A general view is that Schizosaccharomyces pombe undergoes symmetric cell division with two daughter cells inheriting equal shares of the content from the mother cell. Here we show that CTP synthase, a metabolic enzyme responsible for the de novo synthesis of the nucleotide CTP, can form filamentous cytoophidia in the cytoplasm and nucleus of S. pombe cells. Surprisingly, we observe that both c...

Recently, Gutman defined a new graph invariant which is named the Sombor index SO(G) of G and computed via expression = ?u~v? qdeg(u)2 + deg(v)2, where deg(u) represents degree vertex u in summing performed across all unordered pairs adjacent vertices v. Damnjanovic et al. have implemented an earlier result obtained by Wang order to show that, among trees TD that specified sequence D, greedy tr...

Let k be a non-Archimedean local field of characteristic 0. Let D be a division algebra with center k and index n. The group D∗ is a locally compact group which is compact modulo the center. Its complex irreducible representations are finite dimensional. If π is an irreducible representation of D∗ which is self-dual, i.e., if π∨ denotes the dual of π, π∨ ∼= π, then there exists a D∗-invariant, ...

Let G be a graph. The first Zagreb M1(G) of graph G is defined as: M1(G) = uV(G) deg(u)2. In this paper, we prove that each even number except 4 and 8 is a first Zagreb index of a caterpillar. Also, we show that the fist Zagreb index cannot be an odd number. Moreover, we obtain the fist Zagreb index of some graph operations.

In this paper, we investigate the existence and invariant of algebraic attacks, which have been recently shown as an important cryptanalysis method for symmetric-key cryptographical systems. For a given boolean function f in n variables and two positive integers d and e, we observe that the sufficient condition d + e ≥ n, shown in [8] or [9], cannot guarantee the existence of a function g with ...

For integers m ≥ p ≥ 2, let G R = G R (m, m + p) ⊂ RP N be the Plücker embedding of the Grassmannian of m-subspaces in R m+p. We consider a central projection of G R into a projective space RP mp of the same dimension as G R. Although G R may be non-orientable, the topological degree of this projection can be properly defined. Its values are unsigned integers. It turns out that when mp is even,...