a set $s$ of vertices in a graph $g$ is a dominating set if every vertex of $v-s$ is adjacent to some vertex in $s$. the domination number $gamma(g)$ is the minimum cardinality of a dominating set in $g$. the annihilation number $a(g)$ is the largest integer $k$ such that the sum of the first $k$ terms of the non-decreasing degree sequence of $g$ is at most the number of edges in $g$. in this p...

Tick-borne encephalitis virus (TBEV) widespread in the Eurasian continent is a member of the genus Flavivirus, family Flaviviridae. Human TBE cases are registered in more than 30 countries of the world [Charrel RN et al., 2004]. TBEV is subdivided into three main subtypes according to its genetic structure and antigen specificity: European, Siberian, and Far Eastern ones [Holzmann H, et al.1992...

Characteristic for cruciferous plants is their production of N- and S-containing indole phytoalexins with disease resistance and cancer-preventive properties, previously proposed to be synthesized from indole independently of tryptophan. We show that camalexin, the indole phytoalexin of Arabidopsis thaliana, is synthesized from tryptophan via indole-3-acetaldoxime (IAOx) in a reaction catalyzed...

a subset $s$ of vertices in a graph $g$ is called a geodetic set if every vertex not in $s$ lies on a shortest path between two vertices from $s$‎. ‎a subset $d$ of vertices in $g$ is called dominating set if every vertex not in $d$ has at least one neighbor in $d$‎. ‎a geodetic dominating set $s$ is both a geodetic and a dominating set‎. ‎the geodetic (domination‎, ‎geodetic domination) number...

let $p$ be a prime number and $n$ be a positive integer. the graph $g_p(n)$ is a graph with vertex set $[n]={1,2,ldots ,n}$, in which there is an arc from $u$ to $v$ if and only if $uneq v$ and $pnmid u+v$. in this paper it is shown that $g_p(n)$ is a perfect graph. in addition, an explicit formula for the chromatic number of such graph is given.

1. Nelson WE, Vaughan III, VC, McKay, Jr., RJ and Behrman RE, editors. Textbook of pediatrics, Philadelphia, 1979, W B Saunders Company. 2. Rudolph AM, Barnett HL, and Einhorn AH, editors: Pediatrics, ed 16, New York, 1977, Appleton-CenturyCrofts. 3. Irgang S: Lupus erythematosus profundus. Report of an example with clinical resemblance to Darier-Roussy sarcoid, Arch Dermatol 42:97, 1940. 4. Fo...

In this thesis, first, joint with Longzhi Lin, we establish estimates for the harmonic map heat flow from the unit circle into a closed manifold, and use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed geodesic. Second, we prove the uniqueness for ...