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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We argue that the problem of time is not a crucial issue inherent in the quantum picture of the universe evolution. On the minisuperspace model example with the massless scalar field, we demonstrate four approaches to the description of quantum evolution, which give similar results explicitly. The relevance of these approaches to building a quantum theory of gravity is discussed.

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

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

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

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

(1) Context: Cancer triggers significant changes in family dynamics. It is noteworthy that coping and problem-solving skills, particularly in situations involving cancer in children and adolescents, have not been adequately explored in the context of family adaptation. This study aims to analyze the effectiveness of family interventions in coping to improve problem-solving skills in parents and/or caregivers of children and adolescents during and after oncological treatment. (2) Methods: This is a scoping review following the recommendations of the Joanna Briggs Institute and the Systematic Reviews and Meta-Analyses Extension for Scoping Review (PRISMA-ScR), from 2014 to 2024, in the databases LILACS, CINAHL, SCOPUS, Web of Science, and PUBMED. (3) Results: Forty-five studies were eligible. Coping strategies were categorized as follows: (1) positive attitudes (including a sense of courage and hope, family support to enhance resilience, and future planning), (2) caregiver empowerment (involving acceptance of diagnosis, emotional distancing, and coping through religiosity), and (3) communication skills (encompassing professional communication, horizontal dialogue with healthcare teams, and sincere communication with friends and family). (4) Conclusions: Over time, families develop coping and problem-solving strategies that influence changes in family functioning patterns, aiding them in accepting, reinterpreting, and reframing ideas and feelings associated with neoplasia.

Studying the two famous old problems that why the moon can move around the Sun and why the orbit of the Moon around the Earth cannot be broken off by the Sun under the condition that calculating with F=GMm/R^2, the attractive force of the Sun on the Moon is almost 2.2 times that of the Earth. We found that the planet and moon are unified as one single gravitational unit which results in that the Sun cannot have the force of F=GMm/R^2 on the moon. The moon is moved by the gravitational unit orbiting around the Sun. It could indicate that the gravitational field of the moon is limited inside the unit and the gravitational fields of both the planet and moon is unified as one single field interacting with the Sun. The findings are further clarified by reestablishing Newton’s repulsive gravity.

In the paper we present a new test for comparison of the means of multivariate samples with unknown distributions. The test is based on the comparison of the distributions of the distances between the samples’ elements and their means using univariate two-sample Kolmogorov-Smirnov test. The activity of the suggested method is illustrated by numerical analysis of the real-world and simulated data.

Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string.

The asymptotic behavior of the analytic solutions of a family of singularly perturbed q-difference-differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and q-Gevrey. This asymptotic phenomena is observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis-Sibuya theorem.

Decomposed fuzzy sets are the resent extension of intuitionistic fuzzy sets by incorporating functional and dysfunctional points of views to the definition of membership functions. This paper extends the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) method to the Decomposed Fuzzy TOPSIS (DF TOPSIS) method and applies it to a multi-criteria risk-based supplier selection problem under fuzziness. DF TOPSIS involves finding a positive ideal solution and a negative ideal solution and measuring the distance of each alternative to these solutions. The final ranking is obtained based on the proportion of distances to the positive and negative ideal solutions. The developed DF TOPSIS method incorporates the accuracy and consistency of expert judgments, enhancing the decision-making process. A sensitivity analysis is also presented in order to show the robustness of the obtained rankings by DF TOPSIS.

To assist Java programming learning of novice students, we have developed the web-based Java programming learning assistant system (JPLAS). JPLAS provides several types of exercise problems to cultivate code reading/writing skills at various levels. In JPLAS, the code writing problem (CWP) asks a student to write a source code that will pass the test code given in the assignment where the correctness is verified by running them on JUnit. In this paper, to reduce the teacher load at marking process, we present the answer code validation program that verifies all the source codes from a lot of students for each assignment at a time and reports the number of passing tests for each source code in the CSV file. Besides, to test a source code with various input data, we implement the test data generation algorithm that identifies the data type, generates a new data, and replaces it for each test data in the test code. Furthermore, to verify the correctness of the implemented procedure in the source code, we introduce the intermediate state testing in the test code. For evaluations, we applied the proposal to source codes and test codes in a Java programming course in Okayama university, Japan, and confirmed the validity and effectiveness.

Diffuse optical tomography (DOT) is an optical medical imaging method that can assess the structural properties of tissues and their functional characteristics, such as hemoglobin concentration, water content, as well as lipid concentration, via three-dimensional image reconstruction. This paper presents the theoretical basis and working principle of diffuse optical tomography. The paper explains how the optical properties of tissue can be imaged by photon migration techniques based on diffusion theory. The author presents the reasoning for near-infrared (NIR) imaging as the most effective technique in terms of quantitative recovery of spectroscopic optical parameters. This work also listed various advantages, applications, and challenges of DOT. The paper also briefly discusses current progress in near-infrared medical imaging and its future direction.

This paper presents a cooperative parallel tabu search meta-heuristic for the vehicle routing problem with time windows. It is based on the scheme in which several search threads cooperate by asynchronously exchanging information on the best solutions identified. The exchanges are performed through a mechanism called adaptive memory which holds and manages a pool of solutions. This enforces the asynchronous strategy of information exchanges and ensures the independence of the individual search threads. Each of these independent threads implements a tabu search meta-heuristic. Comprehensive computational experiments and comparisons to best known solutions show that the proposed cooperative parallel tabu search algorithm is able to achieve 48 new best solutions on VRPTW benchmark instances.

This study revisits the Reynolds-averaged Navier--Stokes equations (RANS) and finds that the existing literature is erroneous regarding the primary unknowns and the number of independent unknowns in the RANS. The literature claims that the Reynolds stress tensor has six independent unknowns, but in fact the six unknowns can be reduced to three that are functions of the three velocity fluctuation components, because the Reynolds stress tensor is simply an integration of a second-order dyadic tensor of flow velocity fluctuations rather than a general symmetric tensor. This difficult situation is resolved by returning to the time of Reynolds in 1895 and revisiting Reynolds' averaging formulation of turbulence. The study of turbulence modeling could focus on the velocity fluctuations instead of on the Reynolds stress. An advantage of modeling the velocity fluctuations is, from both physical and experimental perspectives, that the velocity fluctuation components are observable whereas the Reynolds stress tensor is not.

Although educational timetabling problems have been studied for decades, one type, the STP, has not developed as quickly as the other two types due to its diversity and complexity. Also, most of the STP research has only focused on the educators’ availabilities when studying the educator aspect, and the educators’ preferences and expertise have not been taken into consideration. This paper proposes a conceptual model for the school timetabling problem considering educators’ availabilities, preferences and expertise as a whole, and chooses a common real-world school timetabling scenario to study. A mathematical model is presented. A Virtual search space for dealing with the large search space is introduced, and the artificial bee colony algorithm is adapted and applied to the proposed model. The proposed approach is simulated with a random-generated large dataset. The experimental results demonstrate that the proposed approach is able to solve the STP and handle a large dataset in an ordinary computer hardware environment, which significantly reduces computational costs. Compared to the traditional CP method, the proposed approach is more effective and can provide more satisfactory solutions in considering educators’ availabilities, preferences, and expertise levels.

In a recent paper [1], I argued against backward in time effects used by several authors to explain delayed choice experiments. I gave an explanation showing that there is no physical influence propagating from the present to the past and modifying the state of the system at a time previous to the measurement. However, though the solution is straightforward in the case of delayed choice experiments involving only one particle, it is subtler in the case of experiments involving two entangled particles because they give rise to EPR-like situations. Considering that a measurement is not an actual change of the physical state of a system and is relative to the observer allows to understand that there is neither backward in time effects nor instantaneous collapse of the second system when the first one is measured, as is often postulated. This allows also to get rid of any non-locality [2]. In this paper, I want to go further into the consequences of this way of considering the measurement, that I have called Convivial Solipsism, and show that even if, in the usual sense, there is no physical effect of the present or of the future on the past, we must nevertheless consider that the observer’s past is sometimes not entirely determined and that it becomes determined only when certain measurements are done latter. This apparent contradiction disappears if one understand that each observer builds, through her own measurements, her own world (that I call the phenomenal world in Convivial Solipsism) which is different from what we are used to consider as the common world shared by everybody.

Based on the Graph Model of Conflict Resolution (GMCR), a two-stage decision framework is developed to reveal the essence of brownfield incidents and facilitate the resolution of brownfield conflicts caused by the incidents. More particularly, the forward GMCR is utilized in Stage I, the negotiation stage, to simulate the evolution of a brownfield conflict (BC) and predict its potential resolution via stability analysis. If no acceptable equilibrium can be obtained, the BC progresses into Stage II, the third-party-intervention stage, where the inverse GMCR is used to assist a third party in intervening the conflict to achieve a desirable outcome. To illustrate the practicality of this framework, a recent BC occurred in Changzhou, China, is taken as a case study. Invaluable insights are provided through the computation and investigation of the corresponding preference relationships.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

In the energy-momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, in a fluid with a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy-momentum densities, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell's stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural explanation for the famous, more than a century old, 4/3 factor in the electromagnetic mass.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

The Physics-Informed Neural Networks (PINNs) improve the efficiency of data utilization by combining physical principles with neural network algorithms and ensure that the predictions are consistent and stable with the physical laws. PINNs opens up a new approach to address inverse problems in fluid mechanics. Based on the single-relaxation-time lattice Boltzmann method (SRT-LBM) with the Bhatnagar-Gross-Krook (BGK) collision operator, the PINN-SRT-LBM model is proposed in this paper for solving the inverse problem in fluid mechanics. The PINN-SRT-LBM model consists of three components. The first component involves a deep neural network that predicts the equilibrium control equations in different discrete velocity directions within SRT-LBM. The second component employs another deep neural network to predict non-equilibrium control equations, enabling inference of the fluid's non-equilibrium characteristics. The third component, a physics informed function translates the outputs of the first two networks into physical infor-mation. By minimizing the residuals of the physical partial differential equations (PDEs), the physics informed function infers relevant macroscopic quantities of the flow. The model evolves two sub-models applicable to different dimensions, named PINN-SRT-LBM-I and PINN-SRT-LBM-II models according to the construction of the physical informed function. The innovation of this work is the introduction of SRT-LBM and discrete velocity models as physical drivers into the neural network through the interpretation function. Therefore, PINN-SRT-LBM allows the neural network to handle inverse problems of various dimensions and focus on problem-specific solving. Experimental results confirm the accurate prediction of flow infor-mation at different Reynolds numbers within the computational domain. Relying on the PINN-SRT-LBM models, inverse problems in fluid mechanics can be solved efficiently.

Petri nets are a graphical notation for describing a class of discrete event dynamic systems whose behaviours are charaterised by concurrency, synchronisation, mutual exclusion and conflict. They have been used over the years for the modelling of various distributed systems applications. With the advent of pervasive systems and the Internet of Things, the Calculus of Context-aware Ambients (CCA) emerged as a suitable formal notation for analysing the behaviours of these systems. In this paper, we are interested in comparing the expressive power of Petri nets to that of CCA. That is, can the class of systems represented by Petri nets be modelled in CCA? To answer this question, an algorithm is proposed that maps any Petri net onto a CCA process. We show that a Petri net and its corresponding CCA process behave the same way through experiments. It follows that CCA is at least as expressive as Petri nets, i.e. any system that can be specified in Petri nets can also be specified in CCA. Moreover, tools developed for CCA can also be used to analyse Petri nets.

I extend earlier work that derived a Born rule for nuclear-decay cloud chamber tracks (Mott problem) without invoking quantum measurement axioms. The key ingredient there was the identification of sites at which the cross section for ionization by a passing charged particle is singular at ionization threshold. This singularity arose from a Penning-like process involving molecular polarization in sub-critical vapor clusters. In the present paper, I propose a simple experiment to determine if similar ionization physics takes place in the mica window of a Geiger counter and drives the collimation of spherically-symmetric wavefunctions outside the counter tube into ion tracks inside. The experiment measures the count rate from a radioactive point source as a function of source-window separation. I have performed a proof-of-concept of this experiment; results are consistent with the singular-ionization picture. I consider implications for the Stern-Gerlach experiment and superconducting qubits. I detail further work required to flesh out these results more rigorously.

We consider a stationary inclusion in a real Hilbert space X, governed by a set of constraints K, a nonlinear operator A and an element f∈X. Under appropriate assumptions on the data the inclusion has a unique solution, denoted by u. We state and prove a covergence criterion, i.e., we provide necessary and sufficient conditions on a sequence {un}⊂X which guarantee its convergence to the solution u. We then present several applications which provide the continuous dependence of the solution with respect to the data K, A and f, on one hand, and the convergence of an associate penalty problem, on the other hand. We use these abstract results in the study of a frictional contact problem with elastic materials which, in a weak formulation, leads to a stationary inclusion for the deformation field. Finally, we apply the abstract penalty method in the anlysis of two nonlinear elastic constitutive laws.

There have been a vast number of studies on reading strategies from different angles performed at various age levels. However, the COVID-19 pandemic has brought a challenge to students´ lives, especially at the university level where they have to struggle with reading many materials online and offline. Therefore, this study investigated the levels of three different strategies of metacognitive awareness: global reading strategy, problem-solving strategy, and support reading strategy among 192 Slovak freshmen university students in a Business English class during the COVID-19 pandemic. The findings reveal that the students used problem-solving strategies the most, followed by global and support reading strategies the least. The results also indicate a difference between male and female students at individual levels of reading strategies. The study proposes a set of recommendations with an alliance of COVID-19 learning environment based on the results such as taking notes while reading and highlighting the most important information with an emphasis on details or showing the importance of previewing the text, asking questions/making predictions about the text, and most importantly paying attention to self-regulation practices in a new school environment.

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order, on the quotient space of isomorphism classes of finite groups, that is well behaved with respect to cardinality. If $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G\leq\mathbb Z_{p_1}^{n_1}\oplus\mathbb Z_{p_2}^{n_2}\oplus\cdots\oplus\mathbb Z_{p_k}^{n_k}$ where $n=p_1^{n_1}p_2^{n_2}\cdots p_{k}^{n_k}$ is the prime factorization of $n$. We find a canonical order for the objects of $G$ and define equivalent objects of $G$, thus finding the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and we are provided with a minimal set of independent equations that define the group. We show how to find all groups of order $n$, and order them. We give examples using all groups with order smaller than $10$, and we find the canonical block form of the symmetry group $\Delta_4$. In the next section, we extend our results to the infinite case, which defines a real number as an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational aspects of these representations.

In recent, Chae found that, at weak gravitational acceleration g_N≲10⁻⁹ms⁻², the observed orbit of the wide binary stars is not accordant with current theory of binary star. Here, we present, this finding should be an observational evidence for that Newtonian theory of orbit perturbation is still valid in galactic scale.

The present paper reports an alternative solution of the measurement problem in quantum theory. The measurement problem can be characterized as that the U-procedure verses the R-procedure. The R-procedure is tested by the Yes/No measurement originally proposed by von Neuman and discussed in details by Penrose. We propose a novel stochastic sampling method to tackle the measurement paradox. Each testing sample produces a pair of Yes-number c and No-number d, which in turn generates a sample phase with respect to the exponential form of (c+id). All the sample phases forms a group G_R. Taking G_R as the sampling potential, combined with the dynamic phase group G_U，we establish a unified model of U-procedure and R-procedure for the evolution of wavefunction. Based on the Born rule, the probability of a sample is given by the squared magnitude of （c+id）. Some metaproperties of the new U-R model, such as natural transformation, consistency, and completeness, are presented. The present work provides a new picture of quantum mechanics and alike. The measurement problem widely exists in dynamic analysis, higher cognition, and large data modeling. Thus, the work reported here has a wide range of applications. Keywords: The measurement problem; U-R procedures; the Yes/No type measurement; stochastic sampling; sample phase; Born probability.

This manuscript presents a novel approach to estimating the potential within Schrödinger equations, with a particular focus on applications to the Navier-Stokes problem in fluid dynamics. By establishing new theoretical estimates, we delve into the intricate dynamics of fluid flow, aiming to unveil previously obscured aspects of the Navier-Stokes equations. Through a rigorous mathematical framework, we explore how these new potential estimates can provide a fresh perspective on fluid mechanics, contributing to the ongoing quest to solve some of its most persistent challenges.

In this paper, a distributed algorithm is proposed to solve a consensus convex optimization problem. It is a Jacobi-proximal alternating direction method of multipliers with a damping parameter $\gamma$ in the iteration of multiplier. Compared with existing algorithms, it has the following nice properties: (1) The restriction on proximal matrix is relaxed substantively, thus alleviating the weight of the proximal term. Therefore, the algorithm has a faster convergence speed. (2) The convergence analysis of the algorithm is established for any damping parameter $\gamma\in(0,2]$, which is larger ones in the literature. In addition, some numerical experiments and an application to a logistic regression problem are provided to validate the effectiveness and the characteristics of the proposed algorithm.

In a series of recent papers we developed a formulation of general relativity in which spacetime and the dynamics of matter evolve with a Poincaré invariant parameter τ. In this paper we apply the formalism to derive the metric induced by a `static’ event evolving uniformly along its t-axis at the spatial origin x=0. The metric is shown to vary with t and τ, as well as spatial distance r, taking its maximum value for a test particle at the retarded time τ=t−r/c. In the resulting picture, an event localized is space and time produces a metric field similarly localized, where both evolve in τ. We first derive this metric as a solution to the wave equation in linearized field theory, and discuss its limitations by studying the geodesic motion it produces for an evolving event. By then examining this solution in the 4+1 formalism, which poses an initial value problem for the metric under τ-evolution, we clarify these limitations and indicate how they may be overcome in a solution to the full nonlinear field equations.

The problem of optimal scheduling in a system with parallel queues and a single server has been extensively studied in the queueing theory. However, such systems have mostly been studied by assuming homogeneous attributes of arrival and service processes, or in heterogeneous case a Markov random process was usually assumed. In this paper, we explore the possibility of combining simulation and neural network paradigms for optimal scheduling in a heterogeneous system with an arbitrary inter-arrival and service time distributions. The service of any queue by the server is exhaustive. Further routing of the server after the queue has been emptied is as instructed by the trained neural network. Any change in the queue that currently has a server is accompanied by a switching cost. The simulated annealing optimization algorithm which is used to optimize the parameters of the neural network was adapted for numerically evaluated average cost function. A Markov decision problem was formulated for the corresponding markovian queueing system to verify the results of solving the optimization problem. In addition to comparing the actual values of the average cost, the parameter values of the neural network trained on the optimal control policy of the Markov model are also used to determine the domains of parameters required for the simulated annealing defined on a finite discrete domain. Numerical analysis shows the effectiveness of this approach. Moreover, a comparison of the results for different distributions illustrates the insensitivity of the optimal control policy to the shape of the distributions for the same two first moments. Thus, the optimal control policy for an exponential model can be used as a suboptimal one for the general system.

Equine Assisted Activities (EAA) are considered a suitable innovative rehabilitative practice for children with neurodevelopmental disorders, including Autism Spectrum Disorder (ASD). While standardized scales have been previously used as a tool to evaluate the effects of EAA on different domains of functioning in ASD children, few studies have considered an ethological approach as a means to describe human-horse interactions in the context of ASD. In this study, we aimed to evaluate the behaviour of 19 children with ASD - in comparison with 19 typically developing children (TD) - during EAA sessions. We developed an ethogram from the video-recordings, to assess spatial relationships, social interactions and communicative behaviours displayed by the child towards the horse, as well as the occurrence of problem behaviours. Results indicate that children’s behaviours during EAA sessions are modulated by sex and age, while previous children’s experience with EAA appeared to improve interpersonal distance and horse handling. Results from this study highlight the importance of exploring children's behavioural response during animal-assisted activities through direct measurements. This may allow linking the quality/strength of the child-horse relationship to the benefits obtained by the child, particularly in the social/communicative domain, a core symptom of ASD.

In an $m$-person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player $k$ in an $m$-person symmetric game is $k$-mode symmetric, and the payoff tensors of two different individuals are the transpose of each other. Furthermore, we reformulate the $m$-person symmetric game as a tensor complementary problem and demonstrate that locating a symmetric Nash equilibrium is equivalent to finding a solution to the resulting tensor complementary problem. Finally, we use the hyperplane projection algorithm to solve the resulting tensor complementary problem, and we present some numerical results to find the symmetric Nash equilibrium.

Complex problem-solving (CPS) tasks have become an increasingly popular tool for understand-ing and assessing cognitive ability. These tasks have been repeatedly shown to be predictors of academic and workplace success above and beyond traditional measures of general intelligence and fluid intelligence. To date, there has been little exploration of the underlying mechanisms that drive this additional predictive utility. In this study, we examined the role of a variety of non-cognitive personality and investment traits that could drive performance on CPS tasks. Adult participants (n = 152) were recruited via M-Turk and completed a battery of personality and in-vestment trait measures, a measure of general mental ability, and a 61-trial microworlds-style CPS task. Generalised linear mixed-effects models revealed a wide variety of personality and in-vestment traits influenced task performance above and beyond general mental ability. Specifical-ly, two clusters of traits emerged as important determinants of performance: one cluster that in-fluenced the capacity to deal with the introduction of system randomness (Conscientiousness and Extraversion) and one cluster that influenced the capacity to deal with the introduction of system delays (NFC, Learning Goal Orientation, and Intellect). These findings suggest that CPS tasks do capture more than just general mental ability and may be good predictors of academic and workplace success because they tap into both cognitive ability and the motivation and willingness to engage in cognitive exploration and mental effort.

Abstract: The increased penetration of renewables in distribution power systems has motivated researchers to take significant interest in local energy transactions. The major goal of Local Energy Markets (LEM) is to promote the participation of small consumers in energy transactions and providing an opportunity for transactive energy systems. Such energy transactions in LEM are considered as a bi-level optimization problem in which all agents at upper and lower levels try to maximize their profits. But typical bi-level problem is very complex as it is inherently nonlinear, discontinued and strongly NP-hard. So, this article proposes the application of hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem of LEM. The proposed CE-CMAES secured the 1st rank in Testbed-2 entitled, “Bi-level optimization of end-users’ bidding strategies in local energy markets (LM)” at international competitions on Smart Grid Problems, held at GECCO 2020 and WCCI 2020. CE method is used for global exploration of search space and CMAES is used for local exploitation as its adaptive step-size mechanism prevents its premature convergence. A practical distribution system with renewable energy penetration is considered for simulation. The comparative analysis shows that the overall cost, mean fitness and Ranking Index (R.I) obtained from CE-CMAES are superior to those obtained from the state-of-the-art participated algorithms. Wilcoxon Signed Rank Statistical test also proves that CE-CMAES is statistically different from the tested algorithms.

In the paper, the authors establish two identities, which can be regarded as nonlinear differential equations, for the generating function of Eulerian polynomials, find two identities for the Stirling numbers of the second kind, and present two identities for Eulerian polynomials and higher order Eulerian polynomials, pose two open problems about summability of two finite sums involving the Stirling numbers of the second kind. Some of these conclusions meaningfully and significantly simplify several known results.

One of the possible mechanisms causing significant emissions of methane into the atmosphere within the Arctic shelf may be the decomposition of gas hydrates. Their accumulations within the Arctic shelf formed during Ice Age almost simultaneously with the formation of permafrost, which contributed to the emergence of a zone of stable existence of gas hydrates. The subsequent flooding of the Arctic shelf led to the degradation of the permafrost and the violation of the conditions for the existence of hydrates. To assess the state of the stability zone, methods of mathematical numerical modeling are used. Standard seismic methods are widely used to localize gas hydrates, but monitoring their physical state requires the development of fundamentally new approaches based on solving multiparameter inverse seismic problems. In particular, the degree of attenuation of seismic energy is one of the objective parameters for assessing the consolidation of gas hydrates: the closer they are to the beginning of decomposition, the higher the attenuation, and hence the lower the quality factor. Thus, the methods of seismic monitoring of the state of gas hydrates in order to predict the possibility of developing dangerous scenarios should be based on solving a multi-parameter inverse seismic problem. This publication is devoted to the presentation of this approach.

This research employs a spatial optimization approach customized for addressing equitable emergency medical facility location problems, through the p-dispersed-median problem (p-DIME). The p-DIME integrates two conflicting classes of spatial optimization problems, dispersion, and median problems, aiming to identify the optimal locations for emergency medical facilities to achieve a balanced spatial distribution of emergency medical services (EMS) while effectively serving demands. To demonstrate the utility of the p-DIME model, we selected Gyeongsangbuk-do in South Korea, recognized as one of the most challenging areas for providing EMS to the elderly population (aged 65 and over). This challenge arises from the significant spatial disparity in the distribution of emergency medical facilities. The results of the model assessment gauge the spatial disparity of EMS, provide significantly enhanced solutions for a more equitable EMS distribution in terms of service coverage, and offer policy implications for future EMS location planning. In addition, to address the computational challenges posed by p-DIME's inherent complexity, involving mixed-integer programming, this study introduces a solution technique through constraint formulations aimed at tightening the lower bounds of the problem's solution space. The computational results confirm the effectiveness of this approach in ensuring reliable computational performance, with significant reductions in solution times, while still producing optimal solutions.

In this study, we introduce a new class of bi-univalent functions using q-Janowski Function. We derive the Fekete-Szegö functional problems for functions in this new subclass, as well as estimates for the Taylor-Maclaurin coefficients |α2| and |α3|. Furthermore, a collection of fresh outcomes are3 presented by customizing the parameters employed in our initial discoveries.

ETS exposure has been shown as an important environmental risk factor in vulnerable population groups. The aim of the project is to analyze the relationships among the ETS and behavior and health in 6−15-year-old children in Slovakia. The status of physical and mental health of children in relation to exposure to tobacco smoke was examined in the representative group of 1478 school children. The methods used, included anonymous questionnaires filled in by parents, Columbia Impairment Scale (CIS), Behavior Problem Index (BPI) and anthropometry. The prevalence of passive smoking is the highest in the capital (27%) and southern cities. Significant relationships have been confirmed between ETS and the age, socio-economic status, the incompleteness of the family, the level of mother's education and the significantly higher prevalence of respiratory diseases (26.7%).The relationships of ETS with emotional (CIS scores ≥16) and behavioral functions (BPI score ≥14) were significant in children exposed to mother‘s and father‘s smoking at home. In the multivariate analysis this association was not significant; the factors such as income and completeness of the family were dominant. The results confirmed the impact of ETS and social factors on health state and health behavior and could be the argumentation for legislative changes.

This paper develops feasible control strategies and associated system responses to bring an autonomous front-axle bicycle robot from specified initial conditions to final conditions such that a specific performance index is minimized. To solve the problem, the following approach is used: The feasible controls derived from the normal equations of optimality are substituted into the state and the costate systems and form a combined control-free state-costate system which is vectorized to enable and ease the application of a numerical method. A computer program written in Matlab computer programming language, codes a fourth-order Runge-Kutta numerical method and then solve the combined state-costate system of ordinary differential equations. The obtained results are the feasible bicycle robot trajectory, the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations are designed and provided to persuade on the effectiveness and the reliability of the approach.

We consider a Cauchy problem for differential equations in a Hilbert space $X$. The problem is stated in a time interval $I$, which can be finite or infinite. Weuse a fixed point argument for history-dependent operators to prove the unique solvability of the problem. Then, we state and prove convergence criteria for both a general fixed point problem and thecorresponding Cauchy problem. These criteria provide necessary and sufficient conditions on a sequence $\{u_n\}$ which guarantee its convergence to the solution of the corresponding problem, in the space of both continuous and continuously differentiable functions. We then specify our results in the study of a particular differential equation governed by two nonlinear operators. Finally, we provide an application in viscoelasticity and give a mechanical interpretation of the corresponding convergence result.

We refute a recently proposed thought experiment namely the Dead-Alive Physicist (DAP) whose authors claim it to be the falsification of the von Neumann interpretation in Quantum Mechanics. We discover major flaws in their model and our justification serves the purpose of disregarding further claims and assertions made in the paper at various stages. Thus, in a yet another situation, it is proven that the formalism advanced by von Neumann is non-trivial and non-falsifiable.

This work has its origin in intuitive physical and statistical considerations. The problem of optimizing an artificial neural network is treated as a physical system, composed of a conservative vector force field. The derived scalar potential is a measure of the potential energy of the network, a function of the distance between predictions and targets. Starting from some analogies with wave mechanics, the description of the sys-tem is justified with an eigenvalue equation that is a variant of the Schr˜odinger equation, in which the potential is defined by the mutual information between inputs and targets. The weights and parameters of the network, as well as those of the state function, are varied so as to minimize energy, using an equivalent of the variational theorem of wave mechanics. The minimum energy thus obtained implies the principle of minimum mutual information (MinMI). We also propose a definition of the potential work produced by the force field to bring a network from an arbitrary probability distribution to the potential-constrained system, which allows to establish a measure of the complexity of the system. At the end of the discussion we expose a recursive procedure that allows to refine the state function and bypass some initial assumptions, as well as a discussion of some topics in quantum mechanics applied to the formalism, such as the uncertainty principle and the temporal evolution of the system. Results demonstrate how the minimization of energy effectively leads to a decrease in the average error between network predictions and targets.

An inverse aeroacoustic problem for a helicopter rotor combined with aerodynamic constraint is proposed based on Ffowcs Williams and Hawkings equation in subsonic. The rotor noise includes thickness noise and loading noise when quadrupole noise is neglected. Thickness noise is related to geometry and motion conditions. Loading noise is related to the pressure on the wall. Therefore, the equation between pressure on the wall and far-field noise can be established, thus the pressure on the wall can be obtained by solving this equation. Since this equation is an ill-posed, the singular value decomposition combined with the regulation method is applied and the aerodynamic constraint is taken into account. The direct noise prediction is verify firstly and then the inverse problem is solved. The reconstruction pressure is compared to the input data. The result is in good agreement with the input value. At the same time, the influence of interference noise is also considered. Under low signal-to-noise ratio, the reconstruction result is also reasonable.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

Previous research on the relative benefits of Augmentative and Alternative Communication Systems (AACs) has indicated controversial results regarding the effectiveness, the ease of use, and the preference for the different systems. The study aims to observe the comparative effectiveness of two different Augmentative and Alternative Communication (AAC) tools, the Picture Exchange Communication System (PECS) and a speech-generating device (SGD), as communication aids for children with autism. Three children with severe autism and minimally verbally or with no functional language participated. The results showed an increase of communicative behavior with both AAC intervention strategies and a speed acquisition time slightly shorter for the SGD training. Two of the three participants showed a preference for the use of the SGD. Reduction in problem behaviors and improvement in vocal production was observed for one of the participants. Results suggest that PECS and SGD are similarly appropriate for the development of initial request skills and that they can encourage vocal production in students with specific prerequisites.

For each $t\in(-1,1)$, exact values of the least upper bounds $$ H(t)=\sup_{\E X=t,\,\E X^2=1} \frac{\E\abs{X}^3}{\E \abs{X-t}^3},\quad \sup_{\E X=t,\,\E X^2=1} \frac{L_1(X)}{L_1(X-t)} $$ are obtained, where $L_1(X)=\E|X|^3/(\E X^2)^{3/2}$ is the non-cental Lyapunov ratio. It is demonstrated that these values are attained only at two-point distributions. As a corollary, S.\,Shorgin's conjecture is proved that states that the exact value is $$ \sup\frac{L_1(X)}{L_1(X-\E X)}= \frac{\sqrt{17 + 7\sqrt7}}{4} = 1.4899\ldots, $$ where the supremum is taken over all non-degenerate distributions of the random variable $X$ with the finite third moment. Also, in terms of the central Lyapunov ratio $L_1(X-\E X)$, an analog of the Berry--Esseen inequality is proved for Poisson random sums of independent identically distributed random variables with the constant $$ 0.3031\cdot H\left(\frac{\E X}{\sqrt{\E X^2}}\right) \left(1-\frac{(\E X)^2}{\E X^2}\right)^{3/2} \le 0.3031\cdot \frac{\sqrt{17 + 7\sqrt7}}{4}<0.4517.$$ where $\Law(X)$ is the common distribution of the summands.

In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three dimensional space defined by energy, temperature and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of large fermion systems with numerical simulation. As an example, we present energies for up to 50 noninteracting fermions and up to 20 interacting fermions at all temperatures and show good agreement with the analytical result for noninteracting case.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained by the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion.

Bandung and Lembang are the cities that are chosen by many tourists (local and foreign) as their destinations. Geographically, these cities are placed side-by-side and each city has its own characteristics. As in Bandung, there are many hotels and culinary spots, meanwhile, in Lembang, there are many scenery tourism spots. Tourists usually have limited time to visit all the destinations on holiday, which makes them choose several tourist destinations to visit. In this paper, the tourism itinerary recommendation system is proposed by calculating the most optimal route between destinations and approaching the Vehicle Routing Problem with Time Windows. The optimal route is defined by using Dijkstra the shortest path algorithm by using the collaboration between the road information (road length, traffic condition, travel time, and weather condition) and criteria weight that is determined using the Analytics Hierarchy Process as the graph weights. According to the simulation results, the criteria weights are 6.9%, 62.7%, 18.6%, and 11.9% for Route Length, Traffic Condition, Travel Time, and Weather Condition respectively. Moreover, the optimal number of tourism itinerary plans for the tourist in this research is 4 destinations. As the usage of computational resources, it takes 31.8% of CPU and 61.9% of Memory usage. For the time processing, it increases exponentially as the increment of number of requested stops. The output of this research is expected to be a solution to the tourist itinerary plan, especially in Bandung and Lembang.

We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

Starting from a very simple economic scenario, we build on it a game and then we introduce a general strategy able to reduce a regression problem to an equivalent binary classification problem. This reduction scheme (that we call adaptive reduction or also dynamic reduction) can be also used to derive a new boosting algorithm for regression problems named bOOst^d. The bOOst^d algorithm is very simple to implement, and it can use any learning algorithm with no priori assumptions. We present a conjecture for bOOst^d performances, which ensures a little error on training set. More important we can also provide a very good theoretical upper bound for the generalization error. We give a set of preliminary experimental results that seems to confirm our conjecture for bOOst^d performances on training set and the theoretical assumptions for the generalization error. We also provide a possible justification of why boosting often does not overfit. Finally, we leave some open problems and argue that in the future an adaptive single boosting (with an unique code) algorithm for binary, multi class and regression problems can be derived.

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}

The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.

Digital competence is one of the 8 key competences for life-long learning developed by the European Commission, and is requisite for personal fulfilment and development, active citizenship, social inclusion and employment in the knowledge society. To accompany young learners in the development of the competence, and to guarantee optimal implementation of ICTs, it is necessary that teachers are, in turn, literate. We had 43 Secondary School teachers in initial training to assess their own level of competence in the 21 sub-competences in 5 areas identified by the DIGCOMP project, using the rubrics provided in the Common Framework for Digital Competence of Teachers (Spanish Ministry of Education). Overall, pre-service teachers' conceptions about their level of Digital Competence was low (Initial). Students scored highest in Information, which refers mostly to the operations they performed while being students. Secondly, in Safety and Communication, excluding Protection of Digital Data and Preservation of the Digital Identity. Lowest values were achieved in Content Creation and Problem Solving, the dimensions most closely related with the inclusion of ICTs to transform teaching-learning processes. The knowledge or skills they exhibit are largely self-taught and, so, we perceive an urgent need to purposefully incorporate relational and didactic aspects of ICT integration.