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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
In this paper we study left amenability of Lau algebras by introducing left approximate diagonal and virtual diagonal for Lau algebras. Some results related to Hahn-Banach theorem property on foundation topological semigroups are obtained. We introduce the left contractibility of Lau algebras. Some examples for clarifying that left contractibility of Lau algebras is stronger than left amenability of them are given.
The problem when a paratopolgical group (or semitopological group) is a topological group is interesting and important. In this paper, we continue to study this problem. It mainly shows that: (1) Let G be a paratopological group and put τ = ω H s(G); then G is a topological group if G is a P τ-space; (2) every co-locally countably compact paratopological group G with ω H s(G) ≦ ω is a topological group; (3) every co-locally compact paratopological group is a topological group; (4) each 2-pseudocompact paratopological group G with ω H s(G) ≦ ω is a topological group. These results improve some results in [11, 13].
Let (R, m) be a Noetherian local ring and M a finitely generated R-module. In this paper, we study some invariants of the idealization R ⋉ M of R and M such as the polynomial type introduced by Cuong [2] and the polynomial type of fractions introduced by Cuong-Minh [3]. As consequences, we characterize the Cohen-Macaulay, generalized Cohen-Macaulay, pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay properties of the idealization R ⋉ M.
We are studying the representations of Artin’s braid group B n .
In this note the proof of a slight generalization of the Maximal Ergodic Inequality is a bit simplified and it is shown that from this generalized inequality Birkhoff’s Pointwise Ergodic Theorem follows almost immediately.
This paper is devoted to studying a q-analogue of Sturm-Liouville operators. We formulate a dissipative q-difference operator in a Hilbert space. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which is based on the method of Pavlov and define its characteristic function. Finally, we prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative q-Sturm-Liouville difference operator.
Two-weight norm estimates for sublinear integral operators involving Hardy-Littlewood maximal, Calderón-Zygmund and fractional integral operators in variable exponent Lebesgue spaces are derived. Operators and the space are defined on a quasi-metric measure space with doubling condition. The derived conditions are written in terms of L p(·) norms and are simultaneously necessary and sufficient for appropriate inequalities for maximal and fractional integral operators mainly in the case when weights are of radial type.
For a large class of arithmetic functions f, it is possible to show that, given an arbitrary integer κ ≤ 2, the string of inequalities f(n + 1) < f(n + 2) < … < f(n + κ) holds for in-finitely many positive integers n. For other arithmetic functions f, such a property fails to hold even for κ = 3. We examine arithmetic functions from both classes. In particular, we show that there are only finitely many values of n satisfying σ2(n − 1) < σ2 < σ2(n + 1), where σ2(n) = ∑ d|n d 2. On the other hand, we prove that for the function f(n) := ∑ p|n p 2, we do have f(n − 1) < f(n) < f(n + 1) in finitely often.
In this paper, a fourth-order nonlinear difference equation is considered. By making use of the critical point theory, we establish various sets of sufficient conditions for the existence and nonexistence of solutions for Neumann boundary value problem and give some new results. Results obtained generalize and complement the existing ones.
In order to give an excellent description of income distributions, although a large number of functional forms have been proposed, but the four-parameter generalized beta model of the second kind (GB2), introduced by J. B. McDonald [18], is now widely acknowledged which is including many other models as special or limiting cases.One of the fundamentals of statistical inference is the estimation problem of a function of unknown parameter in a probability distribution and computing the variance of the estimator or approximating it by lower bounds.In this paper, we consider two famous lower bounds for the variance of any unbiased estimator, which are Bhattacharyya and Kshirsagar bounds. We obtain the general forms of the Bhattacharyya and Kshirsagar matrices in the GB2 distribution. In addition, we compare different Bhattacharyya and Kshirsagar bounds for the variance of any unbiased estimator of some parametric functions such as mode, mean, skewness and kurtosis in GB2 distribution and conclude that in each case, which bound is better to use. The results of this paper can be useful for researchers trying to find the accuracy of the estimators.
More than two centuries ago Malfatti (see [9]) raised and solved the following problem (the so-called Malfatti’s construction problem): Construct three circles into a triangle so that each of them touches the two others from outside moreover touches two sides of the triangle too. It is an interesting fact that nobody investigated this problem on the hyperbolic plane, while the case of the sphere was solved simultaneously with the Euclidean case. In order to compensate this shortage we solve the following exercise: Determine three cycles of the hyperbolic plane so that each of them touches the two others moreover touches two of three given cycles of the hyperbolic plane.
Hirano [On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra, 168 (2002), 45–52] studied relations between the set of annihilators in a ring R and the set of annihilators in a polynomial extension R[x] and introduced quasi-Armendariz rings. In this paper, we give a sufficient condition for a ring R and a monoid M such that the monoid ring R[M] is quasi-Armendariz. As a consequence we show that if R is a right APP-ring, then R[x]=(x n) and hence the trivial extension T(R,R) are quasi-Armendariz. They allow the construction of rings with a non-zero nilpotent ideal of arbitrary index of nilpotency which are quasi-Armendariz.
We introduce Kurosh elements in division rings based on the idea of a conjecture of Kurosh. Using this, we generalize a result of Faith in {xc[3]} and of Herstein in {xc[6]}.
This paper concerns the existence of mild solutions for some fractional Cauchy problem with nonlocal conditions in the α-norm. The linear part of the equations is assumed to generate an analytic compact bounded semigroup, and the nonlinear part satisfies some Lipschitz conditions with respect to the fractional power norm of the linear part. By using a fixed point theorem of Sadovskii, we establish some existence results which generalize ones in the case of fractional order derivative.
In recent years, slash and skew slash distributions have been employed, as flexible models, in various fields. In this paper, we study several properties of these distributions in both univariate and multivariate cases. Some recurrence relations for the probability density functions are derived and the behavior of reliability measures, such as hazard rate and mean residual life, associated to these distributions are investigated.
A ring R is called NLI (rings whose nilpotent elements form a Lie ideal) if for each a ∈ N(R) and b ∈ R, ab − ba ∈ N(R). Clearly, NI rings are NLI. In this note, many properties of NLI rings are studied. The main results we obtain are the following: (1) NLI rings are directly finite and left min-abel; (2) If R is a NLI ring, then (a) R is a strongly regular ring if and only if R is a Von Neumann regular ring; (b) R is (weakly) exchange if and only if R is (weakly) clean; (c) R is a reduced ring if and only if R is a n-regular ring; (3) If R is a NLI left MC2 ring whose singular simple left modules are Wnil-injective, then R is reduced.
A recently published paper [6] considered the total graph of commutative ring R. In this paper, we compute Wiener, hyper-Wiener, reverse Wiener, Randić, Zagreb, ABC and GA indices of zero-divisor graph.
The classification of Bruce and Gaffney respectively Gibson and Hobbs for simple plane curve singularities respectively simple space curve singularities is characterized in terms of invariants. This is the basis for the implementation of a classifier in the computer algebra system singular.
The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.
We study basic properties of the generalized ideal transforms D I (M, N) and the set of associated primes of the modules R i D I (M, N).
A new generalization of the logarithmic series distribution has been obtained as a limiting case of the zero-truncated Mishra’s [10] generalized negative binomial distribution (GNBD). This distribution has an advantage over the Mishra’s [9] quasi logarithmic series distribution (QLSD) as its moments appear in compact forms unlike the QLSD. This makes the estimation of parameters easier by the method of moments. The first four moments of this distribution have been obtained and the distribution has been fitted to some well known data-sets to test its goodness of fit.
An upper bound is given on the size of a k-fan-free 3-graph, and an infinite family reaching this bound is also described.
Applying certain convexity arguments we investigate the existence of a classical solution for a Dirichlet problem for which the Euler action functional is not necessarily differentiable in the sense of Gâteaux.
The aim of this paper is to investigate the semifields of order q 4 over a finite field of order q, q an odd prime power, admitting a Klein 4-group of automorphisms.
The main aim of this paper is to investigate (H p , L p ) and (H p , L p,∞) type inequalities for maximal operators of Riesz logarithmic means of one-dimensional Vilenkin—Fourier series.
In the following text we prove that in a generalized shift dynamical system (X Г, σ φ) for infinite countable Г and discrete X with at least two elements the following statements are equivalent:
- the dynamical system (X Г, σ φ) is chaotic in the sense of Devaney
- the dynamical system (X Г, σ φ) is topologically transitive
- the map φ: Г → Г is one to one without any periodic point.
Let C be a class of some finitely presented left R-modules. A left R-module M is called C-injective, if Ext R 1(C, M) = 0 for each C ∈ C. A right R-module M is called C-flat, if Tor1 R (M, C) = 0 for each C ∈ C. A ring R is called C-coherent, if every C ∈ C is 2-presented. A ring R is called C-semihereditary, if whenever 0 → K → P → C → 0 is exact, where C ∈ C and P is finitely generated projective and K is finitely generated, then K is also projective. A ring R is called C-regular, if whenever P/K ∈ C, where P is finitely generated projective and K is finitely generated, then K is a direct summand of P. Using the concepts of C-injectivity and C-flatness of modules, we present some characterizations of C-coherent rings, C-semihereditary rings, and C-regular rings.
A general class of linear and positive operators dened by nite sum is constructed. Some of their approximation properties, including a convergence theorem and a Voronovskaja-type theorem are established. Next, the operators of the considered class which preserve exactly two test functions from the set {e 0, e 1, e 2} are determined. It is proved that the test functions e 0 and e 1 are preserved only by the Bernstein operators, the test functions e 0 and e 2 only by the King operators while the test functions e 1 and e 2 only by the operators recently introduced by P. I. Braica, O. T. Pop and A. D. Indrea in [4].
The beta generalized half-normal distribution is commonly used to model lifetimes. We propose a new wider distribution called the beta generalized half-normal geometric distribution, whose failure rate function can be decreasing, increasing or upside-down bathtub. Its density function can be expressed as a linear combination of beta generalzed half-normal density functions. We derive quantile function, moments and generating unction. We characterize the proposed distribution using a simple relationship between wo truncated moments. The method of maximum likelihood is adapted to estimate the model parameters and its potentiality is illustrated with an application to a real fatigue data set. Further, we propose a new extended regression model based on the logarithm of the new distribution. This regression model can be very useful for the analysis of real data and provide more realistic fits than other special regression models.
The purpose of this paper is to revise von Neumann’s characterizations of selfadjoint operators among symmetric ones. In fact, we do not assume that the underlying Hilbert space is complex, nor that the corresponding operator is densely defined, moreover, that it is closed. Following Arens, we employ algebraic arguments instead of the geometric approach of von Neumann using the Cayley transform.
In the paper we give some remarks on the article of Janet Mills. In particular, the proof of Lemma 1.2 (in her work) is incorrect, and so the proof of Theorem 3.5 is not valid, too. Using different methods we show the mentioned theorem. Moreover, we find a new equivalent condition to the statements in Theorem 3.5. In particular, an explicit definition of a new class of orthodox semigroups is introduced.
The distance of two-dimensional samples is studied. The distance of two samples is based on the optimal matching method. Simulation results are obtained when the samples are drawn from normal and uniform distributions.
By [12], a ring R is left APP if R has the property that “the left annihilator of a principal ideal is pure as a left ideal”. Equivalently, R is a left APP-ring if R modulo the left annihilator of any principal left ideal is flat. Let R be a ring, (S, ≦) a strictly totally ordered commutative monoid and ω: S → End(R) a monoid homomorphism. Following [16], we show that, when R is a (S, ω)-weakly rigid and (S, ω)-Armendariz ring, then the skew generalized power series ring R[[S ≦, ω]] is right APP if and only if r R(A) is S-indexed left s-unital for every S-indexed generated right ideal A of R. We also show that when R is a (S, ω)-strongly Armendariz ring and ω(S) ⫅ Aut(R), then the ring R[[S ≦, ω]] is left APP if and only if ℓ R(∑a ∈ A ∑s ∈ S Rω s(a)) is S-indexed right s-unital, for any S-indexed subset A of R. In particular, when R is Armendariz relative to S, then R[[S ≦]] is right APP if and only if r R(A) is S-indexed left s-unital, for any S-indexed generated right ideal A of R.
In this study, we investigate approximation properties and obtain Voronovskaja type results for complex modified Szász-Mirakjan operators. Also, we estimate the exact orders of approximation in compact disks and prove that the complex modified Szász-Mirakjan operators attached to an analytic function preserve the univalence, starlikeness, convexity and spirallikeness in the unit disk.
In this paper, the authors investigate the linearization problems associated with two families of generalized Lauricella polynomials of the first and second kinds. By means of their multiple integral representations, it is shown how one can linearize the product of two different members of each of these two families of the generalized Lauricella polynomials. Upon suitable specialization of the main results presented in this paper, the corresponding integral representations are deduced for such familiar classes of multivariable hypergeometric polynomials as (for example) the Lauricella polynomials F A (r) in r variables, the Appell polynomials F 2 in two variables and the multivariable Laguerre polynomials. Each of these integral representations, which are derived as special cases of the main results in this paper, may also be viewed as a linearization relationship for the product of two different members of the associated family of multivariable hypergeometric polynomials.
We give a characterization of all those commutative groups which admit at least one absolutely nonmeasurable homomorphism into the real line (or into the one-dimensional torus). These are exactly those commutative groups (G, +) for which the quotient group G/G 0 is uncountable, where G 0 denotes the torsion subgroup of G.
Let b = 2, 5, 10 or 17 and t > 0. We study the existence of D(−1)-quadruples of the form {1, b, c, d} in the ring
Let N(k, l) be the smallest positive integer such that any set of N(k, l) points in the plane, no three collinear, contains both a convex k-gon and a convex l-gon with disjoint convex hulls. In this paper, we prove that N(3, 4) = 7, N(4, 4) = 9, N(3, 5) = 10 and N(4, 5) = 11.
In this paper we analyse the natural permutation module of an affine permutation group. For this the regular module of an elementary Abelian p-group is described in detail. We consider the inequivalent permutation modules coming from nonconjugate complements. We prove their strong structural similarity well exceeding the fact that they have equal Brauer characters.
The purpose of this paper is to investigate the relations of incomparability between so called convergence classes of the permutations of ℕ. The convergence class of any permutation p of ℕ, denoted by Σ(p), is defined to be the family of all real series Σa
n such that both Σa
n and Σa
p(n) are convergent. A permutation p of ℕ is called a divergent permutation if there exists a conditionally convergent real series Σa
n such that the p-rearranged series Σa
p(n) is divergent.It is proved that for every divergent permutation p of ℕ there exists a family
In this paper, we introduce inclusion ideals I(H) associated to a special class of non uniform hypergraphs H(gC; ɛ; d), namely, the uniformly increasing hypergraphs. We discuss some algebraic properties of the inclusion ideals. In particular, we give an upper bound of the Castelnouvo-Mumford regularity of the special dual ideal I [*](H).
Csáki and Vincze have defined in 1961 a discrete transformation T which applies to simple random walks and is measure preserving. In this paper, we are interested in ergodic and asymptotic properties of T. We prove that T is exact: ∩ k≧1 σ(T k(S)) is trivial for each simple random walk S and give a precise description of the lost information at each step k. We then show that, in a suitable scaling limit, all iterations of T “converge” to the corresponding iterations of the continuous Lévy transform of Brownian motion.
The purpose of this note is to show by constructing counterexamples that two conjectures of Móri and Székely for the Borel-Cantelli lemma are false.
