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We deduce new properties of the orbicyclic function of several variables investigated in a recent paper by V. A. Liskovets. We point out that the function and its connection to the number of solutions of certain linear congruences occur in the literature in a slightly different form. We investigate another similar function considered by Deitmar, Koyama and Kurokawa by studying analytic properties of some zeta functions of Igusa type. Simple number-theoretic proofs for some known properties are also given. [ABSTRACT FROM AUTHOR]

The article examines the impact of two humidification and flattening methods for albumen prints on the surface characteristics of the albumen. The two methods include a Gore-Tex® sandwich and the use of a humidity chamber. For humidification process, variables include the length of time and levels of relative humidity and the parameters measured include the changes in number and/or size of the cracks. It was found that a 10-minute exposure to the Gore-Tex® sandwich method resulted to a significant change to the cracks. Meanwhile, in humidity chamber, there is no change in cracks even after 24 hours. After evaluating several flattening methods after humidification, it was found that the "hard-soft sandwich" developed by Homburger and Korbel is the most effective.

We define a “period-ring-valued beta function” and give a reciprocity law on its special values. The proof is based on some results of Rohrlich and Coleman concerning Fermat curves. We also have the following application. Stark’s conjecture implies that the exponentials of the derivatives at s = 0 s=0 of partial zeta functions are algebraic numbers which satisfy a reciprocity law under certain conditions. It follows from Euler’s formulas and properties of cyclotomic units when the base field is the rational number field. In this paper, we provide an alternative proof of a weaker result by using the reciprocity law on the period-ring-valued beta function. In other words, the reciprocity law given in this paper is a refinement of the reciprocity law on cyclotomic units. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new function space B p , θ , a , ϰ , τ 〈 l 〉 ⁢ (s , G) {B_{p,\theta,a,\varkappa,\tau}^{\langle l\rangle}(s,G)} with parameters of many groups of variables of Besov–Morrey type. In view of the embedding theorems we study some properties of the functions which belong to these spaces. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that bilinear Calderón–Zygmund operators are bounded from products of variable Hardy spaces into variable Lebesgue or Hardy spaces. [ABSTRACT FROM AUTHOR]

Let r : X 2 → X 2 {r\colon X^{2}\rightarrow X^{2}} be a set-theoretic solution of the Yang–Baxter equation on a finite set X. It was proven by Gateva-Ivanova and Van den Bergh that if r is non-degenerate and involutive, then the algebra K ⁢ 〈 x ∈ X ∣ x ⁢ y = u ⁢ v ⁢ if ⁢ r ⁢ (x , y) = (u , v) 〉 {K\langle x\in X\mid xy=uv\text{ if }r(x,y)=(u,v)\rangle} shares many properties with commutative polynomial algebras in finitely many variables; in particular, this algebra is Noetherian, satisfies a polynomial identity and has Gelfand–Kirillov dimension a positive integer. Lebed and Vendramin recently extended this result to arbitrary non-degenerate bijective solutions. Such solutions are naturally associated to finite skew left braces. In this paper we will prove an analogue result for arbitrary solutions r B {r_{B}} that are associated to a left semi-brace B; such solutions can be degenerate or can even be idempotent. In order to do so, we first describe such semi-braces and then prove some decompositions results extending those of Catino, Colazzo and Stefanelli. [ABSTRACT FROM AUTHOR]

In this paper, the author investigates the complete convergence for weighted sums of asymptotically negatively associated (ANA) random variables with different distributions, and obtains some equivalent conditions of complete convergence theorem for weighted sums as well as summation of ANA cases. These results generalize and improve the corresponding ones obtained by Baum and Katz (1965), Peligrad and Gut (1999) and Cai (2006), respectively. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the paper 'Functions without short implicents. Part I: lower estimates of weights'. In Part II we propose various methods of construction of n-place Boolean functions not admitting implicents of k variables. The first of the methods proposed is based on the gradient algorithm, the second and the third ones depend on a certain combinatorial principle of construction, while the fourth method is based on a random choice of elements in the function support. The above methods have different efficiency depending on the value of k. We give upper estimates for the minimal value w ( n, k) of weights of the so-constructed functions. Together with the lower estimates of w ( n, k) from the first part of the paper this allows us to obtain an asymptotically sharp estimate w ( n, k) = Θ (ln n) as n → ∞. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new analytical hybrid methods for the solution of conformable fractional differential equations (CFDE), which are based on the recently proposed conformable fractional derivative (CFD) in R. Khalil, M. Al Horani, A. Yusuf and M. Sababhed, A New definition of fractional derivative, J. Comput. Appl. 264 (2014). Moreover, we use the method of variation of parameters and reduction of order based on CFD, for the CFDE. Furthermore, to show the efficiency of the proposed analytical hybrid method, some examples are also presented. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the relation between the two classes of functions BV * ⁢ (q ; α) {\mathrm{BV}_{*}(q;\alpha)} and Λ * ⁢ BV p {\Lambda_{*}\mathrm{BV}^{p}}. It uses a new shorter proof and extends the results of Gogatishvili, Goginava and Tephnadze. [ABSTRACT FROM AUTHOR]

Srivastava and Panda have studied the simple and multiple generating relations concerning the multivariable H-function. The aim of this paper is to derive the various classes of simple and multiple generating relations involving the multivariable Aleph-function. The generating function is used in the theory of numbers, in physics and other fields of mathematics. We see the particular cases concerning the multivariable I-function, the Aleph-function of two variables and the I-function of two variables. [ABSTRACT FROM AUTHOR]

Let A be an abelian variety. The abelian Ax–Lindemann theorem shows that the Zariski closure of an algebraic flow in A is a translate of an abelian subvariety of A. The paper discusses some conjectures on the usual topological closure of an algebraic flow in A. The main result is a proof of these conjectures when the algebraic flow is given by an algebraic curve. [ABSTRACT FROM AUTHOR]

In this paper, a variable-coefficient and nonisospectral Ablowitz–Kaup–Newell–Segur (vcniAKNS) hierarchy with Lax integrability is constructed by embedding a finite number of differentiable and time-dependent functions into the well-known AKNS spectral problem and its time evolution equation. In the framework of inverse scattering transform method with time-varying spectral parameter, the constructed vcniAKNS hierarchy is solved exactly. As a result, exact solutions and their reduced n-soliton solutions of the vcniAKNS hierarchy are obtained. It is graphically shown that the parity of an embedded time-dependent function has connection with the symmetrical characteristics of the spatial structures and singular points of the obtained one-soliton solutions. [ABSTRACT FROM AUTHOR]

The paper is concerned with estimating the computational complexity of the branch-and-bound method for the subset sum problem. We study the relationship between the way of decomposition of subproblems and the number of the method steps. The standard variant of the branch-and-bound method for the subset sum problem with binary branching is considered: any subproblem is decomposed into two more simple subproblems by assigning values 0 and 1 to a selected branching variable. It is shown that for any set of parameters of the problem the procedure of branching variables selection in the descending order of their weights is optimal. [ABSTRACT FROM AUTHOR]

The theory of multivariate neural network operators in a Kantorovich type version is here introduced and studied. The main results concerns the approximation of multivariate data, with respect to the uniform and Lp norms, for continuous and Lp functions, respectively. The above family of operators, are based upon kernels generated by sigmoidal functions. Multivariate approximation by constructive neural network algorithms are useful for applications to neurocomputing processes involving high dimensional data. At the end of the paper, several examples of sigmoidal functions for which the above theory holds have been presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the fibers of "automorphic word maps", a certain generalization of word maps, on finite groups and on nonabelian finite simple groups in particular. As an application, we derive a structural restriction on finite groups G where, for some fixed nonempty reduced word w in d variables and some fixed ρ ∊ .0; 1], the word map wG on G has a fiber of size at least ρǀGǀd : No sufficiently large alternating group and no (classical) simple group of Lie type of sufficiently high rank can occur as a composition factor of such a group G. [ABSTRACT FROM AUTHOR]

Vieta's classical formulae explicitly determine the coefficients of a polynomial p ∈ 𝔽[x] in terms of the roots of p, where 𝔽 is any commutative ring. In this paper, Vieta's formulae are obtained for slice-regular polynomials over the noncommutative algebra of quaternions, by an argument which essentially relies on induction, without invoking quasideterminants or noncommutative symmetric functions. [ABSTRACT FROM AUTHOR]

The paper puts forward a nontrivial lower estimate 2 1/6 n for the carinality of the domain of a universal function for the class of linear Boolean functions, where n is the number of variables. [ABSTRACT FROM AUTHOR]

In this paper we discuss generalized two-variable Chebyshev polynomials and their relevant relations; in particular, by using their integral representations, we prove some operational identities. The approach is based on the generalized two-variable Hermite polynomials and the integral representations of ordinary Chebyshev polynomials of first and second kind. In addition, we discuss how the families of generalized Chebyshev polynomials can be used to prove some interesting properties related to ordinary Chebyshev polynomials of first and second kind. A fundamental role, as we see, is played by the powerful operational techniques verified by the families of generalized Hermite polynomials. [ABSTRACT FROM AUTHOR]

The following notion of bounded index for complex entire functions was presented by Lepson. function f(z) is of bounded index if there exists an integer N independent of z, such that . . . {. . .} ≥ . . . for all n: The main goal of this paper is extend this notion to holomorphic bivariate function. To that end, we obtain the following definition. A holomorphic bivariate function is of bounded index, if there exist two integers M and N such that M and N are the least integers such that . . . {. . .} ≥ . . . for all m and n: Using this notion we present necessary and sufficient conditions that ensure that a holomorphic bivariate function is of bounded index. [ABSTRACT FROM AUTHOR]

In 1994, Brüdern and Fouvry [1] initiated the investigation of Lagrange's four squares theorem with almost prime variables. In this paper, we prove that every suffi- ciently large integer, congruent to 4 modulo 24, can be represented as a sum of four squares of integers, each of which has at most four prime factors. Instead of the four-dimensional vector sieve developed by Brüdern and Fouvry [1], we establish this result by combining the threedimensional sieve and the switching principle. [ABSTRACT FROM AUTHOR]

The paper is concerned with relations between the correlation-immunity (stability) and the perfectly balancedness of Boolean functions. It is shown that an arbitrary perfectly balanced Boolean function fails to satisfy a certain property that is weaker than the 1-stability. This result refutes some assertions by Markus Dichtl. On the other hand, we present new results on barriers of perfectly balanced Boolean functions which show that any perfectly balanced function such that the sum of the lengths of barriers is smaller than the length of variables, is 1-stable. [ABSTRACT FROM AUTHOR]

In this paper two simplification techniques are used in order to represent geographical distribution patterns of standard Japanese. The first technique is a representation of two-dimensional geographical distribution patterns in one dimension. The second is the plotting of geographical locations making use of railway distances from cultural centres. By simplifying the two-dimensional geographical distribution into one by railway distance, another dimension on a sheet of paper can show one other characteristic of standard Japanese forms. In order to see the patterns of distribution of Japanese standard forms, numerical data based on the Linguistic Atlas of Japan are utilized. Gravity centres of railway distance are calculated for each standard Japanese form, and correspondence with the degree of nationwide usage and the year of first attestation in historical documents is considered. Two-dimensional graphs (scattergrams) of the three factors are considered. [ABSTRACT FROM AUTHOR]

Crack growths processes of various types are widely covered by power laws. Especially, both creep deformation of creep-resistant bulk materials and creep crack growth in such materials can be covered by power laws and possess close exponents in many cases. This paper focuses on the microscopic thermodynamic mechanisms of the correspondence and the power law itself. In this paper, it is shown that the power laws can be considered as certain homogenous kinetic rate laws of local or microscopic internal variables within the thermodynamic framework of Rice and correspond to a certain macroscopic requirement of maximum dissipation. It is revealed that nonlinear phenomenological equations and Onsager reciprocal relations emerge naturally from the framework if each rate is a monotonic increasing and homogeneous function of the same degree in its conjugate force. The homogeneity property transfers exactly from local internal variables to global internal variables. On the basis of the remarkable properties, it is shown that the power laws of crack growth directly lead to the re?ned Gri?th criterion by Rice, and both exponents of creep deformation and creep crack growth can be related by a simple linear relation. [ABSTRACT FROM AUTHOR]

The paper is concerned with the problem of synthesis of two-pole contact circuits implementing n-place Boolean functions and admitting short fault detection and diagnostic tests with respect to closures of contacts. It is shown that almost all n-place Boolean functions are implemented by irredundant two-pole contact circuits admitting single fault detection, complete fault detection and single diagnostic tests of constant length. We also prove that: 1) any Boolean function f( x1,..., xn) may be implemented by an irredundant two-pole contact circuit containing at most one input variable distinct from the variables x1,..., xn and admitting single and complete fault detection tests of length at most 2 n; 2) any Boolean function f( x1,..., xn) may be implemented by an irredundant two-pole contact circuit containing at most two input variables distinct from the variables x1,..., xn and admitting single diagnostic test of length at most 4 n. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of removable isolated singularities for elliptic equations with variable exponents. We give a sufficient condition for removability of the isolated singular point for the equations in . [ABSTRACT FROM AUTHOR]

How to construct a variable coefficient integrable coupling equation hierarchy is an important problem. In this paper, we present new Lax pairs with some arbitrary functions and generate a variable coefficient integrable coupling of Ablowitz-Kaup-Newell-Segur hierarchy from a zero-curvature equation. Then the Hamiltonian structure of the variable coefficient coupling equation hierarchy is derived from the variational trace identity. It is also indicated that this method is an efficient and straightforward way to construct the variable coefficient integrable coupling equation hierarchy. [ABSTRACT FROM AUTHOR]

The paper is concerned with n-place Boolean functions not admitting implicents of k variables, 1 ¢ k < n. Estimates for the minimal possible weight w(n, k) of such functions are obtained. It is shown that w(n, 1) = 2, n = 2, 3,…, and w(n, 2) È log2n as n Ù ∞, and moreover, for k > 2 there exists n0 such that w(n, k) > 2k-2 - log2n for all n > n0. [ABSTRACT FROM AUTHOR]

The paper is concerned with checking problems for failure and state diagnostics of N gates implementing in a working condition a given Boolean function f(x1, . . . , xn). This problem is solved by composing single-output circuits from these gates and analyzing the output values of these circuits on all input tuples of variables. An arbitrary constant malfunction at the output of any single gate is allowed. It is required to minimize the number of circuits required for a check for failure and determination of all states of all gates. Exact values for the minimal possible number of such circuits are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we estimate the order of magnitude of the double Fourier coefficients of a function of the class (⋀1, ⋀2) BV(p(n) ↑ ∞, φ) over [0, 2π]2. [ABSTRACT FROM AUTHOR]

Let L1,L2 be a pair of one-to-one commuting sectorial operators such that each Li for i∈{1,2} satisfies the mi order L² off-diagonal estimates and m1 ≥ m2 > 0. Let HLiP(Rn), i∈{1,2}, and HL1+L2P(Rn) be the Hardy spaces associated, respectively, to the operators Li and L1+L2, where L2:=L2m1/m2 is a fractional power of L2. In this paper, the authors give out some real-variable properties of these Hardy spaces. More precisely, the authors first establish the bounded joint H∞ functional calculus in these Hardy spaces and prove that the abstract Riesz transform Dmi(L1+L2)−1/2 is bounded from HLiP(Rn) to the classical Hardy space Hp(Rn) for all p∈(n/n+mi,1], where i∈{1,2}. Moreover, for all p∈(0,1], the authors show that HL1+L2P (Rn) = HL1P (Rn) + HL2P (Rn) and give a sufficient condition to guarantee HL1P (Rn) ⊂ HL2P (Rn). [ABSTRACT FROM AUTHOR]

This paper is devoted to studying initial value problems for semilinear wave equations with variable coefficients with subcritical exponents for n ( n ≥ 1) space dimensions. We prove that solutions to a certain kind of subcritical wave equations cannot be global if the initial values are positive somewhere and nonnegative no matter how small the initial data are, and also we give the sharp lifespan estimate of solutions for the problems. This solves a part of the famous Strauss' conjecture about semilinear wave equations in the case of subcritical exponents and variable coefficients Cauchy problems. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the problem of recovering smooth functions from their Fourier coefficients. We consider the functions of two variables. Herewith this problem is ill-posed. The problem is studied in the case of given smoothness of the functions as well as when a parameter of smoothness is supposed to be unknown. [ABSTRACT FROM AUTHOR]

In this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable cross-sectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation awell-balanced solver is developed, assuring the C-property and depth positivity. The performance of this method is studied in several test cases focusing on accurate capturing of steady states. [ABSTRACT FROM AUTHOR]

The paper is concerned with the process of fluctuation of the player rating in the Elo model in an infinite series of games with the same adversary. Under some assumptions on the model parameters, this process is shown to have a stationary distribution; its median is found for players of the same skill. [ABSTRACT FROM AUTHOR]

The paper is concerned with the numbers of non-occurring values in intervals of a stationary sequence of m-dependent random variables with N outcomes. These numbers are shown to be asymptotically joint normally distributed, provided that the number N and the lengths of intervals tend to infinity with the same asymptotic order of growth. [ABSTRACT FROM AUTHOR]

In this paper we present an Lp-theory for a class of stochastic partial differential equations (SPDEs in abbreviation) driven by Lévy processes. The SPDEs under consideration can have random coefficients that depend both on the time and space variable. Existence and uniqueness of solutions in various Sobolev spaces are obtained. These Sobolev spaces describe the regularity of the solutions of the SPDEs. [ABSTRACT FROM AUTHOR]

We consider in this paper mixed relaxed-singular stochastic control problems, where the control variable has two components, the first being measure-valued and the second singular. The control domain is not necessarily convex and the system is governed by a nonlinear stochastic differential equation, in which the measure-valued part of the control enters both the drift and the diffusion coefficients. We establish necessary optimality conditions of the Pontryagin maximum principle type satisfied by an optimal relaxed-singular control, which exist under general conditions on the coefficients. The proof is based on the strict singular stochastic maximum principle established by Bahlali-Mezerdi, Ekeland's variational principle and some stability properties of the trajectories and adjoint processes with respect to the control variable. [ABSTRACT FROM AUTHOR]

This paper continues the study of quasigroups isotopic to groups and to Abelian groups. For identities with permutations of a certain kind the notion of the type is introduced; identities with permutations of various types are presented, which characterize quasigroups isotopic to Abelian groups. The approach being used had allowed to establish a number of new unbalanced identities involving four variables in an equasigroup, as well as a number of identities involving three variables in an equasigroup with one nullary operation, each of which characterises a quasigroup isotopic to a group or to an Abelian group. [ABSTRACT FROM AUTHOR]

In this paper we consider a nonlinear problem of simultaneous search of functions , of functional equations with variable parameter p. We formulate and prove existence of formulas for functions , which belong to special classes. [ABSTRACT FROM AUTHOR]

In this paper we study the inverse problem of determining three unknown source terms in the linearized Lotka-Volterra competition-diffusion system of three species with variable coefficients from measured output data in the form of Dirichlet and the final time overdetermination boundary conditions. We use Hasanov's approach based on quasi-solution method and adjoint problem solution for inverse source problems. Further we provide the Fréchet gradient of the cost functional through the solution of the adjoint problem and several necessary and sufficient results to prove the existence of a quasi-solution and also unicity of the considered inverse problem. [ABSTRACT FROM AUTHOR]

The effect of non-axial breaking of relativistic and nonrelativistic cylindrical axially-symmetric nonlinear plasma oscillations was earlier identified and then numerically and analytically studied by the authors within a one-dimensional hydrodynamic model. In this paper, an explicit method of the second order of accuracy (on smooth solutions) is proposed and implemented in Euler variables for the two-dimensional simulation of the indicated effect. The results of calculations admitting comparison with the one-dimensional model are presented. [ABSTRACT FROM AUTHOR]

In this paper we suggest a combined method for solving systems of Boolean polynomial equations based on testing a part of variables and using monomial compatibility criteria for dropping out some values of the tested variables. The complexity of the method is estimated for various parameters of the system. [ABSTRACT FROM AUTHOR]

A power system analyst wants to be absolutely sure, whether the divergence of power flow method is really due to infeasible operation, or failure of the numerical method, while performing power flow studies. Because of the special structure and characteristics of a distribution system, Newton based methods are not very well suited. Forward/backward sweep methods are well suited for these systems, which exploit the structural advantage of distribution systems. An efficient power flow is required for the analysis of ill-conditioned or highly stressed systems, which are more common in unbalanced systems. In this paper, a robust non-divergent power flow is developed for distribution system using optimal multiplier. It is based on Newton-like power flow derived from conventional forward backward sweep distribution power flow. Two versions of the power flow methods (i) normal variable matrix and (ii) constant matrix have been investigated. Results for three sample systems, with different loading conditions, demonstrate the potential of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Let ( T, C, X) be a vector of random variables (rvs) where T, C and X are the interest variable, a right censoring rv and a covariate, respectively. In this paper, we study the kernel conditional quantile estimation in the dependent case and when the covariable takes values in an infinite-dimension space. An estimator of the conditional quantile is given and, under some regularity conditions, among which the small-ball probability for the covariate, its uniform strong convergence with rates is established. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate and present the general properties of the (exponential) bipartitional polynomials. After establishing relations between bipartitional polynomials and polynomial sequences of binomial and trinomial type, a number of identities are deduced. [ABSTRACT FROM AUTHOR]

Simson's identity is a well-known Fibonacci identity in which the difference of certain order 2 products has a particularly pleasing form. Other old and beautiful identities of a similar nature are attributed to Catalan, Gelin and Cesààro, and Tagiuri. Catalan's identity can be described as a family of product difference Fibonacci identities of order 2 with 1 parameter. In Section 2 of this paper we present four families of product difference Fibonacci identities that involve higher order products. Being self-dual, each of these families may be regarded as a higher order analogue of Catalan's identity. We also state two conjectures that give the form of similar families of arbitrary order. In the final section we give other interesting product difference Fibonacci identities. [ABSTRACT FROM AUTHOR]

The bent functions are the Boolean functions of an even number of variables which are at the maximum possible distance from the set of all affine functions. In this paper, it is shown that each isometric mapping of the set of Boolean functions of n variables to itself preserving the class of bent functions is a combination of an affine transformation of coordinates and a shift by an affine function. It is proved that the affine functions are precisely all Boolean functions which are at the maximum possible distance from the class of bent functions. [ABSTRACT FROM AUTHOR]

This paper is devoted to regularization in the process of derivative's approximation of integrated semigroups in time variables. We consider the direct method and also the method based on A. N. Tikchonov's approach. It is shown that discrete derivative converges in strong sense and the order of convergence in general Banach space is obtained. The presentation is given in the abstract framework of discrete approximation scheme, which includes finite element methods, finite difference schemes and projection methods. [ABSTRACT FROM AUTHOR]

Let X and Y be separable Banach spaces and E be a subset of X. By a random operator from X into Y we mean a rule Φ that assigns to each element x ∈ X a unique Y - valued random variable Φ x. Taking into account many circumstances in which the inputs are also subject to the influence of a random environment there arises the need to define the action of Φ on some random inputs. In this paper, some procedures for extending random mappings will be proposed. Some conditions under which a random mapping can be extended to apply to all X-valued random variables will be presented. [ABSTRACT FROM AUTHOR]