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Nowadays, there has been a rapidly increasing number of scientific submissions in multiple research domains. A large number of journals have various acceptance rates, impact factors, and rankings in different publishers. It becomes time-consuming for many researchers to select the most suitable journal to submit their work with the highest acceptance rate. A paper submission recommendation system is more critical for the research community and publishers as it gives scientists another support to complete their submission conveniently. This paper investigates the submission recommendation system for two main research topics: computer science and applied mathematics. Unlike the previous works (Wang et al., 2018; Son et al., 2020) that extract TF–IDF and statistical features as well as utilize numerous machine learning algorithms (logistics regression and multiple perceptrons) for building the recommendation engine, we present an efficient paper submission recommendation algorithm by using different bidirectional transformer encoders and the Mixture of Transformer Encoders technique. We compare the performance between our methodology and other approaches by one dataset from Wang et al. (2018) with 14012 papers in computer science and another dataset collected by us with 223,782 articles in 178 Springer applied mathematics journals in terms of top K accuracy (K = 1 , 3 , 5 , 10). The experimental results show that our proposed method extensively outperforms other state-of-the-art techniques with a significant margin in all top K accuracy for both two datasets. We publish all datasets collected and our implementation codes for further references. 1 1 https://github.com/BinhMisfit/PSRMTE. • Bidirectional transformer encoders can improve the performance of the paper submission recommendation system. • The Mixture of Transformer Encoders framework shows the efficiency in the paper submission recommendation problem. • Proposed techniques can surpass other recent techniques on two datasets related. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we determine the modularities of asymptotically optimal towers found by Maharaj and Wulftange in 2005. This is also a continuation of the work of Elkies in 2002. [Copyright &y& Elsevier]

Abstract: In this short note we point to an error in the proof of a theorem stated in [L. Balková, E. Pelantová, Š. Starosta, On Brlek-Reutenauer conjecture, Theoret. Comput. Sci. 412 (2011) 5649–5655]. By constructing a counterexample, we show that the assertion of the theorem is actually incorrect. Although this theorem is of a technical character, it was used in an argument leading to a corollary of a general interest to the Brlek-Reutenauer conjecture, and thus as a consequence of this note we have that the proof of the mentioned corollary is also flawed. [Copyright &y& Elsevier]

Abstract: A lemma presented by Matkowski requires a proof. [Copyright &y& Elsevier]

The enumerative problem of spanning trees of graphs is one of the fundamental problems in the field of graph theory, which has attracted the attention of mathematicians and physicists. For a connected graph G , let T be a spanning tree of G. In this paper, we call T to be a pm - t r e e of G if T contains a perfect matching. Recently, Li and Yan (Applied Mathematics and Computation, 456 (2023), 128125.) gave an explicit expression for the number of pm-trees in linear hexagonal chains on the plane, cylinder and Möbius strip, respectively. In this paper, we extend the results above and obtain the explicit formula for the number of pm-trees in linear polygonal chains with n polygons of 4 k + 2 vertices on the plane, cylinder and Möbius strip, respectively. [ABSTRACT FROM AUTHOR]

One of the key tools for many fields of applied mathematics is the integral equations. Integral equations are widely utilized in many models, atmosphere–ocean dynamics, fluid mechanics, mathematical physics, and many other physical and engineering disciplines. A new numerical strategy based on the Bernoulli wavelet is introduced to solve system of Fredholm integral equations of second kind. In this paper, the Bernoulli wavelets are first built. Second, the system of Fredholm integral equations has been reduced into an algebraic system. In order to demonstrate the viability, and accuracy of the suggested Bernoulli wavelet approach, some numerical examples are offered at the end. The derived numerical results are examined with those from other numerical techniques and with exact solutions, demonstrating the superiority of the proposed method over those techniques. The novelty of proposed technique is that it can be extended for the numerical solution of two dimensional integral equations and differential equations appearing in engineering models, however some modifications will be required. [ABSTRACT FROM AUTHOR]

Structuralists typically appeal to some variant of the widely popular 'mapping' account of mathematical representation to suggest that mathematics is applied in modern science to represent the world's physical structure. However, in this paper, I argue that this realist interpretation of the 'mapping' account presupposes that physical systems possess an 'assumed structure' that is at odds with modern physical theory. Through two detailed case studies concerning the use of the differential and variational calculus in modern dynamics, I show that the formal structure that we need to assume in order to apply the mapping account is inconsistent with the way in which mathematics is applied in modern physics. The problem is that a realist interpretation of the 'mapping' account imposes too severe of a constraint on the conformity that must exist between mathematics and nature in order for mathematics to represent the structure of a physical system. • This paper presents a critique of the 'mapping' account of mathematical representation. • The 'mapping' account requires that physical systems possess an assumed structure. • This structure is at odds with modern physical theory. • I argue that a realist interpretation of the account imposes a severe constraint on the conformity between math and nature. • The argument is defended through two case studies concerning the differential and variational calculus. [ABSTRACT FROM AUTHOR]

In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a non-constructive way, a polynomial-time recognition of geometric grid classes of permutations and k -letter graphs for a fixed k. However, explicit algorithms are available only for k = 2. In this paper, we present the first explicit polynomial-time algorithm for the recognition of 3-letter graphs over a cyclic decoder. It is based on a structural characterization of graphs in this class. [ABSTRACT FROM AUTHOR]

• Fractional calculus is a fast growing field in mathematics, science and engineering. • This is a bibliographic analysis of 351 articles that use Atangana-Baleanu operators • Articles grow by 80.25% yearly from all countries, especially developing countries. • This shows the influence of this rapidly growing field of applied mathematics. Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation and integration operators. Recently, Atangana and Baleanu proposed operators based on generalized Mittag-Leffler functions to solve fractional integrals and derivatives. These contributions have set off an explosion of new research in fractional calculus, and this paper present a comprehensive bibliometric analysis of the peer-reviewed papers inspired by Atangana and Baleanu. In total, 351 papers in the Scopus database have used Atangana-Baleanu operators and this number is growing at 80.25% each year since 2016. These papers were written by 343 authors, predominantly from Mexico, Saudi Arabia and India. Although these data show that Atangana-Baleanu operators support global and fast growing scientific research, the field is dominated statistically by a few productive individuals. I present citation network of the most prolific authors and show collaboration and citation networks. Finally, I present a thematic analysis of the papers applying Atanagana-Baleanu operators and show how research forms clusters based on: analytical solutions, numerical simulations or applications in science and engineering. [ABSTRACT FROM AUTHOR]

• A two-stage degradation system with two performance characterizes is considered. • A correlated bivariate Wiener process is adopted in modeling. • The explicit expressions of system reliabilities and availabilities are derived. • Two algorithms for the simulations of system reliabilities are given. It is still a challenge to study the degradation mechanisms of complex systems with multiple performance characteristics. This paper develops a two-stage stochastic degradation model. The degeneration processes of two correlated performance characteristics are described by a correlated bivariate Wiener process in the first stage, in which neither of the degradation levels of performance characteristics reaches their thresholds. When one of the degradation levels of performance characteristics reaches its threshold, the system operates defectively in the second stage, and the system degradation process is described by the other performance characteristic which is modeled by a univariate Wiener process. The system fails completely when both the degradation levels of performance characteristics reach their thresholds. Explicit expressions of the system reliability and availabilities are given based on different inspection and maintenance policies. Simulation is also presented, and it shows that the analytical results and the simulation results are in good agreement. Finally, a detailed case study of the rail track geometry degradation is given to demonstrate the results obtained in the paper. [ABSTRACT FROM AUTHOR]

• The Plancherel–Parseval–Rayleigh identities associated with the linear canonical transform (LCT) and 2D LCT are derived. • Based on the derived identities, the weighted moment Heisenberg–Pauli–Weyl uncertainty principles associated with the LCT and 2D LCT are investigated and derived in details. • Examples are provided to show the derived results are sharper than those in the existing literature. • Applications of the derived results in time frequency resolution analysis and signal energy concentrations are also discussed in this paper. The classical uncertainty principle plays an important role in quantum mechanics, signal processing and applied mathematics. With the development of novel signal processing methods, the research of the related uncertainty principles has gradually been one of the most hottest research topics in modern signal processing community. In this paper, the weighted Heisenberg–Pauli–Weyl uncertainty principles for the linear canonical transform (LCT) have been investigated in detail. Firstly, the Plancherel–Parseval–Rayleigh identities associated with the LCT are derived. Secondly, the weighted Heisenberg–Pauli–Weyl uncertainty principles in the LCT domain are investigated based on the derived identities. The signals that can achieve the lower bound of the uncertainty principle are also obtained. The classical Heisenberg uncertainty principles in the Fourier transform (FT) domain are shown to be special cases of our achieved results. Thirdly, examples are provided to show that our weighted Heisenberg–Pauli–Weyl uncertainty principles are sharper than those in the existing literature. Finally, applications of the derived results in time frequency resolution analysis and signal energy concentrations are also analyzed and discussed in detail. [ABSTRACT FROM AUTHOR]

This paper develops and analyzes the optimal weighted upwind finite volume method (OWUFVM) for convection–diffusion equations on nonuniform rectangular meshes. The dual meshes in this method are associated with the local Peclet numbers, which are determined by the convection and diffusion coefficients and the mesh size. We first prove the stability and H 1 -norm error estimate. Then we prove a weak error estimate, which plays a key role in deriving the optimal second-order error estimate in the L 2 norm. The L 2 -norm error estimate is the most important result of this paper. We also briefly examine the discrete maximum principle. Numerical experiments are presented to illustrate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract Fuzzy logic based systems are very widely used for modeling and control of complex non-linear, plants. Fuzzy systems require the knowledge about the structure of the dynamic plant in order to achieve fruitful results. Recurrent Fuzzy systems (RFS) are a variation of fuzzy systems and have the ability to model and control dynamic plants without using the information about the structure of the plant. This paper presents identification and control of non-linear dynamical systems using two different architectures of recurrent fuzzy system (RFS). It highlights the importance of RFS over the conventional type-1 fuzzy based system. The objective of system identification as well as control has been achieved using both the architectures of RFS and the simulation results clearly show their efficiency. This paper also highlights yet another advantage of RFS over the conventional type-1 fuzzy systems which comes into light when dealing with higher order systems. The paper explains how the computational complexity can be greatly reduced by using RFS for higher order dynamical systems. A comparative analysis between the conventional type-1 fuzzy system and the two recurrent fuzzy systems has also been performed. Highlights • Identification and Control without the knowledge about the order and structure of the plants using 2 different recurrent fuzzy structures. • A remarkable reduction in the complexity as compared to conventional fuzzy systems when dealing with higher order systems. • Checking the robustness of the discussed recurrent fuzzy structures against parameter perturbation as well as external disturbances. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a simplified reproducing kernel method to solve the linear Volterra integral equations with variable coefficients. The main idea of the method is to establish a reproducing kernel direct space that can be used in Volterra integral equations. And in the first time, this paper analyzes the convergence order and stability of the approximate solution. Then the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The proposed method is proved to be stable and is not less than the second order convergence. The algorithm is proved to be feasible and stable through some numerical examples. [ABSTRACT FROM AUTHOR]

Abstract This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited number of interface conditions and do not carry out stability or convergence analysis. Our method also retains second-order accuracy in space while preserving the tridiagonal matrix structure of the classical single-layer discretisation. Stability and convergence analysis of the new finite volume method is presented for each of the three classical time discretisation methods: forward Euler, backward Euler and Crank–Nicolson. We prove that both the backward Euler and Crank–Nicolson schemes are always unconditionally stable. The key contribution of the work is the presentation of a set of sufficient stability conditions for the forward Euler scheme. Here, we find that to ensure stability of the forward Euler scheme it is not sufficient that the time step τ satisfies the classical constraint of τ ≤ h i 2 ∕ (2 D i) in each layer (where D i is the diffusivity and h i is the grid spacing in the i th layer) as more restrictive conditions can arise due to the interface conditions. The paper concludes with some numerical examples that demonstrate application of the new finite volume method, with the results presented in excellent agreement with the theoretical analysis. Highlights • Finite volume method for layered diffusion problems is developed. • Proposed method is applicable to general boundary/interface conditions. • Theoretical analysis (stability and convergence) of the schemes is presented. • Finding: interface conditions can lead to more restrictive stability conditions. • Presented numerical results confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, Investigation of global approximation of the generalized Szàsz–Mirakjan type operators in exponential weight spaces is discussed. The paper focuses on calculation of moments, direct results and inverse results for the saturated as well as non-saturated cases. [ABSTRACT FROM AUTHOR]

The theory of single upper and lower tolerances for combinatorial minimization problems was formalized in 2005 for the three types of cost functions sum, product, and maximum, and since then it has shown to be rather useful in creating heuristics and exact algorithms. However, such single tolerances are often used because the assessment of multiple cost changes is considered too complicated. This paper addresses that issue. In this paper we extend this theory from single to set tolerances for these three types of cost functions. In particular, we characterize specific values of set upper and lower tolerances as positive and infinite, and we show a criterion for the uniqueness of an optimal solution to a combinatorial minimization problem. Furthermore, we present one exact formula and several bounds for computing set upper and lower tolerances using the relation to their corresponding single tolerance counterparts. [ABSTRACT FROM AUTHOR]

Abstract Median filter (MF) is a content preserving nonlinear filter, employed to hide traces of image manipulations, affecting the reliability of manipulation detection techniques. Thus, median filter detection is a major concern for digital image forensics (DIF) experts. The methods used for median filter detection (MFD) are computationally expensive as high dimensionality of feature vectors are employed. This paper proposes an effective method for blind median filter detection based on streaking effect of the median filter. The method offered in the paper is built on experimental observation that the percentage streak area (psa) of an image increases on repetitive median filtering of the image, the rate at which psa increases for median filtered images is different from the rate at which psa increases for unfiltered images. A feature vector based on the observation is extracted from three different image datasets UCID, BOSS and Dresden and feed to Support Vector Machine (SVM) to perform 10-fold cross validation using linear kernel. The results obtained, using a three-dimensional feature vector, demonstrates efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

The number of failed components in a failed or operating system is a very useful quantity in terms of replacement and maintenance strategies. These quantities have been studied in several papers for a system consisting of identical components. In this paper, the number of failed components at the time when the system fails and the number of failed components when the system is working are considered for a well-known and widely applicable k -out-of- n structure. The system is assumed to have multiple types of components. That is, the system consists of components having nonidentical failure time distributions. Optimization problems are also formulated to find optimal values of the number of components of each type, and the optimal replacement time. [ABSTRACT FROM AUTHOR]

In a recent paper, we presented an intelligent evolutionary search technique through genetic programming (GP) for finding new analytical expressions of nonlinear dynamical systems, similar to the classical Lorenz attractor's which also exhibit chaotic behaviour in the phase space. In this paper, we extend our previous finding to explore yet another gallery of new chaotic attractors which are derived from the original Lorenz system of equations. Compared to the previous exploration with sinusoidal type transcendental nonlinearity, here we focus on only cross-product and higher-power type nonlinearities in the three state equations. We here report over 150 different structures of chaotic attractors along with their one set of parameter values, phase space dynamics and the Largest Lyapunov Exponents (LLE). The expressions of these new Lorenz-like nonlinear dynamical systems have been automatically evolved through multi-gene genetic programming (MGGP). In the past two decades, there have been many claims of designing new chaotic attractors as an incremental extension of the Lorenz family. We provide here a large family of chaotic systems whose structure closely resemble the original Lorenz system but with drastically different phase space dynamics. This advances the state of the art knowledge of discovering new chaotic systems which can find application in many real-world problems. This work may also find its archival value in future in the domain of new chaotic system discovery. [ABSTRACT FROM AUTHOR]

The three-part paper deals with energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions. The principle of minimum total energy, i.e. the sum of the potential and fracture energies, which stems directly from the Griffith’s theory of cracks, is applied to the problem of arbitrary crack growth in 2D. The proposed formulation enables minimisation of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths to solve for the evolution of the mechanical system over time. The three parts focus, in turn, on (I) the theory of multiple crack growth including competing cracks, (II) the discrete solution by the extended finite element method using the minimum-energy formulation, and (III) the aspects of computer implementation within the Matlab programming language. The key contributions of Part-I of this three-part paper are given as follows. (1) Formulation of the total energy functional governing multiple crack behaviour. (2) Three solution methods to the problem of competing crack growth for different fracture front stabilities, e.g. stable, unstable, or partially stable crack tip configurations; we compare our approach to Budyn et al. (2004) and demonstrate via example cases that the latter approach of resolving competing crack growth is not energy minimal in some cases. Finally, (3), the minimum energy criterion for a set of crack tip extensions is posed as the condition of vanishing rotational dissipation rates with respect to the extension angles. The proposed formulation lends itself to a straightforward application within a discrete framework involving multiple finite-length crack tip extensions. The open-source Matlab code, documentation, benchmark/example cases are included as supplementary material. [ABSTRACT FROM AUTHOR]

In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the solution vector. In this paper we discuss various possibilities to decouple the equations for the different components that result in unconditionally stable schemes. If the spatial discretization uses Cartesian grids, the resulting schemes are Locally One Dimensional (LOD). The stability analysis of these schemes is based on the general stability theory of additive operator-difference schemes developed by Samarskii and his collaborators. The results of the theoretical analysis are illustrated on a 2D numerical example with a smooth manufactured solution. [ABSTRACT FROM AUTHOR]

This paper presents information on the content and resources of the internationally certified Master’s program “Mathematical Modeling and Information Technologies in Photonics” in the field of Applied Mathematics and Physics. The paper investigates scientific achievements of the academic staff, peculiarities of courses currently held, opportunities of available facilities and resources, and prospects for the Master’s worldwide research activities. [ABSTRACT FROM AUTHOR]

The present paper studies both the fixed point property ( FPP for brevity) and the almost fixed point property ( AFPP for short) for Marcus-Wyse ( M -, for short) topological spaces by using an M -retract. Under M -topology, let S N M ( x ) be the smallest open neighborhood of x . In this paper we prove that every M -connected subspace of S N M ( x ) has the FPP . Let S C M 4 be a simple closed M -curve with four elements in Z 2 . Besides, consider an M -topological plane ( X , γ X ) (see Definition 5 ) such that S N M ( x ) ⊂ ( X , γ X ) , where x is a double even point or an even point. Then, proving that S C M 4 is an M -retract of ( X , γ X ) , we propose that every M -topological plane does not have the AFPP . Finally, the present paper proves the following: consider M -connected spaces ( X i , γ X i ) , where X i ⊂ Z , 2 ≤ | X i | ≨ ∞ , i ∈ { 1 , 2 } . Then the Cartesian product as an M -topological subspace ( X 1 × X 2 , γ X 1 × X 2 ) does not have the AFPP . [ABSTRACT FROM AUTHOR]

Non-linear partial derivative equations describe mathematical models of mechanics of plates and shells. Solving such equations analytically and numerically is a huge problem, and it is possible to solve it using Fourier's idea, the method of separation of variables, which goes by the name of Fourier. The combination of Fourier and Bubnov–Galerkin methods revolutionized applied mathematics and numerical methods. In this paper, the symbiosis of the Fourier and Bubnov–Galerkin methods was given for the problems of plate and shell theory: the Bubnov–Galerkin method, Kantorovich–Vlasov method, variational iteration methods, Vaindiner and Agranovskii–Baglai–Smirnov methods, applied to each of these methods, which gives practically exact solutions. A rationale for these methods is for the problems of plate theory concerning non-linearities. A mathematical model was constructed to analyse the stress–strain state of elastic–plastic problems in plate theory, according to the deformation theory of plasticity. The above methods solved the problems in elastic–plastic formulation for different types of boundary conditions and loads. It was noted that the procedure of the Agranovskii–Baglai–Smirnov method in combination with the Bubnov–Galerkin methods in higher approximations, Kantorovich–Vlasov method and variational iteration method makes it possible to obtain a practically exact solution of the problem. It was shown that the variational iteration method is the fastest. It should also be noted that this method does not require a system of approximating functions that satisfy the boundary conditions. • The development of methods based on Fourier and Bubnov–Galerkin ideas was considered. • Mathematical methods for the analysis of the stress-strain state of plates by deformation theory of plasticity were developed. • The methods are based on the idea of reducing partial differential equations to ordinary differential equations. • The paper presents numerical results of the analysis of the stress-strain state of plates using the developed methods. • It was shown that the most efficient and fastest method is the variational iteration method. [ABSTRACT FROM AUTHOR]

Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by k -canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The variable activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to c -sensitivity and provides formulas for the activities and c -sensitivity of general k -canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the c -sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally efficient way to obtain Derrida values of Boolean networks, deterministic or stochastic, that does not involve simulation. [ABSTRACT FROM AUTHOR]

This paper presents a method for determining the nonlinear dynamic responses of structures under moving loads. The load is considered as a four degrees-of-freedom system with linear suspensions and tires flexibility, and the structure is modeled as an Euler–Bernoulli beam with simply supported at both ends. The nonlinear dynamic interaction of the load–structure system is discussed, and Kelvin−Voigt material model is employed for the beam. The nonlinear partial differential equations of the dynamic interaction are derived by using the von Kármán nonlinear theory and D'Alembert's principle. Based on the Galerkin method, the partial differential equations of the system are transformed into nonlinear ordinary equations, which can be solved by using the Newmark method and Newton−Raphson iteration method. To validate the approach proposed in this paper, the comparison are performed using a moving mass and a moving oscillator as the excitation sources, and the investigations demonstrate good reliability. [ABSTRACT FROM AUTHOR]

Recently, in mathematical economics, Even and Lehrer introduced the decomposition integral (Even and Lehrer, 2014). In this paper, general versions of some well-known probabilistic inequalities for the decomposition integrals and the superdecomposition integrals are discussed that are still open for research. The main results of this paper generalize some previous results for particular integral inequalities obtained by several researchers in generalized probability theory. [ABSTRACT FROM AUTHOR]

This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semilinear parabolic equations with the initial point t = t ′ ≥ 0 . If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t ∈ ( 0 , τ ] , τ > 0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given. [ABSTRACT FROM AUTHOR]

In this paper we analyze the approximation of multivariate integrals over the Euclidean space for functions which are analytic. We show explicit upper bounds which attain the exponential rate of convergence. We use an infinite grid with different mesh sizes in each direction to sample the function, and then truncate it. In our analysis, the mesh sizes and the truncated domain are chosen by optimally balancing the truncation error and the discretization error. This paper derives results in comparable function space settings, extended to R s , as which were recently obtained in the unit cube by Dick, Larcher, Pillichshammer and Woźniakowski, see Dick et al. (2011). They showed that both lattice rules and regular grids, with different mesh sizes in each direction, attain exponential rates, hence motivating us to analyze only cubature formula based on regular meshes. We further also amend the analysis of older publications, e.g., Sloan and Osborn (1987) and Sugihara (1987), using lattice rules on R s by taking the truncation error into account and extending them to take the anisotropy of the function space into account. [ABSTRACT FROM AUTHOR]

Ahlswede and Khachatrian’s diametric theorem is a weighted version of their complete intersection theorem, which is itself a well known extension of the t -intersecting Erdős–Ko–Rado theorem. The complete intersection theorem says that the maximum size of a family of subsets of [ n ] = { 1 , … , n } , every pair of which intersects in at least t elements, is the size of certain trivially intersecting families proposed by Frankl. We address a cross intersecting version of their diametric theorem. Two families A and B of subsets of [ n ] are cross t -intersecting if for every A ∈ A and B ∈ B , A and B intersect in at least t elements. The p -weight of a k element subset A of [ n ] is p k ( 1 − p ) n − k , and the weight of a family A is the sum of the weights of its sets. The weight of a pair of families is the product of the weights of the families. The maximum p -weight of a t -intersecting family depends on the value of p . Ahlswede and Khachatrian showed that for p in the range [ r t + 2 r − 1 , r + 1 t + 2 r + 1 ] , the maximum p -weight of a t -intersecting family is that of the family F r t consisting of all subsets of [ n ] containing at least t + r elements of the set [ t + 2 r ] . In a previous paper we showed a cross t -intersecting version of this for large t in the case that r = 0 . In this paper, we do the same in the case that r = 1 . We show that for p in the range [ 1 t + 1 , 2 t + 3 ] the maximum p -weight of a cross t -intersecting pair of families, for t ≥ 200 , is achieved when both families are F 1 t . Further, we show that except at the endpoints of this range, this is, up to isomorphism, the only pair of t -intersecting families achieving this weight. [ABSTRACT FROM AUTHOR]

Pseudorandom binary sequences play a crucial role in cryptography. The classical approach to pseudorandomness of binary sequences is based on computational complexity. This approach has certain weak points thus in the last two decades a new, more constructive and quantitative approach has been developed. Since multidimensional analogs of binary sequences (called binary lattices) also have important applications thus it is a natural idea to extend this new approach to the multidimensional case. This extension started with a paper published in 2006, and since that about 25 papers have been written on this subject. Here our goal is to present a survey of all these papers. [ABSTRACT FROM AUTHOR]

This work is devoted to establish a general expression for calculating the bond incident degree (BID) indices of polyomino chains and to characterize the extremal polyomino chains with respect to several well known BID indices. From the derived results, all the results of the papers (An and Xiong, 2016, Deng et al., 2014, Yarahmadi et al., 2012) and some results of the papers (Rada, 2014, Ali et al., 2015) are obtained as corollaries. [ABSTRACT FROM AUTHOR]

The paper proposes a new approach for function approximation by ‘estimating’ the second derivative, using Taylor series, where the samples of the function and its first derivatives at the sample points are known. Without such ‘estimation’, these initial data, can approximate the function traditionally using the first order Taylor approximation, but with more error. If we desire to improve the approximation via second order Taylor series, then we can estimate the ‘pseudo’ second derivatives of the function in three different ways. All these three ways are investigated in this paper. The pseudo second derivatives help in computing many more sample points of the function within each sampling interval. Thus, the approach acts like a mathematical ‘magnifying glass’. Two examples are treated to compare the efficiencies of the methods. Also, a qualitative study for upper bound of error of the approximations is studied in detail. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the open problem of the global boundedness of the Lü system based on Lyapunov stability theory, which was proposed by Zhang and Mu (2012). The innovation of the paper is that this paper not only proves the Lü system is global bounded according to dynamical systems theory but also gives the bounds of the Lü system. [ABSTRACT FROM AUTHOR]

Let D = ( P , B ) be any nontrivial nonsymmetric 2-( v, k, λ ) design. In this paper we construct a connected, regular and bipartite graph, say IG v , b ( D ) , from D . Some graphic properties of IG v , b ( D ) are investigated. In particular, the results in the paper bridges the equivalency between edge-transitivity of IG v , b ( D ) and flag-transitivity of D . With the equivalency, it is obtained that IG v , b ( D ) is a semisymmetric graph as long as D is a nonsymmetric flag-transitive 2-( v, k, λ ) design. [ABSTRACT FROM AUTHOR]

This is a paper in a series systematically to study toroidal vertex algebras and their (twisted) modules. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that most of the extended affine Lie algebras can be associated to toroidal vertex algebras. [ABSTRACT FROM AUTHOR]