The development and generalization of Digital Volume Correlation (DVC) on X-ray computed tomography data highlight the issue of long term storage. The present paper proposes a new model-free method for pruning the DVC data. The size of the remaining sampled data can be user-defined, depending on the needs concerning storage space. The data pruning procedure is deeply linked to hyper-reduction techniques. The DVC data of a resin-bonded sand tested in uniaxial compression is used as an illustrating example. The relevance of the pruned data is tested afterwards for model calibration. A new Finite Element Model Updating (FEMU) technique coupled with an hybrid hyper-reduction method is used to successfully calibrate a constitutive model of the resin bonded sand with the pruned data only.

Zero-Knowledge Proofs ZKP provide a reliable option to verify that a claim is true without giving detailed information other than the answer. A classical example is provided by the ZKP based in the Graph Isomorphism problem (GI), where a prover must convince the verifier that he knows an isomorphism between two isomorphic graphs without publishing the bijection. We design a novel ZKP exploiting the NP-hard problem of finding the algebraic ideal of a multivariate polynomial set, and consequently resistant to quantum computer attacks. Since this polynomial set is obtained considering instances of GI, we guarantee that the protocol is at least as secure as the GI based protocol.

The capital allocation framework proposed by [] presents capital allocation principles as solutions to particular optimization problems and provides a general solution of the quadratic allocation problem via a geometric proof. However, the widely used haircut allocation principle is not reconcilable with that optimization setting. In this paper we provide an alternative proof of the quadratic allocation problem based on the Lagrange multipliers method to reach the general solution. We show that the haircut allocation principle can be accommodated to the optimization setting with the quadratic optimization criterion if one of the original conditions is relaxed. Two examples are provided to illustrate the accommodation of this allocation principle.

Nowadays, the wasting of resources is one of the fundamental challenges of the industrial sector. The rectangle packing problem can be very effective in this context. Practical applications of this issue in the timing and designing of the industries and businesses are very remarkable. The purpose of this issue is to arrange a set of rectangles with specific dimensions in a rectangular page with a specific width and unlimited height without overlapping. The fundamental challenge in this issue is that this is an NP-complete issue. Therefore, it is difficult to achieve the best arrangement, which has the maximum rate of resource utilization and also has a linear running time. Many algorithms have been presented to estimate a practical solution for this issue. In the past decades, the best fit method has been one of the most useful methods for this purpose. This study presents a combinatorial algorithm based on two algorithms, including the lowest front-line strategy and the best-fit algorithm. The running results indicate that the suggested algorithm performs well, despite its simplicity. The time complexity of the suggested algorithm is O(nm), in which n is the number of input rectangles and m is the number of the created front lines.

Background and Objective: Diabetes Mellitus is a long-term, multifaceted metabolic condition that necessitates ongoing medical management. Hypogonadism is a syndrome that is a clinical and/or biochemical indicator of testosterone deficiency. Cross-sectional studies have reported that 20-80.4 % of all men with Type 2 diabetes have hypogonadism, and Type 2 diabetes is related with low testosterone. This study presents an analysis of the use of ML and EL classifiers in predicting testosterone deficiency. In our study, we compared optimized traditional ML classifiers and three EL classifiers using grid search and stratified k-fold cross-validation. We used the SMOTE method for the class imbalance problem. Methods: This database contains 3397 patients for the assessment of testosterone deficiency. Among these patients, 1886 patients with type 2 diabetes were included in the study. In the data pre-processing stage, firstly outlier/excessive observation analyses were performed LOF and missing value analyses were performed with random forest. The SMOTE is a method for generating synthetic samples of the minority class. Four basic classifiers, namely MLP, RF, ELM and LR, were used as first level classifiers. Tree ensemble classifiers, namely ADA, AGBoost, and SGB, were used as second level classifiers. Results: After SMOTE, while the diagnostic accuracy decreased in all base classifiers except ELM, sensitivity values increased in all classifiers. Similarly, while the specificity values decreased in all classifiers, F1 score increased. The RF classifier gave more successful results on the base-training dataset. The most successful ensemble classifier in the training dataset was the ADA classifier in the original data and in the after SMOTE data. The testing data, XGBoost is the most suitable model for your intended use in evaluating model performance. XGBoost, which exhibits a balanced performance especially when SMOTE is used, can be preferred to correct class imbalance. Conclusions: SMOTE is used to correct the class imbalance in the original data. However, as seen in this study, when SMOTE was applied, the diagnostic accuracy decreased in some models, but the sensitivity increased significantly. This shows the positive effects of SMOTE to better predict the minority class.

Many people, including Horadam, have studied the numbers $W_n$, satisfying the recurrence relation $W_n=u W_{n-1}+v W_{n-2}$ ($n\ge 2$) with $W_0=0$ and $W_1=1$. In this paper, we study the $p$-numerical semigroups of the triple $(W_i,W_{i+2},W_{i+k})$ for integers $i,k(\ge 3)$. For a nonnegative integer $p$, the $p$-numerical semigroup $S_p$ is defined as the set of integers whose nonnegative integral linear combinations of given positive integers $a_1,a_2,\dots,a_\kappa$ with $\gcd(a_1,a_2,\dots,a_\kappa)=1$ are expressed in more than $p$ ways. When $p=0$, $S=S_0$ is the original numerical semigroup. The largest element and the cardinality of $\mathbb N_0\backslash S_p$ are called the $p$-Frobenius number and the $p$-genus, respectively.

In this note, we suggest a one-sample version of the recently proposed two-sample test for comparison of the means of multivariate samples. The test checks a hypothesis that the mean of multivariate sample is equal to a certain value with the alternative hypothesis that the mean does not equal to this value. The suggested test is illustrated by analysis of real-world and simulated data.

Increasing the metacognitive abilities of chemistry students is an indisputable output of the teaching and learning process today. Collaborative problem based learning is a learning method that has been tested and proven to be applied, especially in Western countries in increasing the metacognitive abilities of students, but it is still very minimal applied in Asian countries, including Indonesia. Thus, this study was conducted to explore previous studies that examined collaborative problem-based learning in improving students' metacognitive abilities. The research design used in this study is a Systematic Literature Review with the requirements of the inclusion of articles on collaborative problem-based learning in improving the metacognitive abilities of chemistry students, accredited national and international publications between 2010 and 2020, full text, journal articles, and open access. The results of the exploration that were carried out found 102 articles, then the title and abstract were read into 20 articles, and 4 articles were read in full, which fulfilled all the stipulated inclusion requirements. The results of the systematic literature review conducted in this study provide empirical evidence of literacy that problem based learning improves the metacognitive abilities of chemistry students. However, most of research conducted still uses various instruments, which are not standardized and validated.

This study investigates the effect of dividend policy on firm performance and value in the Korean market, taking into account the unique context of Chaebol ownership structures. Analyzing 5,478 observations from the Korean Composite Stock Price Index, the research employs multiple regression models to explore the effects of various dividend policy measures under alignment and entrenchment theories. The key findings reveal significant impacts of cash dividend payment on firm value, while dividend yield and dividend policy exhibit varying associations. In the Chaebol and non-Chaebol context, mixed results suggest complex interactions between dividend policy and business outcomes. Policy recommendations emphasize transparent communication about dividend policy to mitigate information asymmetry and enhance corporate governance in the Korean market.

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

In this paper we study a bilinear optimal control problem related to a 2D parabolic-elliptic chemo-repulsion system consider a nonlinear chemical signal production term. We prove the existence of global optimal solutions with bilinear control, and applying a result on the existence of Lagrange multipliers in Banach spaces, we derive an optimality system for a local optimal solution.

This paper attempts to clarify an long-standing issue about the number of unknowns in the Reynolds-Averaged Navier-Stokes equations (RANS). This study shows that all perspectives regarding the numbers of unknowns in the RANS stem from the misinterpretation of the Reynolds stress tensor. The current literature consider that the Reynolds stress tensor has six unknown components; however, this study shows that the Reynolds stress tensor actually has only three unknown components, namely the three components of fluctuation velocity. This understanding might shed a light to understand the well-known closure problem of turbulence.

A university canteen is a queueing system characterised by non-stationary time of arrival with limited resources where the arrival rate is time dependent and has different pattern of arrival for different time interval. This means at certain time of the day, the arrival rate is much higher than other time and for a university canteen, the arrival rate of customer during the lunchtime is much higher and the food (resources) is limited. Non-stationary time dependent queueing system is not easily modelled mathematically hence such queueing systems are modelled using simulation tools such as ARENA. In order to model a non-stationary time dependent queueing system with limited resources and solve queueing problems using ARENA, researchers have to depend on their knowledge and experience in identifying the appropriate and relevant parameters for the system and make modifications to these parameters of the system to solve queueing problems by means of trial and error. Hence, this research work explores the potentials of applying a systematic problem solving tool, TRIZ to help users to make better decisions in deriving solutions to improve a non-stationary time dependent queueing system with limited resources. A case study was carried out to minimize the waiting time of the customers at the cafeteria of the Faculty of Engineering, Universiti Putra Malaysia (UPM), which has queueing problems for years during lunchtime. TRIZ was applied in this case study and the results showed that TRIZ can assist researchers to derive a solution model that lead to shorter waiting time without incurring additional cost and resources.

We are encouraged to look beyond ɅCDM as there are no satisfactory explanations for either dark energy or dark matter. A data centred phenomenological approach supports an explanation where dark energy is Holographic Dark Information Energy, HDIE. HDIE explains many effects attributed separately to Ʌ and CDM. HDIE mimics Ʌ with sufficient energy and an equation of state parameter, w= -1.03±0.05 at redshifts z<1.35 to account for accelerating expansion. HDIE is clumped around galaxies at densities that distort space-time, explaining many CDM attributed effects. The present ratio of HDIE/baryons ~2.15, required for the observed expansion history, is equivalent to a dark matter fraction ~68%, consistent with many galaxies. The HDIE/baryon model is based largely on proven physics, provides a common explanation for dark energy and dark matter, and solves the cosmological coincidence problem. At earlier times, z > ~1.35, HDIE was phantom, w = -1.82±0.08, enabling the model to be falsified. HDIE fits Planck dark energy wo-wa plots at least as well as Ʌ, and is consistent with other results that suggest dark energy was phantom at earlier times. A new w-parameterisation is proposed, as the usual CPL parameterisation is biased and unsuitable for distinguishing between HDIE/baryon and ɅCDM models.

We study the robustness of the cμ-rule for the optimal allocation of a resource consisting of one unreliable server to parallel queues with two different classes of customers. The customers in queues can be served with respect to a FCFS retrial discipline, when the customers at the head of queues repeatedly tries to occupy the server in a random time. It is proved that for the scheduling problem in the system without arrivals the cμ-rule minimizes the total average cost. For the system with arrivals it is difficult directly to prove the optimality of the same policy with explicit relations. We derived for an infinite-buffer model a static control policy that also prescribes for the certain values of system parameters the service exclusively for the class-i customers if both of queues are not empty with the aim to minimize the average cost per unit of time. It is also shown that in a finite-buffer case the cμ-rule fails.

Urban design is a complex problem-solving activity that commonly requires the aid of a variety of methods to support the process and enhance the quality of the outcomes. How to help designers with adequate methods to deal with ill-defined urban problems constitutes a major challenge in the urban design domain. In this regard, the use of urban design patterns is considered as a method that can contribute to urban design problem-solving. However, this tool was never investigated to understand its role in the task-related activities that take place during the design process by designers working in team, and its effect on the creativity of the final design outcome as perceived by urban designers and students. Therefore, an empirical research based on a controlled experiment was carried out to explore the aid provided by design patterns during the conceptual stages of the process. The study contributed to gain a better insight into the main design activities derived from the use of patterns as problem-solving tools, and to unveil their contribution to urban design. Implications for design practice and design education are discussed.

Three body systems in which one of the bodies is ejected without escaping the binary system have previously been studied in various restricted forms. However, none of these studies dwells on the problem in a general setting. Thus, to study this phenomenon qualitatively, we try to expand this problem's scope to unequal mass systems and generalize them by considering various configurations of fixed initial points with precisely calculated initial velocities, some zero velocity models and some optimized models. We will see the use of terminology similar to the previous studies done in this domain but incorporate different analytical and evaluation methods.

In this article, we establish the existence of and then compare smallest eigenvalues for nabla fractional boundary value problems involving a fractional difference boundary condition, using the theory of u0-positive operators with respect to a cone in a Banach space.

With an increasing adoption of Battery Electric Bus (BEB) fleets, developing a reliable charging schedule is vital to a successful migration from their fossil fuel counterparts. In this paper, a Simulated Annealing (SA) implementation is developed for a charge scheduling framework for a fixed-schedule fleet of BEBs that utilizes a proportional battery dynamics model, accounts for multiple charger types, allows partial charging, and further considers the total energy consumed by the schedule as well as peak power use. Two generation mechanisms are implemented for the SA algorithm denoted as the "quick" and "heuristic" implementations, respectively. The model validity is demonstrated by utilizing a set of routes sampled from the Utah Transit Authority (UTA) and comparing the results against two other models: the BPAP and the Qin-Modified. The results presented show that both SA techniques offer a means of generating operationally feasible schedules quickly while minimizing the cost of operation and considering battery health.

The present work concerns with presenting an explicit formula for new shifted wavelet (NSW) functions. Wavelet functions have many applications and advantages in both applied and theoretical fields. They are formulated with different orthogonal polynomials to construct new techniques for treating some problems in sciences, and engineering. A new important differentiation property of NSW in terms of NSW themselves is obtained and proved in this paper. Then it is utilized together with the state parameterization technique to find solution of optimal control problem (OCP) approximately. The suggested method converts the OCP into a quadratic programming problem, which can be easily determined on computer. As a result, the approximate solution closes with the exact solution even with a small number of NSW utilized in estimation. The error bound estimation for the proposed method is also discussed. Some test numerical examples are solved to demonstrate the applicability of the suggested method. For comparison, the exact known solutions against the obtained approximate results are listed in Tables.

Machine learning methods used for classification can face challenges due to class imbalance, where a certain class is underrepresented. Over/under-sampling of minority/majority class observations, or model selection for ensemble methods alone, may not be effective if the class imbalance ratio is very high. To address this issue, this paper proposes a method called enhance tree ensemble (ETE) based on generating synthetic data for minority class observations in conjunction with tree selection based on their performance on the training data. The proposed method first generates minority class instances to balance the training data and then uses the idea of tree selection by leveraging out-of-bag (〖ETE〗_OOB) and sub-samples (〖ETE〗_SS) observations, respectively. The efficacy of the proposed method is assessed using twenty benchmark problems for binary classification with moderate to extreme class imbalance, comparing it against other well-known methods such as optimal tree ensemble (OTE), SMOTE random forest (〖RF〗_SMOTE), over-sampling random forest (〖RF〗_OS), under-sampling random forest (〖RF〗_US), k-nearest-neighbor (k-NN), support vector machine (SVM), tree, and artificial neural network (ANN). Performance metrics such as classification error rate and precision are used for evaluation purposes. The analyses of the study revealed that the proposed method, based on data balancing and model selection, yielded better results than the other methods.

Students with disabilities are often framed as “the problem” and have limited opportunities to engage in standards based mathematics, leading to persistent underachievement. In this paper, we investigate a research divide between mathematics educational research for students with and without disabilities, a divide with significant differences in the theoretical orientations and research methodologies used to understand learners. Based on an analysis of 149 mathematics educational research articles published between 2013 and 2015, we found significant differences between articles focused on learners with and without disabilities. For those with disabilities, mathematical problem solving was understood primarily from behavioral and information processing theoretical perspectives, while for those without disabilities, problem solving was understood primarily through constructivist and sociocultural perspectives. While 86% of research on problem-solving including students with disabilities was quantitative, only 35% of research on students without disabilities was quantitative. Fifty percent of problem-solving research on students without disabilities was qualitative, compared to only 6% of research on students with disabilities. Problem solving, then, is studied in very different ways for learners with and without disabilities. Students without disabilities are studied through close analysis of learning, often individual. Students with disabilities are most often studied quantitatively, in groups, with little analysis of individual thinking. By offering only a limited range of methods and theoretical orientations, this research divide reifies deficit constructions of students with disabilities.

Home care centers face both an increase in demand and many variations during the execution of routes, compromising the routes initially planned: robust solutions are not effective enough, it is necessary to move on to resilient approaches. We create a close to reality use case supported by interviews of staff at home health care centers, where caregivers are faced with unexpected events that compromise their initial route. We model, analyze and compare three resilient approaches to deal with these disruptions: a baseline approach without any collaboration, a distributed collaborative approach, and a centralized collaborative approach, where we propose a centralization and sharing of information to improve local decision-making. The latter reduces the number of late arrivals by 11% and the total time of late arrival by 21%, and also halves the number of routes exceeding the end of work time (contrary to the distributed collaborative approach, due to the time wasted reaching colleagues). The use of a device, such as a smartphone application, to centralize and share information thus allows better mutual assistance between caregivers. Moreover, we highlight several possible openings like the coupling of simulation and optimization to propose a more resilient approach.

The center vortex model of quantum chromodynamic states that vortices, closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using non-trivial center regions, that is, regions whose boundary evaluates to a non-trivial center element, a resolution of this issue seems possible. We use such non-trivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

Integrated energy systems (IES) seek to minimize power generating costs in future power grids through the dynamic coupling of different energy technologies. To accommodate fluctuations in load demand due to the penetration of renewable energy sources, flexible operation capabilities must be fully exploited, i.e., even power plants that are traditionally considered as base-load units need to be operated according to unconventional paradigms. Thermomechanical loads induced by frequent power adjustments can accelerate the wear and tear of components. If a unit is flexibly operated without respecting limits on materials and components, the risk of failures of expensive components will eventually increase, nullifying the additional profits ensured by flexible operation. In addition to the limits on power variations (explicit constraints), the solution of the unit dispatch problem needs to meet the limits on temperature, pressure and flow rate variations (implicit constraints). The FARM (Feasible Actuator Range Modifier) module was developed to enable existing optimization algorithms to identify solutions to the unit dispatch problem that are both economically favorable and technologically sustainable. Thanks to the iterative dispatcher-validator scheme, FARM permits addressing all the imposed constraints without excessively increasing the computational costs. In this work, the algorithms constituting the module are described, and the performance was assessed by solving the unit dispatch problem for an IES composed of three units, i.e., Balance of Plant, Gas Turbine, High-Temperature Steam Electrolysis. Finally, FARM module provides dedicated tools for visualizing the response of the process variables of interest during operation transients and a tool aiding the operator at making decisions. These techniques might represent the first step towards the deployment of an Ecological Interface Design (EID) for IES units.

This article examines the impact of network degree distribution on the performance of evolutionary algorithms, specifically in solving the Traveling Salesperson Problem (TSP). It evaluates the integration of various network types to regulate population crossovers, enhancing candidate solutions and their refinement over generations. The experimental analysis includes complex networks like Erdős–Rényi and Barabási–Albert, along with regular graphs such as Balanced trees and Harary graphs. The study focuses on how different network structures influence exploration, convergence, and computational efficiency, particularly in terms of CPU time. Results show that highly connected networks, like Barabási–Albert, facilitate faster convergence and improved solution quality by guiding the search process more effectively. The Harary graph with k=2 demonstrated superior performance, reducing execution times by up to sevenfold compared to traditional approaches. This improvement highlights the advantages of specific degree distributions in balancing exploration and exploitation. Networks with hubs, such as Barabási–Albert, accelerate information flow and the evolutionary process, while more regular networks, like Harary graphs, provide controlled structures that maintain high solution quality. These findings emphasize the importance of network topology in evolutionary algorithms and suggest further exploration of hybrid models and other network types to optimize NP-hard problems.

Abstract. Myopia has become a major health problem around the world. The devel-opment of myopia is starting to appear at an earlier age than in previous generations and its consequences have prompted multiple studies, particularly regarding topical atropine treatment aiming at preventing or slowing myopia progression. Our objective is to review randomized and controlled studies on the efficacy and safety of topical atropine to prevent myopia progression in children. This was a narrative review compiled from literature of PubMed and Cochrane Library, including randomized and controlled clinical trials of atropine eye drops for myopia progression published within 2017 - 2023. Fourteen clinical trials were found in the 7 year-period analyzed. All study atropine concentrations were effective in reducing the progression of myopia compared to the placebo. The highest dose of atropine (1%) showed the best efficacy in reducing the spherical equivalent progression and axial elongation over the lower dose (0.01%). Side-effects were mild or moderate. The use of atropine eye drops to prevent myopia progression has shown benefits without involving serious adverse effects. Higher doses of atropine (0.5% and 1%) have been shown to have more efficacy in preventing myopia progression than lower doses (0.01%), so starting intervention with those doses of at-ropine could be considered for preventing myopic children from becoming severe myopia patients later in life.

Monge-Ampere equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge-Ampere equations with two parameters is investigated based on Guo-Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our main results.

It is a critical issue to allocate redundancy to critical smart grid infrastructure for disaster recovery planning. In this study, we present a framework to combine statistical prediction methods and optimization models for the optimal redundancy allocation problem. First, we develop statistical simulation methods to identify critical nodes of very large-scale smart grid infrastructure based on the topological features of embedding networks, and then present a linear integer programming model based on generalized assignment problem (GAP) for redundancy allocation of critical nodes in smart grid infrastructure. The model is specifically implemented in the context of smart grid infrastructure. The findings demonstrate that the combined approach of statistical simulation and optimization effectively addresses the size limitations inherent in a sole optimization approach. Notably, the optimal solutions for redundancy allocation in very large grid systems highlight that the cost of redundancy is only a fraction of the economic losses incurred due to weather-related outages.

This paper introduces a novel algorithm for solving the point-to-point shortest path problem in a static regular 8-neighbor connectivity (G8) grid. This algorithm can be seen as a generalization of Hadlock algorithm to G8 grids, and is shown to be theoretically equivalent to the relaxed A* (RA*) algorithm in terms of the provided solution's path length, but with substantial time and memory savings, due to a completely different computation strategy, based on defining a set of lookup matrices. Through an experimental study on grid maps of various types and sizes (1290 runs on 43 maps), it is proven to be 2.25 times faster than RA* and 17 times faster than the original A*, in average. Moreover, it is more memory-efficient, since it does not need to store a G score matrix.

High-fidelity patient simulation (HFPS) is widely used in professional training to enhance students’ competence in clinical management. Problem-solving (PS) and clinical reasoning (CR) skills are essential to developing students in professional competence in safe and effective care. These two skills should be initiated at the early training. However, little is known about the effects of HFPS on developing PS and CR skills in first year undergraduate students. Therefore, this pre- and post-experimental study aimed to investigate the effects of HFPS on development of PS and CR skills in first-year nursing students. The students were required to go through four sessions, preparation, pre-briefing and orientation, simulation role-playing, and debriefing, for the HFPS. The study utilized the Problem-Solving Inventory (PSI) and the Nurses Clinical Reasoning Scale (NCRS) to measure problem-solving and clinical reasoning abilities before and after HFPS. Bivariate analysis, one-sample t-test, and independent t-test were performed to evaluate the performance of the PS and CR skills at the two study periods. One hundred eighty-nine students were recruited, with a mean age of 20.56 years, and 73% were female students. The analytic results showed that the PSI, particularly in domains of Problem-Solving Confidence (PSC) (p&lt;0.001) and overall PS (p&lt;0.001), and the CR (p&lt;0.001) had significant improvement after HFPS. The study concluded that HFPS is an effective innovative method to significantly improve students’ problem-solving and clinical reasoning abilities. Nurse educators play an important role in providing explicit learning instructions in a simulation guideline that directs and guides students to learn at each stage of HFPS. Students should take more initiative and engage in their learning through HFPS to enhance their competence in knowledge and higher intellectual skills for personal and professional developments.

Backgrounds: The field of Artificial Intelligence (AI) has seen a major shift in recent years due to the development of new Machine Learning (ML) models such as Generative Pre-trained Transformer (GPT) and AI which are progressively becoming part our everyday lives. GPT has achieved previously unheard-of levels of accuracy in most computerized language processing tasks and their chat-based variations. Aim: The aim of this study was to investigate the problem-solving abilities of ChatGPT using two sets of verbal insight problems, with a known performance level established by a sample of human participants. Material and Methods: A total of 30 problems labelled as “practice problems” and “transfer problems”, as listed by Ansburg and Dominowski (2000), were administered to ChatGPT. The answers provided by ChatGPT received a score of "0" for each problem answered incorrectly and a score of "1" for each correct response, as per the correct solution specified in Ansburg and Dominowski's (2000) study. The highest score that could be attributed to both the practice and transfer problems was 15 out of 15. In order to compare ChatGPT performance to the performance to that of human subjects, the solution rate for each problem (based on a sample of 20 subjects) was used, as indicated by Ansburg and Dominowski (2000). Results: The study highlighted that ChatGPT can be trained in out-of-the-box thinking and demonstrated potential in solving verbal insight problems. The global performance of ChatGPT equalled the most probable outcome for the human sample in both practice problems and transfer problems as well as upon their combination. Additionally, ChatGPT answer combinations were among the 5% of most probable outcomes for the human sample both when considering practice problems and pooled problem sets. These findings demonstrate that ChatGPT performance on both set of problems was in line with the mean rate of success of human subjects, indicating that it performed reasonably well. Conclusions: The use of transformer architecture and self-attention in ChatGPT may have helped to prioritize inputs while predicting, contributing to its potential in verbal insight problem-solving. ChatGPT has shown potential in solving insight problems, thus highlighting the importance of incorporating AI in psychological research. However, it is acknowledged that open challenges still exist. Indeed, further research is needed to fully understand the capabilities and limitations of AI in insight problem-solving.

We propose Reduced Collatz Conjecture that is equivalent to Collatz Conjecture, which states that every positive integer can return to an integer less than it, instead of 1. Reduced Collatz Conjecture should be easier because some properties are presented in reduced dynamics, rather than in original dynamics (e.g., ratio and period). Reduced dynamics is a computation sequence from starting integer to the first integer less than it, and original dynamics is a computation sequence from starting integer to 1. Reduced dynamics is a component of original dynamics. We denote dynamics of x as a sequence of either computations in terms of ``I'' that represents (3*x+1)/2 and ``O'' that represents x/2. Here 3*x+1 and x/2 are combined together, because 3*x+1 is always even and followed by x/2. We formally prove that all positive integers are partitioned into two halves and either presents ``I'' or ``O'' in next ongoing computation. More specifically, (1) if any positive integer x that is i module $2^t$ (i is an odd integer) is given, then the first t computations (each one is either ``I'' or ``O'' corresponding to whether current integer is odd or even) will be identical with that of i. (2) If current integer after t computations (in terms of ``I'' or ``O'') is less than x, then reduced dynamics of x is available. Otherwise, the residue class of x (namely, i module $2^t$) can be partitioned into two halves (namely, i module $2^{t+1}$ and $i+2^t$ module $2^{t+1}$), and either half presents ``I'' or ``O'' in intermediately forthcoming (t+1)-th computation.

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρ_c0 (ρ_c0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.

In this paper new upper limits on the parameters of the Continuous Spontaneous Localization (CSL) collapse model are extracted. To this end the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by collapse models. This study allows to obtain the most stringent limits within a relevant range of the CSL model parameters, with respect to any other method. The collapse rate $\lambda$ and the correlation length $r_C$ are mapped, thus allowing to exclude a broad range of the parameter space.

In a search for a solution of the galaxy rotation problem, a novel view on cosmological gravity is developed. In this view, the origin of gravity is traced back to the basic nuclear field of energy, spread by quarks as elementary pointlike sources. This gives a common basis for gravity, electromagnetism, the strong nuclear force and the weak nuclear force. After a review on gravimagnetism and the causality problem of gravity, a hypothetical concept for the gravity field is proposed, which solves the rotation problem without the need to accept dark matter as the deus ex machina.

The article presents a non-destructive test system based on electrical impedance tomography for monitoring flood embankments. The technology of cyber-physical systems and the Internet of Things with the use of electrical impedance tomography enables real-time monitoring of flood embankments. This solution provides a visual analysis of damage and leaks, which allows for quick and effective intervention and possible prevention of danger. A dedicated solution based on the IT structure, dedicated laboratory models and a dedicated measurement system with various types of sensors and machine learning algorithms for image reconstruction has been developed. The system includes specialized intelligent devices for tomographic measurements. The application contains the analysis of anomalies occurring in the structure of the object as a result of damage or danger and breaking the shaft during the flood. The presented solution enables ongoing monitoring of objects by collecting measurement results, forecasts and simulations. The main advantage of the proposed system is the spatial ability to analyse shafts, high accuracy of imaging and high speed of data processing. The use of tomographic techniques in conjunction with image reconstruction algorithms allow for non-invasive and very accurate spatial assessment of humidity and damages of flood embankments. The presented results show the effectiveness of the presented research.

We consider partition functions, in the form of state sums, and associated probabilistic measures for aperiodic substrates described by model sets and their associated tiling spaces. We propose model set tiling spaces as microscopic models for small scales in the context of quantum gravity. Model sets possess special self-similarity properties that allow us to consider implications on large and observable scales from the underlying (non-ergodic) dynamics. In particular we consider the implication of the underlying aperiodic substrate for the well known problem of time in quantum gravity, and propose a correspondence between small and large scales, the so-called ergodic correspondence, that addresses the emergence of matter properties and spacetime structure. In the process we find a possible bound in the mass spectrum of fundamental particles.

In this paper, we give closed-form expressions of the $p$-Frobenius number for the triple of the generalized star numbers $a n(n-1)+1$ for an integer $a\ge 4$. When $a=6$, it is reduced to the famous star number. For the set of given positive integers $\{a_1,a_2,\dots,a_k\}$, the $p$-Frobenius number is the largest integer $N$ whose number of nonnegative integer representations $N=a_1 x_1+a_2 x_2+\dots+a_k x_k$ is at most $p$. When $p=0$, the $0$-Frobenius number is the classical Frobenius number, which is the central topic of the famous linear Diophantine problem of Frobenius.

In this paper we study a special kind of finite mixture model. The sample drawn from the model consisits of three parts. The first two parts are drawn from specified distributions f1 and f2, while the third one is drawn from the mixture. A problem of interest is whether the two distributions f1 and f2 are the same. To test this hypothesis, we first define the regular location and scale family of distributions and assume that f1 and f2 are regular denisty functions. Then the hypothesis transforms to the equalities of the location and scale parameters, respectively. To utilize the information in the sample, we use Bayes’ theorem to obtain the posterior distribution and give the sampling method. Then we propose the posterior p-value to test the hypothesis. The simulation studies show that our posterior p-value largely improves the power in both normal and logistic cases while nicely controls the Type-I error. A real halibut dataset is used to illustrate the validity of our method.

This paper considers the problem of quantifying the quality of a model selection problem for a graphical model. The model selection problem often uses a distance measure such as the Kulback-Leibler (KL) distance to quantify the quality of the approximation between the original distribution and the model distribution. We extend this work by formulating the problem as a detection problem between the original distribution and the model distribution. In particular, we focus on the covariance selection problem by Dempster, [1], and consider the cases where the distributions are Gaussian distributions. Previous work showed that if the approximation model is a tree, that the optimal tree that minimizes the KL divergence can be found by using the Chow-Liu algorithm [2]. While the algorithm minimizes the KL divergence it does not minimize other measures such as other divergences and the area under the curve (AUC). These measures all depend on the eigenvalues of the correlation approximation measure (CAM). We find expressions for KL divergence, log-likelihood ratio, and AUC as a function of the CAM. Easily computable upper and lower bounds are also found for the AUC. The paper concludes by computing these measures for real and synthetic simulation data.

Based on author's previous work [Sun, B. The Reynolds Navier-Stokes Turbulence Equations of Incompressible Flow Are Closed Rather Than Unclosed. Preprints 2018, 2018060461 (doi: 10.20944/preprints201806.0461.v1)], this paper proposed an explicit representation of velocity fluctuation and formulated the Reynolds stress tensor in terms of the mean velocity field. The proposed closed Reynolds Navier-Stokes turbulence formulations reveal that the mean vorticity is the key source of producing turbulence.

Purpose: This study investigates the implementation and impact of maker culture—viewed as a tool for developing green digital skills—in higher education institutions in Hong Kong. Maker culture, a collaborative educational approach, embraces students’ capacity for self-paced, autonomous learning and applies this knowledge to creative problem-solving and innovation, key aspects of sustainability education. Methods: An empirical study was conducted, focusing on the experiences of teachers in the higher education sector in Hong Kong. Eight individuals were interviewed to gain insights into their perceptions and experiences with maker education within sustainability contexts. The sample was limited to ensure cross-sectional comparability and direct weighting of teachers’ experiences within a singular, complementary educational setting. Results: The findings provide valuable insights into the benefits and challenges of integrating maker education into traditional educational systems to foster green digital skills. It became evident that adequate resources, effective teachers, and improved administrative systems play significant roles in the successful implementation of this approach. Conclusion: Maker education, as a tool for developing green digital skills, offers a promising alternative to traditional performance-based studies. It has the potential to lead to a future of education that is creative, innovative, and student-directed, fostering sustainability competences. Therefore, despite the challenges, with the right support and resources, the integration of maker culture into educational systems could significantly transform teaching and learning processes, advancing sustainability education.

This article investigates the prospect of implementing multidisciplinary and multicultural student teamwork (MMT) involving Case-based Learning (CBL) and Problem-based Learning (PBL) as a sustainable teaching practice. Based on a mixed methods approach, which includes direct observation (both physical and virtual), questionnaire distribution and focus-group interviews the study reveals that MMT through CBL and PBL can both facilitate and hinder sustainable learning. Our findings show that while MMT enhances knowledge sharing, it also poses a wide range of challenges, raising questions about its social significance as a sustainable teaching practice. The study suggests the implementation of certain mechanisms, such as ‘Teamwork Training’ and ‘Pedagogical Mentors’, aiming to strengthen the sustainable orientation of MMT through CBL and PBL.

The article presents a cyber-physical system for acquiring, processing and reconstructing images from measurement data. The technology was based on process tomography, intelligent measurement sensors, machine learning, Big Data, Cloud Computing, Internet of Things as a solution for Industry 4.0. Industrial tomography enables observation of physical and chemical phenomena without the need of internal penetration and allows real-time monitoring of production processes. The application includes specialized intelligent devices for tomographic measurements and dedicated algorithms for solving the inverse problem. The work focuses mainly on electrical tomography and image reconstruction using deterministic methods and machine learning, the reconstruction results were compared, different measurement models were used. The researches were carried out for synthetic data and laboratory measurements. The main advantage of the proposed system is the possibility of spatial data analysis and their high processing speed. The presented research results show that the process tomography gives the possibility to analyse the processes taking place inside the facility without disturbing the production, analysis and detection of obstacles, defects and various anomalies. Knowing the characteristics of a given solution, the application allows you to choose the appropriate method to reconstruct the image.

The article presents the results of research on a new method of spatial analysis of walls and buildings moisture. Due to the fact that destructive methods are not suitable for historical buildings of great architectural significance, a non-destructive method based on electrical tomography has been adopted. A hybrid tomograph with special sensors was developed for the measurements. This device enables the acquisition of data, which are then reconstructed by appropriately developed methods enabling spatial analysis of wet buildings. Special electrodes that ensure good contact with the surface of porous building materials such as bricks and cement were introduced. During the research, a group of algorithms enabling supervised machine learning was analyzed. They have been used in the process of converting input electrical values into conductance depicted by the output image pixels. The conductance values of individual pixels of the output vector made it possible to obtain images of the interior of building walls, both flat intersections (2D) and spatial (3D) images. The presented group of algorithms has a high application value. The main advantages of the new methods are: high accuracy of imaging, low costs, high processing speed, ease of application to walls of various thickness and irregular surface. By comparing the results of tomographic reconstructions, the most efficient algorithms were identified.

We point out an inconsistency in Newton's equations of celestial mechanics. A set of differential equations implied by Newton's equations are shown to be free of this inconsistency. We then investigate the integrals of motion associated with this relative difference system.

The advance of the medical field in the 21st century has influenced the development of many innovations, including in medical education. PBL (problem-based learning) is one of the pedagogical approaches that has been studying and implementing worldwide to attract medical students’ attention with their learning style and learning environment. China is the most significant “receiver” country of foreign students in Asia, and clinical medicine is one of the most chosen majors for undergraduate. In China, PBL has been implementing in some schools, but mostly with the local students and only a few implementations to the international students. International medical students in China faced a variety of challenges during their studies. In this review paper, we give the solution to adapt to the challenges by focusing on the implementation the integrated organ/system curriculum/syllabus with the PBL method to the school system with the support of the school stakeholders and students’ role.

Instead of the conventional 0 and 1 values, bipolar reasoning uses -1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., “uncertain” lies between “impossible” and “totally sure”). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e., William of Ockham and Nicholas of Autrecourt, who embodied a bipolar mode of thought that is eminently modern. Starting from the trivial observation that “once a wheat sheaf is sealed and tied up, the packed down straws display the same orientation”, we work up a new theory of the bipolar nature of networks, suggesting that orthodromic (i.e., feedforward, bottom-up) projections might be functionally coupled with antidromic (i.e., feedback, top-down) projections via the mathematical apparatus of presheaves/globular sets. When an entrained oscillation such as a neuronal spike propagates from A to B, changes in B might lead to changes in A, providing unexpected antidromic effects. Our account points towards the methodological feasibility of novel neural networks in which message feedback is guaranteed by backpropagation mechanisms endowed in the same feedforward circuits. Bottom-up/top-down transmission at various coarse-grained network levels provides fresh insights in far-flung scientific fields such as object persistence, memory reinforcement, visual recognition, Bayesian inferential circuits and multidimensional activity of the brain. Implying that axonal stimulation by external sources might backpropagate and modify neuronal electric oscillations, our theory also suggests testable previsions concerning the optimal location of transcranial magnetic stimulation’s coils in patients affected by drug-resistant epilepsy.

In this review, our goal is to design and test quantum-like algorithms for Artificial Intelligence (AI) in open systems to structure a human-machine team to be able to reach its maximum performance. Unlike the laboratory, in open systems, teams face complexity, uncertainty and conflict. All task domains have complexity levels, some have low, and others high levels. Complexity in this new domain is affected by the environment and the task, which are both affected by uncertainty and conflict. We contrast the individual and interdependence approaches to teams. The traditional and individual approach focuses on building teams and systems by aggregating the best available information for individuals, their thoughts, behaviors and skills. Its concepts are characterized chiefly by one-to-one relations between mind and body, a summation of disembodied individual mental and physical attributes, and degrees of freedom corresponding to the number of members in a team; however, this approach is characterized by the many researchers who have invested in it for almost a century with few effects that can be generalized to human-machine interactions; by the replication crisis of today (e.g., the invalid scales for self-esteem, implicit racism, and honesty); and by its many disembodied concepts. In contrast, our approach is based on the quantum-like nature of interdependence. It allows us to theorize about the bistability of mind and body, but it proposes a measurement problem and a non-factorable nature. Bistability addresses team structure and performance; the measurement problem solves the replication crisis; and the non-factorable aspect of teams reduces the degrees of freedom and the information derivable from teammates to match findings by the National Academies of Science. We begin with a review of the science of teams and a focus on human-machine team research in the laboratory versus the open; justifications for rejecting traditional social science while supporting our approach; a full understand of the complexity of the domain, tasks in the domain, and how teams address both; the mathematics involved; a review of results from our model versus the open field; a discussion of the results; conclusions; and the path forward to successfully advance the science of interdependence and autonomy.

This study proposes a novel flexible bus dispatching system where a fleet of fully automated modular bus units, together with conventional buses, serves the passenger demand. These modular bus units can either operate individually or combined (forming larger modular buses with a higher passenger capacity). This provides enormous flexibility to manage the service frequencies and vehicle allocation, reducing thereby the operating cost and improving passenger mobility. We develop an optimization model used to determine the optimal composition of bus units and the optimal service frequency at which the buses (both conventional and modular) are dispatched across each bus line. We explicitly account for the dynamics of traffic congestion and complex interactions between the modes at the network level based on the recently proposed three-dimensional macroscopic fundamental diagram (3D-MFD). To the best of our knowledge, this is the first application of the 3D-MFD and modular bus units for the frequency setting problem in the domain of bus operations. Numerical results show the improvements in the total system cost made by adapting the number of combined modular bus units and their dispatched frequencies to the evolution of both, the car and the passenger demand. A comparison with the commonly used approach that considers only the bus system (neglecting the complex multimodal interactions and congestion propagation) reveals the value of the proposed modeling framework.

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

Sleep disorders are a frequent problem in pediatrics. The prevalence is variable (from 15 to 50%) although the majority of papers coincide in that 1 every 3 kids can experiment some kind of sleep disorder. Underlying medical problems usually manifest by difficulty to fall asleep or stay asleep. The diagnosis and resolution of the medical problems with the specific treatment should be the prime concern, before starting with the treatment of the sleep behavioral problem

With a software-defined network (SDN), the control plane is separated from the data plane, allowing the control of network flows to be easy and dynamic at the same time. While the controller, which is equipped with various control applications, is capable of analyzing a large amount of data, it may become overburdened when it is faced with a large volume of traffic. The intrusion detection system (IDS) is an example of control applications that can be used to detect intrusions. It is recommended to deploy instances of the IDS across the data plane. This will improve the processing power and detection rate and as a result reduce the load on the controller at the same time. While there is no doubt that an IDS would be beneficial for improving detection rates, installing one at each switch in the data plane would be costly. To address this issue, this paper proposes the deployment of IDS chains across the data plane. The controller directs incoming traffic via alternative paths, including the IDS chain, which increases the detection rate while avoiding overloading. In order to improve transmission efficiency, our study proposes a method of balancing the distribution of flows and assigning them to specific IDS chains. This approach minimizes the cost of flow grouping through the use of a new incoming traffic grouping technique. Our method is tested and evaluated through the use of a test bed and trace-based simulation, and has been proven to effectively reduce delays and hop counts across various traffic scenarios.

The algorithm now known as Kadane’s algorithm for the maximum subarray problem uses many of the ideas that Kadane proposed, but it is not the algorithm that Kadane intended. This paper compares the two algorithms in question. They are both linear in time, employ just a few words of memory, and use a dynamic programming structure. The upshot is two light-weight algorithms for the maximum subarray problem.

The Gestalt psychologists’ theory of insight problem-solving was based on a direct parallelism between perceptual experience and higher-order forms of cognition (e.g., problem-solving). Simi-larly to the sudden recognition of an ambiguous figure, they contended that problem-solving in-volves a restructuring of one's initial representation of the problem’s elements, leading to a sud-den leap of understanding phenomenologically indexed by the "Aha!" feeling. Over the last centu-ry, different scholars discussed the validity of the Gestalt psychologists’ perspective foremost us-ing the behavioral measures available at the time. However, in the last 2 decades, scientists gained a deeper understanding of insight problem-solving due to the advancements in cognitive neuroscience. This review aims to provide a retrospective reading of Gestalt theory based on the knowledge accrued by adopting novel paradigms and investigating their neurophysiological correlates. Among several key points that the Gestalt psychologists underscored, we focus specif-ically on the role of the visual system in marking a discrete switch of knowledge into awareness, as well as the perceptual experience and the holistic standpoints. While the main goal of this paper is to read the previous theory in light of new evidence, we also hope to initiate an academic dis-cussion and encourage further research about the points we raise.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

Service pricing is a bottleneck in the development of innovation services, as it is the issue of most concern between the suppliers and demanders. In this paper, a negotiation pricing model that is based on the multiobjective genetic algorithm is developed for innovation service pricing. Regarding the service pricing process as a multiobjective problem, the objective functions, which include the service price, service efficiency, and service quality, for suppliers and demanders are constructed. As the solution of a multiobjective problem is typically a series of alternatives, another negotiation process is necessary for determining the final decision. A learning strategy is adopted during the negotiation process to simulate reality. Finally, the model is implemented for an innovation service transaction, the objective of which is to identify the optimal price plan. The results demonstrate that the model can provide quantitative decision support for the pricing of an innovation service and ultimately yield a win-win result for both the supplier and demander of the innovation service. Furthermore, the influence of the parameters during the negotiation process is analyzed in detail. The effects of the learning strategy on accelerating the negotiation process, as well as the chosen of reasonable parameters are given.

We have used the varying physical constant approach to resolve the flatness problem in cosmology. Friedmann equations are modified to include variability of speed of light, gravitational constant, cosmological constant and the curvature constant. The continuity equation obtained with such modifications includes scale factor dependent cosmological term as well as the curvature term along with the standard energy-momentum term. The result is that as the scale factor tends to zero (i.e. as the big-bang is approached) the universe becomes strongly curved rather than flatter and flatter in the standard cosmology. We have used the supernovae 1a redshift versus distance modulus data to determine the curvature variation parameter of the new model, which yields a better fit to the data than the standard ΛCDM model. The universe is found to be open type with radius of curvature R_c = 1.64 (1+z)^-3.3 c₀/H₀, where z is the redshift, c₀ is the current speed of light and H₀ is the Hubble constant.

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

A large number of physicists now admit that quantum mechanics is a non-local theory. EPR argument and the many experiences (including recent “loop-hole free” tests) showing the violation of Bell’s inequalities seem to have confirmed convincingly that quantum mechanics cannot be local. Nevertheless, this conclusion can only be drawn inside a standard realist framework assuming an ontic interpretation of the wave function and viewing the collapse of the wave function as a real change of the physical state of the system. We show that this standpoint is not mandatory and that if the collapse is no more considered as an actual physical change, it is possible to recover locality.

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1-control problem for quasi-linear parabolic equation with non-local p[u]-Laplacian and with a cost functional of a tracking type. The main characteristic feature of the considered class of parabolic problems is the fact that the variable exponent p(t,x) and the anisotropic diffusion tensor D(t,x) are not well predefined a priori, but instead these characteristic non-locally depend on a solution of this problem, i.e., pu=p(t,x,u) and Du=D(t,x,u). We prove the existence of optimal pairs with sparse L1-controls using for that the indirect approach and a special family of approximation problems.

This study reports results of focus groups with school nurses and teachers from elementary, middle, and high schools to explore their perceptions of child and adolescent oral health. Participants included 14 school nurses and 15 teachers (83% Female; 31% Hispanic, 21% White, 21% Asian, 14% African American, and 13% Others). Respondents were recruited from Los Angeles County schools and scheduled by school level for six one-hour focus groups, using Zoom. Audio recordings were transcribed, reviewed, and saved with anonymization of speaker identities. NVivo software was used to facilitate content analysis and identify key themes. The nurses’ rate of “Oral Health Education” comments statistically exceeded that of teachers, while teachers had higher rates for “Parental Involvement” and “Mutual Perception” “Need for Care” was perceived to be more prevalent in immigrants to the United States based on student behaviors and complaints. “Access to Care” was seen as primarily the nurse’s role. Strong relationships between community clinics and schools were viewed by some as integral to students achieving good oral health. The results suggest dimensions and questions important to item development for oral health surveys of children and parents to address screening, management, program assessment, and policy planning.

We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users requirements. This approach leads to a convex optimization problem with balance and capacity constraints. We present several decomposition type methods to find a solution of this problem, which exploit its special features. We suggest to apply first the dual Lagrangian method with respect to the total capacity constraint, which gives the one-dimensional dual problem. However, calculation of the value of the dual cost function requires solution of several optimization problems. Our methods differ in approaches of solution of these auxiliary problems. We compare the performance of the suggested methods on several series of test problems. They show rather satisfactory convergence. Nevertheless, proper decomposition technique enhance the convergence essentially.

The etiopathogenesis of autism spectrum disorder (ASD) remains largely unclear. Among other biological hypotheses, researchers have evidenced an imbalance in the endocannabinoid (eCB) system, which regulates some functions typically impaired in ASD, such as emotional responses and social interaction. Also, cannabidiol (CBD), the non-intoxicating component of Cannabis sativa, has been recently approved for treatment-resistant epilepsy. Seizures represent frequent medical comorbidities of ASD and could be responsible for the onset or worsening of behavioral problems. Thus, it has been hypothesized that cannabinoids could be useful in improving some ASD symptoms. Our systematic review was conducted according to the PRISMA guidelines and aimed to summarize the literature regarding the use of cannabinoids in ASD. After searching in Web of Knowledge^TM, PsycINFO, and Embase, we included ten studies (eight papers and two abstracts). Four ongoing trials were retrieved in ClinicalTrials.gov. Findings are promising, as cannabinoids appeared to improve problem behaviors, sleep, hyperactivity, and communication deficits, with limited cardiac and metabolic side effects. Interestingly, they generally allowed to reduce the number of prescribed medications and decreased the frequency of seizures in epileptic patients. Mechanisms of action could be linked to the excitatory/inhibitory imbalance found in people with ASD. However, further trials need to be implemented with better characterization and homogenization of samples, and well-defined outcomes.

This paper aims to outline the effectiveness of modern universal gate quantum computers when utilizing different configurations to solve the B-SAT(Boolean Satisfiability) problem. The quantum computing experiments are performed using Grover’s Search algorithm to find a valid solution. The experiments are performed under different variations to demonstrate their effects on the results. Changing the number of shots, qubit mapping, and using a different quantum processor are all among the experimental variables. The study also branches into a dedicated experiment highlighting a peculiar behavior that IBM quantum processors exhibit when running circuits with a certain number of shots.

The World economy after global crisis of 2008–2009 entered a restructuring era. It defines relevance of researches of its directions and patterns. The principles of determinism and systemic analysis are methodological basis of article. In research were used the methods of processing Big Date, as of continuous changes and the symmetric analysis of macroeconomic indicators according to databases of the IMF, WB, BIS, the Central banks and treasuries. As a result of the research it is proved that depth and globalism of recessionary processes are caused by a combination of crisis of world financial system and civilization problems. Intrinsic signs of risks in the modern economy caused by the duality of the nature of global crises have been identified. There are analyzes: the deficit of resources of the international financial institutions, a negative role of a fixed rate of Yuan, a big share of derivatives and off-balance obligations of banks, use of SPV in structures of deals, growth of debt obligations, trade wars, slowdown in the growth of the Chinese economy, aggravation of contradictions between global and national finances. The thesis is reasonable that deglobalization and dedollarization deepened this conflict, started the rollback mechanism from achievements of globalization, led to tariff wars. By means of a systematization it is proved the key directions of the restructuring of global economy: legal basis, leadership and reserve currency. On the basis of SWOT-analysis of the USA and China it was concluded that the question of leadership of one country should be excluded, but slow transition to use SDR (with a basket from 15–20 currencies) as a reserve.

Signal approximation, is the basic idea of signal processing and mathematical analysis where complex signals can be represented with simpler ones. This paper explores unifying two mathematical fundamentals, Dirichlet-type problems, and hyperbolic series identities, into signal approximation. In this paper, we address a well-known classic topic in mathematical analysis - the Dirichlet problem - to improve (the approximation of) signal using Fourier series. We also discuss using hyperbolic series representations to increase signal modeling flexibility. In this way, we hope to create new links that span some distance along this dimension and result in a somewhat theoretical view of signal behavior - present with the mathematical rigor needed for speculation but absent from an understanding capable of appropriately handling real-world complexity. This paper provides a theoretical investigation of the mechanics at play and reveals by analogy how these mathematical tools can potentially advance signal processing techniques and understanding. This paper illustrates Fourier series and fuzzy logic methods by two case studies on signal processing, satellite communication and financial risk measurement. The first case study performs signal approximation using the Fourier series and hyperbolic function identities to provide insight into how signals behave and are modeled. The second case study deals with applying fuzzy logic for risk evaluation of investment portfolios, emphasizing the utility in evasion systems solving uncertainty and imprecision problems related to financial decisions.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*&gt;0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

Inverse problems of recovering surface fluxes on the boundary of a domain from pointwise observations are considered. Sharp conditions on the data ensuring existence and uniqueness of solutions in Sobolev classes are exposed. They are smoothness conditions on the data, geometric conditions on the location of measurement points, and the boundary of a domain. The proof relies on asymptotics of fundamental solutions to the corresponding elliptic problems and the Laplace transform. The problem is reduced to a linear algebraic system with a nondegerate matrix.

Besides the Lagrangian and the Eulerian descriptions, the motion of a body can also be expressed relative to the present configuration of the body, known as the relative motion description. It is interesting to consider such a relative motion description in general to formulate the basic system of field equations for solid bodies. In doing so, when the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system becomes linear. This will be done for thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Relative Lagrangian formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. Some applications of such a formulation in numerical simulations are briefly reviewed.

In the research we consider a structure-fluid interaction of oscillating piezodevice and acoustic liquid. Such problem requires finding resonance or anti-resonance frequencies of the solid structure to use them in the latter frequency-response analyses step. After finite element discretization of the issue, we need to solve a generalized eigenvalue problem (GEP). The most efficient numerical method for solving the partial GEP is the shift-and-invert Lanczos method. Each step of this algorithm requires solving a large scale system of linear algebraic equations (SLAEs) with special properties. Various ways of ordering grid nodes lead to coefficient matrices with different structure. Several methods are compared in terms of efficiency. The results of the numerical experiments are presented.

We examine a linear q-difference differential equation which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q-analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm log t and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q-difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q-Gevrey type growth.

The zero-catch problem is a key issue in CPUE(Catch Per Unit Effort) standardization, and previous studies have treated all zero-catch data uniformly, but this actually loses some correctly-labeled samples. On the other hand, for the main catches with few zero-catch samples, the problem of low performance of fisheries forecasting remains unsolved even though the forecasting model structure is updating constantly, since we cannot know whether the samples are correctly recorded. In this paper, we propose a method based on confident learning theory to detect anomalous samples in the datasets and unify zero-catch and non-zero samples as noise through an overarching framework of learning with noisy labels, which reveals the heterogeneity among zero-catch samples (as well as among non-zero samples) and the homogeneity between zero-catch samples and non-zero samples. Using three species of tuna in the tropical Atlantic Ocean with the spatial resolution of 0.5 ◦ × 0.5 ◦ and time resolution of days from 2016 to 2019 as experimental material, performance on all three classical machine learning models(Random forest, Support Vector Machine and XGBoost) is significantly improved compared to each baseline.This confirms that we propose a self-adaptive, effective method for detecting and repairing anomalous samples in the fishery dataset.

A lot of previous research have proposed various frameworks and algorithms to optimize routes to reduce the total transportation cost, which accounts for over 70% of overall logistics cost. However, it is very hard to find the cases applied the mathematical models or algorithms to the practical business environment cases, especially daily operating logistics services like convenient stores. Most of previous research have considered the developing an optimal algorithm which can solve the mathematical problem within the practical time while satisfying all constraints such as the capacity of delivery and pick-up, and time windows. For the daily pick-up and delivery service like supporting several convenient stores, it is required to consider the unit transporting container as well as the demand, capacity of trucks, traveling distance and traffic congestion. Especially, the reusable transporting container, trays, should be regarded as the important asset of logistics center. However, if the mathematical model focuses on only satisfying constraints related delivery and not considering the cost of trays, it is often to leave the empty trays on the pick-up points when there is not enough space in the track. In this research, it has been proposed to build the mathematical model for optimizing pick-up and delivery plans by extending the general vehicle routing problem of simultaneous delivery and pickup with time windows while considering left-over cost. With the numerical experiments, it has been proved that the proposed model may reduce the total delivery cost. It may be possible to apply the proposed approach to the various logistics business which uses the reusable transporting container like shipping containers, refrigerating containers, trays, and pallets.

A novel approach was developed that combined LP-based row generation with optimization-based sorting to tackle computational challenges posed by budget allocation problems with combinatorial constraints. The proposed approach dynamically generated constraints using row generation and prioritized them using optimization-based sorting to ensure a high-quality solution. Computational experiments and case studies revealed that as the problem size increased, the proposed approach outperformed simplex solutions in terms of solution search time. Specifically, for a problem with 50 projects (N = 50) and 2,251,799,813,685,250 constraints, the proposed approach found a solution in just 1.4 seconds, while LP failed due to the problem size. The proposed approach demonstrated enhanced computational efficiency and solution quality compared to traditional LP methods.

This article presents a combined route and path planning strategy to guide Skid-Steer Mobile Robots (SSMRs) in scheduled harvest tasks within expansive crop rows with complex terrain conditions. The proposed strategy integrates: i) a global planning algorithm based on the Traveling Salesman Problem under the Capacitated Vehicle Routing approach and Optimization Routing (OR-tools from Google) to prioritize harvesting positions by minimum path length, unexplored harvest points, and vehicle payload capacity, and ii) a local planning strategy using Informed Rapidly-exploring Random Tree (IRRT*) to coordinate scheduled harvesting points while avoiding low-traction terrain obstacles. The global approach generates an ordered queue of harvesting locations, maximizing the crop yield in a workspace map. In the second stage, the IRRT* planner avoids potential obstacles, including farm layout and slippery terrain. The path planning scheme incorporates a traversability model and a motion model of SSMRs to meet kinematic constraints. Experimental results in a generic fruit orchard demonstrated the effectiveness of the proposed strategy. In particular, the IRRT* algorithm outperformed RRT and RRT* with 96.1% and 97.6% smoother paths, respectively. The IRRT* also showed improved navigation efficiency, avoiding obstacles and slippage zones, making it suitable for precision agriculture.

In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject.

For each measurement, at least three objects are needed: a solid, neutral object as a measuring instrument and two objects for comparison. This system of three spatial dimensions per object has a common time. All measurements are based on orbits relative to the firmament and coincidences of the spatial coordinates of the objects after rotations with π and provide the energy of the system. These results in the most suitable coordinate system with dimensions of powers of π in which the radius is curved, as are the longitude and latitude. Polynomials P(2π) correspond to neutral objects, in addition to P(π) for charge, spin, isospin. In addition, it is assumed that the cosmos consists of a single type of particle with a speed of light c. Normalizing to the rest mass of the electron, the neutrinos are ντ=π, νμ=1, and νe=1/π. The energy of an electron is: Ee=gfreq(π)+1−1/π. An algorithm is derived from a Christoffel symbol and similar to a lattice gauge calculation. It provides exact residual masses for neutrons, protons, muons, tauons, quarks u, d, and pions. The theory can be applied to the inner planetary system and the cosmos and explains the hierarchy problem.

This paper presents an interpretable support vector machine (SVM) and its application to rehabilitation assessment. We introduce the concept of nearest boundary point to standardize the one-class SVM decision function and determine the shortest path for data from abnormal cases to become those from normal cases. This analytical approach is computationally simple and provides a unique solution. The nearest boundary point of abnormal data can also be used to analyze the cause of abnormal classification and indicate countermeasures for normalization. These properties render the proposed interpretable SVM valuable for medical assessment applications and other problems that require careful consideration of classification results for treatment. Simulation and application results demonstrate the feasibility and effectiveness of the proposed method.

The marketing industry is rapidly evolving, necessitating educational programs to adapt and equip graduates with relevant skills and knowledge. This systematic literature review with bibliometric analysis (SLRBA) explores the integration of Problem-Based Learning (PBL) in marketing education. PBL is an instructional strategy that empowers students to solve real-life problems by integrating theory and practice, thus fostering critical thinking and decision-making skills. Our review synthesizes data from 71 sources, highlighting the definition of PBL, strategies to promote its implementation in marketing education, and the benefits and challenges associated with this approach. The findings indicate that PBL enhances student engagement, provides hands-on experience, and prepares students for real-world marketing challenges. Strategies such as using social media, serious games, e-learning, and feedback mechanisms are discussed for their effectiveness in promoting active learning and student participation. Despite its advantages, PBL faces challenges such as resource intensiveness, student resistance, and information integrity issues. This review underscores the importance of PBL in bridging the gap between theoretical knowledge and practical application, ultimately preparing marketing students to meet the demands of the industry. The paper concludes with recommendations for future research and best practices for implementing PBL in marketing education.

Topological defects such as magnetic monopoles that may have formed during cosmological phase transitions in the early universe. The Kibble mechanisms govern the formation of this defects and their abundance is influenced by the correlation length and the temperature-dependent Higgs mass. The Magnetic monopoles are particularly interested but their excessive production poses the monopole problem which is challenge to the standard model. Many solutions including symmetry breaking patterns and thermal pair production have been proposed to mitigate the monopole problem. Detecting monopoles would offer valuable insights into high-energy physics and the early universe. Detection of (even) a single monopole could revolutionize our current knowledge of the universe.

The quickest path problem in the multistate flow networks, also known as the quickest path reliability problem (QPRP), aims at calculating the probability of transmitting a minimum of d units of flow/dat/commodity from a source node to a destination node through one single path within T units of time. Several exact and approximation algorithms have been proposed in the literature to address this problem. Most of the exact algorithms in the literature need prior knowledge of all the network’s minimal paths (MPs), which is considered a weak point. In addition to the time, the budget is always limited in real-world systems, making it an essential consideration in the analysis of systems’ performance. Hence, this study considers the QPRP under the cost constraints and provides an efficient approach based on the node-child matrix to address the problem without knowing the MPs. We show the correctness of the algorithm, compute its complexity results, illustrate it through a benchmark example, and conduct extensive experimental results on the known benchmarks and one thousand randomly generated test problems to demonstrate its practical superiority compared to the existing algorithms in the literature.

Different variants of thinning for discrete random variables are studied. The thinning procedure allows to introduce an analog of scale parameter for positive integer-valued random variables. Sufficient and necessary conditions for the existence of such a scale are given.

Research has shown that hands-on projects promote stem education, namely, via problem-solving. CanSat, literally 'satellite in a can', is a stem educational project promoted by the European Space Agency. This paper addresses this issue by researching this STEM project, which demonstrates how problem-solving can be achieved in secondary-level students within the framework of the CanSat. We use qualitative techniques of data collection and analysis. The results showed that students use sophisticated thinking strategies to process information within this interdisciplinary project: (a) cognitive testing, cognitive organization, cognitive regulation, and monitoring, in addition to computer language and physical–mathematical calculations, are cognitive and metacognitive behavior strategies revealed in the CanSat; (b) problem-solving was suggested as a specific model, where students’ higher cognitive and metacognitive ordering processes deepen in project development; (c) computational, lateral, or divergent and convergent thinking were detected as thinking types of students associated with and mobilized in the course of problem-solving, The findings of this research have practical implications for STEM education in space science. Hands-on projects using problem-solving are an essential strategy to promote STEM education. Additionally, they are a starting point to promote meaningful learning and new thinking types.

We studies the initial value problem for the fractional Navier-Stokes-Coriolis equations, which obtained by replacing the Laplacian operator in the Navier-Stokes-Coriolis equation by the more general operator $(-\Delta)^\alpha$ with $\alpha>0$. We introduce function spaces of the Besove type characterized by the time evolution semigroup associated with the general linear Stokes-Coriolis operator. Next, we establish the unique existence of global in time mild solutions for small initial data belonging to our function spaces characterized by semigroups in both the scaling subcritical and critical settings.

Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author’s earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.

Considering the significant advancements in autonomous vehicle technology, research in this field is of interest to researchers. To automatic parking, controlling steer angle, gas hatch, and brakes need to be learned. Due to the increase in the number of cars and road traffic, car parking space has decreased. Its main reason is information error. Because the driver does not receive the necessary information or receives it too late, he cannot take appropriate action against it. This paper uses two phases: the first phase, for goal coordination, was used genetic algorithms and the Cuckoo search algorithm was used to increase driver information from the surroundings. Using the Cuckoo search algorithm and considering the limitations, it increases the driver’s level of information from the environment. Also, by exchanging information through the application, it enables the information to reach the driver much more quickly and the driver reacts appropriately at the right time. The suggested protocol is called the MODM-based solution. Here, the technique is assessed through extensive simulations performed in the NS-3 environment. Based on the simulation outcomes, it is indicated that the parking system performance metrics are enhanced based on the detection rate, false-negative rate, and false-positive rate.

The Kolkata Paise Restaurant Problem is a very challenging game, where n agents have to decide where they will have lunch on a busy day during their lunch break. The game is very interesting because there are exactly n restaurants and each restaurant can accommodate only one agent. If two or more agents happen to choose the same restaurants, only one gets served and the others have to return back to work hungry. In this paper, we tackle this problem from an entirely new angle. We abolish certain implicit assumptions, which allows us to propose a novel strategy with greater utilization of the restaurants and overall efficiency. We emphasize the spatially distributed nature of our approach, which, for the first time, perceives the locations of the restaurants as uniformly distributed in the entire city area. This critical change in perspective has profound ramifications in the topological layout of the restaurants, which now makes it completely realistic to assume that every agent has a second chance. Every agent now may visit, in case of failure, more than one restaurants, within the predefined time constraints. From the point of view of each agent, the situation now resembles more that of the iconic travelling salesman, who must compute an optimal route through n cities. Following this shift in paradigm, we advocate the use of metaheuristics, as exacts solution of the TSP are prohibitively expensive, because they can produce near-optimal solutions in a very short amount of time. The use of metaheuristics enables each agent to compute her own personalized solution, incorporating her preferences, and providing alternative destinations in case of successive failures. We analyze rigorously the resulting situation, proving probabilistic formulas that confirm the advantages of this policy and the increase in utilization. The detailed mathematical analysis of our scheme demonstrates that it can achieve utilization ranging from .85 to 0.95 from the first day, while rapidly attaining steady state utilization 1.0. Moreover, the equations we have developed generalize previously presented formulas in the literature, which can be shown to be special cases of our results.

This paper presents a discrete particle swarm optimization (DPSO) algorithm with heterogeneous (non-uniform) parameter values for solving the dynamic travelling salesman problem (DTSP). The DTSP can be modelled as a sequence of static sub-problems, each of which is an instance of the TSP. We present a method for automatically setting the values of the DPSO parameters without three parameters, which can be defined based on the size of the problem, the size of the particle swarm, the number of iterations, and the particle neighbourhood size. We show that the diversity of parameter values has a positive effect on the quality of the generated results. We compare the performance of the proposed heterogeneous DPSO with two ant colony optimization (ACO) algorithms. The proposed algorithm outperforms the base DPSO and is competitive with the ACO.

The impact of instructional guidance on learning outcomes in higher biomedical education is subject of intense debate. There is the teacher-centered or traditional way of teaching (TT) and, on the other side, the notion that students learn best under minimal guidance (problem-based learning, PBL). Although the benefits of PBL are well-known, there are aspects susceptible to improvement. Hence, a format merging TT and PBL (hybrid-PBL, h-PBL) may advance education in biomedical sciences. Here, we systematically reviewed studies that employed h-PBL in higher biomedical education compared to TT and/or pure PBL. We found that h-PBL resulted in better overall students’ performance and perception than TT or pure PBL. These findings encourage more research on investigating the pedagogical benefits of h-PBL and posit an eclectic system in which the pedagogical tools from TT and PBL are used cooperatively in the best interest of the education and satisfaction of the students.

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

News recommendation schemes utilize features of the news itself and information about users to suggest and recommend relevant news items to the users towards the interest they have. However, the effectiveness of the existing news recommendation scheme is limited in the occurrence of new user cold start problems. Therefore, we designed a news recommender system using hybrid approaches to address new user cold start problems to ease and suggest more related news articles for new users. To achieve the objective mentioned above, user demographic data with a hybrid recommendation system that contains the scheme of both content-based and collaborative filtering approaches is proposed. To evaluate the effectiveness of the proposed model, an extensive experiment is conducted using a dataset of news articles with user rating value and user demographic data. The performance of the proposed model is done by two ways of experiment. So, the performance of the proposed model performs around 68.05% of Precision, 42.46% of Recall and 52.1% of the average F1 score for the experiment based on individual user similarity in the system. And also performs around 93.75% of precision, 40.25% of recall and 56.31% F1-score for the similarity of users based on the similarity of users within the same category which is better than the first experiment.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

The time evolution of the continuous measure symmetry for the system built of the three bodies interacting via the potential U(r)~1/r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the case of the pure gravitational interaction the three-body-system deviated from its initial symmetrical location, described by the Lagrange equilateral triangle, comes to collapse, accompanied by the growth of the continuous measure of symmetry. When three point bodies interact via the Coulomb repulsive interaction, the time evolution of CMS is quite different. CMS calculated for all of studied initial configurations of the point charges and all of their charge-to-mass ratios always comes to its asymptotic value with time, evidencing the stabilization of the shape of the triangle, constituted by the interacting bodies.

For more than one hundred years, scientists dispute the correct interpretation of Lorentz transformations within the framework of the special theory of relativity of Albert Einstein. On the one hand, the changes in length, time and mass with increasing velocity are interpreted as apparent due to the observer dependence within special relativity. On the other hand, real changes are described corresponding to the experimental evidence of mass increase in particle accelerators or of clock delay. This ambiguity is accompanied by an ongoing controversy about valid Lorentz-transformed thermodynamic quantities such as entropy, pressure and temperature. In this paper is shown that the interpretation problem of the Lorentz transformations is genuinely anchored within the postulates of special relativity and can be solved on the basis of the thermodynamic approach of matter-energy equivalence, i.e. an energetic distinction between matter and mass. It is suggested that the velocity-dependent changes in state quantities are real in each case, in full agreement with the experimental evidence.

This paper discusses a possible approach to validate the Goldbach conjucture which states that all even numbers can be expressed as a summation of two prime numbers. For this purpose the paper begins with the concept of successive-addition-of-digits-of-an-integer-number (SADN) and its properties in terms of basic algebraic functions like addition, multiplication and subtraction. This concept of SADN forms the basis for classifying all odd numbers into 3 series- the S1, S3 and S5 series- which comprise of odd numbers of SADN(7,4,1), SADN(3,9,6) and SADN(5,2,8) respectively and follow a cyclical order. The S1 and S5 series are of interest in the analysis since they include both prime and composite numbers while the S3 series exclusively consists of composite numbers. Furthermore, the multiplicative property of SADN shows why composites on the S1 series are derived as products of intra-series elements of the S1 and S5 series while composites on the S5 series are derived as products of inter-series elements of the S1 and S5 series. The role of SADN is also important in determining the relevant series for identifying the combination of primes for a given even number since it shows why such combinations for even numbers of SADN(1,4,7) will be found on the S5 series while those for even numbers of SADN(2,5,8) will lie on the S1 series and both the series have a role to play in identifying the prime number combinations for even numbers with SADN(3,6,9). Thereafter, the analysis moves to calculating the total number of acceptable combinations for a given even number that would include combinations in the nature of two composites (c1+c2), one prime and one composite (p+c) and two primes (p1+p2). A cyclical pattern followed by even numbers is also discussed in this context. Identifying the c1+c2 and p+c combinations and thereafter subtracting them from the total number of combinations will yield the number of p1+p2 combinations. For this purpose the paper discusses a general method to calculate the number of composites on the S1 and S5 series for a given number and provides a detailed method for deriving the number of c1+c2 combinations. The paper presents this analysis as a proof to validate the Goldbach conjecture. Since even numbers can be of SADN 1 to 9 and the relation between nTc (i.e. total number of acceptable combinations) and nc(i.e. number of composites) for all even numbers can either be of nTc > nc or nTc ≤ nc, the paper shows that the Goldbach conjecture is true for both these categories of even numbers. In this manner this analysis is totally inclusive of all even numbers in general terms and since the analysis of every even number is common in methodology but unique in compilation, apart from being totally inclusive, it is also mutually exclusive in nature. This proves that the Goldbach conjecture which states that all even numbers can be expressed as atleast one combination of two prime numbers holds true for all even numbers, across all categories possible. Additionally this approach proves that the identification of p1+p2 combinations which would validate the Goldbach conjecture lies in the identification of c1+c2 combinations.

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem