共查询到20条相似文献,搜索用时 15 毫秒
1.
Ulrich Albrecht 《Results in Mathematics》1990,17(3-4):179-201
We discuss faithfully flat abelian groups in conjunction with the following: A class C of abelian groups with full A-socle is A-balanced closed if it is closed with respect to finite direct sums and subgroups with full A-socle, ker ? ε C for all ? ε Horn (G, H) and G, H ε C, and A is projective with respect to all exact sequences of elements of C. A self-small group A admits an A-balanced closed class C which contains ⊕IA for all index-sets I exactly if it is faithfully flat as an E(A)-module. We show that Corner's as well as Dugas' and Göbel's realization theorems yield abelian groups that are faithfully flat as E(A)-modules. Several applications of these results are given, some of which yield an answer to part a of Fuchs' Problem 84 and a partial respond to part c of the same problem. 相似文献
2.
In an ordinary list multicoloring of a graph, the vertices are “colored” with subsets of pre‐assigned finite sets (called “lists”) in such a way that adjacent vertices are colored with disjoint sets. Here we consider the analog of such colorings in which the lists are measurable sets from an arbitrary atomless, semifinite measure space, and the color sets are to have prescribed measures rather than prescribed cardinalities. We adapt a proof technique of Bollobás and Varopoulos to prove an analog of one of the major theorems about ordinary list multicolorings, a generalization and extension of Hall's marriage theorem, due to Cropper, Gyárfás, and Lehel. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 179–193, 2007 相似文献
3.
Z. A. Chanturiya 《Mathematical Notes》1975,18(2):695-700
In this paper we generalize the Bernshtein-Szász and Zygmund-Szász theorems on the absolute convergence of Fourier series in the classes Lip α. 相似文献
4.
Satoru Niki 《Mathematical Logic Quarterly》2020,66(4):484-493
Ishihara's problem of decidable variables asks which class of decidable propositional variables is sufficient to warrant classical theorems in intuitionistic logic. We present several refinements to the class proposed by Ishii for this problem, which also allows the class to cover Glivenko's logic. We also treat the extension of the problem to minimal logic, suggesting a couple of new classes. 相似文献
5.
《Historia Mathematica》2004,31(1):76-86
Around 1931 Zermelo had an extended correspondence with the young Reinhold Baer concerning the edition of Cantor's collected works. Some of the letters also deal with Skolem's paradox and Gödel's first incompleteness theorem. Whereas Zermelo's letters are lost, most of Baer's letters are contained in the Zermelo Nachlass. Besides giving insight into Zermelo's reaction to Skolem's and Gödel's results, the letters also demonstrate Baer's clear understanding of the behavior of models of set theory and of the relevance of Gödel's first incompleteness theorem. 相似文献
6.
Joel Spencer 《Combinatorica》1981,1(3):303-307
We compare extremal theorems such as Turán’s theorem with their corresponding partition theorems such as Ramsey’s theorem.
We derive a general inequality involving chromatic number and independence number of symmetric hypergraphs. We give applications
to Ramsey numbers and to van der Waerden numbers. 相似文献
7.
《Journal of Mathematical Analysis and Applications》1987,122(2):393-407
We provide some new Caratheodory-type selection theorems, i.e., selections for correspondences of two variables which are continuous with respect to one variable and measurable with respect to the other. These results generalize simultaneously Michael's [21]continuous selection theorem for lower-semicontinuous correspondences as well as a Caratheodory-type selection theorem of Fryszkowski [10]. Random fixed point theorems (which generalize ordinary fixed point theorems, e.g., Browder's [6]) follow as easy corollaries of our results. 相似文献
8.
Krishnaswami Alladi 《The Ramanujan Journal》2012,29(1-3):339-358
We analyze a two-parameter q-series identity in Ramanujan’s Lost Notebook that generalizes the product part of the fundamental one-parameter Lebesgue identity. From reformulations of this two-parameter identity, we deduce new partition theorems including variants of the Gauss triangular number identity and Euler’s pentagonal number theorem. We discuss connections with a partial theta identity of Ramanujan and with several classical results such as those of Sylvester and Göllnitz–Gordon. 相似文献
9.
In this article, we first investigate the properties of modular Frobenius groups. Then, we consider the case that G' is a minimal normal subgroup of a modular Frobenius group G. We give the complete classification of G when G' as a modular Frobenius kernel has no more than four conjugacy classes in G. 相似文献
10.
We prove that the conjugate convolution operators can be used to calculate jumps for functions. Our results generalize the
theorems established by He and Shi. Furthermore, by using Lukács and Móricz’s idea, we solve an open question posed by Shi
and Hu. 相似文献
11.
In a recent paper Lovász, Neumann-Lara, and Plummer studied Mengerian theorems for paths of bounded length. Their study led to a conjecture concerning the extent to which Menger's theorem can fail when restricted to paths of bounded length. In this paper we offer counterexamples to this conjecture. 相似文献
12.
13.
Stephan G. Wagner 《The Ramanujan Journal》2007,14(1):43-68
We study the set of integers with a given sum of digits with respect to a linear recurrent digit system. An asymptotic formula for the number of integers ≤N with given sum of digits is determined, and the distribution in residue classes is investigated, thus generalizing results due to Mauduit and Sárközy. It turns out that numbers with fixed sum of digits are uniformly distributed in residue classes under some very general conditions. Namely, the underlying linear recurring sequence must have the property that there is no prime factor P of the modulus such that all but finitely many members of the sequence leave the same residue modulo P. The key step in the proof is an estimate for exponential sums using known theorems from Diophantine approximation. 相似文献
14.
The paper concerns the investigation of two classes of nonlinear singular integral equations with Cauchy kernel important in the applications. There are given uniqueness and existence theorems, the last by a novel application of Schauder's fixed point theorem to this type of equations. 相似文献
15.
Fioralba Cakoni 《Mathematical Methods in the Applied Sciences》2000,23(5):441-466
We investigate a three‐dimensional mathematical thermoelastic scattering problem from an open surface which will be referred to as a screen. Under the assumption of the local finite energy of the unified thermoelastic scattered field, we give a weak model on the appropriate Sobolev spaces and derive equivalent integral equations of the first kind for the jump of some trace operators on the open surface. Uniqueness and existence theorems are proved, the regularity and the singular behaviour of the solution near the edge are established with the help of the Wiener–Hopf method in the halfspace, the calculus of pseudodifferential operators on the basis of the strong ellipticity property and Gårding's inequality. An improved Galerkin scheme is provided by simulating the singular behaviour of the exact solution at the edge of the screen. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
16.
《Mathematische Nachrichten》2017,290(8-9):1347-1373
Building upon the results of M. C. Matos and extending previous work of J. D. Farmer, W. B. Johnson and J. A. Chávez‐Domínguez we define a Lipschitz mixed summable sequence as the pointwise product of a strongly summable sequence and a weakly Lipschitz summable one. Then we introduce classes of Lipschitz maps satisfying inequalities between Lipschitz mixed summable sequence and strongly summable sequences analogously to the linear case. These classes generalize the classes of Lipschitz summable maps considered earlier in the literature. We use standard techniques to establish several basic properties, showing that these classes of maps are ideals and some relationships between them. We establish various composition and inclusion theorems between different classes of Lipschitz summing maps and several characterizations. Furthermore, we prove that the classes of Lipschitz p‐summing maps coincide and the nonlinear “Pietsch Domination Theorem” for the case . We also identify cases where all Lipschitz maps are in the aforementioned classes of Lipschitz maps and discuss a sufficient condition for a Lipschitz composition formula as in the linear case. 相似文献
17.
18.
Much of extremal graph theory has concentrated either on finding very small subgraphs of a large graph (such as Turán's theorem [Turán, P., On an extremal problem in graph theory (in Hungarian), Matematiko Fizicki Lapok 48 (1941), 436–452]) or on finding spanning subgraphs (such as Dirac's theorem [Dirac, G.A., Some theorems on abstract graphs, Proc. London Math. Soc. s3-2 (1952), 69–81] or more recently work of Komlós, Sárközy and Szemerédi [Komlós, J., G. N. Sárközy and E. Szemerédi, On the square of a Hamiltonian cycle in dense graphs, Random Struct. Algorithms 9 (1996), 193-211; Komlós, J., G. N. Sárközy and E. Szemerédi, Proof of the Seymour Conjecture for large graphs, Ann. Comb. 2 (1998), 43–60] towards a proof of the Pósa-Seymour conjecture). Only a few results give conditions to obtain some intermediate-sized subgraph. We contend that this neglect is unjustified. To support our contention we focus on the illustrative case of minimum degree conditions which guarantee squared-cycles of various lengths, but also offer results, conjectures and comments on other powers of paths and cycles, generalisations thereof, and hypergraph variants. 相似文献
19.
Thomas Powell 《Mathematical Logic Quarterly》2020,66(3):300-310
We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem, which presents a simple condition under which the converse holds. Our approach is inspired by proof theory, and in particular Gödel's functional interpretation, which we use to establish quantitative versions of both of these results. 相似文献
20.
H. Allouba 《随机分析与应用》2013,31(5):787-810
We prove Girsanov's theorem for continuous orthogonal martingale measures. We then define space-time SDEs, and use Girsanov's theorem to establish a oneto- one correspondence between solutions of two space-time SDEs differing only by a drift coefficient. For such stochastic equations, we give necessary conditions under which the laws of their solutions are absolutely continuous with respect to each other. Using Girsanov's theorem again, we prove additional existence and uniqueness results for space-time SDEs. The same one-to-one correspondence and absolute continuity theorems are also proved for the stochastic heat and wave equations 相似文献