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91.
Başak Karpuz 《Journal of Difference Equations and Applications》2017,23(12):1929-1942
We consider difference equations with a single delay term and obtain sufficient conditions for both oscillation and nonoscillation. Moreover, our nonoscillation theorem improves the affirmative answer to Ladas’ corrected conjecture given by Tang and Yu in [Comput. Math. Appl. 38(11–12) (1999), pp. 229–237]. We also present a detailed discussion with examples to emphasize the significance and the sharpness of the new results. 相似文献
92.
本文利用Luthar-Passi方法,研究了五次交错群A_5与六阶二面体群D_6直积的整群环的挠单位,得到了该群的Zassenhaus猜想成立. 相似文献
93.
Tutte's 5‐flow conjecture from 1954 states that every bridgeless graph has a nowhere‐zero 5‐flow. It suffices to prove the conjecture for cyclically 6‐edge‐connected cubic graphs. We prove that every cyclically 6‐edge‐connected cubic graph with oddness at most 4 has a nowhere‐zero 5‐flow. This implies that every minimum counterexample to the 5‐flow conjecture has oddness at least 6. 相似文献
94.
Hans Schoutens 《代数通讯》2017,45(1):262-274
We prove Hochster’s small maximal Cohen–Macaulay conjecture for three-dimensional complete F-pure rings. We deduce this from a more general criterion, and show that only a weakening of the notion of F-purity is needed, to wit, being weakly F-split. We conjecture that any complete ring is weakly F-split. 相似文献
95.
In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of d-th syzygy of R-modules of finite length, provided R is an isolated singularity. Based on this result, it is shown that under a mild assumption on the base ring R, satisfying the Auslander–Reiten conjecture behaves well under completion and reduction modulo regular elements. In addition, it will turn out that, if R is a commutative Noetherian ring and 𝒬 a finite acyclic quiver, then the Auslander–Reiten conjecture holds true for the path algebra R𝒬, whenever so does R. Using this result, examples of algebras satisfying the Auslander–Reiten conjecture are presented. 相似文献
96.
Yu Fu 《Mathematische Nachrichten》2015,288(7):763-774
We obtain a complete classification of proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces with arbitrary dimension. Precisely, together with known results of Balmu?‐Montaldo‐Oniciuc, we prove that compact orientable proper biharmonic hypersurfaces with at most three distinct principal curvatures in sphere spaces are either the hypersphere or the Clifford hypersurface with and . Moreover, we also show that there does not exist proper biharmonic hypersurface with at most three distinct principal curvatures in hyperbolic spaces . 相似文献
97.
Guangcun Lu 《Journal of Functional Analysis》2011,261(2):542-589
In lines 8-11 of Lu (2009) [18, p. 2977] we wrote: “For integer m?3, if M is Cm-smooth and Cm−1-smooth L:R×TM→R satisfies the assumptions (L1)-(L3), then the functional Lτ is C2-smooth, bounded below, satisfies the Palais-Smale condition, and all critical points of it have finite Morse indexes and nullities (see [1, Prop. 4.1, 4.2] and [4])”. However, as proved in Abbondandolo and Schwarz (2009) [2] the claim that Lτ is C2-smooth is true if and only if for every (t,q) the function v?L(t,q,v) is a polynomial of degree at most 2. So the arguments in Lu (2009) [18] are only valid for the physical Hamiltonian in (1.2) and corresponding Lagrangian therein. In this note we shall correct our arguments in Lu (2009) [18] with a new splitting lemma obtained in Lu (2011) [20]. 相似文献
98.
In this paper we verify the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds when n=3,4. We also give an almost sharp lifespan for the subcritical case 2?p<pc when n=3. The main ingredients include a Keel-Smith-Sogge type estimate with 0<μ<1/2 and weighted Strichartz estimates of order two. 相似文献
99.
Benny Sudakov 《Advances in Mathematics》2011,(1):601
The Ramsey number r(G) of a graph G is the minimum N such that every red–blue coloring of the edges of the complete graph on N vertices contains a monochromatic copy of G. Determining or estimating these numbers is one of the central problems in combinatorics.One of the oldest results in Ramsey Theory, proved by Erd?s and Szekeres in 1935, asserts that the Ramsey number of the complete graph with m edges is at most . Motivated by this estimate Erd?s conjectured, more than a quarter century ago, that there is an absolute constant c such that for any graph G with m edges and no isolated vertices. In this short note we prove this conjecture. 相似文献
100.
对于不小于7素数p,设1≤k≤p-1,则使用同余方法可证明方程n=pkp-1d(n)无正整数解,从而pkp-1不是优美指数,进而可以肯定"存在无穷多个正整数不是优美指数". 相似文献