Browse Our Mathematics and Statistics Journals
Mathematics and statistics journals publish papers on the theory and application of mathematics, statistics, and probability. Most mathematics journals have a broad scope that encompasses most mathematical fields. These commonly include logic and foundations, algebra and number theory, analysis (including differential equations, functional analysis and operator theory), geometry, topology, combinatorics, probability and statistics, numerical analysis and computation theory, mathematical physics, etc.
Mathematics and Statistics
We study point processes associated with coupon collector’s problem, that are defined as follows. We draw with replacement from the set of the first n positive integers until all elements are sampled, assuming that all elements have equal probability of being drawn. The point process we are interested in is determined by ordinal numbers of drawing elements that didn’t appear before. The set of real numbers is considered as the state space. We prove that the point process obtained after a suitable linear transformation of the state space converges weakly to the limiting Poisson random measure whose mean measure is determined.
We also consider rates of convergence in certain limit theorems for the problem of collecting pairs.
The class CR of completely regular semigroups considered as algebras with binary multiplication and unary operation of inversion forms a variety. Kernel, trace, local and core relations, denoted by K, T, L and C, respectively, are quite useful in studying the structure of the lattice L(CR) of subvarieties of CR. They are equivalence relations whose classes are intervals. Their ends are used for defining operators on L(CR).
Starting with a few band varieties, we repeatedly apply operators induced by upper ends of classes of these relations and characterize corresponding classes up to certain variety low in the lattice L(CR). We consider only varieties whose origin are “central” band varieties, that is those in the middle column of the lattice L(B) of band varieties. Several diagrams represent the (semi)lattices studied.
We prove that if I k are disjoint blocks of positive integers and n k are independent random variables on some probability space (Ω,F,P) such that n k is uniformly distributed on I k , then has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0, 1),B, λ), where B is the Borel σ-algebra and λ is the Lebesgue measure. We also investigate the case when n k have continuous uniform distribution on disjoint intervals I k on the positive axis.
Let G be a finite simple connected domain in the complex plane C, bounded by a Carleson curve Γ := ∂G. In this work the direct and inverse theorems of approximation theory by the algebraic polynomials in the weighted generalized grand Smirnov classes ε p),θ(G,ω) and , 1 < p < ∞, in the term of the rth, r = 1, 2,..., mean modulus of smoothness are proved. As a corollary the constructive characterizations of the weighted generalized grand Lipschitz classes are obtained.
In this article, we give some reviews concerning negative probabilities model and quasi-infinitely divisible at the beginning. We next extend Feller’s characterization of discrete infinitely divisible distributions to signed discrete infinitely divisible distributions, which are discrete pseudo compound Poisson (DPCP) distributions with connections to the Lévy-Wiener theorem. This is a special case of an open problem which is proposed by Sato (2014), Chaumont and Yor (2012). An analogous result involving characteristic functions is shown for signed integer-valued infinitely divisible distributions. We show that many distributions are DPCP by the non-zero p.g.f. property, such as the mixed Poisson distribution and fractional Poisson process. DPCP has some bizarre properties, and one is that the parameter λ in the DPCP class cannot be arbitrarily small.
Let R be a ring. The purpose of this paper is to study the existence and the representation for the anti-triangular matrix under some conditions, where a, b, c ∈ R. The results extend recent works given in the literature.
In this paper, we introduce a new concept of q-bounded radius rotation and define the class R* m (q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S* q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.
In this paper, we prove the existence of infinitely many solutions for the following class of boundary value elliptic problems where Ω is a bounded domain in R N (N ≥ 2), Δλ is a strongly degenerate elliptic operator, V (x) is allowing to be sign-changing and f is a function with a more general super-quadratic growth, which is weaker than the Ambrosetti-Rabinowitz type condition.
The purpose of this work is to present a new geometric approach to some problems in differential subordination theory. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.
A space X is star-C-Hurewicz if for each sequence (U n : n ∈ N) of open covers of X there exists a sequence (K n : n ∈ N) of countably compact subsets of X such that for each x ∈ X, x ∈ St(K n , Un n ) for all but finitely many n. In this paper, we investigate the relationship between star-C-Hurewicz spaces and related spaces, and study topological properties of star-C-Hurewicz spaces.
We give estimates for the number of quadratic residue and primitive root values of polynomials in two variables over finite fields.
A space X is weakly linearly Lindelöf if for any family U of non-empty open subsets of X of regular uncountable cardinality κ, there exists a point x ∈ X such that every neighborhood of x meets κ-many elements of U. We also introduce the concept of almost discretely Lindelöf spaces as the ones in which every discrete subspace can be covered by a Lindelöf subspace. We prove that, in addition to linearly Lindelöf spaces, both weakly Lindelöf spaces and almost discretely Lindelöf spaces are weakly linearly Lindelöf.
The main result of the paper is formulated in the title. It implies that every weakly Lindelöf monotonically normal space is Lindelöf, a result obtained earlier in [3].
We show that, under the hypothesis 2ω < ω ω, if the co-diagonal Δ c X = (X × X) \Δ X is discretely Lindelöf, then X is Lindelöf and has a weaker second countable topology; here Δ X = {(x, x): x ∈ X} is the diagonal of the space X. Moreover, discrete Lindelöfness of Δ c X together with the Lindelöf Σ-property of X imply that X has a countable network.
This paper is concerned with the existence of solutions to a class of p(x)-Kirchhofftype equations with Robin boundary data as follows: in Ω, on ∂Ω, where β ∈ L ∞ (∂Ω) and f : Ω × → satisfies the Carathéodory condition. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions.
We classify the extreme 2-homogeneous polynomials on 2 with the hexagonal norm of weight ½. As applications, using its extreme points with the Krein-Milman Theorem, we explicitly compute the polarization and unconditional constants of .
In this article, we define general normal forms for any logic that has propositional part and whose non-propositional connectives distribute over finite disjunctions. We do not require the non-propositional connectives to be closed on the set of formulas, so our normal forms cover logics with partial connectives too. We also show that most of the known normal forms in the literature are in fact particular cases of our general forms. These general normal forms are natural improvement of the distributive normal forms of J. Hintikka [6] and their modal analogues, e.g. [1] and [4].
We compute the second differential osp(n|2)-relative cohomology of the Lie superalgebra К(n) of contact vector fields with coefficients in the superspace of weighted densities on the (1, n)-dimensional real superspace, n > 1, where osp(n|2) is the orthosymplectic Lie superalgebra. We explicitly give 2-cocycles spanning theses cohomology spaces. This work is the simplest generalization of a result by Basdouri [ On osp(1|2)-Relative Cohomology on S 1|1. Communications in Algebra 42:4, 1698–1710 (2014)].
This paper deals with a class of algebraic hyperstructures called ternary semihypergroups. In this paper, we introduce the notion of generalized quasi (bi)-hyperideals in ternary semihypergroups and study their structure. Some related properties of them are investigated. Several characterizations of ternary semihypergroups in terms of minimal generalized quasi(bi)-hyperideals are provided. Also, the n-left simple, m-right simple, (p, q)-lateral simple and (m, (p, q), n)-quasi-simple ternary semihypergroups are defined and investigated.
We present the algorithms for computing the normal form of unimodular complete intersection surface singularities classified by C. T. C. Wall. He indicated in the list only the μ-constant strata and not the complete classification in each case. We give a complete list of surface unimodular singularities. We also give the description of a classifier which is implemented in the computer algebra system Singular.
The aim of this paper is to obtain some new bounds having Riemann type quantum integrals within the class of strongly convex functions. The results obtained are sharp on limit q → 1. These new results reduce to Tariboon-Ntouyas, Merentes-Nikodem and other previously known results when q → 1, where 0 < q < 1. The sharpness of the results of Tariboon-Ntouyas and Merentes-Nikodem is proved as a consequence.
We prove that the local time process of a planar simple random walk, when time is scaled logarithmically, converges to a non-degenerate pure jump process. The convergence takes place in the Skorokhod space with respect to the M1 topology and fails to hold in the J1 topology.
Consider a two-dimensional discrete random variable (X, Y) with possible values 1, 2, . . . , I for X and 1, 2, . . . , J for Y. For specifying the distribution of (X, Y), suppose both conditional distributions of X given Y and Y given X are specified. In this paper, we address the problem of determining whether a given set of constraints involving marginal and conditional probabilities and expectations of functions are compatible or most nearly compatible. To this end, we incorporate all those information with the Kullback-Leibler (K-L) divergence and power divergence statistics to obtain the most nearly compatible probability distribution when the two conditionals are not compatible, under the discrete set up. Finally, a comparative study is carried out between the K-L divergence and power divergence statistics for some illustrative examples.
The Rayleigh distribution is an important model in applications such as noise theory, height of the sea waves and wave length. In this paper, we first study the reliability characteristics of Morgenstern type bivariate Rayleigh distribution (MTBRD). Then, we investigate some properties on concomitants of order statistics and record values in MTBRD. Finally, we propose the best linear unbiased estimator for a parameter of MTBRD using both complete and censored samples based on concomitants of order statistics.
In this paper, we get integral representations for the quintic Airy functions as the four linearly independent solutions of differential equation y (4) + xy = 0. Also, new integral representations for the products of these functions are obtained in terms of the Bessel functions and the Riesz fractional derivatives of these products are given.
The appropriate estimation of incurred but not reported (IBNR) reserves is traditionally one of the most important task for property and casualty actuaries. As certain claims are reported considerably later after their occurrence, the amount and appropriateness of the reserves have a substantial effect on the financial results of institutions. In recent years, stochastic reserving methods have become increasingly widespread, supported by broad actuarial literature, describing development models and evaluation techniques.
The cardinal aim of the present paper is to compare the appropriateness of several stochastic estimation methods, supposing different distributional underlying development models. For lack of analytical formulae in most of the model settings relevant from a practical perspective, due to the complex behavior of summed variables, simulations are performed to approximate distributions and results. Considering that the number of runoff triangles is generally limited, stochastically simulated scenarios contribute to feasible solutions. Stochastic reserving is taken into account as a stochastic forecast, thus comparison techniques developed for stochastic forecasts can be applied, opening up new informative perspectives beyond classical prediction measures, such as the mean square error of prediction.
Based on an original idea, i.e., a special way of choosing the indexes of the involved mappings, we propose a new iterative algorithm for approximating common fixed points of a sequence of nonexpansive nonself mappings, and some convergence theorems are established in the framework of CAT(0) spaces. Our results extend the previous results restricted to the situation of a single mapping.
A space X is of countable type (resp. subcountable type) if every compact subspace F of X is contained in a compact subspace K that is of countable character (resp. countable pseudocharacter) in X. In this paper, we mainly show that: (1) For a functionally Hausdorff space X, the free paratopological group FP(X)and the free abelian paratopological group AP(X) are of countable type if and only if X is discrete; (2) For a functionally Hausdorff space X, if the free abelian paratopological group AP(X) is of subcountable type then X has countable pseudocharacter. Moreover, we also show that, for an arbitrary Hausdorff μ-space X, if AP 2(X) or FP 2(X) is locally compact, then X is a topological sum of a compact space and a discrete space.
In this paper, we study the existence of multiple solutions for a class of impulsive perturbed elastic beam equations of Kirchhoff-type. We give a new criteria for guaranteeing that the impulsive perturbed elastic beam equations of Kirchhoff-type have at least three generalized solutions by using a variational method and a critical points theorem of B. Ricceri.
By making use of the critical point theory, we establish some new existence criteria to guarantee that a 2nth-order nonlinear difference equation containing both advance and retardation with p-Laplacian has a nontrivial homoclinic orbit. Our conditions on the potential are rather relaxed, and some existing results in the literature are improved.
Let {F n } n ≥0 be the sequence of Fibonacci numbers. The aim of this paper is to give linear independence results over for the infinite series with certain nonprincipal real Dirichlet characters χ j . We also deduce the irrationality results for the special principal Dirichlet characters and for other multiplicative functions.
Hujter and Lángi defined the k-fold Borsuk number of a set S in Euclidean n-space of diameter d > 0 as the smallest cardinality of a family F of subsets of S, of diameters strictly less than d, such that every point of S belongs to at least k members of F.
We investigate whether a k-fold Borsuk covering of a set S in a finite dimensional real normed space can be extended to a completion of S. Furthermore, we determine the k-fold Borsuk number of sets in not angled normed planes, and give a partial characterization for sets in angled planes.
In this paper we study rings R with the property that every finitely generated ideal of R consisting entirely of zero divisors has a nonzero annihilator. The class of commutative rings with this property is quite large; for example, noetherian rings, rings whose prime ideals are maximal, the polynomial ring R[x] and rings whose classical ring of quotients are von Neumann regular. We continue to study conditions under which right mininjective rings, right FP-injective rings, right weakly continuous rings, right extending rings, one sided duo rings, semiregular rings and semiperfect rings have this property.
A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. It was conjectured in [10], that for any two graphs G and H, b(G[H]) ≦ b(G) − 1|V (H)| + Δ(H) + 1 and b(G ⊠ H) ≦ max {b(G)(Δ(H) + 1), b(H) Δ(G) + 1)}, where G[H] and G ⊠ H denotes the lexicographic product and the strong product of G and H, respectively. In this paper, we disprove both conjectures.
A new concept of Walsh-Lebesgue points is introduced for higher dimensions and it is proved that almost every point is a modified Walsh-Lebesgue point of an integrable function. It is shown that the Walsh-Fejér means σ n f of a function f ∈ L 1[0, 1) d converge to f at each modified Walsh-Lebesgue point, whenever n→∞ and n is in a cone. The same is proved for other summability means, such as for the Weierstrass, Abel, Picard, Bessel, Cesàro, de La Vallée-Poussin, Rogosinski and Riesz summations.
We propose a new two-parameter continuous model called the extended arcsine distribution restricted to the unit interval. It is a very competitive model to the beta and Kumaraswamy distributions for modeling percentages, rates, fractions and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating and quantile functions, Shannon entropy and order statistics. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. We demonstrate by means of two applications to proportional data that it can give consistently a better fit than other important statistical models.
In this paper, we study dissipative q-Sturm—Liouville operators in Weyl’s limit circle case. We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm—Liouville operators. Using Livšic’s theorems, we prove a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm—Liouville operators.
In [14] we investigated some Vilenkin—Nörlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H 1/(1+α) to the space weak-L 1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H 1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Nörlund means with non-increasing coefficients are not bounded from the Hardy space H 1/(1+α) to the space L 1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.
We present here characterizations of the most recently introduced continuous univariate distributions based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the 1th order statistic; (iii) truncated moments of certain functions of the n th order statistic; (iv) truncated moment of certain function of the random variable. We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We will also point out that some of these distributions are infinitely divisible via Bondesson’s 1979 classifications.
A subgroup H of G is called M p -embedded in G, if there exists a p-nilpotent subgroup B of G such that H p ∈ Syl p (B) and B is M p -supplemented in G. In this paper, we use M p -embedded subgroups to study the structure of finite groups.
In this paper we establish approximation properties of Cesàro (C, −α) means with α ∈ (0, 1) of Vilenkin—Fourier series. This result allows one to obtain a condition which is sufficient for the convergence of the means σ n −α (f, x) to f(x) in the L p -metric.
In this paper, we concern the Principal Ideal Theorem (PIT) for w-Noetherian rings. Let R be a w-Noetherian ring and a be a nonzero nonunit element of R. If p is a prime ideal of R minimal over (a), then ht p ≦ 1.
In this paper, we study the k-th order Kantorovich type modication of Szász—Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, we present a quantitative Voronovskaya theorem for differentiated Szász—Mirakyan operators in weighted spaces. The approximation properties such as rate of convergence and simultaneous approximation by the new constructions are also obtained.
In this article we characterize the classification of stably simple curve singularities given by V. I. Arnold, in terms of invariants. On the basis of this characterization we describe an implementation of a classifier for stably simple curve singularities in the computer algebra system SINGULAR.
We investigate the pointwise and uniform convergence of the symmetric rectangular partial (also called Dirichlet) integrals of the double Fourier integral of a function that is Lebesgue integrable and of bounded variation over ℝ2. Our theorem is a two-dimensional extension of a theorem of Móricz (see Theorem 3 in [10]) concerning the single Fourier integrals, which is more general than the two-dimensional extension given by Móricz himself (see Theorem 3 in [11]).
In this paper, we shall establish some Hadamard-type inequalities for differentiable coordinated convex functions in a rectangle from the plane in two variables. Through these inequalities, more precise estimates could be obtained. Some examples and applications to cubature formulas are also provided.
Let α be an infinite ordinal. Let RCA α denote the variety of representable cylindric algebras of dimension α. Modifying Andréka’s methods of splitting, we show that the variety RQEA α of representable quasi-polyadic equality algebras of dimension α is not axiomatized by a set of universal formulas containing only finitely many variables over the variety RQA α of representable quasi-polyadic algebras of dimension α. This strengthens a seminal result due to Sain and Thompson, answers a question posed by Andréka, and lifts to the transfinite a result of hers proved for finite dimensions > 2. Using the modified method of splitting, we show that all known complexity results on universal axiomatizations of RCA α (proved by Andréka) transfer to universal axiomatizations of RQEA α . From such results it can be inferred that any algebraizable extension of L ω,ω is severely incomplete if we insist on Tarskian square semantics. Ways of circumventing the strong non-negative axiomatizability results hitherto obtained in the first part of the paper, such as guarding semantics, and /or expanding the signature of RQEA ω by substitutions indexed by transformations coming from a finitely presented subsemigroup of ( ω ω, ○) containing all transpositions and replacements, are surveyed, discussed, and elaborated upon.
In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of asymptotically stable solutions of some nonlinear functional integral equations in the space of continuous and bounded functions on R+ = [0,∞). We also give some examples satisfying the conditions our existence theorem.
The consistent way of investigating rings with involution, briefly *-rings, is to study them in the category of *-rings with morphisms preserving also involution. In this paper we continue the study of *-rings and the notion of *-reduced *-rings is introduced and their properties are studied. We introduce also the class of *-Baer *-rings. This class is defined in terms of *-annihilators and principal *-biideals, and it naturally extends the class of Baer *-rings. The use of *-biideals makes this concept more consistent with the involution than the use of right ideals in the notion of Baer *-rings. We prove that each *-Baer *-ring is semiprime. Moreover, we show that the property of *-Baer extends to both the *-corner and the center of the *-ring. Finally, we discuss the relation between *-Baer and quasi-Baer *-rings; the generalization of Baer *-ring.
In this paper we introduce differential subordination and superordination properties for certain subclasses of analytic functions involving certain linear operator, and obtain sandwich-type results for the functions belonging to these classes.
Let forb(m, F) denote the maximum number of columns possible in a (0, 1)-matrix A that has no repeated columns and has no submatrix which is a row and column permutation of F. We consider cases where the configuration F has a number of columns that grows with m. For a k × l matrix G, define s · G to be the concatenation of s copies of G. In a number of cases we determine forb(m, m α · G) is Θ(m k+α). Results of Keevash on the existence of designs provide constructions that can be used to give asymptotic lower bounds. An induction idea of Anstee and Lu is useful in obtaining upper bounds.
We investigate some equivalent conditions for the reverse order laws (ab)# = b † a # and (ab)# = b # a † in rings with involution. Similar results for (ab)# = b # a* and (ab)# = b*a # are presented too.
