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
A new model, in terms of finite bipartite graphs, of the free pseudosemilattice is presented. This will then be used to obtain several results about the variety SPS of all strict pseudosemilattices: (i) an identity basis for SPS is found, (ii) SPS is shown to be inherently non-finitely based, (iii) SPS is shown to have no irredundant identity basis, and (iv) SPS is shown to have no covers and to be ∩-prime in the lattice of all varieties of pseudosemilattices. Some applications to e-varieties of locally inverse semigroups are also derived.
Let K ⊂ ℝ2 be an o-symmetric convex body, and K* its polar body. Then we have |K| · |K*| ≧ 8, with equality if and only if K is a parallelogram. (|·| denotes volume). If K ⊂ ℝ2 is a convex body, with o ∈ int K, then |K| · |K*| ≧ 27/4, with equality if and only if K is a triangle and o is its centroid. If K ⊂ ℝ2 is a convex body, then we have |K| · |[(K − K)/2)]*| ≧ 6, with equality if and only if K is a triangle. These theorems are due to Mahler and Reisner, Mahler and Meyer, and to Eggleston, respectively. We show an analogous theorem: if K has n-fold rotational symmetry about o, then |K| · |K*| ≧ n 2 sin2(π/n), with equality if and only if K is a regular n-gon of centre o. We will also give stability variants of these four inequalities, both for the body, and for the centre of polarity. For this we use the Banach-Mazur distance (from parallelograms, or triangles), or its analogue with similar copies rather than affine transforms (from regular n-gons), respectively. The stability variants are sharp, up to constant factors. We extend the inequality |K| · |K*| ≧ n 2 sin2(π/n) to bodies with o ∈ int K, which contain, and are contained in, two regular n-gons, the vertices of the contained n-gon being incident to the sides of the containing n-gon. Our key lemma is a stability estimate for the area product of two sectors of convex bodies polar to each other. To several of our statements we give several proofs; in particular, we give a new proof for the theorem of Mahler-Reisner.
We give optimal bounds for Kloosterman sums that arise in the estimation of Fourier coefficients of Siegel modular forms of genus 2.
Recently Khan and Orhan have proved that an ordinary (single) sequence is A-strongly convergent if and only if it is A-statistically convergent and A-uniformly integrable. In this paper we consider the similar problem for multidimensional sequences when A is a multivariable-to-single matrix. We also study the same question when A is a multivariable-to-multivariable matrix.
Let ν be a positive Borel measure on ℝ̄+:= [0;∞) and let p: ℝ̄+ → ℝ̄+ be a weight function which is locally integrable with respect to ν. We assume that
The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.
We construct an infinite dimensional quasi-polyadic equality algebra
For two locally compact groups G and H, we show that if L 1(G) is strictly inner amenable, then L 1(G × H) is strictly inner amenable. We then apply this result to show that there is a large class of locally compact groups G such that L 1(G) is strictly inner amenable, but G is not even inner amenable.
We study some properties of representable or I-stable local homology modules H i I (M) where M is a linearly compact module. By duality, we get some properties of good or at local cohomology modules H I i (M) of A. Grothendieck.
The sub-bifractional Brownian motion, which is a quasi-helix in the sense of Kahane, is presented. The upper classes of some of its increments are characterized by an integral test.
Let {X n } n∈ℕ be a sequence of i.i.d. random variables in ℤd. Let S k = X 1 + … + X k and Y n(t) be the continuous process on [0, 1] for which Y n(k/n) = S k/n 1/2 for k = 1, … n and which is linearly interpolated elsewhere. The paper gives a generalization of results of ([2]) on the weak limit laws of Y n(t) conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on ℤd: d ≧ 2 is the Brownian motion.
Characterizations of the Amoroso distribution based on a simple relationship between two truncated moments are presented. A remark regarding the characterization of certain special cases of the Amoroso distribution based on hazard function is given. We will also point out that a sub-family of the Amoroso family is a member of the generalized Pearson system.
We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.
In this paper, we have used Eryilmaz’s (2008) multi-colour Pólya urn model to obtain joint distributions of runs of t-types of exact lengths (k 1, k 2, …, k t), at least lengths (k 1, k 2, …, k t), non-overlapping runs of lengths (k 1, k 2, … k t) and overlapping runs of lengths (k 1, k 2, … k t) when counting of runs is done in a circular setup. We have also derived joint distributions of longest runs of various types under similar conditions. Distributions of runs have found applications in fields of reliability of consecutive-k-out-of n: F system, consecutive k-out-of-r-from n: F system, start-up demonstration test, molecular biology, radar detection, time sharing systems and quality control. The literature is profound in discussion of marginal distribution and joint distribution of runs of various types under linear and circular setup using techniques like urn model with balls of two or more colours, probability generating function and compounding discrete distribution with suitable beta functions. Through this paper for first time effort been made to discuss joint distributions of runs of various lengths and types using Multi-colour urn model.
Suppose X is a locally convex space, Y is a topological vector space and λ(X)βY is the β-dual of some X valued sequence space λ(X). When λ(X) is c 0(X) or l ∞(X), we have found the largest M ⊂ 2λ(X) for which (A j) ∈ λ(X)βY if and only if Σ j=1 ∞ A j(x j) converges uniformly with respect to (x j) in any M ∈ M. Also, a remark is given when λ(X) is l p(X) for 0 < p < + ∞.
Let G be a finite group and H a subgroup of G. H is said to be S-quasinormal in G if HP = PH for all Sylow subgroups P of G. Let H sG be the subgroup of H generated by all those subgroups of H which are S-quasinormal in G and H sG the intersection of all S-quasinormal subgroups of G containing H. The symbol |G|p denotes the order of a Sylow p-subgroup of G. We prove the followingTheorem A. Let G be a finite group and p a prime dividing |G|. Then G is p-supersoluble if and only if for every cyclic subgroup H of Ḡ (G) of prime order or order 4 (if p = 2), Ḡ has a normal subgroup T such that H sḠ and H∩T=H sḠ ∩T.Theorem B. A soluble finite group G is p-supersoluble if and only if for every 2-maximal subgroup E of G such that O p′ (G) ≦ E and |G: E| is not a power of p, G has an S-quasinormal subgroup T with cyclic Sylow p-subgroups such that E sG = ET and |E ∩ T|p = |E sG ∩ T|p.Theorem C. A finite group G is p-soluble if for every 2-maximal subgroup E of G such that O p′ (G) ≦ E and |G: E| is not a power of p, G has an S-quasinormal subgroup T such that E sG = ET and |E ∩ T p = |E sG ∩ T|p.
We introduce the concept of nil-McCoy rings to study the structure of the set of nilpotent elements in McCoy rings. This notion extends the concepts of McCoy rings and nil-Armendariz rings. It is proved that every semicommutative ring is nil-McCoy. We shall give an example to show that nil-McCoy rings need not be semicommutative. Moreover, we show that nil-McCoy rings need not be right linearly McCoy. More examples of nil-McCoy rings are given by various extensions. On the other hand, the properties of α-McCoy rings by considering the polynomials in the skew polynomial ring R[x; α] in place of the ring R[x] are also investigated. For a monomorphism α of a ring R, it is shown that if R is weak α-rigid and α-reversible then R is α-McCoy.
Suppose that A is either the Banach algebra L 1(G) of a locally compact group G, or measure algebra M(G), or other algebras (usually larger than L 1(G) and M(G)) such as the second dual, L 1(G)**, of L 1(G) with an Arens product, or LUC(G)* with an Arenstype product. The left translation invariant closed convex subsets of A are studied. Finally, we obtain necessary and sufficient conditions for LUC(G)* to have 1-dimensional left ideals.
Let K be a finite field and let X* be an affine algebraic toric set parameterized by monomials. We give an algebraic method, using Gröbner bases, to compute the length and the dimension of C X* (d), the parameterized affine code of degree d on the set X*. If Y is the projective closure of X*, it is shown that C X* (d) has the same basic parameters that C Y (d), the parameterized projective code on the set Y. If X* is an affine torus, we compute the basic parameters of C X* (d). We show how to compute the vanishing ideals of X* and Y.
The smallest monoid containing a 2-testable semigroup is defined to be a 2-testable monoid. The well-known Brandt monoid B 2 1 of order six is an example of a 2-testable monoid. The finite basis problem for 2-testable monoids was recently addressed and solved. The present article continues with the investigation by describing all monoid varieties generated by 2-testable monoids. It is shown that there are 28 such varieties, all of which are finitely generated and precisely 19 of which are finitely based. As a comparison, the sub-variety lattice of the monoid variety generated by the monoid B 2 1 is examined. This lattice has infinite width, satisfies neither the ascending chain condition nor the descending chain condition, and contains non-finitely generated varieties.
Реэюме
Abstract
The main objective of this paper is a study of some new multidimensional Hilbert type inequalities with a general homogeneous kernel. We derive a pair of equivalent inequalities, and also establish the conditions under which the constant factors included in the obtained inequalities are the best possible. Some applications in particular settings are also considered.
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We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vallée Poussin sums on the sets C β q H ω of Poisson integrals of functions from the class H ω generated by convex upwards moduli of continuity ω(t) which satisfy the condition ω(t)/t → ∞ as t → 0. As an implication, a solution of the Kolmogorov-Nikol’skii problem for de la Vallée Poussin sums on the sets of Poisson integrals of functions belonging to Lipschitz classes H α, 0 < α < 1, is obtained.
A system of m nonzero vectors in ℤn is called an m-icube if they are pairwise orthogonal and have the same length. The paper describes m-icubes in ℤ4 for 2 ≦ m ≦ 4 using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in ℤ4.
Motivated by a remark and a question of Nicholas Katz, we characterize the tangent space of the space of Fuchsian equations with given generic exponents inside the corresponding moduli space of logarithmic connections: we construct a weight 1 Hodge structure on the tangent space of the moduli of logarithmic connections such that deformations of Fuchsian equations correspond to the (1, 0)-part.
This paper mainly discusses how Devaney chaos and Li-Yorke sensitivity carry over to product systems. First, two results on the periodic points of product systems are obtained. By using them, the following two results are Proved: (1) A finite product system is mixing and Devaney chaotic if and only if each factor system is mixing and Devaney chaotic. (2) An infinite product map Π i=1 ∞ f i is mixing and Devaney chaotic if and only if each factor map f i is mixing and Devaney chaotic and sup {min P(f i): i ∈ ℕ} < + ∞, where P(f i) is the set of all periods of f i. Besides, we obtain that the product system is Li-Yorke sensitive (sensitive) if and only if there exists a factor system that is Li-Yorke sensitive (sensitive).
We introduce the concept of double uniform density of subsets of ℕ×ℕ and the study the corresponding convergence (namely, I u-convergence) of double sequences. Further we solve an inequality related to the I u-limit superior of bounded double sequences in line of [5].
We give a new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique borrowed from additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most d + 1 MUBs in ℂd. It may also yield a proof that no complete system of MUBs exists in some composite dimensions — a long standing open problem.
López-Blázquez and Weso lowski [6] introduced the top-k-lists sequence of random vectors and elaborated the usefulness of such data. They also developed the distribution of top-k-lists and their properties arising from various probability distributions, such as standard exponential distribution and uniform distribution on (0, 1). In this paper, we study the linearity of regressions inside top-k-lists and then based on this study we present characterizations of certain distributions.
Let D be a division ring with center F. We say that D is a division ring of type 2 if for every two elements x, y ∈ D, the division subring F(x, y) is a finite dimensional vector space over F. In this paper we investigate multiplicative subgroups in such a ring.
Let k, n be natural numbers with k ≦ n/2 and let X n,k denote the set of k-element subsets of {1, 2, … n}. The symmetric group S n acts in a natural way on the set X n,k. Motivated by a question of Robert Guralnick, we investigate the size of a minimal base for this action. We give constructions providing a minimal base if n = 2k or if n ≧ k 2. We also describe a general process providing a base of size at most c times bigger than the size of a minimal base for some universal constant c
A ring R is called left p.q.-Baer if the left annihilator of a principal left ideal is generated, as a left ideal, by an idempotent. It is first proved that for a ring R and a group G, if the group ring RG is left p.q.-Baer then so is R; if in condition G is finite then |G|−1 ∈ R. Counterexamples are given to answer the question whether the group ring RG is left p.q.-Baer if R is left p.q.-Baer and G is a finite group with |G|−1 ∈ R. Further, RD ∞ is left p.q.-Baer if and only if R is left p.q.-Baer.
Let R be a domain with quotient field K. It is proved that R is an integrally closed domain if and only if every nonzero t-ideal of R is complete, if and only if every nonzero v-ideal of R is complete. We also obtain that every prime ideal of an integrally closed domain is integrally closed, and every strongly prime ideal of a domain is integrally closed. Moreover, we introduce the notion of w-cancellation ideals and give some equivalent characterizations of PVMDs. In particular, it is proved that R is a PVMD if and only if every w-ideal of R is complete.
We give an upper bound for the Stanley depth of the edge ideal I of a k-partite complete graph and show that Stanley’s conjecture holds for I. Also we give an upper bound for the Stanley depth of the edge ideal of a s-uniform complete bipartite hypergraph.
If A is a minimal algebra (that is, has no proper subalgebras) then the set S 2(A) of all subalgebras of A 2 has a natural structure of ordered involutive monoid. This paper gives a characterization of monoids S that appear in the role of this monoid if A is finite, weakly diagonal (every subalgebra of A 2 contains the graph of an automorphism of A) and has a majority term.
Abstract
In this paper we look at the security of two block ciphers which were both claimed in the published literature to be secure against differential crypt-analysis (DC). However, a more careful examination shows that none of these ciphers is very secure against... differential cryptanalysis, in particular if we consider attacks with sets of differentials. For both these ciphers we report new perfectly periodic (iterative) aggregated differential attacks which propagate with quite high probabilities. The first cipher we look at is GOST, a well-known Russian government encryption standard. The second cipher we look at is PP-1, a very recent Polish block cipher. Both ciphers were designed to withstand linear and differential cryptanalysis. Unhappily, both ciphers are shown to be much weaker than expected against advanced differential attacks. For GOST, we report better and stronger sets of differentials than the best currently known attacks presented at SAC 2000 [32] and propose the first attack ever able to distinguish 16 rounds of GOST from random permutation. For PP-1 we show that in spite of the fact, that its S-box has an optimal theoretical security level against differential cryptanalysis [17], [29], our differentials are strong enough to allow to break all the known versions of the PP-1 cipher.
Abstract
Sealed bid auctions are a popular means of high-stakes bidding, as they eliminate the temporal element from the auction process, allowing participants to take less emotional, more thoughtful decisions. In this paper, we propose a digital communication protocol for conducting sealed bid auctions with high stakes, where the anonymity of bids as well as other aspects of fairness must be protected. The Dining Cryptographers’ Protocol (denoted by DC) was presented by David Chaum in 1988. The protocol allows the participants to broadcast a message anonymously. In a recent paper (Another Twist in the Dining Cryptographers’ Protocol, submitted to the Journal of Cryptology) the authors propose a variant of the original DC eliminating its main disadvantages. In this paper we present a cryptographic protocol realizing anonymous sealed bid auctions, such as first price or Vickrey auction, based on this variant. The proposed scheme allows to identify at least one dishonest participant violating the protocol without using of Trusted Third Parties. Additionally, we require that bids are binding. It is achieved by enabling all participants acting in concert (the so-called “angry mob”) to find out the identity of the winner, in case the winner fails to make the purchase.
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In this paper, we present several methods for the construction of elliptic curves with large torsion group and positive rank over number fields of small degree. We also discuss potential applications of such curves in the elliptic curve factorization method (ECM).
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In recent papers [14], [15] I studied collision and avalanche effect in families of finite pseudorandom binary sequences. Motivated by applications, Mauduit and Sárközy in [13] generalized and extended this theory from the binary case to k-ary sequences, i.e., to k symbols. They constructed a large family of k-ary sequences with strong pseudorandom properties. In this paper our goal is to extend the study of the pseudorandom properties mentioned above to k-ary sequences. The aim of this paper is twofold. First we will extend the definitions of collision and avalanche effect to k-ary sequences, and then we will study these related properties in a large family of pseudorandom k-ary sequences with “small” pseudorandom measures.
Abstract
This paper considers security implications of k-normal Boolean functions when they are employed in certain stream ciphers. A generic algorithm is proposed for cryptanalysis of the considered class of stream ciphers based on a security weakness of k-normal Boolean functions. The proposed algorithm yields a framework for mounting cryptanalysis against particular stream ciphers within the considered class. Also, the proposed algorithm for cryptanalysis implies certain design guidelines for avoiding certain weak stream cipher constructions. A particular objective of this paper is security evaluation of stream cipher Grain-128 employing the developed generic algorithm. Contrary to the best known attacks against Grain-128 which provide complexity of a secret key recovery lower than exhaustive search only over a subset of secret keys which is just a fraction (up to 5%) of all possible secret keys, the cryptanalysis proposed in this paper provides significantly lower complexity than exhaustive search for any secret key. The proposed approach for cryptanalysis primarily depends on the order of normality of the employed Boolean function in Grain-128. Accordingly, in addition to the security evaluation insights of Grain-128, the results of this paper are also an evidence of the cryptographic significance of the normality criteria of Boolean functions.
Abstract
In our constribution we explore a combination of local reduction with the method of syllogisms and the applications of generic guessing strategies in the cryptanalysis of the block cipher GOST. Our experiments show that GOST with 64/128/256 bit key requires at least 12/16/22 rounds to achieve full bit security against the method of syllogisms combined with the “maximum impact” strategy.
Abstract
The weighted averages of a sequence (c k ), c k ∈ ℂ, with respect to the weights (p k ), p k ≥ 0, with {fx135-1} are defined by {fx135-2} while the weighted average of a measurable function f: ℝ+ → ℂ with respect to the weight function p(t) ≥ 0 with {fx135-3}. Under mild assumptions on the weights, we give necessary and sufficient conditions under which the finite limit σ n → L as n → ∞ or σ(t) → L as t → ∞ exists, respectively. These characterizations may find applications in probability theory.
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The non-trivial hereditary monocoreflective subcategories of the Abelian groups are the following ones: {G ∈ Ob Ab | G is a torsion group, and for all g ∈ G the exponent of any prime p in the prime factorization of o(g) is at most E(p)}, where E(·) is an arbitrary function from the prime numbers to {0, 1, 2, …,∞}. (o(·) means the order of an element, and n ≤ ∞ means n < ∞.) This result is dualized to the category of compact Hausdorff Abelian groups (the respective subcategories are {G ∈ Ob CompAb | G has a neighbourhood subbase {G α } at 0, consisting of open subgroups, such that G/G α is cyclic, of order like o(g) above}), and is generalized to categories of unitary R-modules for R an integral domain that is a principal ideal domain. For general rings R with 1, an analogous theorem holds, where the hereditary monocoreflective subcategories of unitary left R-modules are described with the help of filters L in the lattice of the left ideals of the ring R. These subcategories consist of those left R-modules, for which the annihilators of all elements belong to L. If R is commutative, then this correspondence between these subcategories and these filters L is bijective.
Abstract
The distance d G (u, v) between two vertices u and v in a connected graph G is the length of the shortest uv-path in G. A uv-path of length d G (u, v) is called a uv-geodesic. A set X is convex in G if vertices from all ab-geodesics belong to X for any two vertices a, b ∈ X. The convex domination number γcon(G) of a graph G equals the minimum cardinality of a convex dominating set. In the paper, Nordhaus-Gaddum-type results for the convex domination number are studied.
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We prove that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right seminormal bands.
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We give a very short survey of the results on placing of points into the unit n-dimensional cube with mutual distances at least one. The main result is that into the 5-dimensional unit cube there can be placed no more than 40 points.
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In this paper, we establish some new refinements for the celebrated Fejér’s and Hermite-Hadamard’s integral inequalities for convex functions.
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We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semigroups (a step that has previously proved to be awkward). We also put some earlier work of Gantos into a wider and clearer context, and pave the way for further progress.
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We prove that partially ordered semigroups with local units are strongly Morita equivalent if and only if they have a joint enlargement, which in turn happens if and only if the Cauchy completions of the semigroups are equivalent.
