-Difference sequence spaces of fuzzy numbers

In this paper, using the difference operator of order m and an Orlicz function, we introduce and examine some classes of sequences of fuzzy numbers. We give the relations between the strongly Cesàro type convergence and statistical convergence in these spaces. Furthermore, we study some of their properties like completeness, solidity, symmetricity, etc. We also give some inclusion relations related to these classes.     

Error-correcting codes from permutation groups

We replace the usual setting for error-correcting codes (i.e. vector spaces over finite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncovering-by-bases, related to covering designs, and construct some examples of these. We also analyse the complexity of the algorithm.We then formulate a conjecture about uncoverings-by-bases, for which we give some supporting evidence and prove for some special cases. In particular, we consider the case of the symmetric group in its action on 2-subsets, where we make use of the theory of graph decompositions. Finally, we discuss the implications this conjecture has for the complexity of the decoding algorithm.     

Defective intertwining property and generator domain

We discuss the defective intertwining property of generators of semigroups. We give some equivalent conditions in terms of generator, resolvent and semigroup. As an application, using this property, we give an example in which we can determine the exact generator domain of a Schrödinger operator.     

Critical point approaches to Gradient-Type systems on the Sierpi\'{n}ski Gasket

We investigate the existence of multiple solutions for parametric quasi-linear systems of the gradient-type on the Sierpi\''{n}ski gasket. We give some new criteria to guarantee that the systems have at least three weak solutions by using a variational method and some critical points theorems due to Ricceri. We extend and improve some recent results. Finally, we give two examples to illustrate the main results.     

Local Expansions of Periodic Spline Interpolation with Some Applications

In this paper we prove some asymptotic expansions of the error of interpolation on equally spaced nodes with periodic smoothest splines of arbitrary degree on a uniform partition. We obtain a local expansion in terms of derivatives of the interpolate. Afterwards we apply this result to the asymptotic study of the numerical solution of periodic integral equations of the second kind by means of ϵ – collocation methods. We show some new superconvergence results and give particular forms of these expansions depending on the choices of the parameter ϵ. We finally give some numerical experiments, which corroborate the theory.     

Equidistribution for meromorphic transforms and the dd<Superscript>c</Superscript>-method

In this paper we give an introduction to the notion of meromorphic transform. We describe some equidistribution problems and their solution, using the dd^c-method. In particular, we give some statistical properties of the equilibrium measure for meromorphic maps on compact Kähler manifolds: K-mixing, exponential decay of correlations and central limit theorem.     

Distribution of Points and Hardy Type Inequalities in Spaces of Homogeneous Type

In the setting of spaces of homogeneous type, we study some Hardy type inequalities, which notably appeared in the proofs of local T(b) theorems. We give some sufficient conditions ensuring their validity, related to the geometry and distribution of points in the homogeneous space. We study the relationships between these conditions and give some examples and counterexamples in the complex plane.     

Approximation Properties For Modified q-Bernstein-Kantorovich Operators

The purpose of this article is to give a generalization of q-Bernstein-Kantorovich operators. We present some approximation theorems. We compute the rate of convergence and error estimation of these operators by means of the modulus of continuity. Furthermore, we give some numerical examples to show comparisons in illustrative graphics for the convergence of these operators to various functions.     

Finiteness theorems for the Picard objects of an algebraic stack

We prove some finiteness theorems for the Picard functor of an algebraic stack, in the spirit of SGA 6, exp. XII and XIII. In particular, we give a stacky version of Raynaud?s relative representability theorem, we give sufficient conditions for the existence of the torsion component of the Picard functor, and for the finite generation of the Néron–Severi groups or of the Picard group itself. We give some examples and applications. In Appendix A, we prove the semicontinuity theorem for a (non-necessarily tame) algebraic stack.     

Paley type group schemes and planar Dembowski–Ostrom polynomials

In this paper we give some necessary and sufficient conditions for Dembowski–Ostrom polynomials to be planar. These conditions give a simple explanation of the Coulter–Matthews and Ding–Yin commutative semifields and enable us to obtain permutation polynomials from some of the Zha–Kyureghyan–Wang commutative semifields. We then give a generalization of Feng’s construction of Paley type group schemes in extra-special p-groups of exponent p and construct a family of Paley type group schemes in what we call the flag groups of finite fields. We also determine the strong multiplier groups of these group schemes. In the last section of this paper, we give a straightforward generalization of the twin prime power construction of difference sets to a construction of Hadamard designs from twin Paley type association schemes.     

Characterization of the D w -Laguerre-Hahn Functionals

We give some characterization theorems for the D w -Laguerre-Hahn linear functionals and we extend the concept of the class of the usual Laguerre-Hahn functionals to the D w -Laguerre-Hahn functionals, recovering the classic results when w tends to zero. Moreover, we show that some transformations carried out on the D w -Laguerre-Hahn linear functionals lead to new D w -Laguerre-Hahn linear functionals. Finally, we analyze the class of the resulting functionals and we give some applications relative to the first associated Charlier, Meixner, Krawtchouk and Hahn orthogonal polynomials.     

The Mann–Whitney <Emphasis Type="Italic">U</Emphasis>-statistic for α-dependent sequences

We give the asymptotic behavior of the Mann–Whitney U-statistic for two independent stationary sequences. The result applies to a large class of short-range dependent sequences, including many nonmixing processes in the sense of Rosenblatt [17]. We also give some partial results in the long-range dependent case, and we investigate other related questions. Based on the theoretical results, we propose some simple corrections of the usual tests for stochastic domination; next we simulate different (nonmixing) stationary processes to see that the corrected tests perform well.     

Equidistribution for meromorphic transforms and the ddc-method

In this paper we give an introduction to the notion of meromorphic transform. We describe some equidistribution problems and their solution, using the dd^c-method. In particular, we give some statistical properties of the equilibrium measure for meromorphic maps on compact Kähler manifolds: K-mixing, exponential decay of correlations and central limit theorem.

     

Lattices Derived from Hyperlattices

In this article, by considering the notion of a hyperlattice and a superlattice, we give some examples of them, and we study their structures and their quotient structure with a regular relation. We introduce the relation ν on a hyperlattice L, and we let ν* be the transitive closure of ν. We show that ν* is a fundamental relation on a hyperlattice. The quotient L/ν* is called the fundamental lattice. Notice that the most important relations in hyperstructure theory are the fundamental ones. Finally, we give some interesting results about the fundamental lattices.     

α-型及其应用

本文以α型为基本工具研究代数问题，给出了Abian结果的一个进一步的结果，并给出了域上的无限线性方程组有解的一点判定准则。     

Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

We analyse collocation methods for nonlinear homogeneous Volterra—Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and give conditions for such existence and uniqueness in some cases. Finally, we illustrate these methods with an example of a collocation problem and give some examples of collocation problems that do not fit in the cases studied previously.     

Hardy–Sobolev inequalities in half-space and some semilinear elliptic equations with singular coefficients

We study some semilinear elliptic equations with singular coefficients which relate to some Hardy–Sobolev inequalities. We obtain some existence results for these equations and give a theorem for prescribing the Palais–Smale sequence for these equations. Moreover, we find some interesting connections between these equations and some semilinear elliptic equations in hyperbolic space. Using these connections, we obtain many new results for these equations.     

Matrix-valued continued fractions

We discuss the properties of matrix-valued continued fractions based on Samelson inverse. We begin to establish a recurrence relation for the approximants of matrix-valued continued fractions. Using this recurrence relation, we obtain a formula for the difference between mth and nth approximants of matrix-valued continued fractions. Based on this formula, we give some necessary and sufficient conditions for the convergence of matrix-valued continued fractions, and at the same time, we give the estimate of the rate of convergence. This paper shows that some famous results in the scalar case can be generalized to the matrix case, even some of them are exact generalizations of the scalar results.     

Compactification of Drinfeld modular varieties and Drinfeld modular forms of arbitrary rank

We give an abstract characterization of the Satake compactification of a general Drinfeld modular variety. We prove that it exists and is unique up to unique isomorphism, though we do not give an explicit stratification by Drinfeld modular varieties of smaller rank which is also expected. We construct a natural ample invertible sheaf on it, such that the global sections of its k-th power form the space of (algebraic) Drinfeld modular forms of weight k. We show how the Satake compactification and modular forms behave under all natural morphisms between Drinfeld modular varieties; in particular we define Hecke operators. We give explicit results in some special cases.     

A mathematical programming problem with singular mixed pointwise-integral constraints

We investigate an infinite dimensional optimization problem which constraints are singular integral-pointwise ones. We give some partial results of existence for a solution in some particular cases. However, the lack of compactness, even in L¹ prevents to conclude in the general case. We give an existence result for a weak solution (as a measure) that we are able to describe. The regularity of such a solution is still an open problem.