Cosmic inflation has presented solutions for a number of important cosmological problems, yet left some unanswered. In this paper, we present a cosmological model based on the quantization of the zero-point field which is consistent with empirical data, requires fewer assumptions, and presents answers to some of those unanswered questions. A comparison between standard cosmology and the theory presented in this paper is given below. Vacuum energy density: Standard inflationary model needs both Hubble’s constant and Matter density to estimate it. But, new cosmological model needs only Hubble’s constant. Non-vacuum energy density: Standard model can’t predict it. But, the new model can predict using only Hubble’s constant. Ratio of vacuum energy to total energy: Standard model can’t predict it. But, new model can predict it, that too without using Hubble’s constant. Energy conservation: In standard model, total energy is not conserved before inflation. But, in the new model, energy is conserved right from beginning of the universe whose net energy (including gravitational potential energy) is always zero. Flatness and homogeneity: Standard model needs Inflaton field with a specific potential energy distribution to explain it. But, new model doesn’t need any such hypothetical field, just the zero-point field is sufficient. Based on the new cosmological model, in the conclusion, realistic possibility for existence of multiverse and a mechanism for end of universe are discussed.

Quantum Field Theory (QFT) and General Relativity (GR) are pillars of modern physics, each supported by extensive experimental evidence. QFT operates within Lorentzian spacetime, while GR ensures local Lorentzian geometry. Despite their successes, these frameworks diverge significantly in their estimations of vacuum energy density, leading to the cosmological constant problem—a discrepancy where QFT estimates exceed observed values by 123 orders of magnitude. This paper addresses this inconsistency by tracing the cooling evolution of the universe's gauge symmetries—from \(SU(3) \times SU(2) \times U(1)\) at high temperatures to \(SU(3)\) alone near absolute zero—motivated by the experimental Meissner effect. This symmetry reduction posits that \(SU(3)\) forms the fundamental "atoms" of vacuum energy. Our analysis demonstrates that the calculated number of \(SU(3)\) vacuum atoms reconciles QFT's predictions with empirical observations, effectively resolving the cosmological constant problem. The third law of thermodynamics, by preventing the attainment of absolute zero, ensures the stability of \(SU(3)\) vacuum atoms, providing a thermodynamic foundation for quark confinement. This stability guarantees a strictly positive mass gap, defined by the vacuum energy density, and implies a Lorentzian quantum structure of spacetime. Moreover, it offers insights into the origins of both gravity/gauge duality and gravity/superconductor duality.

The 3x+1 problem is a problem of continuous iteration for integers. According to the basic theorem of arithmetic and the way of iteration, we derive a general formula for continuous iteration for odd integers. Through this formula, we can construct a loop iteration equation and obtain the result of the equation: the equation has only one positive integer solution. In addition, this general formula can be converted into a linear indeterminate equation. The process of solving this equation shows that the relationship between the iteration result and the odd number being iterated is linear. Extending this result to all positive even numbers, we get the answer to the 3x + 1 question.

Because of hyper complexity, difficulty to define, multiple stakeholders with conflicting perspectives, and lack of clear-cut solutions, wicked problems necessitate innovative and adaptive strategies. Operations Research has been a valuable tool for managers to make informed decisions for years. However, as we face increasingly complex and messy problems, it has become apparent that relying solely on either hard or soft OR approaches is no longer sufficient. We need to explore more innovative methodologies to address these wicked problems effectively. This study has bridged the research gap by proposing a structured process encompassing a subdivision-based problem structuring method for defining the wicked problem, a multi-attribute decision-making (MADM) for prioritizing sub-problems, and a hard OR technique, data envelopment analysis (DEA) for tackling one of the most critical sub-divisions. The proposed methodology, implemented in a case study, focuses on a higher education institution experiencing a decline in student admissions and involves five steps. First, a diverse group of stakeholders is formed to ensure comprehensive consideration of perspectives. Second, the wicked problem is defined, considering long-term consequences, multiple stakeholders, and qualitative stakeholder opinions. Third, a hierarchical structure is created to break down the wicked problem into manageable sub-problems. Fourth, a multi-criteria decision-making (MCDM) method prioritizes sub-problems. Finally, the sub-problems are addressed one by one using a combination of soft and hard OR tools. The findings highlight the benefits of integrating hard and soft OR approaches. The article concludes with reflections on the implications of using a combined OR approach to tackle wicked problems in higher education and beyond.

Cutting and packing problems have been studied for decades and are of concern for a wide variety of industries to reduce costs and material utilization. This paper addresses the one-dimensional cutting stock problem, focusing on minimizing total stock usage. Procedures that address this problem include linear programming methods and metaheuristics. However, linear programming methods are limited to low-complexity instances, while most metaheuristics require extensive parameter tuning. In this paper, we develop a Petri-net model to construct cutting patterns. Using the reachability tree of the Petri net, the filtered beam search algorithm is implemented to find the best solution. Our algorithm is compared with the Least Lost Algorithm and the Generate & Solve algorithm over five datasets of instances. These algorithms share some characteristics with ours and have proven to be effective and efficient. Experimental results demonstrate that our algorithm effectively finds optimal solutions for both low and high-complexity instances. These findings confirm that Petri nets are suitable for modeling and solving the one-dimensional cutting stock problem.

The cosmological model presented here rests on the postulate that the universe can be described as an interacting attraction (exerted by matter) and repulsion (exerted by the excitation energy of the quantum vacuum) system in virial equilibrium. The basic parameters of the model, the matter density and the excitation energy of the quantum vacuum are determined by observations and are not adjusted to the model. The model requires only a few assumptions that can be deduced from the laws of conventional physics and from the rules of quantum field theory. Existing problems in standard cosmology, such as the flatness and the horizon problems, among others, can be resolved in a straightforward way without inflation and without recourse to dark matter and dark energy.

We study a localization of gravity through the matching point between non-inertial frames and local inertial frames. This localization of gravity is done through defining relative gravitational red-shift. This lead to an emergence of a timeless state in a mathematically consistent way. In this timeless state of gravity, we find a geometric interpretation of the speed of light and mass. The experimental support of the timeless state is the quantum entanglement and internal symmetries that are independent of time. Therefore gravity would be responsible for measurements independent of time including quantum entanglement. Timeless state in that sense explain why do we have gravity/gauge correspondence. We conjecture that the universe emerged from a black hole with a global $SU(3)\times SU(2)\times U(1)$ symmetry on its event horizon that produces gauge fields Electromagnetism, weak and strong nuclear force through localization of this global symmetry. Through the localization in the gravity field, the timeless measurements such as spin will be correlated with the varying of timeless measurement which is relative gravitational red-shift. We present a gravitational or geometric interpretation of spin-0, spin-1, and spin-1/2 states. We present an interpretation of why do we measure matter rather than anti-matter. We found that the Higgs scalar field is represented by the gravitational red-shift at every point in the space around the black hole. We derive the numerical value of the cosmological constant that agrees with experimental observations.

In this paper, I introduce a new concept of representing numbers in base ; in other words, I have found new series for any number similar to series that could be written according to the collatz sequence which is called zi(n) in this article. These series need to end with 1. Then, we use two sets of rules to make a diagram which then proves the existence of such series for any number.In this diagram, by branching numbers into different branches in accordance to the modularity of 4 and continuing branching to the point that their numbers have enough common terms in their collatz series, we could reduce zi(n) to zi(k) so that k<n in any branch by Rule Number One. This diagram shows that zi(n) exists for every number, in other words, this proves the theorem (A) or zi-existence theorem. The proof of zi-existence theorem leads to a proof of the collatz conjecture because the collatz series could be written as a linear combination of such series that all of them end with 1, so the collatz series for any number ends with 1.

Although general relativity has been successful in explaining many astronomical phenomena, few problems about the contents and evolution of the universe have remained mysterious since last century. Most important of them is the cosmological constant problem in which conventional calculation of vacuum (or dark) energy density using quantum mechanics leads to a value ~10¹¹⁴ J/m³ which is ~10¹²³ times more than the vacuum energy (5.3×10^-10 J/m³) estimated from astronomical observations of expanding universe. Similarly, cosmic coincidence problem questions why the matter energy density (ordinary plus dark matter) is of the same order as the vacuum energy density at present time. Finally, the mechanism responsible for spatial flatness and expansion of the universe are not clearly understood. In this paper, by taking the vacuum as a finite and closed quantum oscillator, we solve all of the above-mentioned problems. At first, by using purely quantum mechanical approach, we predict that the dark energy density is c⁴/(GR²) = 5.27×10^-10 J/m³ (where R is radius of 3-sphere of universe) and matter energy density is c⁴/(2GR²) = 2.6×10^-10 J/m³ which match well with astronomical observations. We also prove that the dark energy has always been ~66.7% and matter energy has been ~33.3% of total energy and hence, the so called cosmic coincidence problem doesn’t exist. Next, we show how flatness of space could be maintained since the early stage of universe. Finally, using our model, we derive the expression for age and radius of universe which match well with the astronomical data.

This article introduces a novel three-phase angular perturbation technique for solving the School Bus Problem (SBP), an NP-hard combinatorial optimization challenge. The three phases—initial solution, global and local search, and solution exploration—focus on optimizing school bus routes by minimizing sharp turns and reducing travel distances. The performance of three metaheuristic algorithms (GAACOSA-AP, BFSPSO-AP, RL-AP) is evaluated, and significant improvements in routing efficiency are observed. we evaluated the performance of our hybrid algorithm against the industry-leading optimization software, CPLEX, and other optimization techniques across multiple school scenarios. The results show that the GAACOSA-AP algorithm consistently outperforms its counterparts, achieving substantial reductions in travel distances, particularly for complex routes with numerous stops. The integration of Angular Perturbation was key to improving route geometry by, reducing sharp turns, and enhancing overall path optimization by an average reduction of 27.12% compared to 22.37% without Angular Perturbation.

This paper proposes a novel formulation of the fuzzy newsvendor problem for inventory management applications. This new formulation allows the use of any profit function. A new credibility estimation is proposed to explore the neighborhood around the most impactful demand scenarios. Further, a simulation procedure was designed for the different demand scenarios, which allows the comparison of the proposed approach with probabilistic demand curves. The fuzzy newsvendor problem is solved using a modified genetic algorithm (GA), where an initialization mechanism with null values is proposed. The new formulation of the fuzzy newsvendor problem together with the modified GA have shown to improve the average profit up to 55% in problems with low-budget scenarios.

The augmenting commitment in the entrepreneurial learning process, both at academic and industry level, has led to new mechanisms and methodologies. Entrepreneurship literature has shown evidence of raising interest in the problem-based learning (PBL) methodology with regard to upcoming events from the surrounding learning context. This paper presents a Systematic Bibliographic Literature Review (SBLR) with respect to the application of PBL throughout distinct entrepreneurial processes either in higher education, or in industry. It aimed to identify relevant entrepreneurial opportunities for PBL. Bibliographic databases were searched for documents published between 2002 and May 2024 to categorize key topics discussed in the literature on PBL and entrepreneurship. The review process identified 142 empirical and non-empirical papers on entrepreneurship related PBL. Data analysis revealed diverse subthemes for PBL uses in entrepreneurship in both higher education institutions and industry. The research questions “What is the interplay of problem-based learning methodology with entrepreneurship?” guided the study. The central output of the research is the discovery of the varying uses of PBL to cope with diverse events arising within entrepreneurship context. Future research directions are suggested.

Problem-Based Learning (PBL) has emerged as an innovative and effective pedagogical methodology in medical education. This student-centered approach promotes the development of critical thinking, problem-solving, and self-directed learning skills, essential for the training of competent physicians. This article explores the theoretical foundations of PBL, its implementation methodology, and the benefits it offers to medical students as well as to the quality of medical care. Through a comprehensive literature review and analysis of experiences in different contexts, the importance of PBL as a tool to improve medical training is highlighted and recommendations are offered for its effective implementation.

On the H-type group G⊂Rm×Rn, we study the existence of solutions for the Brezis-Nirenberg problem

The container relocation problem (CRP) is one of the important topics in container terminals, which aims to find the optimal sequence of movements to minimize the total number of relocations needed to retrieve all the containers within a bay according to a given specific layout and retrieval order. However, determining such an order may be difficult due to uncertainty. Various CRP solution methods proposed so far show a common pitfall concerning the complexity of the solving process, whose scale grows exponentially with the number of containers. Considering the retrieval operation process of the inbound containers in a bay consists of several operation rounds, this paper focuses on the real-time operation scenario of each round to minimize the actual number of relocations during the pick-up process, i.e., starting from the initial layout of the bay, we minimize the sum of the incremental number of blocking containers due to the layout change and the number of reallocated containers unrelated to the target container. We present a heuristic algorithm (called SPFH) based on the three rules (LL, MSS, and FSS), considering the adjustment of the pick-up order of containers. Numerical experiments on a set of instances generated from the literature are performed. The proposed methodology excels in both execution efficiency and solution quality and is capable of solving instances that were impossible to solve before. This also makes our methods appealing for being applied in practice. The source codes are available at https://github.com/zhou-sf/rt-scrp.

The paper proposes an approach to solving the inverse epidemiological problem, written in terms of the “mean field” theory. Finding the coefficients of the epidemiological SIR mean field model is reduced to solving an optimization problem, for the solution of which only zero-order methods can be used. The Nelder-Mead method was chosen as such a method. The algorithm for solution of the inverse coefficient problem is proposed. Computational experiments were carried out to compare the obtained solutions with respect to synthetic and real data. The results of computational experiments have shown the efficiency of this approach. Ways to further improve the approach have also been determined.

This paper proposes an electric vehicle routing problem with considering states of charging stations and suggests solution strategies. Charging of electric vehicles is a main issue in the field of electric vehicle routing problem. There are many studies to find locations of charging stations, recharging functions for batteries of vehicles, and so on. However, states of charging stations significantly affect the routes of electric vehicles, which is not much explored. The states may include open or close of charging stations, occupied or empty of charging slots, and so on. This paper investigates how the states of charging stations are estimated and routing strategies are determined. We formulate a mixed integer programming model and suggest how to solve the problem with exact method. Numerical examples provide the optimal routing strategies of electric vehicles in the changing environments of the states of charging stations.

The Fuzzy Transportation Problem (FTP) represents a significant extension of the Classical Transportation Problem (TP) by introducing uncertainly and imprecision into the parameters involved. Various algorithms have been proposed to solve the FTP, including fuzzy linear programming, metaheuristic algorithms and fuzzy mathematical programming techniques combined with Artificial Neural Networks. This paper presents the application of Trigonometric Acceleration Coefficients-PSO (TrigAc-PSO), a variation of the Classical Particle Swarm optimization algorithm, which is an innovative algorithm originally developed for solving the TP. TrigAC-PSO, has demonstrated remarkable success in optimizing various problem domains in crisp environments.

In this paper, improved matrix Reduction Method is proposed for the solution of fuzzy transportation problem in which all inputs are taken as fuzzy numbers. Since ranking fuzzy number is important tool in decision making, Fuzzy trapezoidal number is converting in to crisp set by using Mean techniques and solved by proposed method for fuzzy transportation problem. We give suitable numerical example for unbalanced and compare the optimal value with other techniques. The Result shows that the optimum profit of transportation problem using proposed technique under robust ranking method is better than the other method. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms.

The emerging working mode of coordinated trucks and drones has demonstrated significant practical potential in various fields, including logistics and delivery, intelligence surveillance reconnaissance, area monitoring, and patrol. The seamless collaboration between trucks and drones is garnering widespread attention in academia and has emerged as a key technology for achieving efficient and secure transportation. This paper provides a comprehensive and in-depth review of the research status on the routing problem for coordinated trucks and drones, covering aspects such as application background, cooperative modes, configurations, issues have been taken into consideration, and solution methodologies.

There are many problems based on solving non-autonomous differential equations of the form x¨(t)+ω2(t)x(t)=0, where x(t) represents the coordinate of a material point and ω is the angular frequency. The inverse problem involves finding the bounded coefficient ω. Continuity of the function ω(t) is not required. The trajectory x(t) is unknown, but the initial and final values of the phase variables are given. The variation principle of minimum time for the entire dynamic process allows for the determination of the optimal solution {x(t),ω(t)}. Thus, the inverse problem is an optimal control problem. No simplifying assumptions were made.

(1) Background: There is not much research about obesity in nursing homes although knowledge will help us to develop customized treatment plans and prevention strategies, which may help to decrease the burden for all persons involved. The objective of conducting this study was to describe the prevalence of obesity and the association between obesity and care problems in nursing home patients. (2) Methods: This study is a secondary data analysis of data collected in an annually performed cross-sectional study called “Nursing Quality Measurement 2.0”. A standardized and tested questionnaire was used to collect data. (3) Results: 1236 nursing home patients took part and 16.7% of them were obese. The multivariate logistic regression analysis results show that urinary incontinence is significantly associated with the presence of obesity (OR 2.111). The other care problems of pressure injuries, fecal and double incontinence, physical restraints, falls and pain were not associated with obesity. (4) Conclusion: The results indicate that, in the nursing home setting, health care staff should pay special attention to the patients’ nutritional and continence status and help patients maintain a normal, healthy weight. Conducting more studies with larger sample sizes is recommended, as this will allow differentiation among different obesity classes.

Laboratory diagnosis of leishmaniasis remains a major challenge, demonstrating variable efficacy in detecting infected mammalian hosts. Thus, there is a great need for the accuracy of the identification of appropriate antigens to also improve diagnostic tests. This review brings to the fore the sensitivity of the balance in canine and human leishmaniasis, which greatly influences the progression of the disease and especially the diagnostic methods. The problem of diagnosis arises in asymptomatic leishmaniasis, since in these conditions the methods considered as reference in the diagnosis of leishmaniasis no longer show certainty, being influenced for the most part by the immune response of the host, which is different according to the presence of other associated diseases or even according to the breed, when we talk about dogs. Consequently, the diagnosis and surveillance of leishmaniasis cases remains an open topic, with the need for new methods adapted to the immunological status of the host.

The brain’s ability to create a unified conscious representation of an object by integrating information from multiple perception pathways is called perceptual binding. Binding is crucial for normal cognitive function. Some perceptual binding errors and disorders have been linked to certain neurological conditions, brain lesions, and conditions that give rise to illusory conjunctions. However, the mechanism of perceptual binding remains elusive. Here, we present a computational model of binding using two sets of coupled oscillatory processes that are assumed to occur in response to two different percepts. We use the model to study the dynamic behavior of coupled processes to characterize how these processes can modulate each other and reach a temporal synchrony. We identify different oscillatory dynamic regimes that depend on coupling mechanisms and parameter values. The model can also discriminate different combinations of initial inputs that are set by initial states of coupled processes. Decoding brain signals that are formed through perceptual binding is a challenging task, but our modeling results demonstrate how crosstalk between two systems of processes can possibly modulate their outputs. Therefore, our mechanistic model can help one gain a better understanding of how crosstalk between perception pathways can affect the dynamic behavior of the systems that involve perceptual binding.

The research develops the vehicular routing problem for the distribution of refrigerated products in a multinational company. The mathematical model corresponds to the vehicle routing problem with hard time windows and stochastic service (VRPTW-ST) time model applied in the city of Santiago de Chile. For optimization of the model, optimization methods tabu search, chaotic search and general algebraic modeling were used. The results allow to validate the meta-heuristic chaotic search to solve the VRPTW-ST; chaotic search method obtains superior performance than tabu search method for solving a real problem in a large city.

In a previous paper we defined the Black-and-White SAT problem which has exactly two solutions, where each variable is either true or false. We showed that Black-and-White $2$-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonbogl\'{a}r model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a Black-and-White SAT problem. We prove a powerful theorem, the so called Transitions Theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as Blask-and-White SAT problems. We show that the Balatonbogl\'{a}r model is between the strong and the weak model, and it generates $3$-SAT problems, so the Balatonbogl\'{a}r model represents strongly connected communication graphs as Black-and-White $3$-SAT problems. Our motivation to study these models is the following: The strong model generates a $2$-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonbogl\'{a}r model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonbogl\'{a}r model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: SAT problem and directed graphs.

Internet-led labour market has become so competitive forcing many organisations from different sectors to embrace e-recruitment. However, realising the value of the e-recruitment from a Requirements Engineering (RE) analysis perspective is challenging. This research is motivated by the results of a failed e-recruitment project conducted in military domain which is used as a case study in this research. After reviewing the various challenges faced in that project through a number of related research domains, this research focuses on two major problems which are the (1) difficulty of scoping, representing, and systematically transforming recruitment problem knowledge towards e-recruitment solution specification; and (2) the difficulty of documenting e-recruitment best practices for reuse purposes in an enterprise recruitment environment. In this paper, a Problem-Oriented Conceptual Model (POCM) with a complementary Ontology for Recruitment Problem Definition (Onto-RPD) is proposed to contextualise the various recruitment problem viewpoints from an enterprise perspective and to elaborate those problem viewpoints towards a comprehensive recruitment problem definition. The POCM and Onto-RPD are developed incrementally using action-research conducted on three real case studies: (1) Secureland Army Enlistment, (2) British Army Regular Enlistment, and (3) UK Undergraduate Universities and Colleges Admissions Service (UCAS). They are later evaluated in a focus group study against a set of criteria. The study showed that the POCM and Onto-RPD provide a strong foundation for representing and understanding the e-recruitment problems from different perspectives.

The paper studies some cases in physics such as Galilean inertia motion and etc., and presents a logical schema of recursive abduction, from which we can derive the universality of physical laws in an effective logical path without requiring infinite inductions. Recursive abduction provides an effective logical framework to connect a universal physical law with finite empirical observations based on both quasi-law tautologies and suitable recursive dimensions, two new concepts introduced in this paper. Under the viewpoint of recursive abduction, the historical difficulty from Hume’s problem naturally vanishes. In Hume’s problem one always misunderstood a time-recursive issue as an infinitely inductive problem and, thus, sank into an inescapable quagmire. With this new effective logical schema, the paper gives a concluding discussion to Hume’s problem and justifies the validity of probability argument for natural laws.

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

Starting with a positive odd integer $n$, apply a function $f(n)$ repetitively such that $f(n) = 3n + 1$ if $n \not\equiv 0 (\text{mod}\:2)$ or $f(n) = n/2$ if $n \equiv 0 (\text{mod}\:2)$. Let the sequence of all the odd integers obtained form an orbit $n, f^1(n) , f^2(n), \ldots, f^k(n), f^{k + 1}(n)$. The $k^{th}$ odd integer is written as $f^k(n) = (3^k + \mathbf{B(k)})/2^{\mathbf{z(k)}}$ where $\mathbf{B(k)}$ is the collection of terms without the coefficient $n$. We show that when $1 - \mathbf{B(k)}/(2^{\mathbf{z(k)}} n) \approx 1$, the condition for unbounded orbit is given by OEIS A022921. Further, if there exists at least one orbit for which $f^{k + 1}(n) = n$ when $(k + 1) < 3$, we show that there exists no orbit with $k + 1 > 3$ for which $f^{k + 1}(n) = n$. The final result is that the odd integers that can violate the Collatz conjecture are smaller than 5.

Health issues of children with intellectual disabilities (ID) have gained significant attention as a key focus of China health goals. This study aimed to compare the differences in displacement skills and problem behaviors among children with varying degrees and types of ID, while also exploring their relationship. The study included 90 participants who were children with ID and had completed TGMD-2 displacement skills and Strengths and Difficulties Questionnaire (SDQ) assessments. Covariance, partial correlation, and multiple linear regression analyses were conducted to examine the differences and correlations between these factors. The findings revealed that higher severity of intellectual disability was associated with lower scores in locomotor skills and increased manifestation of problem behaviors. Notably, there were significant variations in locomotor skills and problem behaviors among children with different types of intellectual disabilities. There is a positive correlation between locomotor skills and problem behaviors in children with intellectual disabilities, where locomotor skills can predict the occurrence of problem behaviors. In Conclusion, the research confirms that the development of locomotor skills can have a positive impact on the accompanying problem behaviors of children with developmental disabilities.

Proposed article deals with analyses on trends of problem-solving robotic applications in manu-facturing, especially in transportations and manipulations. Intelligent agent-based manufacturing systems with robotic agents are observed. Intelligent core of such units must be able to propose the plan of problem-solving in form of strategy. The logical model of adaptive strategies planning for intelligent robotic system is described in form of predicates with presentation of data processing on base of set theory descriptions. Dynamic structure of workspace and possible change of goals are considered as reasons for functional strategies adaptation. Proposed formal descriptions are sup-ported by model of mobile robotic platform, acting in warehouse.

A given problem in physics can be solved if it is well formulated. Well formulated means that it has a bijective correspondence to physical reality. Mass Gap Problem has no bijective correspondence with the physical reality and is that’s why not solvable mathematically. It can be solved in the frame of quantum mechanics by the formulation of the photon’s mass accordingly to the Planck-Einstein relation.

Recent advances in the theory of quantum gravity show that the Ricci flow serves as the time evolution operator for the vacuum energy density and that in the presence of baryonic matter, the Ricci flow is analogous to the heat equation in the presence of a heat sink. Here we show using the equations of quantum gravity, that quantum information can be modelled as a thermal fluid consisting of a superposition of weakly excited eigenstates of a quantum field and that each eigenstate vector has an associated eigenstate potential well. The depth of the potential well depends on the amplitude of the eigenstate vector. Measurement is then considered as a selection by tuning process which only allows an eigenstate resonating with the detector to be detected. During the detection process, the resonating eigenstate vector increases in amplitude, deepening its potential well such that the other weakly excited states rapidly drain their small excitation energies into it via the principle of minimum action. This draining process is the act of collapsing the wave function to a specific state. Also, the presence of the eigenstate potential wells is what cancels out the infinities from high energy interactions.

This paper investigates an inverse problem of option pricing in the extended Black--Scholes model. We identify the model coefficients from the measured data and attempt to find arbitrage opportunities in financial markets using a Bayesian inference approach. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by Markov Chain Monte Carlo (MCMC), which explores the posterior state space. The efficient sampling strategy of MCMC enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown drift and volatility coefficients from the measured data.

This paper investigates the inverse option problems (IOP) in the extended Black--Scholes model arising in financial markets. We identify the volatility and the drift coefficient from the measured data in financial markets using a Bayesian inference approach, which is presented as an IOP solution. The posterior probability density function of the parameters is computed from the measured data. The statistics of the unknown parameters are estimated by a Markov Chain Monte Carlo (MCMC) algorithm, which exploits the posterior state space. The efficient sampling strategy of the MCMC algorithm enables us to solve inverse problems by the Bayesian inference technique. Our numerical results indicate that the Bayesian inference approach can simultaneously estimate the unknown trend and volatility coefficients from the measured data.

This paper deals with a non-standard finite difference scheme defined on a quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow of an incompressible fluid past a flat plate for a wide range of the magnetic parameter. We show how to improve the obtained numerical results via a mesh refinement and a Richardson extrapolation. The obtained numerical results are favourably compared with those available in the literature.

In this paper, we explore the surprising behavior of certain discrete maps, drawing inspiration from Collatz-like problems and advanced techniques in analytic number theory, dynamical systems, and differential geometry. Specifically, we investigate a driven cubic-quintic Duffing equation and predict the number of limit cycles around equilibrium points. Furthermore, we develop a novel theoretical framework for chaos suppression in damped-driven systems, leveraging sequences derived from Collatz-like problems. Our study also focuses on analyzing the density of these sequences in both Euclidean and Riemannian metric spaces, providing a comparative analysis of their distribution properties. We estimate the growth rate of sequence density analytically and numerically, highlighting the sensitivity of the density values to the choice of parameters in both metric spaces. Our results present new insights into the behavior of these sequences and their implications for number theory, chaotic dynamics, and geometric analysis.

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, the coherent eigenstates of a complete set of operators in a given representation, defined with respect to a shared continuous parameterization. Formulating such eigenstates for a single relativistic particle with spin, and applying them to the description of many-body states, presents well-known challenges. In this paper, we review the covariant theory of relativistic spin and entanglement in a framework first proposed by Stueckelberg and developed by Horwitz, Piron, et.\ al. This approach modifies Wigner's method by introducing an arbitrary timelike unit vector $n^\mu$ on which one induces a representation of $SL(2,C)$, rather than induce on the spacetime momentum $p^\mu$. Generalizing this approach, we construct relativistic spin states on an extended phase space $\{(x^\mu,p^\mu),(\zeta^\mu,\pi^\mu)\}$, inducing a representation on the momentum $\pi^\mu$, thus providing a novel dynamical interpretation of the timelike unit vector $n^\mu = \pi^\mu / M$. Studying the unitary representations of the Poincar\'e group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states, and relate these to experiments involving temporal interference, analogous to the spatial interference known from double slit experiments.

The Fading Affect Bias (FAB) occurs in autobiographical memory when unpleasant emotions fade faster than pleasant emotions and the phenomenon appears to be a form of emotion regulation. As emotion regulation is positively related to problem-solving, the current study examined FAB in the context of problem-solving. In-person and online studies asked participants to provide basic demographics, describe their problem-solving abilities, and rate various healthy and unhealthy variables including emotional intelligence and positive problem-solving attitudes. Participants also completed an autobiographical event memory form for which they recalled and described 2 pleasant and 2 unpleasant problem-solving and non-problem-solving events and rated the initial and current affect and rehearsals for those events. We found a robust FAB effect that was larger for problem-solving events than for non-problem-solving events in Study 1 but not in Study 2. We also found that FAB was positively related to healthy variables, such as grit, and negatively related to unhealthy variables, such as depression. Moreover, many of these negative relations were inverted at high levels of positive problem-solving attitudes, and these complex interactions were partially mediated by talking rehearsals and thinking rehearsals.

This paper investigates the periodic and quasi-periodic orbits in the symmetric collinear four-body problem through a variational approach. In Section 3, we analyze the conditions under which homographic solutions minimize the action functional. We demonstrate that these solutions for four equal masses arranged in a linear configuration are indeed the minimizers of the action functional and compute the minimum value of the action functional for these solutions. Additionally, we employ numerical experiments using Poincaré sections to explore the existence and stability of periodic and quasi-periodic solutions within this dynamical system. Our results provide a deeper understanding of the variational principles in celestial mechanics and reveal complex dynamical behaviors that are crucial for further studies in multi-body problems. The findings have significant implications for theoretical research and practical applications in astrodynamics and space mission planning.

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

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 Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. [J. Optim. Theory Appl. 2023, 196, 1036–1055.] and Yu et al. [Mathematics, 2023, 11, 2000] provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong’s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.

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.

Diffuse optical tomography (DOT) is a medical imaging procedure using light to measure the geometric and working properties of cells, for instance, oxygen consumption, water content, and fat percentage in the tissue by performing three-dimensional visualization of the tissue. This paper aims to explain the theory behind diffuse optical tomography imaging and how the technology works. The paper explains how photon migration techniques based on diffusion theory can be used to image the optical properties of tissue. There are several reasons why near-infrared (NIR) imaging is the most effective method in terms of recovering optical parameters quantitatively in the near-infrared region. The author discusses the methods in detail. This research also presents various advantages, practical uses, and potential problems that have been related to DOT in this work. There is also a brief discussion of current research developments in medical imaging using near-infrared wavelengths, and what the future holds for that area.

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

The aim of this survey is to review some recent developements in devising efficient preconditioners for sequences of linear systems A x = b. Such a problem arise in many scientific applications, such as discretization of transient PDEs, solution of eigenvalue problems, (Inexact) Newton method applied to nonlinear systems, rational Krylov methods for computing a function of a matrix. Full purpose preconditioners such as the Incomplete Cholesky (IC) factorization or approximate inverses are aimed at clustering eigenvalues of the preconditioned matrices around one. In this paper we will analyze a number of techniques of updating a given IC preconditioner (which we denote as P0 in the sequel) by a low-rank matrix with the aim of further improving this clustering. The most popular low-rank strategies are aimed at removing the smallest eigenvalues (deflation) or at shifting them towards the middle of the spectrum. The low-rank correction is based on a (small) number of linearly independent vectors whose choice is crucial for the effectiveness of the approach. In many cases these vectors are approximations of eigenvectors corresponding to the smallest eigenvalues of the preconditioned matrix P0 A. We will also review some techniques to efficiently approximate these vectors when incorporated within a sequence of linear systems all possibly having constant (or slightly changing) coefficient matrices. Numerical results concerning sequences arising from discretization of linear/nonlinear PDEs and iterative solution of eigenvalue problems show that the performance of a given iterative solver can be very much enhanced by the use of low-rank updates.

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.

This paper attempts to clarify an issue regarding the lasting unsolved problem of turbulence, namely the closure problem. This study shows that all perspectives regarding the numbers of un- known quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor. The current literatures have a consensus that the Reynolds stress tensor has six unknowns; however, this study shows that the Reynolds stress tensor actually has only three ones, namely the three components of fluctuation velocity. With this new understanding, the closed turbulence equations for incompressible flows are proposed.

This paper shown that turbulence closure problem is not an issue at all. All mistakes in the literature regarding the numbers of unknown quantities in the Reynolds turbulence equations stem from the misunderstandings of physics of the Reynolds stress tensor, i.e., all literatures have stated that the symmetric Reynolds stress tensor has six unknowns; however, it actually has only three unknowns, i.e., the three components of fluctuation velocity. We shown the integral-differential equations of the Reynolds mean and fluctuation equations have exactly eight equations, which equal to the numbers of quantities in total, namely, three components of mean velocity, three components of fluctuation velocity, one mean pressure and one fluctuation pressure. That is why we claim in this paper, that the Reynolds Navier-Stokes turbulence equations of incompressible flow are closed rather than unclosed. This study may help to solve the puzzle that has eluded scientists and mathematicians for centuries.

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.

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.

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.

The capacitated lot-sizing problem with product recovery (CLSP-RM) holds significant importance in reverse logistics but is notoriously complex (NP-hard). In this study, two techniques are introduced to confront this challenge. The first technique entails devising a linear optimization task that eliminates capacity limitations across a wide problem spectrum, yielding a remarkably accurate approximation of the optimal solution. This adaptable approach presents a potent alternative and holds potential for extension to diverse problem categories owing to its versatile nature. The second technique employs a simulation methodology utilizing Halton’s uniform random numbers to address the issue. This randomized production search method sidesteps considerations of production costs, inventory expenditures, and production order when determining production batches. The research’s novelty lies in its application of these techniques to the problem. The suggested methods undergo evaluation via a benchmark dataset of approximately 4200 instances, with comparison against solutions derived through the Gurobi solver. The results underscore the efficacy and resilience of the introduced methodology in tackling the CLSP-RM predicament.

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.

Use of MS Excel as a platform for teaching simple iterative solution of partial differential equations runs into issues of reliability of the computation because of the large number of calculations required. This article documents the problem and an empirical solution. The cause of this unreliability was found by detailed examination of the numerical results from three simultaneous iterations. Computers of several types from different manufacturers were found to fail occasionally in updating variables in the numerical iteration. A simple work-around is suggested and was tested on several platforms.

Generative artificial intelligence tools are flourishing across various sciences, particularly in the educational domain. ChatGPT, with its versions 3.5 and 4.0, stands out for its multilingual capabilities, catering to both students and educators. This research aimed to evaluate the performance differences between these versions, and importantly, to compare the accuracy of ChatGPT's responses in English versus Arabic. In our study, we presented ChatGPT with 39 chemistry problems related to 6th-7th grade curriculum, including twenty-five open questions and fourteen multiple-choice questions. Each response was categorized as accurate, partially accurate, or inaccurate. Our analysis, focused on trends across versions and languages, revealed significant enhancements in version 4.0, particularly in its ability to process Arabic. However, despite these improvements, our findings indicate that responses in English consistently outperformed those in Arabic in terms of accuracy. In light of this discrepancy, we suggest that ChatGPT either incorporates additional Arabic databases into its training regimen or develops a code that adopts the following strategy to ensure more accurate responses in science education: questions should first be translated from Arabic to English, addressed, and then retranslated into Arabic before being presented to the user. This approach takes advantage of the greater accuracy of responses in English to benefit Arabic-speaking users, and it may also improve outcomes for speakers of other languages who experience less precise answers in the fields of chemistry or science education.

Continuous cropping of Platycodon produces problems that significantly impact its yield and quality making it a pressing issue that requires immediate attention. In this study, the sandwich method is employed to evaluate the allelopathic activity of different plant parts (leaves, stems, and roots) of Platycodon. The inhibitory effects of the various Platycodon plant parts were quantified based on their effects on lettuce seedlings growth by Sandwich method, with the following average inhibition percentages at 1 mg/ml (agar) of : leaves (79.4%, 61.8%), stems (58.0%, 45.7%), and roots (53.4%, 49.3%) for lettuce radicals and hypocotyls, respectively. At a concentration of 5 mg/ml, the inhibitory effects were as follow: leaves (91.9%, 72.2%), stems (79.5%, 60.3%), and roots (71.4%, 65.2%). Also, by employing the Plant Box method, it was determined that Platycodon root exudation. The growth inhibition rates of lettuce seedling roots and hypocotyls were 45.5% and 18.9%, respectively. The effect of activated carbon on the adsorption of allelopathic substances was investigated, and the results of the sandwich method with a concentration of 1 mg/ml showed the following growth inhibitory effects on lettuce seedlings and hypocotyls: roots (27.8%, 25.7%), leaves (13.3%, 25.7%), and stem (9.07%, 13.6%). The Plant Box method revealed average rates of inhibition of -16.7% and -4.70% on the growth of lettuce seedlings and hypocotyls, respectively. The results of this study demonstrated that activated carbon has a mitigating effect on the allelopathic inhibition associated with the different plant parts and root exudation of Platycodon, thus may provide a potential solution for overcoming obstacles associated with continuous cropping of Platycodon.

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.

The capacitated team orienteering problem with time windows (CTOPTW) is a NP-hard combinatorial optimization problem. In the CTOPTW, a set of customers is given each with a profit, a demand, a service time and a time window. A homogeneous fleet of vehicles is available for serving customers and collecting their associated profits. Each vehicle is constrained by a maximum tour duration and a limited capacity. The CTOPTW is concerned with the determination of a preset number of vehicle tours that begin and end at a depot, visit each customer no more than once while satisfying the time duration, time window and vehicle capacity constraints on each tour. The objective is to maximize the total profit collected. In this study we propose an iterated local search (ILS) algorithm to deal with the CTOPTW. ILS is a single solution based meta-heuristic that successively invokes a local search procedure to explore the solution space. A perturbation operator is used to modify the current local optimum solution in order to provide a starting solution for the local search procedure. As different problems and instances have different characteristics, the success of the ILS is highly dependent on the local search procedure, the perturbation operator(s) and the perturbation strength. The basic ILS uses a single perturbation operator and the perturbation strength remains the same during the optimization process. To address these issues, we use three different perturbation operators and a varying perturbation strength which changes as the algorithm progresses. The idea is to assign a larger perturbation strength in the early stages of the search in order to focus on exploring the search space. The perturbation strength is gradually decreased so that we focus more on exploitation. The computational results show that the proposed ILS algorithm is able to generate high quality solutions on the CTOPTW benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both the solution quality and computational time. Moreover, the proposed ILS produces 21 best known results and 5 new best solutions.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

The present work studies a swelling porous-elastic system with viscoelastic damping. We establish a general and optimal decay estimate which generalizes some recent results in the literature. Our result is established without imposing the usual equal-wave-speed condition associated with similar problems in literature.

We compute explicitly trace of one-dimensional diffusion process which can be regarded as a Dirichlet form on graphs and we study its conservativeness property. Finally, we give an example of a discretization of one dimensional diffusion of Bessel's process with order $\nu$.

Background: Underreporting of Visceral Leishmaniasis (VL) in India remains a problem to public health controls. Effective and reliable surveillance systems are critical for monitoring disease outbreaks and public health control programs. However, in India, government surveillance systems are affected by levels of scarcity in resources and therefore, uncertainty surrounds the true incidence of asymptomatic and clinical cases, affecting morbidity and mortality rates. The State of Bihar alone contributes up to the 40\% of the worldwide VL cases. The inefficiency of surveillance systems occurs because of multiple reasons including delay in seeking health care, accessing non-authentic health care clinics, and existence of significant asymptomatic self healing infectious cases. This results in a failure of the system to adequately report true transmission rates and number of symptomatic cases that have sought medical advice (thus, high underreporting of cases). Objectives and Methods: There are several methods to estimate the extent of underreporting in the surveillance system. In this research, we use a mathematical dynamic model and two different types of data sets, namely, monthly incidence for 2003-2005 and yearly incidence from 2006-2012 from the Bihar's 21 most VL affected districts out of its 38 districts. The goals of the study are to estimate critical metrics to measure level of transmission and to evaluate the estimation process between the two data sets and 21 districts. In particularly, our focus is on (i) estimating infection transmission potential, underreporting level in incidence and proportion of self-healing cases, (ii) quantifying reproduction number of the$R_0$, and (iii) comparing underreporting incidence levels and proportion of self-healing cases between the two periods 2003-2005 and 2006-2012 and between 21 districts. Results: Our research suggests that the number of asymptomatic individuals in the population who eventually self-heal may have a significant effect on the dynamics of VL spread. The estimated mean self-healing proportion (out of all infected) is found to be $\sim 0.6$ with only 7 out of 21 affected districts having self-healing proportion less than $0.5$ for both data sets. The estimated mean underreporting level is at least $64$\% for the state of Bihar. The estimates of the basic reproduction numbers obtained are similar in magnitude for most of the districts, being in the range of (0.88, 2.79) and (0.98, 1.01) for 2003-2005 and 2006-2012, respectively. Conclusions: The estimates for the two types (monthly and yearly) of temporal data suggest that monthly data are better for estimation if less number of data points are available, however, in general, using such data set results in larger variances in parameters as compared to estimates obtained through aggregated yearly data. Estimated values of transmission related metrics are lower than those obtained from earlier analyses in the literature, and the implications of this for VL control are discussed. The spatial heterogeneity in these control metrics increases the risk of epidemics and makes the control strategies more complex.

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.

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.

We focus on macromolecules which are modelled as sequentially growing dual scale-free networks. The dual networks are built by replacing star-like units of the primal treelike scale-free networks through rings, which are then transformed in a small-world manner up to the complete graphs. In this respect, the parameter γ describing the degree distribution in the primal treelike scale-free networks regulates the size of the dual units. The transition towards the networks of complete graphs is controlled by the probability p of adding link between non-neighbouring nodes of the same initial ring. The relaxation dynamics of the polymer networks is studied in the framework of generalized Gaussian structures by using the full eigenvalue spectrum of the Laplacian matrix. The dynamical quantities on which we focus here are the averaged monomer displacement and the mechanical relaxation moduli. For several intermediate values of the parameter’s set (γ, p) we encounter for these dynamical properties regions of constant in-between slope.

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.

We present a very computationally light and fast approximation algorithm and then verify it with genetic algorithm and simulated annealing. We show that our algorithm is on par with GA and SA in terms of output produced while having a tightly bounded time complexity. Our algorithm works best when there is a strong positive correlation between the reliability of a component and its cost. We present two algorithms with the same essence. One of them is system cost bounded and the other is target reliability bounded. Our proposed algorithm works on a subsystem level redundancy instead of component level redundancy.

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.

In this study, we focus on the vibration-damping devices within the renowned physical experimental apparatus—STM. Utilizing GeoGebra software and Python, we meticulously elucidate the principle by which the vibrations of the damper are damped in a magnetic field, thereby achieving the vibration-damping functionality of the entire system. This approach not only fosters a clear physical conceptualization but also ensures the acquisition of accurate and comprehensive knowledge. Furthermore, the inquiry demonstrates the process of problem clarification facilitated by the use of software tools and then we compare the power of the widlely programming language--Python and the GeoGebra.

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.

This article describes an approach for optimising sensor-controlled systems through minimal intervention, utilising Fuzzy Linear Systems of Equations (FLSE). Staring with a generalised model of the system behaviour, incorporating an array of control units, environmental sensors, and an expert knowledge base. The described problems of detecting the level of intervention needed to change the system state to another is handled with the help of developed methods for solving the inverse problem for FLSE. By achieving minimal intervention, we ensure that system adjustments effective, economically optimal and non-intrusive. A MATLAB-based implementation is presented.

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.

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.

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.

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.

The dynamics of the main photosynthetic structures is studied by mathematical modeling methods in this article. Chlorophyll portion variability in phytoplankton and the formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their participation in the growth of specific biomass. Computational experiments are presented that simulate various degrees of environmental friendliness. The corresponding functions are built in accordance with seasonal fluctuations throughout the year in the Far East region of Russia. The stability of model solutions in long-term dynamics is also investigated. The models were tested for biological adequacy and their effectiveness was compared. For the model selected as a result of the comparison, the optimal control problem has been formulated and solved. It is shown that in this way it is possible to reduce the space of the initial components of the model system.

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.

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.

The development of the smart city concept and the inhabitants’ need to reduce travel time, as well as society’s awareness of the reduction of fuel consumption and respect for the environment, lead to a new approach to the classic problem of the Travelling Salesman Problem (TSP) applied to urban environments. This problem can be formulated as “Given a list of geographic points and the distances between each pair of points, what is the shortest possible route that visits each point and returns to the departure point?” Nowadays, with the development of IoT devices and the high sensoring capabilities, a large amount of data and measurements are available, allowing researchers to model accurately the routes to choose. In this work, the purpose is to give solution to the TSP in smart city environments using a modified version of the metaheuristic optimization algorithm TLBO (Teacher Learner Based Optimization). In addition, to improve performance, the solution is implemented using a parallel GPU architecture, specifically a CUDA implementation.

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.

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.

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.

In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, which special cases can be found in many important engineering practical applications such as image recognizing, signal processing and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results.