core countries such as China, the United States, and Germany playing a dominant role in the network and playing a crucial role in network robustness, but also increasing network vulnerability. In terms of unweighted assortativity, all four networks exhibit the characteristic of "small countries relying on hubs," while the weighted assortativity of the downstream network is positive, indicating enhanced network resilience. In terms of node resilience, countries exhibit significant differences and dynamic changes. China demonstrates strong resilience and adaptability, while the United States maintains its core position. China's influence in the downstream network has significantly increased, and India has rapidly emerged in the recycling network. To enhance network resilience, it is necessary to increase diversity and redundancy, establish effective emergency response mechanisms, and promote the diversification and green transformation of the supply chain.

Background/Aim: Performing emergency surgery for bowel obstruction continues to place a significant strain on the healthcare system. Conventional assessment methods for outcomes in bowel obstruction cases often concentrate on isolated factors, and the evaluation of results for individuals with bowel obstruction remains poorly studied. This study aimed to examine the risk factors associated with major postoperative complications. Methods: We retrospectively analyzed 99 patients undergoing surgery from 2015 to 2022. We divided the patients into two groups: 1) benign related obstruction (n=68), 2) cancer related obstruction (n=31). We used logistic regression, KNN and XGBOOST. We calculated the receiver operating characteristic curve, and accuracy of the model. Results: Colon obstructions were more frequent in the cancer group (p=0.005). Operative time, intestinal resection and stoma were significantly more frequent in the cancer group. Major complications were 41% for the cancer group vs. 20 in the benign group (p=0.03). Uni-and multivariate analysis shows that significant risk factors for major complication were cancer related obstruction and CRP. The best model was KNN with an accuracy of 0.82. Conclusion. Colonic obstruction is associated with a tumor-related blockage. Malignant cancer and an increase in C-reactive protein (CRP) are significant risk factors for patients who have undergone emergency surgery due to major complications. KNN could improve the process of counseling and the perioperative management of patients with intestinal obstruction in emergency settings.

Seventy-seven percent of Irish primary school children do not meet recommended physical activity (PA) guidelines [1]. The Daily Mile (TDM) is a primary school initiative designed to increase children’s PA output. This study evaluates TDM’s perceived effect on Irish primary school children’s health-related metrics. A mixed-methods study, comprising two data collection phases, used the RE-AIM framework to evaluate TDM [2]. Phase one involved teachers, principals and classroom assistants (n = 191) from TDM-registered schools completing a questionnaire. Two TDM-registered schools participated in phase two where, (i) interviews were conducted with each principal, (ii) a teacher sub-sample (n = 4) participated in a focus group and (iii) a child sub-sample (n = 14) participated in separate focus groups. TDM was perceived to positively impact markers of children’s health, including their PA behaviour, physical fitness and social wellbeing. Inclement weather (66.5%) and a lack of time (56.5%) were reported as the top-ranked implementation barriers. Moreover, TDM’s repetitive nature often left children feeling disinterested and resulted in some teachers modifying the initiative to maintain engagement levels. Maintaining the long-term implementation of TDM and its health benefits in primary schools may require bespoke amendments to the original format to preserve children’s engagement.

It was the aim of this study to compare the ratio of salbutamol and its major metabolite salbutamol-4’-O-sulfate as well as the quantity excreted renally after oral and inhalative administration. Additionally, the excretion pattern after application of racemic salbutamol opposed to the pure enantiomer levosalbutamol was evaluated. For quantitation of the sulfonated metabolite of salbutamol, reference material was synthesized and characterized by NMR and HRMS. Urine samples were analyzed by ultrahigh performance liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS). Salbutamol is mainly metabolized by sulfotransferase 1A3 (SULT1A3), which is most abundantly found in the jejunum. A high first pass effect occurs upon oral administration, which leads to a higher amount of salbutamol-4’-O-sulfate in urine compared to unchanged salbutamol excreted within the first hour post administration. Thus, when administered orally, the proportion of metabolite to total salbutamol was higher than for inhalative administration in the early urinary excretion. Levosalbutamol is the favored enantiomer of SULT1A3 and therefore metabolized at a higher rate whereas racemic salbutamol shows a reduced proportion between metabolite and parent compound. The amount of sulfoconjugate was found higher than that of the parent compound for all urine samples except for those excreted in the first hour after inhalative administration.

Our environment has been significantly impacted by man-made pollutants, primarily due to industries make substantial use of synthetic chemicals, resulting in significant environmental consequences. In this research investigation, the co-precipitation approach was employed for the synthesis of cellulose-based ferric oxide (Fe₂O₃/cellulose) and copper oxide nanoparticles (CuOx-NPs). Scanning electron microscopy (SEM) analyses were conducted to determine the properties of the newly synthesised nanoparticles. Furthermore, the synthesized nanoparticles were employed for eliminating chromium from aqueous media under various conditions, including temperature, contact time, adsorbent concentration, adsorbate concentration, and pH. Additionally, the synthesised materials were used to recover Cr(VI) ions from real samples, including tap water, seawater, and industrial water, and the adsorptive capacity of both materials evaluated under optimal conditions. The synthesis of Fe₂O₃/cellulose and CuOx-NPs proved to be effective, as indicated by the outcomes of the study.