For any graph G, let V (G) and E(G) denote the vertex set and the edge set of G respectively. The Boolean function graph B(G, L(G), NINC) of G is a graph with vertex set V (G) ∪ E(G) and two vertices in B(G, L(G), NINC) are adjacent if and only if they correspond to two adjacent vertices of G, two adjacent edges of G or to a vertex and an edge not incident to it in G. For brevity, this graph is denoted by B1(G). In this paper, structural properties of B1(G) and its complement including traversability and eccentricity properties are studied. In addition, solutions for Boolean function graphs that are total graphs, quasi-total graphs and middle graphs are obtained.
In the paper we find conditions on the pair (ω1, ω2) which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space Mp,ω1 to another Mp,ω2 , 1 < p < ∞, and from the space M1,ω1 to the weak space WM1,ω2 . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.
Let µ_{n-1}(G) be the algebraic connectivity, and let µ_{1}(G) be the Laplacian spectral radius of a k-connected graph G with n vertices and m edges. In this paper, we prove that {\mu _{n - 1}}(G) \geqslant \frac{{2n{k^2}}}{{(n(n - 1) - 2m)(n + k - 2) + 2{k^2}}} , with equality if and only if G is the complete graph Kn or Kn − e. Moreover, if G is non-regular, then {\mu _1}(G) < 2\Delta - \frac{{2(n\Delta - 2m){k^2}}}{{2(n\Delta - 2m)({n^2} - 2n + 2k) + n{k^2}}} , where ▵ stands for the maximum degree of G. Remark that in some cases, these two inequalities improve some previously known results., Xiaodan Chen, Yaoping Hou., and Obsahuje seznam literatury
The article presents an analysis of two short stories by Shen Congwen (1902-1988), the foremost Chinese writer of the Republican period (1912-1949). The peculiar anti-idyllic quality of "Aboard and on Shore", a local-mood prose piece with marked autobiographical coloring, and "Sansan", an early example of the writer´s famous pastoral stories, is scrutinized using M. Bakhtin´s concept of "chronotop". Examination of the stories´ spatio-temporal layout reveals the presence of a shared semantic structure: the rise and subsequent demise of an idyllic space. The unstable chronology, a quality inherent not only to the two pieces under scruting but also to a series of Shen Congwen´s work from the late 1920s and early 1930s, is discussed as being possibly a product of the writer´s effort to express nostalgia.
Cartesian products of intuitionistic fuzzy sets have been defined using the min-max and the product-probabilistic sum operations. In this paper we introduce and analyse the properties of a generalized cartesian product of intuitionistic fuzzy sets using a general triangular norm and conorm. In particular we investigate the emptiness, the commutativity, the distributivity, the interaction with respect to generalized unions and intersections, the distributivity with respect to the difference, the monotonicity and the cutting in terms of level-sets.
We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing literature.
The cellular processes underlying individual differences in the Woring Memory Capacity (WMC) of humans are essentially unknown. Psychological experiments suggest that subjects with lower working memory capacity (LWMC), with respect to subjects with higher capacity (HWMC), take more time to recall items from a list because they search through a larger set of items and are much more susceptible to interference during retrieval. However, a more precise link between psychological experiments and cellular properties is lacking and very difficult to investigate experimentally. In this paper, we investigate the possible underlying mechanisms at the single neuron level by using a computational model of hippocampal CA1 pyramidal neurons, which have been suggested to be deeply involved in the recognition of specific items. The model makes a few experimentally testable predictions on the cellular processes underlying the cumulative latency in delayed free recall experimentally observed in humans under different testing conditions. The results suggest, for the first time, a physiologically plausible explanation for individual performances, and establish a proof of principle for the hypothesis that HWMC individuals use a larger portion of the apical tree with a correlated higher level of synaptic background noise.