Search

In this paper, we classify the invariant complex structures on four-dimensional, solvable, simply-connected real Lie groups with commutator of dimension three. The resulting complex surfaces corresponding to these structures are also determined. The classification is based on the determination of certain complex subalgebras of the complexifications of the corresponding real Lie algebras.

Accurate sky identification is one of the most important functions of an automated telescope mount. The more accurately the robotic telescope is navigated to the investigated part of the sky, the better the observations and discoveries made. In this paper, we present mathematical methods for accurate sky identification (celestial coordinates determination). They include the automatic selection of the reference stars, preliminary and full sky identification, as well as an interaction with international databases, which are a part of the astrometric calibration. All described methods help to receive accurately calculated astrometric data and use it for the positional calibration and better navigation of the automated telescope mount. The developed methods were successfully implemented in the Collection Light Technology (CoLiTec) software. Through its use, more than 1600 small solar system objects were discovered. It has been used in more than 700,000 observations and successful sky identifications, during which, five comets were discovered. Additionally, the accuracy indicators of the processing results of the CoLiTec software are provided in the paper, which shows benefits of the CoLiTec software and lower standard deviation of the sky identification in the case of low signal-to-noise ratios.

In this paper some non existence results are given for smooth varieties of dimension bigger then 1, embedded in projective spaces with low codimension, by the pluricanonical system |mK X |, withm≥2. The only meaningful cases of codimension 2 are surfaces in P4 and threefolds in P5, whose existence is excluded. When the codimension is 3, for surfaces in P5 is proven thatm=2, while for three-folds in P6 and fourfolds in P7 only two numerical possibilities for the degree are given.

In the present paper, a necessary and sufficient condition for an element of the semigroup BX (D) defined by semilattices of the class Σ1(X, 5) to be regular is given. Moreover, formulas for calculation of regular elements are derived.

The new L-LLC resonant bidirectional DC-DC converter (L-LLC-BDC) will produce a large resonance current and voltage inrush during the startup, posing a threat to the safe operation of the power device. Although a very high starting frequency can effectively suppress the inrush, it will also increase the output current demand of the driving ICs. This paper proposes a phase-shifting soft-start control strategy based on the current-limiting curve. Using operating mode analysis, the peak value of the resonant current is limited according to the output voltage and the phase shift angle of the switch, with the limit current curve at the startup stage drawn. By this current curve, a one-to-one correspondence between the output voltage and the phase shift angle of the switch is obtained. The phase-shifted soft-start control strategy can quickly establish the output voltage on the basis of a resonant frequency and can effectively suppress the resonance current inrush. An experimental prototype with a power of 6 kW and an input of 760 V and an output of 380 V is built. The experimental results prove the correctness and effectiveness of the soft start control strategy proposed in this paper.

A simulation model, and more generically, a model, is founded on its assumptions. Assurance of the model’s correctness and correct use is needed to achieve accreditation. Often the exercise of working with a specific code misunderstands the overall process, focusing the resources on the model coding and forgetting the needed resources to ensure the validation of every step of the model definition and coding. The goal of this work is to present a methodology to help in the definition and use of the assumptions in the modeling process. To do so, we present a process to conduct a simulation project, an assumptions taxonomy, and a method that simplifies working with those assumptions. We propose to extend the traditional Validation, Verification, and Accreditation processes to a process composed of eight Validation, Verification, and Accreditation phases that cover the overall life cycle of a model. Although this paper is focused on a simulation model, we can extend the proposed method to a more general modeling approach.

In this paper we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equation, where uniform trace estimates on the half-line are shown., Comment: Some typos corrected. Accepted for publication in Mathematische Nachrichten

In this paper, optimal sizing of a photovoltaic (PV) pumping system with a water storage tank (WST) is developed to meet the water demand to minimize the life cycle cost (LCC) and satisfy the probability of interrupted water (pIW) constraint considering real region data. The component sizing, including the PV resources and the WST, is determined optimally based on LCC and pIW using a new meta-heuristic method named enhanced artificial rabbits optimization (EARO) via a nonlinear inertia weight reduction strategy to overcome the premature convergence of its conventional algorithm. The WST is sized optimally regarding the lack of irradiation and inaccessibility of the pumping system so that it is able to improve the water supply reliability. The LCC for water extraction heights of 5 and 10 m is obtained at 0.2955 M$ and 0.2993 M$, respectively, and the pIW in these two scenarios is calculated as zero, which means the complete and reliable supply of the water demand of the customers using the proposed methodology based on the EARO. Also, the results demonstrated the superior performance of EARO in comparison with artificial rabbits optimization (ARO) and particle swarm optimization (PSO); these methods have supplied customers’ water demands with higher costs and lower reliability than the proposed EARO method. Also, during the sensitivity analysis, the results showed that changes in the irradiance and height of the water extraction have a considerable effect on the cost and ability to meet customer demand.

Nowadays, ICT play a fundamental role in education, as they are essential in all areas of knowledge at any educational stage. Specifically, in the area of mathematics, within the Primary Education stage, they are also very valid resources. This is demonstrated by the latest scientific studies. In recent times, the scientific literature has provided evidence of all this through different research studies. The aim of this paper is to analyze all those publications that deal with the teaching–learning processes of mathematics through ICT in primary education. The aim is to show the current state of the scientific literature and what elements and aspects to highlight are common to the documents analyzed. By means of the systematic literature review method, we analyzed 11 articles indexed in Scopus and the Web of Science, with the result that the use of ICT in this area is still scarce, as the volume of publications in this respect is very low. This could also indicate a prevalence of traditional methodologies associated with the teaching of mathematics that could hinder students’ acquisition of mathematical competence. However, those studies that show the use of ICT demonstrate that its use leads to an improvement in performance, motivation, and problem solving.

This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of adeles $\bA$ by using infinite tensor products of Hilbert spaces. The adele ring is roughly speaking a subring of the direct product of all possible ($p$-adic and Archimedean) completions $\bQ_p$ of the field of rational numbers $\bQ$ with some conditions at infinity. Using our technique, we prove that $L^2(\bA)=\otimes_{e,p\in\{\infty,2,3,5,...}}L^2({\bQ}_{p})$ is the infinite tensor product of the spaces $L^2({\bQ}_{p})$ with a stabilization $e=(e_p)_p$, where $e_p(x)=\Omega(|x|_p)\in L^2({\bQ}_{p})$, and $\Omega$ is a characteristic function of the unit interval $[0,\,1]$, $\bQ_p$ is the field of $p$-adic numbers, $p=2,3,5,...$; $\bQ_\infty=\bR$. This description allows us to construct an infinite family of Haar wavelet bases on $L^2(\bA)$ which can be obtained by shifts and multi-delations. The adelic multiresolution analysis (MRA) in $L^2(\bA)$ is also constructed. In the framework of this MRA another infinite family of Haar wavelet bases is constructed. We introduce the adelic Lizorkin spaces of test functions and distributions and give the characterization of these spaces in terms of wavelet functions. One class of pseudo-differential operators (including the fractional operator) is studied on the Lizorkin spaces. A criterion for an adelic wavelet function to be an eigenfunction for a pseudo-differential operator is derived. We prove that any wavelet function is an eigenfunction of the fractional operator. These results allow one to create the necessary prerequisites for intensive using of adelic wavelet bases and pseudo-differential operators in applications., Comment: 45 pages

In this paper, we study a finite capacity queue where the arrival process is a special case of the discrete time Markov modulated Poisson process, the service times are generally distributed, and the server takes repeated vacations when the system is empty. The buffer acceptance strategy is based on a generalized push-out scheme: when the buffer is full, an arriving customer pushes out the Nth customer in the queue, where N takes values between 2 and the capacity of the system, and the arriving customer joins the end of the queue. Such a strategy is important when, as well as short waiting times for served customers, the time a pushed-out customer occupies a buffer space is also an important performance measure. The Laplace transform of the waiting time of a served customer is determined. Numerical examples show the influence of the bustiness of the input process and also the trade-off between the average waiting time of served customers and the occupancy of the buffer space of pushed-out customers.

This is the first of a series of three papers devoted to the regularity of solutions of elliptic problems on nonsmooth domains in ℝ3. The present paper introduces various weighted spaces and countably weighted spaces in the neighbourhood of edges and vertices of polyhedral domains, and it concentrates on exploring the structure of these spaces, such as the embeddings of weighted Sobolev spaces, the relation between weighted Sobolev spaces and weighted continuous function spaces, and the relations between the weighted Sobolev spaces and countably weighted Sobolev spaces in Cartesian coordinates and in the spherical and cylindrical coordinates. These well-defined spaces are the foundation for the comprehensive study of the regularity theory of elliptic problems with piecewise analytic data in ℝ3, which are essential for the design of effective computation and the analysis of the h – p version of the finite element method for solving elliptic problems in three-dimensional nonsmooth domains arising from mechanics and engineering.

Certificateless cryptography aims at combining the advantages of public key cryptography and identity based cryptography to avoid the certificate management and the key escrow problem. In this paper, we present a novel certificateless public key encryption scheme on the elliptic curve over the ring, whose security is based on the hardness assumption of Bilinear Diffie-Hellman problem and factoring the large number as in an RSA protocol. Moreover, since our scheme requires only one pairing operation in decryption, it is significantly more efficient than other related schemes. In addition, based on our encryption system, we also propose a protocol to protect the confidentiality and integrity of information in the scenario of Internet of Things with constrained resource nodes.

The use of Artificial Intelligence (AI) and Big Data analysis algorithms is complementary to theory-driven analysis approaches and becoming more popular also in social sciences. This paper describes the use of Big Data and computational approaches in social sciences by bibliometric analyses of articles indexed between 2015 and 2020 in Social Sciences Citation Index (SSCI) of the Web of Science repository. We have analysed especially the recent research direction called Computational Social Sciences (CSS) that bridges computer analytical approaches with social science challenges, generating new methodologies of Big Data and AI analytics for social sciences. The results indicate that AI and Big Data practices are not confined to CSS only and are diffused in a wide variety of disciplines under Social Sciences and are made use of in many main research lines as well. Thus, the anticipated overlap between the Social Sciences & AI specialization and CSS has yet to be crystallised. Moreover, the impact of computational social science studies is not permeated to social science citation networks yet. Lastly, we demonstrate that the AI and Big Data publications that appear under the SSCI index are more oriented towards computational studies than addressing social science concepts, concerns, and challenges.

The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves.

We study the obstruction space T 2 {T^2} for minimally elliptic surface singularities. We apply the main lemma of our previous paper [3] which relates T 2 {T^2} to deformations of hypersurface sections. To use this we classify general hypersurface sections of minimally elliptic singularities. As in the rational singularity case there is a simple formula for the minimal number of generators for T 2 {T^2} as a module over the local ring. This number is in many cases (e.g. for cusps of Hilbert modular surfaces) equal to the vector space dimension of T 2 {T^2} .

In this paper, for the mapping of a sphere into a compact orientable manifold S n → M , n ⩾ 1 , we solve the problem of determining whether it represents a nontrivial element in the homotopy group of the manifold π n ( M ) πn(M ). For this purpose, we consistently use the theory of iterated integrals developed by K.-T. Chen. It should be noted that the iterated integrals as repeated integration were previously meaningfully used by Lappo-Danilevsky to represent solutions of systems of linear differential equations and by Whitehead for the analytical description of the Hopf invariant for mappings f : S 2 n - 1 → S n , n ⩾ 2 . We give a brief description of Chen’s theory, representing Whitehead’s and Haefliger’s formulas for the Hopf invariant and generalized Hopf invariant. Examples of calculating these invariants using the technique of iterated integrals are given. Further, it is shown how one can detect any element of the fundamental group of a Riemann surface using iterated integrals of holomorphic forms. This required to prove that the intersection of the terms of the lower central series of the fundamental group of a Riemann surface is a unit group.

Let A n , G n , H n (respectively, A' n , G' n , H' n ) denote the unweighted arithmetic, geometric, harmonic means of $ x_1,\dots ,x_n $ (respectively, $ 1-x_1,\dots ,1-x_n $ ), where $ x_j\in{(0,1/2]}\ (j=1,\dots ,n) $ . In 1984, Wang and Wang established¶¶ $ \left(\frac{G_n}{G_n'}\right)^n\leq {\left(\frac{A_n}{A_n'}\right)^{n-1}\frac{H_n}{H_n'}} $ ,¶which refines the well-known Ky Fan inequality $ G_n/G_n' \leq {A_n/A_n'} $ . The validity of the converse inequality¶¶ $ \left(\frac{H_n}{H_n'}\right)^{n-1}\frac{A_n}{A_n'} \leq{\left(\frac{G_n}{G_n'}\right)^n} $ (0.1)¶was conjectured in 1988. In this paper we give a proof for (0.1).

In this paper, we present new homogenization results of a stochastic model for flow of a single-phase fluid through a partially fissured porous medium. The model is a double-porosity model with two flow fields, one associated with the system of fissures and the other associated with the porous system. This model is mathematically described by a system of nonlinear stochastic partial differential equations defined on perforated domain. The main tools to derive the homogenized stochastic model are the Nguetseng’s two-scale convergence, tightness of constructed probability measures, Prokhorov and Skorokhod compactness process and Minty’s monotonicity method.

In this paper, we consider the following Schrödinger equation (0.1) − Δ u − μ u | x | 2 + V ( x ) u = K ( x ) | u | 2 ∗ − 2 u + f ( x , u ) , x ∈ R N , u ∈ H 1 ( R N ) , where N ⩾ 4, 0 ⩽ μ < μ ‾, μ ‾ = ( N − 2 ) 2 4 , V is periodic in x, K and f are asymptotically periodic in x, we take advantage of the generalized Nehari manifold approach developed by Szulkin and Weth to look for the ground state solution of (0.1).

In this paper, we discuss methods and approaches for definition of multiplication of distributions, which is not defined in general in the classical theory. We show that this problem is related to the fact that the operator of multiplication by a smooth function is nonclosable in the space of distributions. We give the general method of construction of new objects called new distributions, or mnemofunctions, that preserve essential properties of usual distributions and produce algebras as well. We describe various methods of embedding of distribution spaces into algebras of mnemofunctions. All ideas and considerations are illustrated by the simplest example of the distribution space on a circle. Some effects arising in study of equations with distributions as coefficients are demonstrated by example of a linear first-order differential equation.

In this paper, we consider initial-boundary value problem on semiaxis for generalized Kawahara equation with higher-order nonlinearity. We obtain the result on existence and uniqueness of the global solution. Also, if the equation contains the absorbing term vanishing at infinity, we prove that the solution decays at large time values.

This paper is devoted to the study of the qualitative properties of solutions to boundary-value problems for strongly elliptic differential-difference equations. Some results for these equations such as existence and smoothness of generalized solutions in certain subdomains of Q were obtained earlier. Nevertheless, the smoothness of generalized solutions of such problems can be violated near the boundary of these subdomains even for infinitely differentiable right-hand side. The subdomains are defined as connected components of the set that is obtained from the domain Q by throwing out all possible shifts of the boundary Q by vectors of a certain group generated by shifts occurring in the difference operators. For the one dimensional Neumann problem for differential-difference equations there were obtained conditions on the coefficients of difference operators, under which for any continuous right-hand side there is a classical solution of the problem that coincides with the generalized solution. 2 Also there was obtained the smoothness (in Sobolev spaces W k ) of generalized solutions of the second and the third boundary-value problems for strongly elliptic differential-difference equations in subdomains excluding -neighborhoods of certain points. However, the smoothness (in Ho lder spaces) of generalized solutions of the second boundary-value problem for strongly elliptic differential-difference equations on the boundary of adjacent subdomains was not considered. In this paper, we study this question in Ho lder spaces. We establish necessary and sufficient conditions for the coefficients of difference operators that guarantee smoothness of the generalized solution on the boundary of adjacent subdomains for any right-hand side from the Ho lder space.

On the base of boundary-value, spectral and initial-boundary value problems studied earlier for the case of single domain, we consider corresponding problems generated by sesquilinear form for two domains. Arising operator pencils with corresponding operator coefficients acting in a Hilbert space and depending on two parameters are studied in detail. In the perturbed and unperturbed cases, we consider two situations when one of the parameters is spectral and the other is fixed. In this paper, we use the superposition principle that allow us to present the solution of the original problem as a sum of solutions of auxiliary boundary-value problems containing inhomogeneity either in the equation or in one of the boundary conditions. The necessary and sufficient conditions for the correct solvability of boundary-value problems on given time interval are obtained. The theorems on properties of the spectrum and on the completeness and basicity of the system of root elements are proved.

This paper has two main goals: (a) establish several statistical properties—consistency, asymptotic distributions, and convergence rates—of stationary solutions and values of a class of coupled nonconvex and nonsmooth empirical risk-minimization problems and (b) validate these properties by a noisy amplitude-based phase-retrieval problem, the latter being of much topical interest. Derived from available data via sampling, these empirical risk-minimization problems are the computational workhorse of a population risk model that involves the minimization of an expected value of a random functional. When these minimization problems are nonconvex, the computation of their globally optimal solutions is elusive. Together with the fact that the expectation operator cannot be evaluated for general probability distributions, it becomes necessary to justify whether the stationary solutions of the empirical problems are practical approximations of the stationary solution of the population problem. When these two features, general distribution and nonconvexity, are coupled with nondifferentiability that often renders the problems “non-Clarke regular,” the task of the justification becomes challenging. Our work aims to address such a challenge within an algorithm-free setting. The resulting analysis is, therefore, different from much of the analysis in the recent literature that is based on local search algorithms. Furthermore, supplementing the classical global minimizer-centric analysis, our results offer a promising step to close the gap between computational optimization and asymptotic analysis of coupled, nonconvex, nonsmooth statistical estimation problems, expanding the former with statistical properties of the practically obtained solution and providing the latter with a more practical focus pertaining to computational tractability.

Utilizing (p, q)-numbers and (p, q)-concepts, in 2016, Duran et al. considered (p, q)-Genocchi numbers and polynomials, (p, q)-Bernoulli numbers and polynomials and (p, q)-Euler polynomials and numbers and provided multifarious formulas and properties for these polynomials. Inspired and motivated by this consideration, many authors have introduced (p, q)-special polynomials and numbers and have described some of their properties and applications. In this paper, using the (p, q)-cosine polynomials and (p, q)-sine polynomials, we consider a novel kinds of (p, q)-extensions of geometric polynomials and acquire several properties and identities by making use of some series manipulation methods. Furthermore, we compute the (p, q)-integral representations and (p, q)-derivative operator rules for the new polynomials. Additionally, we determine the movements of the approximate zerosof the two mentioned polynomials in a complex plane, utilizing the Newton method, and we illustrate them using figures.

In this paper, q-Gaussian distribution, q-analogy of Gaussian distribution, is introduced to characterize the prior information of unknown parameters for inverse problems. Based on q-Hermite polynomials, we propose a spectral likelihood approximation (SLA) algorithm of Bayesian inversion. Convergence results of the approximated posterior distribution in the sense of Kullback–Leibler divergence are obtained when the likelihood function is replaced with the SLA and the prior density function is truncated to its partial sum. In the end, two numerical examples are displayed, which verify our results.

The main objective of this paper is to study and describe the hypercentre of a finite group associated with saturated formations, in terms of some subgroup embedding properties related to permutability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra System (CAS) technology (calculator and software) into the senior secondary mathematics curriculum and examination assessment in three phases, starting with a research-based pilot from 2000, followed by parallel implementation of CAS and non-CAS subjects from 2006 and culminating in transition to CAS-assumed subjects in 2010. This paper reports reflections on these developments over two decades from the perspectives of a researcher and the state mathematics manager (the authors) in consultation with four implementing teachers (the consultants). The authors critically examined the strategic design decisions that were made for the initiative over time. Then, with contributions from the four consultants, technical design issues relating to assessment and to teaching and the changes over a decade were investigated. A range of modifications have been made over the two decades, driven by changes in device capability and progressively increasing teaching expertise. The place of CAS in senior mathematics is now widely accepted, partly because an examination component not allowing any technology has been implemented. Examination questions have become more general, which may have added difficulty, but more questions involve setting up a real situation mathematically.

The Rosenau–Korteweg-deVries–Kawahara equation describes the dynamics of dense discrete systems or small-amplitude gravity capillary waves on water of a finite depth. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem.

In this paper, we obtain the criterion of boundedness of maximal operators associated with smooth hypersurfaces. Also we compute the exact value of the boundedness index of such operators associated with arbitrary convex analytic hypersurfaces in the case where the height of a hypersurface in the sense of A. N. Varchenko is greater than 2. Moreover, we obtain the exact value of the boundedness index for degenerated smooth hypersurfaces, i.e., for hypersurfaces satisfying conditions of the classical Hartman-Nirenberg theorem. The obtained results justify the Stein-Iosevich-Sawyer hypothesis for arbitrary convex analytic hypersurfaces as well as for smooth degenerated hypersurfaces. Also we discuss some related problems of the theory of oscillatory integrals.

A classical result of K. L. Chung and W. Feller deals with the partial sums S k S_k arising in a fair coin-tossing game. If N n N_n is the number of “positive” terms among S 1 S_1 , S 2 S_2 , …, S n S_n then the quantity P ( N 2 n = 2 r ) P(N_{2n} = 2r) takes an elegant form. We lift the restriction on an even number of tosses and give a simple expression for P ( N 2 n + 1 = r ) P(N_{2n+1} = r) , r = 0 r = 0 , 1 1 , 2 2 , …, 2 n + 1 2n+1 . We get to this ansatz by adaptating the Feynman–Kac methodology.

The technological development in the field of information and communication has been accompanied by the emergence of security challenges related to the transmission of information. Encryption is a good solution. An encryption process is one of the traditional methods to protect the plain text, by converting it into inarticulate form. Encryption implemented can be occurred by using some substitute techniques, shifting techniques, or mathematical operations. This paper proposed a method with two branches to encrypt text. The first branch is a new mathematical model to create and exchange keys, the proposed key exchange method is the development of Diffie-Hellman. It is a new mathematical operations model to exchange keys based on prime numbers and the possibility of using integer numbers. While the second branch of the proposal is the multi-key encryption algorithm. The current algorithm provides the ability to use more than two keys. Keys can be any kind of integer number (at least the last key is a prime number), not necessarily to be of the same length. The Encryption process is based on converting the text characters to suggested integer numbers, and these numbers are converted to other numbers by using a multilevel mathematical model many times (a multilevel process depending on the number of keys used), while the decryption process is a one-level process using just one key as the main key, while the other keys used as secondary keys. The messages are encoded before encryption (coded by ASCII or any suggested system). The algorithm can use an unlimited number of keys with a very large size (more than 7500 bytes), at least one of them a prime number. Exponentiation is also used for keys to increase complexity. The experiments proved the robustness of the key exchange protocol and the encryption algorithm in addition to the security. Comparing the suggested method with other methods ensures that the suggested method is more secure and flexible and easy to implement.

In the pandemic era of COVID19, software engineering and artificial intelligence tools played a major role in monitoring, managing, and predicting the spread of the virus. According to reports released by the World Health Organization, all attempts to prevent any form of infection are highly recommended among people. One side of avoiding infection is requiring people to wear face masks. The problem is that some people do not incline to wear a face mask, and guiding them manually by police is not easy especially in a large or public area to avoid this infection. The purpose of this paper is to construct a software tool called Face Mask Detection (FMD) to detect any face that does not wear a mask in a specific public area by using CCTV (closed-circuit television). The problem also occurs in case the software tool is inaccurate. The technique of this notion is to use large data of face images, some faces are wearing masks, and others are not wearing masks. The methodology is by using machine learning, which is characterized by a HOG (histogram orientation gradient) for extraction of features, then an SVM(support vector machine) for classification, as it can contribute to the literature and enhance mask detection accuracy. Several public datasets for masked and unmasked face images have been used in the experiments. The findings for accuracy are as follows: 97.00%, 100.0%, 97.50%, 95.0% for RWMFD (Real-world Masked Face Dataset)& GENK14k, SMFDB (Simulated Masked Face Recognition Dataset), MFRD (Masked Face Recognition Dataset), and MAFA (MAsked FAces)& GENK14k for databases, respectively. The results are promising as a comparison of this work has been made with the state-of-the-art. The workstation of this research used a webcam programmed by Matlab for real-time testing.

The converse of the Borel–Cantelli Lemma states that if { A i } i = 1 ∞ is a sequence of independent events such that ∑ P ( A i ) = ∞ , then almost surely infinitely many of these events will occur. Erdős and Renyi proved that it is sufficient to weaken the condition of independence to pairwise independence. Later, several other weakenings of the condition appeared in the literature. The aim of this paper is to provide a collection of conditions, all of which imply that almost surely infinitely many of the events occur, and determine the complete implicational relationship between them. Many of these results are known, or follow from known results, however, they are not widely known among non-specialists. Yet, the results can be extremely useful for areas outside of probability theory, as evidenced by the original motivation of this paper emerging from infinite combinatorics. Our proofs are aimed to be accessible to a general mathematical audience.

The aim of this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on variable exponent Morrey spaces of an integral form. As an application of the boundedness of the maximal operator, we establish Sobolev-type inequalities for Riesz potentials $$I_{\alpha (\cdot )}f$$ of variable order $$\alpha (\cdot )$$ of functions f in variable exponent Morrey spaces of an integral form.

In this paper, we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak -coercivity theory. All eigenvalues are proved to be bifurcation points and the bifurcating branches are investigated both theoretically and numerically. In a one-dimensional model example we obtain the existence of infinitely many bifurcating branches that are mutually disjoint, unbounded, and consist of solutions with a fixed nodal pattern.

Part of the work was done while the authors were visiting the South China University of Science and Technology (SUSTech), Shenzhen, in 2018, and we are grateful (in particular to Professor Cai Heng Li) for the hospitality that we received.The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Groups, representations and applications: new perspectives (supported by EPSRC grant no.EP/R014604/1), where further work on this paper was undertaken. In particular we acknowledge a Simons Fellowship (Cameron) and a Kirk Distinguished Visiting Fellowship (Praeger) during this programme. Schneider thanks the Centre for the Mathematics of Symmetry and Computation of The University of Western Australia and Australian Research Council Discovery Grant DP160102323 for hosting his visit in 2017 and acknowledges the support of the CNPq projects Produtividade em Pesquisa (project no.: 308212/2019-3) and Universal (project no.:421624/2018-3). Diagonal groups are one of the classes of finite primitive permutation groups occurring in the conclusion of the O'Nan-Scott theorem. Several of the other classes have been described as the automorphism groups of geometric or combinatorial structures such as affine spaces or Cartesian decompositions, but such structures for diagonal groups have not been studied in general. The main purpose of this paper is to describe and characterise such structures, which we call diagonal semilattices. Unlike the diagonal groups in the O'Nan-Scott theorem, which are defined over finite characteristically simple groups, our construction works over arbitrary groups, finite or infinite. A diagonal semilattice depends on a dimension m and a group T. For m=2, it is a Latin square, the Cayley table of T, though in fact any Latin square satisfies our combinatorial axioms. However, for m≥3, the group T emerges naturally and uniquely from the axioms. (The situation somewhat resembles projective geometry, where projective planes exist in great profusion but higher-dimensional structures are coordinatised by an algebraic object, a division ring.) A diagonal semilattice is contained in the partition lattice on a set Ω, and we provide an introduction to the calculus of partitions. Many of the concepts and constructions come from experimental design in statistics. We also determine when a diagonal group can be primitive, or quasiprimitive (these conditions turn out to be equivalent for diagonal groups). Associated with the diagonal semilattice is a graph, the diagonal graph, which has the same automorphism group as the diagonal semilattice except in four small cases with m

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates. We go outside Boolean realm and consider circuits built of any fixed set of gates on an arbitrary large finite domain. From the complexity point of view this is strictly connected with the problems of solving equations (or systems of equations) over finite algebras. The research reported in this work was motivated by a desire to know for which finite algebras $\mathbf A$ there is a polynomial time algorithm that decides if an equation over $\mathbf A$ has a solution. We are also looking for polynomial time algorithms that decide if two circuits over a finite algebra compute the same function. Although we have not managed to solve these problems in the most general setting we have obtained such a characterization for a very broad class of algebras from congruence modular varieties. This class includes most known and well-studied algebras such as groups, rings, modules (and their generalizations like quasigroups, loops, near-rings, nonassociative rings, Lie algebras), lattices (and their extensions like Boolean algebras, Heyting algebras or other algebras connected with multi-valued logics including MV-algebras). This paper seems to be the first systematic study of the computational complexity of satisfiability of non-Boolean circuits and solving equations over finite algebras. The characterization results provided by the paper is given in terms of nice structural properties of algebras for which the problems are solvable in polynomial time., 50 pages

This paper proposes corresponding teaching methods and instructional modes based on predecessors’ research on mathematics instructional mode and the current state of mathematics teaching. In addition, this paper constructs a teaching evaluation model based on DL algorithm based on an in-depth study of DL-related theories in order to accurately and scientifically analyze the problems that exist in mathematics teaching. This paper constructs an instructional quality evaluation index system based on rationality and fairness, and uses the BPNN evaluation model to train and study a set of instructional quality data. Finally, the experimental results show that this system has a high level of stability, with a 96.37 percent stability rate and a 95.42 percent evaluation accuracy rate. The results of this paper’s evaluation of the mathematical instructional quality model are objective and reasonable. It can accurately assess instructional quality while also assessing problems in the teaching process based on the instructional quality scores and making reasonable recommendations for teaching improvement based on the weak links in the teaching process. It has the potential to provide a workable system for assessing instructional quality.

In this paper, we introduce new relaxations for the hypograph of composite functions assuming that the outer function is supermodular and concave extendable. Relying on a recently introduced relaxation framework, we devise a separation algorithm for the graph of the outer function over P, where P is a special polytope to capture the structure of each inner function using its finitely many bounded estimators. The separation algorithm takes [Formula: see text] time, where d is the number of inner functions and n is the number of estimators for each inner function. Consequently, we derive large classes of inequalities that tighten prevalent factorable programming relaxations. We also generalize a decomposition result and devise techniques to simultaneously separate hypographs of various supermodular, concave-extendable functions using facet-defining inequalities. Assuming that the outer function is convex in each argument, we characterize the limiting relaxation obtained with infinitely many estimators as the solution of an optimal transport problem. When the outer function is also supermodular, we obtain an explicit integral formula for this relaxation.

The bilevel program is an optimization problem in which the constraint involves solutions to a parametric optimization problem. It is well known that the value function reformulation provides an equivalent single-level optimization problem, but it results in a nonsmooth optimization problem that never satisfies the usual constraint qualification, such as the Mangasarian–Fromovitz constraint qualification (MFCQ). In this paper, we show that even the first order sufficient condition for metric subregularity (which is, in general, weaker than MFCQ) fails at each feasible point of the bilevel program. We introduce the concept of a directional calmness condition and show that, under the directional calmness condition, the directional necessary optimality condition holds. Although the directional optimality condition is, in general, sharper than the nondirectional one, the directional calmness condition is, in general, weaker than the classical calmness condition and, hence, is more likely to hold. We perform the directional sensitivity analysis of the value function and propose the directional quasi-normality as a sufficient condition for the directional calmness. An example is given to show that the directional quasi-normality condition may hold for the bilevel program.

This paper defines a general framework to study infinitely repeated games with time-dependent discounting in which we distinguish and discuss both time-consistent and -inconsistent preferences. To study the long-term properties of repeated games, we introduce an asymptotic condition to characterize the fact that players become more and more patient; that is, the discount factors at all stages uniformly converge to one. Two types of folk theorems are proven without the public randomization assumption: the asymptotic one, that is, the equilibrium payoff set converges to the feasible and individual rational set as players become patient, and the uniform one, that is, any payoff in the feasible and individual rational set is sustained by a single strategy profile that is an approximate subgame perfect Nash equilibrium in all games with sufficiently patient discount factors. We use two methods for the study of asymptotic folk theorem: the self-generating approach and the constructive proof. We present the constructive proof in the perfect-monitoring case and show that it can be extended to time-inconsistent preferences. The self-generating approach applies to the public-monitoring case but may not extend to time-inconsistent preferences because of a nonmonotonicity result.

In this paper, we introduce the notion of infinity branches and approaching surfaces. We obtain an algorithm that compares the behavior at the infinity of two given algebraic surfaces that are defined by an irreducible polynomial. Furthermore, we show that if two surfaces have the same asymptotic behavior, the Hausdorff distance between them is finite. All these concepts are new and represent a great advance for the study of surfaces and their applications., Agencia Estatal de Investigación

Surrogate endpoints have been used to assess the efficacy of a treatment and can potentially reduce the duration and/or number of required patients for clinical trials. Using information theory, Alonso et al. (2007) proposed a unified framework based on Shannon entropy, a new definition of surrogacy that departed from the hypothesis testing framework. In this paper, a new family of surrogacy measures under Havrda and Charvat (H-C) entropy is derived which contains Alonso’s definition as a particular case. Furthermore, we extend our approach to a new model based on the information-theoretic measure of association for a longitudinally collected continuous surrogate endpoint for a binary clinical endpoint of a clinical trial using H-C entropy. The new model is illustrated through the analysis of data from a completed clinical trial. It demonstrates advantages of H-C entropy-based surrogacy measures in the evaluation of scheduling longitudinal biomarker visits for a phase 2 randomized controlled clinical trial for treatment of multiple sclerosis.

This paper presents a simplified model of the population migration problem, addressed to first-year engineering students in order to show them the use of linear algebra tools. The study consists of predicting the census in the city centre and in the suburbs, determining the city population equilibrium point, and making a sociological interpretation of population flows. This practical problem is part of the seminar “Applications of Linear Algebra in Engineering”, which is being held at the Universitat Politècnica de Catalunya-BarcelonaTech (UPC). This seminar consists in the learning of linear algebra by the implementation of real applications where mathematical tools are required to resolve them. This paper presents an application of linear algebra to the population migration problem and analyses students’ appreciation through anonymous surveys and personal interviews. The surveys assessed students’ motivation towards the subject of linear algebra and their learning of mathematical concepts. Personal interviews were conducted for students in order to let them express in detail their opinion about the seminar. The results confirm that the introduction of real applications in the learning of mathematics increases students’ motivation and involvement, which implies an improvement in students’ performance in the first courses of STEM degrees. Peer Reviewed Objectius de Desenvolupament Sostenible::4 - Educació de Qualitat

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and G&auml, hler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending G&auml, hler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology&mdash, a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology&mdash, a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on G&auml, hler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).

In this paper, we introduce an algorithm for computing p-adic integrals on bad reduction hyperelliptic curves. For bad reduction curves, there are two notions of p-adic integration: Berkovich-Coleman integrals which can be performed locally; and abelian integrals with desirable number-theoretic properties. By covering a bad reduction hyperelliptic curve by annuli and basic wide open sets, we reduce the computation of Berkovich-Coleman integrals to the known algorithms on good reduction hyperelliptic curves. These are due to Balakrishnan, Bradshaw, and Kedlaya, and to Balakrishnan and Besser for regular and meromorphic 1-forms on good reduction curves, respectively. We then employ tropical geometric techniques due to the first-named author with Rabinoff and Zureick-Brown to convert the Berkovich-Coleman integrals into abelian integrals. We provide examples of our algorithm, verifying that certain abelian integrals between torsion points vanish., Comment: Comments Welcome! figure taken from arxiv::1606.09618; v2 minor revisions

We study approximation of multivariate periodic functions from Besov and Triebel–Lizorkin spaces of dominating mixed smoothness by the Smolyak algorithm constructed using a special class of quasi-interpolation operators of Kantorovich-type. These operators are defined similar to the classical sampling operators by replacing samples with the average values of a function on small intervals (or more generally with sampled values of a convolution of a given function with an appropriate kernel). In this paper, we estimate the rate of convergence of the corresponding Smolyak algorithm in the L q -norm for functions from the Besov spaces B p , θ s ( T d ) and the Triebel–Lizorkin spaces F p , θ s ( T d ) for all s > 0 and admissible 1 ≤ p , θ ≤ ∞ as well as provide analogues of the Littlewood–Paley-type characterizations of these spaces in terms of families of quasi-interpolation operators.

Support vector machines regression (SVMR) is an important part of statistical learning theory. The main difference between SVMR and the classical least squares regression (LSR) is that SVMR uses the ϵ-insensitive loss rather than quadratic loss to measure the empirical error. In this paper, we consider SVMR method in the field of functional data analysis under the framework of reproducing kernel Hilbert spaces. The main tool used in our theoretical analysis is the concentration inequalities for suprema of some appropriate empirical processes. As a result, we establish explicit convergence rates of the prediction risk for SVMR, which coincide with the minimax lower bound obtained recently in literature for LSR.