The Wiener matrix and the hyper-Wiener number of a tree (acyclic structure), higher Wiener numbers of a tree that can be represented by a Wiener number sequence W, W,W.... whereW = W is the Wiener index, and R W k K    ,.... 2 , 1 is the hyper-Wiener number. The concepts of the Wiener vector and hyper-Wiener vector of a graph are introduced for the molecular graph of bi-phenylene. Moreover, ...

In this paper, we investigate the growth of solutions of the differential equation f (k) +Ak−1 (z) f (k−1) + · · ·+A1 (z) f ′ +A0 (z) f = F, where A0 (z) , . . . , Ak−1 (z) , F (z) / ≡ 0 are entire functions, and we obtain general estimates of the hyper-exponent of convergence of distinct zeros and the hyper-order of solutions for the above equation.

X iv :0 81 2. 43 67 v1 [ cs .D M ] 2 3 D ec 2 00 8 ON SOME CLASSES OF FUNCTIONS AND HYPERCUBES DIMITER STOICHKOV KOVACHEV Abstra t. In this paper, some lasses of dis rete fun tions of k-valued logi are onsidered, that depend on sets of their variables in a parti ular way. Obtained results allow to " onstru t" these fun tions and to present them in their tabular, analyti al or matrix form, that ...

For a full semi-AFL K, B(K) is defined as the family of languages generated by all K-extended basic macro grammars, while H(K) 5 B(K) is the smallest full hyper-AFL containing K, a full basic-AFL is a full AFL K such that B(K) = K (hence every full basic-AFL is a full hyper-AFL). For any full semi-AFL K, K is a full basic-AFL if and only if B(K) is substitution closed if and only if H(K) is a f...

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semiAFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type...

Abstract Hyper-Kamiokande (Hyper-K) is a next generation underground large water Cherenkov detector. Its tank will be filled with 260000 metric tons of ultra-pure fiducial volume 0.19 Mtons, which about 8 times larger than that its predecessor Super-Kamiokande. In volume, light produced by neutrino interactions and detected newly developed photo sensors installed in dedicated frame. Two differe...

Carbachol-stimulated accumulation of labeled IP4 or of total Ins 1,3,4,5-P4 in rat brain cortical slices was maximal in buffer containing 10 mM K+. Iso-osmotic elevation of extracellular K+ to 30 mM did not affect total Ins 1,3,4,5-P4 accumulation but did enhance carbachol stimulated Ins 1,4,5-P3 accumulation. Iso-osmotically elevated K+ suppressed carbachol stimulated accumulation of labeled I...

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...