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121.
Carl Johan Casselgren Hrant H. Khachatrian Petros A. Petrosyan 《Discrete Mathematics》2018,341(3):627-637
An interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors. A cyclic interval-coloring of a multigraph is a proper edge coloring with colors such that the colors of the edges incident with every vertex of are colored by consecutive colors, under the condition that color is considered as consecutive to color . Denote by () and () the minimum and maximum number of colors in a (cyclic) interval coloring of a multigraph , respectively. We present some new sharp bounds on and for multigraphs satisfying various conditions. In particular, we show that if is a -connected multigraph with an interval coloring, then . We also give several results towards the general conjecture that for any triangle-free graph with a cyclic interval coloring; we establish that approximate versions of this conjecture hold for several families of graphs, and we prove that the conjecture is true for graphs with maximum degree at most . 相似文献
122.
Oscar Fernández-Ramos 《代数通讯》2013,41(6):1921-1933
Consider an ideal I ? K[x 1,…, x n ], with K an arbitrary field, generated by monomials of degree two. Assuming that I does not have a linear resolution, we determine the step s of the minimal graded free resolution of I where nonlinear syzygies first appear, we show that at this step of the resolution nonlinear syzygies are concentrated in degree s + 3, and we compute the corresponding graded Betti number β s, s+3. The multidegrees of these nonlinear syzygies are also determined and the corresponding multigraded Betti numbers are shown to be all equal to 1. 相似文献
123.
J.E. Macías-Díaz Anna Szafrańska 《Journal of Difference Equations and Applications》2013,19(7):989-1004
Departing from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity, the boundedness and the spatial and the temporal monotonicity. The main results provide conditions that guarantee the existence and the uniqueness of monotone and bounded solutions of our scheme. The technique was implemented and tested computationally, and the results confirm both a good agreement with respect to the travelling-wave solutions reported in the literature and the preservation of the mathematical features of interest. 相似文献
124.
125.
Weida D. Chen A. Xavier Kohll Bichlien H. Nguyen Julian Koch Reinhard Heckel Wendelin J. Stark Luis Ceze Karin Strauss Robert N. Grass 《Advanced functional materials》2019,29(28)
In this paper the practical density of long‐term DNA storage is increased. Specifically, the DNA weight loading of silica sphere DNA storage is increased to 3.4 wt%, a ten‐fold increase compared to the previous state‐of‐the‐art. By applying a Layer‐by‐Layer (LbL) design with alternating layers of DNA and a polycationic molecule, namely polyethyleneimine (PEI), another dimension to DNA surface binding onto magnetic nanoparticles is added. A protective silica layer is grown on top of the multilayered nanoparticles to shield the DNA from external sources of damage. Accelerated aging experiments of the nanoparticles and the subsequent quantification of DNA stability via qPCR show a significantly lower degradation rate compared to unprotected DNA. The novel material is compared to previous DNA storage technologies, outperforming those in DNA storage density as well as stability. Finally, the storage of an 83 kB digital file in DNA through a successful readout of a 4991 oligonucleotide pool is demonstrated from particle encapsulation, through accelerated aging, to sequencing. 相似文献
126.
The old well-known result of Chartrand, Kaugars and Lick says that every k-connected graph G with minimum degree at least 3k/2 has a vertex v such that G−v is still k-connected. In this paper, we consider a generalization of the above result [G. Chartrand, A. Kaigars, D.R. Lick, Critically n-connected graphs, Proc. Amer. Math. Soc. 32 (1972) 63–68]. We prove the following result:Suppose G is a k-connected graph with minimum degree at least 3k/2+2. Then G has an edge e such that G−V(e) is still k-connected.The bound on the minimum degree is essentially best possible. 相似文献
127.
In this paper, we present new structural results about the existence of a subgraph where the degrees of the vertices are pre-specified. Further, we use these results to prove a 16-edge-weighting version of a conjecture by Karoński, ?uczak and Thomason, an asymptotic 2-edge-weighting version of the same conjecture, and a version of Louigi's Conjecture. 相似文献
128.
We show that in every r-coloring of the edges of K n there is a monochromatic double star with at least \(\frac{n(r+1)+r-1}{r^2}\) vertices. This result is sharp in asymptotic for r = 2 and for r≥ 3 improves a bound of Mubayi for the largest monochromatic subgraph of diameter at most three. When r-colorings are replaced by local r-colorings, our bound is \(\frac{n(r+1)+r-1}{r^2+1}\). 相似文献
129.
B-SERIES METHODS CANNOT BE VOLUME-PRESERVING 总被引:1,自引:0,他引:1
Volume preservation is one of the qualitative characteristics common to many dynamical systems. However, it has been proved by Kang and Shang that e.g. Runge–Kutta (RK) methods can not preserve volume for all linear source-free ODEs (let alone nonlinear ODEs). On the other hand, certain so-called Exponential Runge–Kutta (ERK) methods do preserve volume for all linear source-free ODEs. Do such ERK methods perhaps also preserve volume for all nonlinear ODEs? Here we prove that the answer to this question is negative; B-series methods (which include RK, ERK and several more classes of methods) cannot preserve volume for all source-free ODEs. The proof is presented via the theory of K-loops, which is an extension of the theory of classical rooted trees. 相似文献
130.
用4种不同浓度的条浒苔多酚(Enteromorpha clathrata polyphenols, ECPs)溶液处理新鲜加州鲈鱼块后置于4℃贮藏,结合感官评分、菌落总数、挥发性盐基氮(TVB-N)、硫代巴比妥酸(TBA)值、肌原纤维蛋白巯基含量、表面疏水性、肌肉色差和质地剖面分析(TPA)等指标,综合评估其对鱼块货架期的影响.结果表明,在4℃贮藏条件下, ECPs处理能有效抑制鲈鱼贮藏期间TVB-N值、TBA值和菌落总数的增加,减缓蛋白氧化和品质劣化进程,从而达到延长货架期的作用.当ECPs浓度为0.20%时,其对鲈鱼鱼块的保鲜效果最佳,能延长鲈鱼货架期6 d. 相似文献