共查询到20条相似文献,搜索用时 390 毫秒
1.
Yong Kong 《Journal of Difference Equations and Applications》2013,19(15):1265-1271
The Goulden–Jackson cluster method is a powerful method to find generating functions of pattern occurrences in random sequences [1]. The method is clearly explained, extended and implemented by Noonan and Zeilberger [2]. In this paper, we elaborate on one of the several extensions in [2], namely the extension from symmetrical Bernoulli sequences where the occurrences of each symbol have equal probability, to asymmetrical Bernoulli sequences with different probabilities of symbol generations. An explicit formula is derived for the extension, which is implicitly embedded in the treatment of [2]. The extended result is then compared with the method of Régnier–Szpankowski [3], a method which was developed independently to tackle the same problem. By manipulating some matrix inversions, we show that the Régnier–Szpankowski method can be simplified to the extended Goulden–Jackson method. 相似文献
2.
Be’eri Greenfeld 《代数通讯》2017,45(11):4783-4784
We construct a ring which admits a 2-generated, faithful torsion module but lacks a cyclic faithful torsion module. This answers a question by Oman and Schwiebert [1, 2]. 相似文献
3.
Mihajlo Cekić 《偏微分方程通讯》2017,42(11):1781-1836
In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy. 相似文献
4.
Stéphane Launois 《代数通讯》2017,45(3):1294-1313
Cauchon [5] introduced the so-called deleting derivations algorithm. This algorithm was first used in noncommutative algebra to prove catenarity in generic quantum matrices, and then to show that torus-invariant primes in these algebras are generated by quantum minors. Since then this algorithm has been used in various contexts. In particular, the matrix version makes a bridge between torus-invariant primes in generic quantum matrices, torus orbits of symplectic leaves in matrix Poisson varieties and totally non-negative cells in totally non-negative matrix varieties [12]. This led to recent progress in the study of totally non-negative matrices such as new recognition tests [18]. The aim of this article is to develop a Poisson version of the deleting derivations algorithm to study the Poisson spectra of the members of a class 𝒫 of polynomial Poisson algebras. It has recently been shown that the Poisson Dixmier–Moeglin equivalence does not hold for all polynomial Poisson algebras [2]. Our algorithm allows us to prove this equivalence for a significant class of Poisson algebras, when the base field is of characteristic zero. Finally, using our deleting derivations algorithm, we compare topologically spectra of quantum matrices with Poisson spectra of matrix Poisson varieties. 相似文献
5.
Christian Lomp 《代数通讯》2017,45(6):2735-2737
In this note we answer the question raised by Han et al. in [3] whether an idempotent isomorphic to a semicentral idempotent is itself semicentral. We show that rings with this property are precisely the Dedekind-finite rings. An application to module theory is given. 相似文献
6.
Thomas Laurent 《偏微分方程通讯》2013,38(12):1941-1964
The purpose of this work is to develop a satisfactory existence theory for a general class of aggregation equations. An aggregation equation is a non-linear, non-local partial differential equation that is a regularization of a backward diffusion process. The non-locality arises via convolution with a potential. Depending on how regular the potential is, we prove either local or global existence for the solutions. Aggregation equations have been used recently to model the dynamics of populations in which the individuals attract each other (Bodnar and Velazquez, 2005; Holm and Putkaradze, 2005; Mogilner and Edelstein-Keshet, 1999; Morale et al., 2005; Topaz and Bertozzi, 2004; Topaz et al., 2006). 相似文献
7.
8.
The pioneering work of Brezis-Merle [7], Li-Shafrir [27], Li [26], and Bartolucci-Tarantello [3] showed that any sequence of blow-up solutions for (singular) mean field equations of Liouville type must exhibit a “mass concentration” property. A typical situation of blowup occurs when we let the singular (vortex) points involved in the equation (see (1.1) below) collapse together. However in this case, Lin-Tarantello in [30] pointed out that the phenomenon: “bubbling implies mass concentration” might not occur and new scenarios open for investigation. In this paper, we present two explicit examples which illustrate (with mathematical rigor) how a “nonconcentration” situation does happen and its new features. Among other facts, we show that in certain situations, the collapsing rate of the singularities can be used as blow-up parameter to describe the bubbling properties of the solution-sequence. In this way, we are able to establish accurate estimates around the blow-up points which we hope to use toward a degree counting formula for the shadow system (1.34) below. 相似文献
9.
Max Engelstein 《偏微分方程通讯》2017,42(10):1524-1536
We show that each connected component of the boundary of a parabolic NTA domain in ?2 is given by a graph. We then apply this observation to classify blowup solutions in ?2 to a free boundary problem for caloric measure first considered by Hofmann, Lewis and Nyström [16]. 相似文献
10.
Yingying Zhang 《代数通讯》2017,45(6):2726-2729
Mutation of τ-tilting modules is a basic operation to construct a new support τ-tilting module from a given one by replacing a direct summand. The aim of this paper is to give a positive answer to the question posed in [2, Question 2.31] about mutation of τ-tilting modules. 相似文献
11.
Elisabeth Remm 《代数通讯》2017,45(7):2956-2966
The notion of breadth of a nilpotent Lie algebra was introduced and used to approach problems of classification up to isomorphism in [5]. In the present paper, we study this invariant in terms of characteristic sequence, another invariant, introduced by Goze and Ancochea in [1]. This permits to complete the determination of Lie algebras of breadth 2 studied in [5] and to begin the work for Lie algebras with breadth greater than 2. 相似文献
12.
Jeremy Marzuola 《偏微分方程通讯》2013,38(5):775-790
In this note, we further develop the methods of Burq and Zworski (2005) to study eigenfunctions for billiards which have rectangular components: these include the Bunimovich billiard, the Sinai billiard, and the recently popular pseudointegrable billiards (Bogomolny et al., 1999). The results are an application of a “black-box” point of view as presented in Burq and Zworski (2004). 相似文献
13.
Viktoriya Ozornova 《代数通讯》2017,45(4):1760-1784
A recent theorem of Dobrinskaya [20] states that the K(π,1)-conjecture holds for an Artin group G if and only if the canonical map BM→BG is a homotopy equivalence, where M denotes the Artin monoid associated to G. The aim of this paper is to give an alternative proof by means of discrete Morse theory and abstract homotopy theory. Moreover, we exhibit a new model for the classifying space of an Artin monoid, in the spirit of [13], and a small chain complex for computing its monoid homology, similar to the one of [44]. 相似文献
14.
Sei-Qwon Oh 《代数通讯》2017,45(1):76-104
A Poisson algebra ?[G] considered as a Poisson version of the twisted quantized coordinate ring ?q,p[G], constructed by Hodges et al. [11], is obtained and its Poisson structure is investigated. This establishes that all Poisson prime and primitive ideals of ?[G] are characterized. Further it is shown that ?[G] satisfies the Poisson Dixmier-Moeglin equivalence and that Zariski topology on the space of Poisson primitive ideals of ?[G] agrees with the quotient topology induced by the natural surjection from the maximal ideal space of ?[G] onto the Poisson primitive ideal space. 相似文献
15.
《Optimization》2012,61(6):777-793
In this article, we consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function [1–3,14,15,32] together with the convex separation principle for the study of necessary optimality conditions for D.C. bilevel set-valued optimization problems. We give optimality conditions in terms of the strong subdifferential of a cone-convex set-valued mapping introduced by Baier and Jahn 6 and the weak subdifferential of a cone-convex set-valued mapping of Sawaragi and Tanino 28. The bilevel set-valued problem is transformed into a one level set-valued optimization problem using a transformation originated by Ye and Zhu 34. An example illustrating the usefulness of our result is also given. 相似文献
16.
Julia Porcino 《代数通讯》2015,43(1):84-101
We analyze the structure of ideals generated by some classes of 2 × 2 permanents of hypermatrices, generalizing [9] on 2 × 2 permanental ideals of generic matrices. We compare the obtained structure to that of the corresponding determinantal ideals in [11]: as expected, the permanental ideals have many more (minimal) components. In the last two sections, we examine a few related classes of permanental ideals. 相似文献
17.
Sara Madariaga 《代数通讯》2017,45(1):183-197
In this paper, we define pre-Malcev algebras and alternative quadri-algebras and prove that they generalize pre-Lie algebras and quadri-algebras, respectively, to the alternative setting. We use the results and techniques from [4, 14] to discuss and give explicit computations of different constructions in terms of bimodules, splitting of operations, and Rota–Baxter operators. 相似文献
18.
Yu-Ting Chen 《随机分析与应用》2013,31(5):897-910
Abstract In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where only downward jumps are allowed. 相似文献
19.
A graph Γ is said to be End-regular if its endomorphism monoid End(Γ) is regular. D. Lu and T. Wu [25] posed an open problem: Given a ring R, when does the zero-divisor graph Γ(R) have a regular endomorphism monoid? and they solved the problem for R a commutative ring with at least one nontrivial idempotent. In this paper, we solve this problem for zero-divisor graphs of group rings. 相似文献
20.
Héctor Suárez 《代数通讯》2017,45(10):4569-4580
Pre-Koszul and Koszul algebras were defined by Priddy [15]. There exist some relations between these algebras and the skew PBW extensions defined in [8]. In [24] we gave conditions to guarantee that skew PBW extensions over fields it turns out homogeneous pre-Koszul or Koszul algebra. In this paper we complement these results defining graded skew PBW extensions and showing that if R is a finite presented Koszul 𝕂-algebra then every graded skew PBW extension of R is Koszul. 相似文献