In this research first, a sequence of properties called delta is assigned to each prime number and then examined. Deltas are only dependent on the distribution of prime numbers, so the results obtained for the delta distribution can be considered as a proxy for the distribution of prime numbers. The first observation was that these properties are not unique and different prime numbers may have the same value of delta of a given order. It was found that a small number of deltas cover a large portion of prime numbers, so by recognizing repetitive deltas, the next prime numbers can be predicted with a certain probability, but the most important observation of this study is the normal distribution of deltas. This research has not tried to justify the obtained observations and instead of answering the questions, it seeks to ask the right question.

This research offers an extensive analysis of a family of prime-generating polynomials \( P_k(n) = n^2 - (2k - 79)n + [41 + (k - 39)(k - 40)] \), designed to generate prime numbers for integer values of \( n \) up to \( k \) where \( k \in \{1, 2, \ldots, 80\} \). We elaborate on mathematical clarity, consistency in proofs, error bounds, prime repetition analysis, and cryptographic implications. This study provides in-depth inductive proofs, graphical error bounds analysis, prime repetition statistics, and cryptographic security assessments, offering novel insights and future directions for research in number theory and secure prime generation.

Integer is either a composite number or a prime number. Therefore, detecting composite numbers is important for solving prime numbers. The study of prime numbers, apart from satisfying human curiosity, can be very important. In this article, the order of composite numbers has been detected. And explained with a simple method and a simple function. And, a method has been developed in which all composite numbers and therefore prime numbers can be determined by using the specified methods, functions and formulas.

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 $g_{n}<{\sqrt {p_{n}}}$. This note presents a proof of Oppermann's conjecture using the square root function on inequalities involving prime numbers. This proof simultaneously establishes Andrica's, Legendre's, and Brocard's conjectures.

Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P\bigcap S=\emptyset In this article, we introduce several results concerning graded S-prime ideals. Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals. We say that P is a graded weakly S-prime ideal of R if there exists s\in S such that for all x, y\in h(R), if 0\neq xy\in P, then sx\in P or sy\in P. We show that graded weakly S-prime ideals have many acquaintance properties to these of graded weakly prime ideals.

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.

We developed some questions regarding twin prime conjecture by examining the bounded gaps between composite numbers and explained the relations between the formulas regarding composite numbers. Then we proved the twin prime conjecture to answer the new questions raised by proving the expression: \[ \liminf_{n\to\infty} (c_n_+_1 - c_n) \ge 10. \] In addition, we prove many different approaches have been and it has been proved that there must be a twin prime in the range $(p_k_2\cdot p_k_1, p^2_k_1)$, where $p \neq 2$.

In this paper, we study the symmetry between the supersingular prime number according to smallest sphenic number. With this symmetry, we show that the elements of sporadic group generates all prime numbers with the order by a simple application.

We talk about random when it is not possible to determine a pattern on the observed outcomes. A computer follows a sequence of fixed instructions to give any of its output, hence the difficulty of choosing numbers randomly from algorithmic approaches. However, some algorithms based on mathematical formulas like the Linear Congruential algorithm and the Lagged Fibonacci generator appear to produce "true" random sequences to anyone who does not know the secret initial input [1]. Up to now, we cannot rigorously answer the question on the randomness of prime numbers [2, page 1] and this highlights a connection between random number generator and the distribution of primes. From [3] and [4] one sees that it is quite naive to expect good random reproduction with prime numbers. We are, however, interested in the properties underlying the distribution of prime numbers, which emerge as sufficient or insufficient arguments to conclude a proof by contradiction which tends to show that prime numbers are not randomly distributed. To achieve this end, we use prime gap sequence variation. The algorithm that we produce makes possible to deduce, in the case of a binary choice, a uniform behavior in the individual consecutive occurrence of primes, and no uniformity trait when the occurrences are taken collectively.

I had previously developed an approach called Gocgen approach, which claimed to prove twin prime conjecture. In this paper, I processed the previously developed Gocgen approach with the zeta function and explained the relationship between the zeta function with some formulas to offer another perspective on the zeta function, and also created a new function that explains the Gocgen approach using the zeta function. Understanding the new function created will provide insight into the frequency of prime numbers.

Throughout this paper, we will establish a comprehensive theoretical foundation and rigorously develop the methodology to investigate the structure of quotient ring S/P under the influence of symmetric generalized n-derivations, where S represents an arbitrary ring, and P signifies a prime ideal of S satisfying certain algebraic identities acting on prime ideal P without relying on the assumption of primeness or semi-primeness of the ring.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation is central, then the ring is commutative. In the present paper, we extend this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we establish *-version of Vukman’s theorem [48, Theorem 1]. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the *-version of Vukman’s theorem, we show that if a 2-trosion free semiprime ring A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in a spirit of the classical result due to Bell and Martindale [19, Theorem 3]. As the applications, we extends and unify several classical theorems proved in [6],[25,[42], and [48] . Finally, we conclude our paper with a direction for further research.

The Ramanujan primes are the least positive integers Rn having the property that if m ≥ Rn, then π_m − π_(m/2) ≥ n. This document develops several bounds related to the Ramanujan primes, sharpening the currently known results. The theory presented is by no means exhaustive, however it provides insights for future research work. Alternatively, we may say that it is a road map which may be followed to make further discoveries.

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 part “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 proof for twin prime conjecture.

The primary purpose of this article is to study the asymptotic and numerical estimates in detail for higher degree polynomials in $\pi(x)$ having a general expression of the form, \begin{align*} P(\pi(x)) - \frac{e x}{\log x} Q(\pi(x/e)) + R(x) \end{align*} $P$, $Q$ and $R$ are arbitrarily chosen polynomials and $\pi(x)$ denotes the \textit{Prime Counting Function}. The proofs require specific order estimates involving $\pi(x)$ and the \textit{Second Chebyshev Function} $\psi(x)$, as well as the famous \textit{Prime Number Theorem} in addition to certain meromorphic properties of the \textit{Riemann Zeta Function} $\zeta(s)$ and results regarding its non-trivial zeros. A few generalizations of these concepts have also been discussed in detail towards the later stages of the paper, along with citing some important applications.

In this paper, we propose a novel stochastic model to study prime distribution in almost-short intervals, inspired by a corollary of the Maynard-Guth theorem. The model uses the equation \[ x_{n+1} = x_n + \frac{y}{\log x_n} + \epsilon_n, \] where \(\epsilon_n\) follows a Laplace distribution, and demonstrates that our new bound surpasses both Walfisz and Maynard-Guth bounds, particularly for large \(x\): \[ \left| \pi(x + y) - \pi(x) - \frac{y}{\log x} \right| \leq C \cdot y \exp(-\sqrt[4]{\log x}). \] Additionally, we explore a modulated Hamiltonian \(\hat{H}(x)\), derived from a potential \(V(x)\) and a test function \(f(x)\), that exhibits behavior akin to the energy levels of the heavy nucleus \(H_{38}\). The gaps between these energy levels resemble the distribution of zeros of the Riemann zeta function near the critical line, suggesting that \(\zeta(0.5 + i \hat{H}(x))\) corresponds to the energy levels of \(\hat{H}(x)\), thus supporting a quantum mechanical interpretation of the Riemann hypothesis. Furthermore, assuming the Elliott-Halberstam conjecture, which implies that prime gaps can be as small as 12, we find that the transition rate \(\Gamma_{p \to p+12}\) between quantum states associated with prime numbers increases with larger primes. This observation indicates that the distribution of prime gaps reflects an underlying discrete structure in the "energy" landscape of primes, offering a novel perspective on the connection between number theory and quantum physics.

The present study aims to show on the one hand how easily one can get confused when doing research on the internet. Different platforms, fora and homepages supply the visitor with different - and sometimes contradictory - information. On the other hand, we show how to overcome these contradictions and produce valuable research based on almost all sources. For our study, we use the example of the Feit-Thompson conjecture, which is - in opposite to the well-known Feit-Thompson theorem - not widely known. We try to clarify the scientific literature on this topic and we embed our own result into the present state of art. We prove that pq−1p−1 does not divide qp−1q−1 if p and q are twin primes, i.e. p=q+2. Thus we prove that the Feit-Thompson conjecture is true for twin prime numbers.

Around 1637, Pierre de Fermat famously wrote in the margin of a book that he had a proof for the equation $a^n + b^n = c^n$ having no positive integer solutions for exponents $n$ greater than 2. This statement, now known as Fermat's Last Theorem, remained unproven for centuries, despite the efforts of countless mathematicians. Andrew Wiles' work in 1994 finally provided a rigorous proof of Fermat's Last Theorem. However, Wiles' proof relied on advanced mathematical techniques that were far beyond the scope of Fermat's time, raising questions about whether Fermat could have truly possessed a proof using the methods available to him. Wiles's achievement was widely celebrated, and he was awarded the Abel Prize in 2016 in recognition of his groundbreaking work. The citation for the award described his proof as a "stunning advance" in mathematics. The present work offers a potential solution to Fermat's Last Theorem that may be more aligned with the original approach that Fermat claimed to have used.

The Diophantine equation for which p is prime 2^n = p^2 + 7 and n is integers with p > 0, is examined in this work. It is demonstrated by examining the characteristics of the equation that the only solutions meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7. In order to analyze the above equation, it is necessary to look at the properties of primes and how they relate to powers of two. These results advance our knowledge of prime numbers and how they behave in certain mathematical problems.

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.

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.

The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers. This paper presents theoretical results which originated with a researchin the subject of the maximal prime gaps. the document presents the sharpest upper bound for the maximal prime gaps ever developed. The result becomes the Supremum bound on the maximal prime gaps and subsequently culminates with the conclusive proof of the Firoozbakht's Hypothesis No 30. Firoozbakht's Hypothesis implies quite a bold conjecture concerning the maximal prime gaps. In fact it imposes one of the strongest maximal prime gaps bounds ever conjectured. Its truth implies the truth of a greater number of known prime gaps conjectures, simultaneously, the Firoozbakht's Hypothesis disproves a known heuristic argument of Granville and Maier. This paper is dedicated to a fellow mathematician, the late Farideh Firoozbakht.

The rising importance of Big Data in modern information analysis is supported by vast quantities of user data, but it is only possible to collect sufficient data for all tasks within certain data-gathering contexts. There are many cases where a domain is too novel, too niche, or too sparsely collected to adequately support Big Data tasks. To remedy this, we have created ADG Engine that allows for the generation of additional data that follows the trends and patterns of the data that’s already been collected. Using a database structure that tracks users across different activity types, ADG Engine can use all available information to maximize the authenticity of the generated data. Our efforts are particularly geared towards data analytics by identifying abnormalities in the data and allowing the user to generate normal and abnormal data at custom ratios. In situations where it would be impractical or impossible to expand the available dataset by collecting more data, it can still be possible to move forward with algorithmically expanded data datasets.

Flammability was evaluated and the results showed the values of critical flux at extinguishment (CFE) as 49.5kW/㎡ on average, total heat release (Qt) as 0.21MJ on average, and peak heat release rate (Qp) as 0.66kW on average, which satisfied all of the thresholds presented by the IMO. Therefore, flame-retardant plywood, of which the flame-retardant performance was evaluated, was determined to be an applicable finishing material that satisfies fire safety standards.

A prime number is a natural number with no divisors other than itself and the number 1. There are many unsolved problems related to prime numbers. One such problem is finding a general method for identifying prime numbers. Although it is known that all prime numbers fall under the categories of 2, 3, or 6n±1 (where n≥1), a formalized method for eliminating composite numbers (non-prime numbers) from these categories has yet to be developed. This paper aims to explore a possible method for such elimination, which involves checking whether there exists an n that satisfies n = 6km+k+m or n = 6km+k-m (where k and m are non-zero integers). This method is expected to be a major step forward in the derivation of prime numbers.

Bacillus Calmette-Guérin (BCG) is the only widely used prophylactic tuberculosis (TB) vaccine that can prevent severe TB in infants. However, it provides poor protection in adults, and therefore, there in ongoing research on new TB vaccines and immunization strategies with more durable immune effects. The recombinant BCG and BCG prime-protein booster are two important vaccine strategies that have recently been developed based on BCG and could improve immune responses. In this study, three immune strategies based on four protective antigens, namely, ESAT-6, CFP-10, nPPE18, and nPstS1, were applied to construct recombinant rBCG-EPCP009, EPCP009 subunit protein, and BCG prime-EPCP009 booster vaccine candidates. The short- and long-term immune effects after vaccination in Balb/c mice were evaluated based on humoral immunity, cellular immunity, and the ability of spleen cells to inhibit in vitro mycobacterial growth. At 8 and 12 weeks after the initial immunization, splenocytes from mice inoculated with the BCG prime-EPCP009 protein booster secreted higher levels of PPD- and EPCP009-specific IFN-γ, IL-2, TNF-α, IL-17, GM-CSF, and IL-12 and had a higher IFN-γ⁺CD4⁺ TEM:IL-2⁺CD8⁺ TCM cell ratio than splenocytes from mice inoculated with the rBCG-EPCP009 and EPCP009 proteins. In addition, the EPCPE009-specific IgG2a/IgG1 ratio was slightly higher in the BCG prime-EPCP009 protein booster group than in the other two groups. The in vitro mycobacterial inhibition assay showed that the splenocytes of mice from the BCG prime-EPCP009 protein booster group exhibited stronger inhibition of Mycobacterium tuberculosis （M. tuberculosis）growth than the splenocytes of mice from the other two groups. These results indicate that the BCG prime-EPCP009 protein booster exhibited superior immunogenicity and M. tuberculosis growth inhibition to the parental BCG, rBCG-EPCP009, and EPCP009 proteins under in vitro conditions. Thus, the BCG prime-EPCP009 protein booster may be important for the development of a more effective adult TB vaccine.

In this study, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings in [17]. Firstly we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hyper-modules, then we give some relevant properties of the hypermodule in this topological hyperspace.

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

This research paper aims to explicate the complex issue of the Riemann's Hypothesis and ultimately presents its elementary proof. The method implements one of the binomial coefficients, to demonstrate the maximal prime gaps bound. Maximal prime gaps bound constitutes a comprehensive improvement over the Bertrand's result, and becomes one of the key elements of the theory. Subsequently, implementing the theory of the primorial function and its error bounds, an improved version of the Gauss' offset logarithmic integral is developed. This integral serves as a Supremum bound of the prime counting function Pi(n). Due to its very high precision, it permits to verify the relationship between the prime counting function Pi(n) and the offset logarithmic integral of Carl Gauss. The collective mathematical theory, via the Niels F. Helge von Koch equation, enables to prove the RIemann's Hypothesis conclusively.

In this paper, a "local" algorithm is determined for the construction of two recurrent sequences of positive primes ( ) and ( ), (( ) dependent of ( ) ), such that for each integer n their sum is equal to 2n . To form this, a third sequence of primes ( ) is defined for any integer n by : = Sup( p ∈ : p ≤ 2n - 3 ) , where is the infinite set of primes. The Goldbach conjecture has been proved for all even integers 2n between 4 and 4. In the table of terms of Goldbach sequences given in appendix 10 , values of the order of 2n = are reached. This " finite ascent and descent " method proves the binary Goldbach conjecture ; an analogous proof by recurrence is established and an increase in by 0.7( is justified. Moreover, the Lagrange-Lemoine-Levy conjecture and its generalization, the Bezout-Goldbach conjecture, are proven by the same type of procedure.

Prime number-related issues can be viewed from drastically different perspectives by examining the close connections between prime numbers and composite numbers. We think that multiple perspectives are the pillars on the path to solutions so we have created this study. As a result of the study, we proposed two new formulas by presenting three theorems and one proof for each theorem, a total of three proofs. We proved that the formula p · n + p returns a composite number in the first of the theorems, which is the preliminary theorem. Our first theorem except the preliminary theorem is that the formula p · n + p returns all composite numbers, and we proved that too. Finally, we created Theorem II using Theorem I to use in our other work and proved that the formula 2 · n · p + p returns all odd composite numbers, which is Theorem II. Afterward, we presented the similarities of the 2 · n · p + p formula we put forth with another known formula.

This paper presents proof of Riemann's hypothesis by utilizing the golden ratio and the ellipse's eccentricity in six dimensions. This proof extends across all scientific fields. this research introduces logical and mathematical principles for distributing, recognizing, and categorizing prime numbers. It also explores the relationship between prime numbers and the complex conjugate of five prime numbers in various dimensions. Accordingly, it delves into the classification of even numbers based on prime numbers. This study examines the proof of Riemann's hypothesis from a geometric dimension perspective. Based on this, the mathematical structure of an integrated theory is defined. properties and principles associated with prime numbers reveal connections between quantum mechanics and general relativity.

The Riemann hypothesis is the assertion that all non-trivial zeros are complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. There are several statements equivalent to the famous Riemann hypothesis. Robin's criterion states that the Riemann hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma} \cdot n \cdot \log \log n$ holds for all natural numbers $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function of $n$, $\gamma \approx 0.57721$ is the Euler-Mascheroni constant and $\log$ is the natural logarithm. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. In this note, using Robin's criterion on superabundant numbers, we prove that the Riemann hypothesis is true.

When discussing the Diophantine quintic equation $p(a^5 + b^5) = q(c^5 + d^5)$ where p is a prime and q is an integer, there is a clear gap between the mathematical literature and online forums. Because of the intrinsic complexity of parameterizing fifth-degree equations, this equation re- mains largely unexplored. In this work, we approach this quintic problem through algebraic methods with the goal of providing numerical solutions that illuminate its properties and behaviors.Our research uncovers in- triguing patterns and connections that shed light on the enigmatic nature of Diophantine quintic equations in this particular form.

One of the most important unresolved mysteries in mathematics is the Riemann Hypothesis, which suggests a fundamental connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers. Here, we explore the fascinating union of trigonometric functions, prime numbers, and the Riemann zeta function through an examination of the zeros in the statement ln(sec(π·n log(n))). We demonstrate a strong mathematical connection between these components, providing information on the mysterious properties of prime numbers and their complex relationships to basic mathematical operations. Our thorough investigation adds to the current discussion of the Riemann Hypothesis by offering possible solutions and deepening our comprehension of the intricate relationship between number theory and analytic functions.

This paper serves as a seamless continuation of the previous work titled "Special Spirals are Produced by the ROTASE Galactic Spiral Equations with the Sequential Prime Numbers." Upon revisiting the data, a noteworthy observation emerged: the special spirals can be meticulously aligned with the prime spiral on a point-by-point basis through careful scaling and rotation for the parameter ρ remaining a constant greater than one. As ρ increases, both the scaling factor and rotation angle exhibit a corresponding augmentation, albeit with an intriguing caveat—the rotation angle asymptotically approaches its limit of 90°. Notably, the galactic spiral can be perceived as a remarkably close approximation of the Archimedean spiral, with the degree of proximity increasing as ρ grows larger. Furthermore, an intriguing correspondence arises when ρ takes on a value of 1; at this value, the galactic spiral bears a striking resemblance to the Fermat spiral, the space between two consecutive spiral loops undergoes a continuous reduction as the loop's radius expands, yet it never diminishes to zero; simultaneously, the area between two successive loops experiences an augmentation with the value of ρ.

Let's define $\delta(x) = (\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often. Let's also define $S(x) = \theta(x) - x$, where $\theta(x)$ is the Chebyshev function. It is known that $S(x)$ changes sign infinitely often. We define the another function $\varpi(x) = \left(\sum_{{q\leq x}}{\frac{1}{q}}-\log \log \theta(x)-B \right)$. We prove that when the inequality $\varpi(x) \leq 0$ is satisfied for some number $x \geq 3$, then the Riemann hypothesis should be false. The Riemann hypothesis is also false when the inequalities $\delta(x) \leq 0$ and $S(x)\geq 0$ are satisfied for some number $x \geq 3$ or when $\frac{3 \times \log x + 5}{8 \times \pi \times \sqrt{x} + 1.2 \times \log x + 2} + \frac{\log x}{\log \theta(x)} \leq 1$ is satisfied for some number $x \geq 13.1$.

Let {$\Gamma(k)$} denote {$(k-1)!$}, and let {$\Gamma_{n}(k)$} denote {$(k-1)!$}, where {$n \in \{3,\ldots,16\}$} and {$k \in \{2\} \cup [2^{\textstyle 2^{n-3}}+1,\infty) \cap \mathbb N$}. For an integer {$n \in \{3,\ldots,16\}$}, let $\Sigma_n$ denote the following statement: if a system of equations {${\mathcal S} \subseteq \{\Gamma_{n}(x_i)=x_k:~i,k \in \{1,\ldots,n\}\} \cup \{x_i \cdot x_j=x_k:~i,j,k \in \{1,\ldots,n\}\}$} with $\Gamma$ instead of $\Gamma_{n}$ has only finitely many solutions in positive integers {$x_1,\ldots,x_n$}, then every tuple {$(x_1,\ldots,x_n) \in (\mathbb N \setminus \{0\})^n$} that solves the original system ${\mathcal S}$ satisfies {$x_1,\ldots,x_n \leqslant 2^{\textstyle 2^{n-2}}$}. Our hypothesis claims that the statements {$\Sigma_{3},\ldots,\Sigma_{16}$} are true. The statement {$\Sigma_6$} proves the following implication: if the equation {$x(x+1)=y!$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(1,2),(2,3)\}$}. The statement {$\Sigma_6$} proves the following implication: if the equation {$x!+1=y^2$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(4,5),(5,11),(7,71)\}$}. The statement {$\Sigma_9$} implies the infinitude of primes of the form {$n^2+1$}. The statement {$\Sigma_9$} implies that any prime of the form {$n!+1$} with {$n \geqslant 2^{\textstyle 2^{9-3}}$} proves the infinitude of primes of the form {$n!+1$}. The statement {$\Sigma_{14}$} implies the infinitude of twin primes. The statement {$\Sigma_{16}$} implies the infinitude of Sophie Germain primes.

The field of 3D model generation has become essential across various industries, including gaming, virtual and augmented reality (VR/AR), architecture, and medical imaging. Traditionally reliant on manual efforts, 3D content creation is now being transformed by deep generative models, enabling more efficient, scalable, and dynamic generation of complex shapes and environments. This survey provides a comprehensive review of key backbone architectures used for 3D generation, including autoencoders, variational autoencoders (VAEs), generative adversarial networks (GANs), autoregressive models, diffusion models, normalizing flows, attention-based models, CLIP-guided models, and procedural generation techniques. We explore each model’s role in 3D generation, highlighting their strengths—such as the precision of VAEs, the realism of GANs, the stability of diffusion models, and the scalability of procedural methods—alongside their limitations, such as training instability, high computational costs, and the difficulty in handling multi-modal data. Additionally, we discuss the increasing relevance of attention-enhanced models and the integration of text-based CLIP supervision for improved semantic alignment in 3D outputs. The survey concludes with an analysis of open challenges, including balancing efficiency with expressiveness, managing training complexity, and addressing dataset limitations. It also identifies future research directions, such as few-shot learning, hybrid architectures, and neural-symbolic approaches, which promise to advance the field by improving the generalization and versatility of 3D generation models. This paper aims to guide researchers and practitioners in navigating the evolving landscape of 3D generative methods and inspire new innovations in the creation of realistic, high-quality 3D content.

this paper we present approaches for generating random numbers along with potential applications. Rather than trying to provide extensive coverage of several techniques or algorithms that have appeared in the scientific literature, we focus on some representative approaches presenting their workings and properties in detail. Our goal is to delineate their strengths and weaknesses as well as their potential application domains so as the reader can judge what would be the best approach for the application in hand, possibly a combination of the available approaches. For instance, a physical source of randomness can be used for the initial seed, then suitable preprocessing can enhance its randomness and then the output of the preprocessing can feed different types of generators, e.g. a linear congruential generator, a cryptographically secure one and one based on the combination of one way hash functions and shared key cryptoalgorithms in various modes of operation. Then, if desired, the outputs of the different generators can be combined giving the final random sequence. Moreover, we present a set of practical randomness tests which can be applied on the outputs of random number generators in order to assess their randomness characteristics. In order to demonstrate the importance of unpredictable random sequences, we present an application of cryptographically secure generators in domains where unpredictability is one of the major requirements, i.e. eLotteries and cryptographic key generation.

Background : The current corruption case in Indonesia are severely problematic since it is normalized by society. As a response, the current agenda of the Indonesian government to tackle it is by raising awareness of youth towards Indonesia’s corruption case. Aim : This study aims to knowing the importance of anti-corruption education and its applications among students. Method : The methodology of this study is the use of a qualitative survey on Faculty of Pharmacy students and interviews with representatives of students of the Faculty of Pharmacy. The population of this study is students of Airlangga University. The sample of this study is 52 students of class C the Faculty of Pharmacy Result : Students have awareness about corruption and even proposed that the current anti-corruption education is not enough to tackle corruption. Recommendation : The researcher suggests that students can be brave to campaign about the importance of anti-corruption education to the public. Limitation : The limitation of this study is that it is difficult to conduct research because in the online pandemic era, this results in delays in the research process.

Pancasila is the identity of the Indonesian nation, which means that Pancasila is a national characteristic that cannot be found in any country. Pancasila points are taken from the noble values of the Indonesian state. These principles contain culture, customs, and national character known as manners, cooperation, and high nationalism. As the successor to Indonesian culture, the young generation must be able to preserve and develop Pancasila. In this era of globalization, there are many challenges for the younger generation in preserving Pancasila. This study aims to provide an overview of the decline of Pancasila identity among the younger generation due to the impact of globalization. The research question that has been determined is how the practice behaviour of the younger generation towards the implementation of Pancasila, the solutions and efforts that all Indonesian people can make regarding the crisis of Pancasila identity in the era of globalization. This research method uses a literature review. The research sources were conducted from the latest journals and books published in 2019 until 2021 related to the theme of Pancasila and the millennial generation. The results showed that globalization has greatly facilitated foreign cultures to enter Indonesia. The younger generations use this foreign culture as a lifestyle without filtering it, whether it contains Pancasila values or not. This causes Pancasila has been forgotten and no longer applied in their everyday life. Young people can make various efforts to preserve the national identity, namely Pancasila. Apart from the role of the young generation itself, Indonesian society can also play an essential role in supporting the younger generation to continue implementing Pancasila in their lives. By conducting this research, it is hoped that Indonesia's young generation can understand, select, and stay away from the negative impacts of globalization that enter Indonesia freely. The solution that can be given from this research is that the younger generation must love their own culture more and practice every principle in Pancasila. Parents, educational institutions, and the government must also support the younger generation to maintain national identity, Pancasila values. The limitation of this research is that the researcher did not conduct any primary data, which means the data were not directly from the source. This causes the accuracy of this study to be less guaranteed. The recommendation that the researchers can give for further research is to obtain primary data to ensure accuracy and explore research topics regarding the fading of Pancasila identity in the younger generation in this era of globalization.

Technological developments, as a result of globalization, indirectly affect human lifestyles, one of which is the Indonesian people. In a situation of change towards the Industrial Revolution 4.0, Pancasila has a role as a guide for the Indonesian people to be what by the noble values ​​of the nation. However, the role of the millennial generation in maintaining these noble values ​​is important considering that they are the spearhead of the country's development. From this statement, this study aims to identify and formulate steps to maintain the noble values ​​of Pancasila among the millennial generation so that it does not eliminate national identity and understand the urgency of implementing the Pancasila lifestyle in the era of globalization. By using the literature review method, it can be seen that "grounding" and strengthening the essence of Pancasila values ​​can be a solution so that the existence of Pancasila continues to shine. The Pancasila lifestyle deserves to be implemented because it regulates all behaviors of speech, thought, behavior, action, and good manners so that it must be expressed in the life of the nation and state as well as our everyday life.

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. An ideal I of R disjoint with S is called a weakly S-primary ideal if there exists s∈S such that whenever 0≠ab∈I for a,b∈R, then sa∈√I or sb∈I. The relationships among S-prime, S-primary, weakly S-primary and S-n-ideals are investigated. For an element r in any general ZPI-ring, the (weakly) S_{r}-primary ideals are charctarized where S={1,r,r²,⋯}. Several properties, characterizations and examples concerning weakly S-primary ideals are presented. The stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal are studied. Furthermore, weakly S-decomposable ideals and S-weakly Laskerian rings which are generalizations of S-decomposable ideals and S-Laskerian rings are introduced.

As the international community attaches importance to environmental and climate issues, carbon dioxide emissions in various countries have been subject to constraints and limits. Carbon trading market, as a market tool to reduce greenhouse gas emissions, has gone through a development process from a pilot carbon market to a national carbon market in China. At present, the industries included in the national carbon market are mainly the electric power industry, and the carbon emissions of the electric power industry account for about 40% of the national carbon emissions. According to the construction history of foreign carbon markets, China's future carbon quota allocation will gradually transition from free allocation to auction allocation,the auction mechanism will bring a heavy economic burden to the electric power industry, especially the thermal power generation industry. Therefore, this study takes Guangdong Province as an example to optimize the power generation mix with the objective of minimizing the total economic cost after the innovative introduction of the carbon quota auction mechanism and constructs an optimization model of the power generation mix based on the auction ratio by comprehensively applying the system dynamics model and the multi-objective linear programming model and systematically researches the power generation structure under different auction ratios with the time scale of months and quantitatively evaluates the economic inputs needed to reduce the greenhouse gas emissions.The results of the study show that after comprehensively comparing the total economic cost, renewable energy development and carbon emissions, it is the most scientific and reasonable to set the auction ratio of carbon allowances at 20%, which achieves the best level of economic and environmental benefits.

Paraphrase Generation is one of the most important and challenging tasks in the field of Natural Language Generation. The paraphrasing techniques help to identify or to extract/generate phrases/sentences conveying the similar meaning. The paraphrasing task can be bifurcated into two sub-tasks namely, Paraphrase Identification (PI) and Paraphrase Generation (PG). Most of the existing proposed state-of-the-art systems have the potential to solve only one problem at a time. This paper proposes a light-weight unified model that can simultaneously classify whether given pair of sentences are paraphrases of each other and the model can also generate multiple paraphrases given an input sentence. Paraphrase Generation module aims to generate fluent and semantically similar paraphrases and the Paraphrase Identification systemaims to classify whether sentences pair are paraphrases of each other or not. The proposed approach uses an amalgamation of data sampling or data variety with a granular fine-tuned Text-To-Text Transfer Transformer (T5) model. This paper proposes a unified approach which aims to solve the problems of Paraphrase Identification and generation by using carefully selected data-points and a fine-tuned T5 model. The highlight of this study is that the same light-weight model trained by keeping the objective of Paraphrase Generation can also be used for solving the Paraphrase Identification task. Hence, the proposed system is light-weight in terms of the model’s size along with the data used to train the model which facilitates the quick learning of the model without having to compromise with the results. The proposed system is then evaluated against the popular evaluation metrics like BLEU (BiLingual Evaluation Understudy):, ROUGE (Recall-Oriented Understudy for Gisting Evaluation), METEOR, WER (Word Error Rate), and GLEU (Google-BLEU) for Paraphrase Generation and classification metrics like accuracy, precision, recall and F1-score for Paraphrase Identification system. The proposed model achieves state-of-the-art results on both the tasks of Paraphrase Identification and paraphrase Generation.

In this paper, the distribution of prime numbers is expressed based on proving the Riemann hypothesis. The relationship between three numbers, three, six, and nine, and the modality to the distribution of prime numbers, is one of the results of Riemann's zeta function. Prime numbers are classified into six groups of single-digit numbers. There are no prime numbers in groups of three, six, and nine. The groups are made based on the sum of the internal digits. And for each set, there is an angle in the complex plane. The distance between the prime numbers in each group has a regular pattern. This pattern is a multiple of the numbers three, six, and nine. According to Euler's number, for an angle of 60 degrees, the real part of the cosine is 1/2. Accordingly, all prime numbers are related to angles greater than 60 degrees to 90 degrees. As a result, based on the relationship between the golden spiral and the complex conjugate of the zeta function, the function in The 1/2 point becomes zero based on the prime numbers.

This article provides a proof that the Ramanujan's Inequality given by, \begin{align*} \pi(x)^2 < \frac{e x}{\log x} \pi\left(\frac{x}{e}\right) \end{align*} holds unconditionally for every $x\geq \exp(43.5102146)$. In case for an alternate proof of the result stated above, we shall exploit certain estimates involving the Chebyshev Theta Function, $\vartheta(x)$ in order to derive appropriate bounds for $\pi(x)$, which'll lead us to a much improved condition for the inequality proposed by Ramanujan to satisfy unconditionally.

Sialyllactose (SL) is a functional human milk oligosaccharide essential for immune support, brain development, intestinal maturation, and antiviral defense. However, despite its established health benefits, the effect of SL on exercise performance and muscle mass in mice remains unknown. Here, we aimed to investigate, for the first time, the effects of 6′-SL on muscle functions. Seven-week-old male C57BL/6J mice were administered 100 mg/kg 6′-SL for 12 weeks, after which exhaustive treadmill performance, muscle strength, and muscle phenotype were examined. The administration of 6′-SL significantly improved exhaustive treadmill performance metrics, including distance and exhaustion time. Grip strength was also increased by 6′-SL administration. Additionally, 6′-SL increased muscle mass in both the gastrocnemius (GAS) and soleus. 6′-SL administration led to an increase in the minimum Feret’s diameter and the protein expression of total myosin heavy chain in the GAS muscle. In conclusion, 6′-SL administration in vivo led to increased running distance and time by increasing muscle mass and strength. These findings collectively indicate that 6′-SL is a potential agent for improving muscle health and exercise performance.

Genetic engineering has become an essential element in developing climate-resilient crops and environmental sustainable solutions to respond to the increasing need for global food security. Genome editing using CRISPR/Cas [Clustered regulatory interspaced short palindromic repeat (CRISPR)-associated protein (Cas)] technology is being applied to a variety of organisms, including plants. This technique has become popular because of its high specificity, effectiveness, and low production cost. Therefore, this technology has the potential to revolutionize agriculture and contribute to global food security. Over the past few years, increasing efforts have been seen in its application in developing higher-yielding, nutrition rich, disease resistant, stress-tolerant “crops” fruits and vegetables. Cas proteins such as Cas9, Cas12, Cas13, and Cas14, among others, have distinct architectures and have been used to create new genetic tools that improve features that are important for agriculture. The versatility of Cas has accelerated genomic analysis and facilitated the use of CRISPR/Cas to manipulate and alter nucleic acid sequences in cells of different organisms. This review provides the evolution of CRISPR technology exploring its mechanisms and contrasting it with traditional breeding and transgenic approaches to improve different stress tolerance. We have also discussed the CRISPR/Cas system and explored three Cas proteins that are currently known to exist: Cas12, Cas13, and Cas14 and their potential to generate foreign DNA free or non-transgenic crops that could be easily regulated for commercialization in most countries.

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.

Prime numbers are the atoms of mathematics and mathematics is needed to make sense of the real world. Finding the Prime number structure and eventually being able to crack their code is the ultimate goal in what is called Number Theory. From the evolution of species to cryptography, Nature finds help in Prime numbers. One of the most important advances in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In that paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function defined by: Where ζ(z) is a function of a complex variable z that analytically continues the Dirichlet series. Riemann also formulated a conjecture about the location of the zeros of RZF, which fall into two classes: the "trivial zeros" -2, -4, -6, etc., and those whose real part lies between 0 and 1. Riemann's conjecture Riemann hypothesis [RH] was formulated as this: [RH] The real part of every nontrivial zero z* of the RZF is 1/2. Proving the RH is, as of today, one of the most important problems in mathematics. In this paper we will provide a proof of the RH. The proof of the RH will be built following these five parts: PART 1: Description of the RZF PART 2: The C-transformation PART 3: Application of the C-transformation to in Re(z) 0 to obtain ζ(z)=X(z)-Y(z) PART 4: Analysis of the values of z such that X(z)=Y(z), and |X(z)|=|Y(z)|, that equates to ζ(z)=0 Proof that |X(z)|=|Y(z)| only if Re(z)=1/2 Conclude that ζ(z)=0 only if Re(z)=1/2 for Re(z) 0 PART 5: We will also prove that all non-trivial zeros of ζ(z) in the critical line of the form are not distributed randomly. There is a relationship between the values of those zeros and the Harmonic function that leads to an algebraic relationship between any two zeros.

In this study, a simple approach to solving the Riemann Hypothesis, one of the most prominent unsolved problems in the field of Number Theory in mathematics and one of the “Millenium Prize Problems”, is presented. The Riemann Hypothesis, a conjecture about distribution of prime numbers, has remained unsolved since it was first proposed by German mathematician, Bernhard Riemann in 1859. This paper introduces an analytic continuation of the Zeta Function as well as symmetric approach through integration by parts to address this hypothesis. The proposed solution is obtained through analytical continuation in the critical strip 0<Re(s)<1 to establish that Re(s)=1/2.

For each non-prime odd number as F=pq , if we consider m/n as an approximation for q/p and choose k=mn , then by proving some lemmas and theorems, we can compute the values of m and n. Finally, by using Fermat’s factorization method for F and 4kF as difference of two non-consecutive natural numbers, we should be able to find the values of p and q. Then we introduce two new and powerful sieves for separating composite numbers from prime numbers.

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.

The raw material purchasing (RMP) problem is to determine the purchasing quantities of raw materials in given periods or cycles. Raw material purchasing optimization is crucial for large-scale steel plants because it is closely related to the supply of raw materials and cost savings. The raw material purchasing of large-scale steel enterprises is characterized by many varieties, large quantities, and high costs. The RMP objective is to minimize the total purchasing cost consisting of the price of raw materials, purchasing set-up costs, and inventory costs and meet product demand. We present a mixed integer linear programming (MILP) model and a column generation (CG) solution for the resulting optimization problem. The column generation algorithm is the generalization of the branch & bound algorithm with solving the linear programming (LP) relaxation of MILP using column generation (CG), and its advantage is to handle large-sized MILPs. Experimental results show the effectiveness and efficiency of the solution.

We discuss a formalism which allows for the calculation of a higher harmonic current response to an applied electric field for disordered superconducting systems described on the basis of tight-binding models. The theory is based on an expansion of the density matrix in powers of the field amplitudes where we solve the equation of motion for the individual components. This allows the evaluation of higher order response functions on significantly larger lattices than one can achieve with a previously used approach, which is based on a direct temporal integration of the equation of motion for the complete density matrix. In case of small lattices, where both methods can be applied by including also the contribution of collective modes, we demonstrate the agreement of the corresponding results.

Asphaltene is a component of crude oil that, if mishandled, may create substantial transportation and industrial concerns. It is a solid by nature, with a diverse set of molecular compositions. Furthermore, the oil industry has identified emulsion generation and clogging precipitate as key concerns. The emulsified water droplets in the process are just what give the raw oil its increased viscosity; hence, power is squandered to transport the oil around. The information has been separated into sections based on simulation, solubilization, agglomeration, precipitation, and evidence of model chemicals in the literature. We have included research that investigates the bulk rheology and interfacial rheology of asphaltene to describe its interfacial activity more clearly.

Introduction: Industrial revolution 4.0 in the current era of globalization plays an active role in the modern era in Indonesia. The influence of increasingly advanced technology affects the millennial generation as the nation's next generation to make Pancasila the basis of the State or the foundation of a State. In addition, the millennial generation has begun to shift the guidelines of life from Pancasila so that the appreciation of Pancasila values is starting to disappear along with the development of the times and in line with the progress of Science and Technology (IPTEK). If this continues, then the values of Pancasila will be replaced by a new ideology that will cause behavioural changes in society. Purpose: this study aims to provide the proper application to millennial life using Pancasila values, knowing the behaviour of the millennial generation towards the implementation of Pancasila values, and making Pancasila a way of life. Methods: the method used in this research is Literature Review and takes sources from journals published in 2019 to 2021 related to the Pancasila theme and the millennial generation. Results: the study results show that with the existence of Pancasila as the ideology and principle of the State, it is expected to strengthen the attitude and nature of the community in accepting things outside the norms that exist in Indonesia. In addition, the younger generation is expected to be able to apply Pancasila values along with the development of science and technology in the modern era and current globalization. The research question is how to make the millennial generation implement Pancasila in life in the contemporary period and what solutions can continue to instil Pancasila values ​​in the 4.0 industrial revolution. Recommendation: the conclusion drawn is that Pancasila can become a unifying tool for the nation if the current generation or millennial generation still desires to maintain its values ​​, even though they are in a modern era and many influences from its outside cultures. Limitation: the limitation of this research is not getting all the data directly from the source. The researcher recommends using primary data for the following study to ensure its truth and accuracy better because the researcher directly obtains it.

This paper definitively settles the longstanding conjecture regarding odd perfect numbers. A perfect number is one whose sum of divisors equals itself doubled. While Euclid's method for constructing even perfect numbers is well-known, the existence of odd ones has remained elusive. By employing elementary techniques and analyzing the properties of the divisor sum function, we conclusively prove that no odd perfect numbers exist.

Prime numbers are the building blocks of number theory, and their properties have intrigued mathematicians for centuries. In this paper, we explore a specific categorization of primes, which we refer to as "twin primes", “cousin primes” and "sexy primes". We begin by examining the form of prime numbers greater than 7 and analyze their potential to be expressed in terms of $6n + 5$ or $6n + 7$. This investigation leads to the identification of conditions under which prime numbers can form twin, cousin and sexy pairs. We further develop a general framework to characterize the product of all twin (except 15), cousin (except 21) and sexy primes, providing insights into their algebraic structure.

We demonstrate a new quantitative method to the sieve of Eratosthenes, which is an alternative to the sieve of Legendre. In this method, every element of a given set is sifted out once only, and therefore, this method is free of the Mobius function and of the parity barrier. Using this method, we prove that every sufficiently large even number is the sum of two primes, and that every even number is the difference of two primes in infinitely many ways.

The paper presents two novel mathematical approaches to prove Goldbach's conjecture. The conjecture states that every even number greater than or equal to 6 can be expressed as the sum of two odd prime numbers. We propose that the conjecture has only four genetic codes, and as long as one of them remains valid, the conjecture continues to hold. Through these new mathematical ideas, we aim to prove the validity of Goldbach's conjecture comprehensively.

The Riemann hypothesis, renowned for its deep connection to the distribution of prime numbers, remains a central problem in mathematics. Understanding the distribution of primes is crucial for developing efficient algorithms and advancing our knowledge of number theory. The Riemann hypothesis is the assertion that all non-trivial zeros are complex numbers with real part $\frac{1}{2}$. It is considered by many to be the most important unsolved problem in pure mathematics. Several equivalent formulations of the Riemann hypothesis exist. Robin's criterion for the Riemann hypothesis is based on an inequality that divisor sum function $\sigma$ must satisfy at natural numbers greater than 5040. We require the properties of superabundant numbers, that is to say left to right maxima of $n \mapsto \frac{\sigma(n)}{n}$. By using Robin's criterion on superabundant numbers, we present a novel approach that culminates in a complete proof of the Riemann hypothesis. This work is an expansion and refinement of the article "Robin's criterion on divisibility", published in The Ramanujan Journal.

In the article, we define a sequence F: F(0) = 2, F(1) = 10, F(2) = 16, F(3) = 22, F(4) = 26, F(4) = 28, · · · , F(i) = F(i − 1) + l, where the number l ≤ 8 is defined by using prime numbers and matrix algebra. The sequence includes only even numbers and can be used to define a series of numbers F(i) + 1, the non-Goldbach sequence, that contains all numbers that cannot be written as the sum of two primes. The result is related to Goldbach’s conjecture. The famous Goldbach conjecture states that every even integer greater than 2 can be expressed as the sum of two primes.

Based on recent popular money priming research results, which conclude that money makes self-sufficient (e.g. less interest in other people), we assumed that people are less interested in finding out whether others are lying or telling the truth. In a laboratory experiment, 163 students (85 women, 78 men, M_Age = 23.08, ranging from 18 to 36 years) were primed by actively handling money (versus paper sheets). Afterwards, they classified 24 video statements as true or deceptive (senders describing their most/least favorite movie), rated their classification confidence for each decision and then answered control questions. Results revealed no influence of priming condition on judgmental bias, classification accuracy, and classification confidence. Also the level of self-reported motivation to find out who lied or told the truth did not differ between conditions. Higher motivation was correlated to higher classification confidence. Additionally, and in line with Reinhard (2010) and Reinhard et al. (2011), higher classification accuracy correlated to a higher use of verbal content cues for classification decisions. Thus, while we were able to replicate these findings, our results contradict the assumption of a money prime influence on lie detection ability. Concluding, our results make self-sufficiency in this context questionable and offer next steps for research.

In this paper, the sequential prime numbers are used as variables for the galactic spiral equations which were developed from the ROTASE model. Special spiral patterns are produced when prime numbers are treated with the unit of radian. The special spiral patterns produced with the first 1000 prime numbers have 20 spirals arranged in two groups. The two groups have perfect central symmetry with each other and are separated with two spiral gaps. The special spiral pattern produced with natural numbers from 1 to 7919 shows 6 spirals in the central area and 44 spirals in the outer area. The whole 7919 spiral points can be plotted with either 6-spiral pattern or 44-spiral pattern. For the spirals only produced by the prime numbers in the 6-spiral pattern plotting, the spiral 2 and spiral 3 each has only one spiral point produced by prime number 2 and 3, respectively, all other spiral points produced by other prime numbers are located on the spiral 1 and spiral 5. The special spiral pattern is well explained with careful analysis, it is concluded that all prime numbers greater than 3 must meet one of the equations: P₁ = 1 + 6 * n (n > 0) P₅ = 5 + 6 * n (n ≥ 0) In other words, every prime number greater than 3 is either a P₁ prime number or a P₅ prime number, no exception. Matching one of the equations is a necessary condition for a number to be a prime number, not a sufficient condition. Hope such sufficient condition can be found in the future. The number of P₁ prime numbers roughly equal the number of P₅ prime number in the first 2 billion prime numbers. The galactic spiral equations with golden angle can duplicate Vogel’s result for the simulation of sunflower seed head pattern, and a pinwheel pattern can be produced also with galactic spiral equations and 1 degree more than golden angle.

This project aims to create a virtual assistant with AI integration to improve Siemens Energy's internal processes. Using cloud-based technologies, microservice architecture, and large language models (LLMs), the project seeks to create a reliable, effective, and user-friendly assistant customized to Siemens Energy's requirements. The first significant business difficulty identified by the study was the time engineers had to spend looking for information in large volumes of company papers. The proposed virtual assistant responds with precision and context awareness to optimize productivity. The assistant uses a microservice architecture to guarantee scalability, flexibility, and integration for various use scenarios. Tasks like document retrieval, translation, summarization, and comparison can now be handled effectively. Utilizing Amazon Web Services (AWS) for cost-effectiveness and scalability, the backend is cloud-deployed, backed by a frontend created for natural user interaction. To increase precision and relevance, the system uses cutting-edge AI, such as vector databases and Retrieval Augmented Generation (RAG). The assistant expedites document management procedures, improves data accessibility, and reduces search time. The results highlight how it may enhance workflow efficiency for Siemens Energy engineers and how flexible it can be for future AI-driven applications.

While digital libraries offer essential benefits for the digital age such as constant availability and accessibility, they often fail in providing a similarly enjoyable browsing experience that benefits engagement and serendipitous exploration inherent to traditional library experiences. In this paper, we propose a virtual reality (VR) library environment that emulates a traditional library promoting an engaging browsing experience that benefits browsing enjoyment and serendipity. The implemented system uses procedural content generation to dynamically generate a library-like environment, wherein each room corresponds to a specific category of the digital library. To assess the usability of the implemented system, we conducted an A/B study comparing the VR environment with the web interface of Project Gutenberg. The results of the study suggest that while the physical demand for using the VR environment is higher, the system can significantly benefit the browsing experience and entice users’ curiosity. Furthermore, the study suggests that the system can increase user engagement and users generally felt that using the system was rewarding.

Advanced lithography requires highly sensitive photoresists to improve lithographic efficiency, and it is critical yet challenging to develop high-sensitivity photoresists and imaging strategies. Here, we report a novel strategy for ultra-high sensitivity using hexafluoroisopropanol (HFIP)-containing fluoropolymer photoresists. The incorporation of HFIP, with its strong electrophilic property and electron-withdrawing effect of the fluorine atoms, significantly increases the acidity of the photoresist after exposure, enabling imaging without conventional photoacid generators (PAGs). The HFIP-containing photoresist has been evaluated by electron beam lithography to achieve a trench of ~40 nm at an extremely low dose of 3 μC/cm2, which shows sensitivity enhancement by ~10 times to the commercial PAGs involved system, revealing its high-sensitivity and high-resolution features. Our results demonstrate a new type of PAGs and a novel approach to higher-performance imaging beyond conventional photoresist performance tuning.

Given the imperative of security, sustainability of supply, strategic considerations, and energy independence, there is a widely acknowledged need to persist in utilizing coal as the primary fuel for electricity generation in power plants. However, in order to combat the rising levels of CO2 in the atmosphere, it is crucial to advance the development of carbon capture and storage (CCS) technologies that enable fossil fuel power plants to achieve zero emissions. These technologies play a pivotal role in capturing and effectively storing CO2, thus ensuring that coal-based power generation can continue while significantly reducing its environmental impact. By implementing CCS solutions, fossil fuel power plants can transition towards a more sustainable and environmentally friendly energy future.The utilization of chemical solvents for CO2 absorption, coupled with long-term storage, presents an intriguing and commercially viable technology for CO2 capture. However, the significant energy demands of the solvent regeneration process necessitate optimization, particularly in large-scale power plants. While the current cost of CO2 capture stands at approximately #55,000.00(Naira) per ton of CO2, the objective is to reduce this cost to below #25,000.00(Naira) per ton of CO2. This reduction in cost is essential to ensure the economic feasibility and widespread adoption of CO2 capture technologies in power generation.This research paper explores various approaches to address the energy demands associated with amine scrubbing integration in a commercial power plant. It provides a comprehensive analysis, both technically and economically, of the performance of these different approaches. While some of the proposed schemes may result in minor efficiency reductions, the key objective is to calculate the specific cost per ton of CO2 captured. The primary focus is on identifying the most suitable configuration to implement large-scale, cost-effective schemes that can serve as a foundation for CO2 capture demonstration projects. By determining the optimal configuration, this research aims to pave the way for the successful implementation of efficient and economically viable CO2 capture technologies in the power generation sector.

This study investigates the impact of narrow-band terahertz pulses on the ferroelectric order parameter in Ba0.8Sr0.2TiO3 films on various substrates. The 375 nm thick BST film on an MgO (001) substrate exhibits enhanced THz-induced second harmonic generation when excited by THz pulses with a central frequency of 1.6 THz, due to the resonant excitation of the soft phonon mode. Conversely, the BST film on a Si (001) substrate shows no enhancement, due to its polycrystalline state. The 800 nm thick BST film on an MgO (111) substrate demonstrates maximum of second harmonic generation signal when excited by THz pulses at 1.8 THz, that is also very close to it`s soft mode frequency (1.9 THz). Notably, the frequency spectrum of the BST/MgO (111) film reveals peaks at both the fundamental and doubled frequencies, highlighting the quadratic dependence of SHG intensity on the THz pulse's electric field strength.

Metal halide perovskites (MHPs), in particular lead-based halide perovskites have earned a recognized fame in several fields for their outstanding optoelectronics properties including direct generation of free charge carriers, optimal ambipolar charge carrier transport properties, high absorption coefficient, point-defect tolerance, and compositional versatility. Nowadays, this class of materials represents a real and promising alternative of silica for the photovoltaic technologies. This worthy success led to a growing interest in the exploration of MHP materials in other hot research fields such as the solar-driven photocatalytic water splitting towards hydrogen production, CO2 reduction to CO and CH4, useful organic reactions such as organic synthesis (formation of C-C, C-N, and C-O bonds), and pollutants and dye degradation. Nevertheless, many of these perovskite materials showed air and moisture instability problems that considerably hinder their practical application for photocatalytic water splitting and photodegradation of CO2. Moreover, if the chemical instability is a problem that can be in part mitigated by the optimization of the lattice structure, the presence of lead represents a real problem for the practical application of these type of materials in commercial devices. To successfully overcome this problem, lead-free metal halide perovskites (LFMHPs) have gained increasing interest thanks to their promising optoelectronic properties, comparable to lead-based materials, and their eco-friendly nature. Among all the lead-free perovskite alternatives, this mini review will focus the attention on the bismuth-based perovskites and perovskite derivatives with specific focus on solar-driven photocatalysis application for H2 evolution.

The conversion of methane into chemicals is of interest to achieve a decarbonized future. Fuel cells are electrochemical devices commonly used to obtain electrical energy, but can be utilized either for chemicals production or both energy and chemicals cogeneration. In this work, the partial oxidation of methane in fuel cells for electricity generation and valuable chemicals production at the same time is reviewed. For this purpose, different types of methane-fed fuel cells, both low temperature fuel cells, such as PEMFCs and AAEMFCs, and high temperature fuel cells, such as SOFCs, have been used. Also if few works have been devoted to this topic, the promising results drive the development of fuel cells using methane as the source for the cogeneration of power and valuable chemicals.

Background: In the current era of globalization, the Indonesian government's problem today is the weakening of nationalism and patriotism among the millennial generation. The large number of foreign cultures that have entered Indonesia has caused a sense of nationalism and patriotism. In addition, Indonesia is also facing the problem of spreading the Covid-19 virus. During the pandemic, various policies set by the government received protests from some circles because they felt their freedom was restricted. Therefore, the awareness of millennial generation nationalism is needed, especially during the Covid-19 pandemic like today. This research aims to make millennials aware of nationalism sense, which mainly to prevent the spread of Covid-19. This research is used to answer the questions of what the problems that arise due to the waning of the spirit of nationalism during the pandemic are? and what efforts should be made to maintain the spirit of nationalism? Methods: This research is a qualitative study using the literature review method. The articles used are research published in 2019 to 2021 in Google Scholar, with keywords that match the topic of millennial generation nationalism in the Covid-19 pandemic. Results and Discussion: The results of the study found that the spirit of Indonesian nationalism during the Covid-19 pandemic was decreasing. The decline in the sense of nationalism is due to several government policies that impact the psychology of society and the Indonesian economy. As a result, society, particularly the millennial generation, must play a role in breaking the chain of the Covid-19 virus's propagation by following the government's health standards. Conclusion: The government and society need to work together to understand nationalism in the millennial generation, especially in dealing with problems caused by the Covid-19 pandemic. Based on this, various efforts need to be made to foster the spirit of nationalism and overcome the Covid-19 pandemic. So that later, it can produce a generation that upholds the value of nationalism in everyday life.

Introduction: Indonesia consists of a plural society with different ethnic, religious, racial, skin color, and other cultures. The difference must be understood by everyone, especially the younger generation in the digital age. If the younger generation does not have a sufficient understanding of multicultural education values, it will impact the moral crisis of the Indonesian nation. This research emphasizes the importance of multicultural education to the younger generation to understand the differences (pluralism) in society and respect them. Method: The method uses a qualitative method with the literature review method by collecting data on ten journals published in 2019, 2020, 2021. Results: The rise of socio-cultural conflicts in Indonesia is why applying multicultural values to the younger generation. Multiculturalism is needed to establish morals and sensitivity for a young person in the face of various social problems and symptoms at a growing age. Conclusion: Multicultural education is vital to the younger generation considering Indonesia has diverse nations and cultures. The efforts that can make to improve the morale of the nation's children, namely by learning citizenship education and religious education and utilizing information technology to spread things related to the values of multicultural education to the broader community

Introduction: Pancasila was born as the ideology of the Indonesian nation, which reflects the values cultural values, ethics, morals, and the spirit of the nation. Pancasila was born as a form of national character, which reflects divinity, nationality, unity, togetherness, and justice. The purpose of this research is to know the practice of Pancasila values ​​in the life of the nation and the state. Especially, the implementation of the life of the younger generation in the 21st century today. Methods: This study is literature research where data is collected using keywords in the database. Literature source search carried out with the help of Boolean operators and using the PICOS format. The results of selecting articles, using PRISMA Flow Diagrams. The search results found 125 articles that match the research theme. After checking for duplication, 82 articles were excluded because of the similarity in the results of the discussion. In the end, there were 43 articles used as a literature source. Results: Based on the analysis of research findings, which are supported by literature sources, it shows that the current values ​​of Pancasila are worrying. This can be seen, where people's behavior has been contaminated by external cultures due to technological sophistication. At present, it can be said that the ethics and morals of society do not reflect the values ​​of Pancasila. Conclusion: In order to re-install the values ​​of Pancasila in people's lives, the participation of all parties is necessary. This is especially so, for today's younger generation. Therefore, it is necessary to develop a model for teaching Pancasila to be carried out by schools and colleges. So that later, it can produce a generation of ethics and morals who love the country.

Three computer algorithms are presented. One reduces a network $\CALN$ to its interior, $\CALI$. Another counts all the triangles in the network, and the last randomly generates networks similar to $\CALN$ given just its interior $\CALI$. But these algorithms are not the usual numeric programs that manipulate a matrix representation of the network; they are set-based. Union and meet are essential binary operators; contained_in is the basic relational comparator. The interior $\CALI$ is shown to have desirable formal properties and to provide an effective way of revealing ``communities'' in social networks.

In this paper, we revisit the hydrodynamics supporting the design and development of the RiverCat class of catamaran ferries operating in Sydney Harbor since 1991. More advanced software is used here. This software accounts for the hydrodynamics of the transom demisterns which experience partial or full ventilation, depending on the vessel speed. This ventilation gives rise to the hydrostatic drag, which adds to the total drag of the vessel. The presence of the transom also creates a hollow in the water. This hollow causes an effective hydrodynamic lengthening of the vessel, which leads to a reduction in the wave resistance. Hence a detailed analysis is required in order to optimize the size of the transom. It is demonstrated that the drag of the vessel and the wave generation can be predicted with good accuracy. Finally, the software is also used to optimize the vessel further by means of affine transformations of the hull geometry.

In present work, the effects of bioflavonoids (ginkgetin and sciadopitysin) on stimulus-induced superoxide generation, tyrosyl and serine/threonine phosphorylation of proteins in human neutrophils, and the translocation of cytosolic compounds (p47phox, p67phox and Rac) to cell membrane were studied, which were isolated from the needles of Taxus media var. Hicksii. Meanwhile, three normal flavonoids (apigenin, quercetin and isoquercetin) were involved as contrasts. The results indicated that ginkgetin and sciadopitysin were capable of concentration-dependently inhibitory effects on the superoxide generation induced by N-formyl-methionyl-leucyl-phenylalanine (fMLP), arachidonic acid (AA) and phorbol-12-myristate 13-acetate (PMA). And they also suppressed fMLP- and AA- induced tyrosyl or PMA-induced serine/threonine phosphorylation and the translocation of cytosolic compounds (p47phox, p67phox and Rac) to cell membrane, which were in parallel with the suppression of the stimulus-induced superoxide generation. The effect of these compounds on the radical-scavenging was also investigated. Ginkgetin and sciadopitysin did not show remarkable effect on DPPH radical-scavenging activity, and they didn’t display the radical-scavenging activity on superoxide anion generated by phenagine methoxysulfate (PMS)-NADH system. Apparently, ginkgetin and sciadopitysin had great performance in pharmacological value and they are worthy of in-depth study.

When a microgrid is grid-tied to a distribution system, it can provide surplus power generation to the distribution system, if any abnormality or interruption occurs in the distribution system, the microgrid can operate in standalone mode to isolate the impact of the abnormality or interruption. However, if the microgrid can not collect enough information from the distribution system, it may cause the failure of generation transferring of distribution feeders, or even further influence the stability of the distribution system. In this paper, a strategy for the resilient control of a microgrid is proposed. It can solve the above-mentioned problem, reduce the duration of the outage of loads. This strategy is experimented in the microgrid in the Institute of Nuclear Energy Research (INER), the reliability is also analyzed to evaluate the unavailability of the microgrid in INER, and it is verified that the proposed strategy can reduce the duration of the outage of loads, and hence the reliability of a microgrid can be upgraded.

New challenges arise in the face of global climate change which impact every ecosystem on earth, including aquatic systems. This is evident in observations made in regard to the world’s oceans, which show trends of incremental changes in ocean surface temperatures, sea levels, and ocean acidity. These environmental shifts impact human resources such as fisheries and aquaculture. In addition, according to the World Bank, the increase in human population will also require more food and nutrient production, which include industries such as aquaculture. With this increasing demand in aquaculture and fisheries, we must develop efficient and productive methods to operate these industries. We can use genetic methods, specifically transcriptomic information to better understand the biology of our source of nutrition. With the advent of RNASeq techniques, we can provide a better understanding about growth and development, immune function and stress, and adaptations. The use of population genetics or (genomics) to detect Single Nucleotide Polymorphisms (SNPs) between populations or closely related species can provide greater insight from stock structure to fishery-induced evolution. In addition, candidate loci can be investigated further to better understanding evolutionary processes, which provide clues on physiological adaptations and gene expression patterns that can help elucidate how these organisms respond to their current environment. In addition, the use of transcriptomic analyses such as differential gene expression can be used to determine resilience in various environmental conditions such as pollution, hypoxic/anoxic conditions, fluctuations in salinity, and temperature extremes. There has been an increase in transcriptomic studies for many aquaculture species, which has aimed at improving our understanding of growth, development, and metabolism, providing vital information for fisheries and aquaculture industries to make adjustments to environmental conditions such as oxygen availability, nutrition, and salinity. All of these aspects provide insightful information for advancing our knowledge of aquaculture, fisheries and conservation management.

MicroRNAs (miRNAs) dysregulation contribute the cancer pathogenesis. However, the miRNA profile of canine oral melanoma (COM), one of the frequent malignant melanoma in dog is still unrevealed. The aim of this study is to reveal the miRNA profile in canine oral melanoma. MicroRNAs profile of oral tissues from normal healthy dogs and COM patients were compared by next-generation sequencing. Along with tumour suppressor microRNAs (miRNAs), we report 30 oncogenic miRNAs in COM. Expression of miRNAs were further confirmed by quantitative real-time PCR (qPCR). Pathway analysis showed that deregulated miRNAs impact on cancer and signalling pathways. Three oncogenic miRNAs targets (miR-450b, 301a, and 223) from human study also were down-regulated in COM and had significant negative co-relation with their respective miRNA. Furthermore, we found that miR-450b expression is higher in metastatic cells and regulated MMP9 expression through a PAX9-BMP4-MMP9 axis. In silico analysis indicated that miR-126, miR-20b, and miR-106a regulated the highest numbers of differentially expressed transcription factors in respect to human melanoma. Chromosomal enrichment analysis revealed the X chromosome was enriched with oncogenic miRNAs. We comprehensively analyzed the miRNA’s profile in COM which will be a useful resource for developing therapeutic interventions in both species.

Modern electrical power systems integrate renewable generation, with solar generation being one of the pioneers worldwide. In Latin America, the greatest potential and development of solar generation is found in Chile through the National Electric System. However, its energy matrix faces a crisis of drought and reduction of emissions that limits hydroelectric generation and involves the definitive withdrawal of coal generation. The dispatch of these plants is carried out by the system operator, who uses a simplified mechanism, called “economic merit list” and which does not reflect the real costs of the plants to the damage of the operating and marginal cost of the system. This inefficient dispatch scheme fails to optimize the availability of stored gas and its use over time. Therefore, a real-time redispatch model is proposed that minimizes the operation cost function of the power plants, integrating the variable generation cost as a polynomial function of the net specific fuel consumption, adding gas volume stock restrictions and water reservoirs. In addition, the redispatch model uses an innovative "maximum dispatch power" restriction, which depends on the demand associated with the automatic load disconnection scheme due to low frequency. Finally, by testing real simulation cases, the redispatch model manages to optimize the operation and dispatch costs of power plants, allowing the technical barriers of the market to be broken down with the aim of integrating ancillary services in the short term, using the power reserves in primary (PFC), secondary (SCF), and tertiary (TCF) frequency control.

Large language models (LLMs) excel in providing natural language responses that sound authoritative, reflect knowledge of the context area, and can present from a range of varied perspectives. Agent Based Models and Simulation consist of simulated agents that interact within a simulated environment to explore societal, social, and ethical, among other, problems. Agents generate large volumes of data over time and discerning useful and relevant content is an onerous task. LLMs can help in communicating agents’ perspectives on key events by providing natural language narratives. However, these narratives need to be factual, transparent, and reproducible. To this end, we present a structured narrative prompt for sending queries to LLMs. Chi-square tests and Fisher’s Exact tests are applied to assess statistically significant difference in sentiment scores of the narrative messages between simulation generated narratives, ChatGPT-generated narratives, and real tweets. The narrative prompt structure effectively yields narratives with the desired components from ChatGPT. This structure is expected to be extensible across LLMs. In 14 out of 44 categories, ChatGPT generated narratives which has sentiment scores that were not discernibly different, in terms of statistical significance (alpha level of 0.05), from the sentiment expressed in real tweets. Three outcomes are provided: (1) a list of benefits and challenges for LLMs in narrative generation; (2) a structured prompt for requesting narratives of a LLM based on simulated agents’ information; and (3) an assessment of statistical significance in the sentiment prevalence of the generated narratives compared to real tweets. This indicates significant promise in the utilization of LLMs for helping to connect simulated agent’s experiences with real people.

As one of the world's most populous countries, Indonesia is struggling with the composition of its people, the majority of whom are unemployed productive-age individuals with low education levels. Another issue is the high poverty rate, which is followed by issues of gender inequality. The government cannot solve these social issues on its own. There is a need for community support to solve these problems through sustainable social entrepreneurship activities. Using the Theory of Planned Behavior and Outcome Expectation, this study will determine the factors that influence the interest of individuals known as the Z and Millennial generation, aged 18 to 34 years old, in becoming social entrepreneurs. This study applied a quantitative approach with a judgmental sampling technique to a sample of Generation Z and Millennials who have ever participated in social activities but have not yet started their own business. The study gathered 210 respondents, who were then analyzed using the PLS-SEM method with multiple group analysis generation-based comparison. According to the findings, the Millennial Generation's Attitude Toward Behavior, Subjective Norms, and Outcome Expectation all had a positive impact on Social Entrepreneurial Intention. Meanwhile, Subjective Norms had no effect on Social Entrepreneurial Intention in the Z Generation. Only attitude toward behavior, perceived behavioral control, and outcome expectation have a positive effect on the development of social entrepreneurial intentions. Furthermore, the findings of this study confirm that subjective norms influence attitude toward behavior and Perceived Behavioral Control in both Generation Z and millennials.

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

VITEK MS PRIME (bioMerieux), a newly developed Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS) system, alongside VITEK PICKME Pen (PICKME), offers easy sample preparation for bacteria and yeast. VITEK MS PRIME also offers two software platforms for filamentous fungi: the IVD database and the RUO database. Our study evaluated its identification agreement on 320 clinical isolates of bacteria and yeasts, comparing PICKME and traditional wooden toothpick sampling techniques against ASTA Mi-croIDSys Elite results. Additionally, we assessed the IVD (v3.2) and SARAMIS (v4.16) RUO data-bases on 289 filamentous fungi against molecular sequencing. The concordant rates for spe-cies-level identification of bacteria and yeasts were about 89.4% (286/320) between the PICKME and wooden toothpick, about 83.4-85.3% between VITEK MS PRIME and ASTA MicroIDSys Elite. Retesting with PICKME improved concordance to 91.9%. For filamentous fungi, species-level identification reached 71.3% with the IVD database and 85.8% with RUO, which significantly enhanced basidiomycetes' identification from 35.3% to 100%. Some strains in the IVD database, like Aspergillus vesicolor, Exophiala xenobiotica, and Nannizzia gypsea failed to be identified. VITEK MS PRIME with PICKME offers reliable and efficient microorganism identification. For fila-mentous fungi, combining the use of the RUO database can be beneficial, especially for basidi-omycetes.

In this paper for every number field K generated by a root α of a trinomial x⁷ + ax + b ∈ Z[x] and for every prime integer p, we calculate ν_p(i(K)), the highest power of p dividing the index i(K) of the field K. In particular, we calculate the index i(K). As application, when the index of K is not trivial, then K is not monogenic.

The energy supply for isolated systems remains a current challenge in Brazil and worldwide, particularly when known solutions are compared regarding cost, the ability to supply energy on demand, and sustainability. In this context, green hydrogen, which has been considered one of the main paths for the decarbonization of the energy chain, is also seen as a potential solution for energy supply in isolated systems. Based on a literature review of articles addressing the topics of green hydrogen and isolated systems, an analysis is conducted on the application of green hydrogen as an energy supply solution for isolated systems. The review identified and collected data on important parameters for comparing solutions, such as CAPEX, OPEX, energy cost, and the price per kilogram of hydrogen. Using these data, analyses were performed to provide an overview of the application of green hydrogen in isolated systems. One of the objectives of this work is to present a comprehensive analysis of the green hydrogen chain and its application in the context of electricity generation, particularly for isolated systems in Brazil.

The increasing demand for energy, driven by technological advances, population growth, and economic expansion, has intensified the focus on efficient energy management. Tri-generation systems, such as Combined Cooling, Heating, and Power (CCHP) systems, are of particular interest due to their efficiency and sustainability. Integrating renewable energy sources like solar power with traditional fossil fuels further optimizes CCHP systems. This study presents a novel method for enhancing CCHP system efficiency by identifying optimal design parameters and assisting decision-makers in selecting the best geometric configurations. A mathematical programming model using the Harris Hawks optimizer was developed to maximize net power and exergy efficiency while minimizing CO2 emissions in a solar-assisted CCHP system. The optimization resulted in 100 Pareto optimal solutions, offering various choices for performance improvement. This method achieved higher net power output, satisfactory exergy efficiency, and lower CO2 emissions compared to similar studies. The study shows that maximum net power and exergy efficiency, with reduced CO2 emissions, can be achieved with a system having a low compression ratio and low combustion chamber inlet temperature. The proposed approach surpassed the response surface method, achieving at least a 4.2% reduction in CO2 emissions and improved exergy values.

The objective of this research was to analyze the evolution and trend of the generation gap and nursing education from 1968 to 2021 through bibliometric indicators. The method used is a bibliometric, descriptive and retrospective study of documents in Scopus, with descriptors “Nursing educat*”, “generation* and the Boolean operator “AND”, N= 653 web documents from 1968 to 2021, and filters of the type bib, csv. The search was carried out on October 9, 2021, using the Bibliometrix R Package software and the Biblioshiny tool. The Results indicate high scientific production in 2020 (54 articles disclosed). This study demonstrates patterns and lines of research in nursing education, such as educational models, interpersonal relationships, and organizational innovation.

Boutique hotels emerged in the late 1970s since then the product has become more mainstream. The draw of boutique hotels is more personalized services. When marketing and providing services to a niche market it is smart to be able to differentiate potential guests to best meet their needs. The generational cohort theory states that a population may be divided into segments based on their generation. This research focuses on Generation X to find out what they are seeking in a boutique hotel product. Based upon how they chose their travel destination there were significant differences between culinary experience, attractions/activities, and cost/budget.

Pancreatic cancer stands out as one of the most lethal forms of malignancies, representing 2% of all cancer cases and contributing to 5% of cancer-related fatalities. Therefore, early detection of pancreatic cancer is crucial for enhancing treatment outcomes. Various hereditary cancer syndromes have been linked to an elevated risk of developing pancreatic cancer, suggesting potential benefits from surveillance strategies for individuals at risk. Presently, precision medicine employs PARP inhibitor therapy for pancreatic cancer patients carrying germline variants in Homologous Recombination Repair (HRR) genes. Our objective was to ascertain the occurrence of germline pathogenic/likely pathogenic variants in genes predisposing to cancer among pancreatic cancer patients. Methodologically, we analyzed 184 pancreatic cancer patients referred to our laboratory for genetic examination. Utilizing a Next-Generation Sequencing (NGS) approach, we scrutinized 52 genes implicated in hereditary cancer predisposition. Our findings revealed that 21% of the patients analyzed harbored germline pathogenic/likely pathogenic variants. Within this subset, 48% exhibited positive results in pancreatic cancer susceptibility genes, namely ATM (17%), BRCA1 (12%), BRCA2 (7%), CDKN2A (7%), and PALB2. Significantly, 64.3% of the pathogenic variants were associated with genes involved in the HRR pathway (ATM, BRCA1, BRCA2, BRIP1, CHEK2, FANCL, MRE11, PALB2, RAD50, RAD51B and RAD51C). In conclusion, our study underscores the significance of multigene genetic testing for pancreatic cancer patients, with 21% of individuals yielding findings linked to pancreatic or other cancer predisposition. Moreover, patients carried pathogenic/likely pathogenic variants in HRR genes, potentially benefiting from targeted therapies such as PARP inhibitors or platinum-based treatments.

Pairs of potential and flow variables have long been established for interfacing object-oriented component models of physical systems. Recently, however, the use of triplets has been discovered for the purpose of robust modeling. New and powerful Modelica libraries have been developed such as the DLR ThermoFluid Stream library or the introduction of the Dialectic Mechanics library. Their use of triplets is entangled with a special modeling approach that uses Linear Implicit Equilibrium Dynamics. In this paper, we study the basic motivation of this approach, its benefits and drawbacks before we finally demonstrate how it beneficially impacts the generation of corresponding simulation code.

This paper aims to explore how climate change affects electricity generation (fossil-fueled power plants, hydroelectric stations, wind systems and photovoltaics) and energy demand in residential buildings in Greece for the period up to 2050. In both cases RCP scenarios results are considered in the appropriate spatial and temporal dimension. Energy supply technologies were examined through statistical regression models and/or mathematical equations correlating climatic parameters with energy productivity. With respect to energy demand, bottom-up models were developed that integrate behavioral and policy aspects. The analysis showed that climate change is expected to mainly affect electricity generation from hydro and thermal power plants, while the impacts on solar and wind energy are significantly lower. The range of impacts on hydro potential and electricity generation depends on the geographical location of the power plants and shows significant uncertainty due to the corresponding uncertainty in climate models estimates regarding precipitation and runoff changes while showing significant geographical variations. With respect to energy demand, climate change is expected to affect energy consumption, but the expected range of effects depends on both the implementation and the characteristics (deep vs. shallow renovation) of measures for upgrading the thermal performance of the building stock and the intensity of climate change.

This paper aims to study and analyze a new Peltier cell layout using a PCM in biphasic mode, with the liquid phase encapsulating the p-n junctions and the solid one playing the role of heat sink. The selected PCM is an organic compound that operates within a temperature range corresponding to the melting process. The phase change zone encompasses the working temperature of the Peltier cell, avoiding thermal gradient variation across the cell section and maintaining the operating conditions and the cell efficiency. PCM encapsulates the Peltier cell thermocouples, creating a layer that increases the power generation as the thickness reduces. We simulated the performance of the new configuration for different temperature gaps between both sides of the cell, obtaining an improvement in power generation from 1.65 to 7.93. This power increase ratio depends on the temperature gap and transient time to reach the steady working temperature. The control of the layer thickness, transient time, and working temperatures resides in the external heating power source, which varies the operating conditions regulating the heat power and the airflow. Maximum output power from the cell prototype is 36.5 W, while conventional Peltier cells operating in similar conditions produce 7.3 W, which represents a power gain of 500%.

This paper performs a comprehensive analysis of the wind energy potential of onshore regions in Greece with emphasis on quantifying the volume risk and the spatial covariance structure. Optimization techniques are employed to derive efficient wind capacity allocation plans (also known as generation portfolios) incorporating different yield aspirations. The generation profile of minimum variance and other optimal portfolios along the efficient frontier are subject to rigorous evaluation using a fusion of descriptive and statistical methods. In particular, principal component analysis is employed to estimate factor models and investigate the spatiotemporal properties of wind power generation, providing valuable insights into the persistence of volume risk. The overarching goal of the study is to employ a set of statistical and mathematical programming tools guiding investors, aggregators and policy makers in their selection of wind energy generating assets. The findings of this research challenge the effectiveness of current policies and industry practices, offering a new perspective on wind energy harvesting with a focus on the management of volume risk.

The sandwich generation caregivers provide simultaneous care for multiple generations. Caregiving is a dynamic process, and each generation has its unique set of needs. Moreover, studies have indicated a growing population within this group. However, despite extensive research efforts, the caregiving practices employed by the sandwich generation remain inadequately explained. Therefore, the objective of this study was to shed light on the caregiving practices offered by the sandwich generation. The grounded theory approach was selected as the conceptual framework for investigating the research objective. Purposive and snowball sampling methods were utilized to recruit 18 participants from the sandwich generation. The data collected through interviews and observations were analyzed using the 2015 version of Corbin and Strauss methodology. The findings revealed that sandwich generation caregivers are influenced by prominent personality traits, issues related to the elderly, and dependencies and interdependencies within the caregiving process. Sandwich caregivers employ a range of strategies influenced by intervening and background factors. Throughout this process, caregivers encounter both positive and negative consequences. Consequently, policymakers and planners should prioritize the establishment and expansion of support systems for caregiving.