let $d=(v,a)$ be a finite simple directed graph. a function$f:vlongrightarrow {-1,0,1}$ is called a twin minus dominatingfunction (tmdf) if $f(n^-[v])ge 1$ and $f(n^+[v])ge 1$ for eachvertex $vin v$. the twin minus domination number of $d$ is$gamma_{-}^*(d)=min{w(f)mid f mbox{ is a tmdf of } d}$. inthis paper, we initiate the study of twin minus domination numbersin digraphs and present some lo...

We classify the smallest two fold blocking sets with respect to the (n−k)-spaces in PG(n, 2). We show that they either consist of two disjoint k-dimensional subspaces or are equal to a (k+1)-dimensional space minus one point.

Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...

The manufacture and use of triple-barreled microelectrodes, which are capable of simultaneous in vivo measurement of intracellular pH and the activities of K+ or NO3- and cell membrane potential (Em), are described. Scanning electron micrographs showed that the three tips were aligned and that the overall tip diameter was approximately 0.8 [mu]m. When filled with 100 mM KCl, all three barrels s...

In this paper, for a CM abelian extension K/k of number fields, we propose conjecture which describes completely the Fitting ideal minus part Pontryagin dual T-ray class group K set T primes as Gal(K/k)-module. Here, emphasize that consider full group, and do not throw away ramifying (the object study is quotient by subgroup generated classes primes). We prove our consequence equivariant Tamaga...

Thyroid hormones have diverse effects on growth and metabolism. Specific "receptor" proteins which bind triiodothyronine and other biologically active analogs and which may be involved in thyroid hormone action have been recently found in nuclei of responsive tissues. This report presents studies of these receptors in rat liver nuclei. Confirming previous reports, a Scatchard analysis of the bi...

This paper studies the maximum-clique independence problem and some variations of clique transversal such as {k}-clique, maximum-clique, minus clique, signed k-fold problems from algorithmic aspects for k-trees, suns, planar graphs, doubly chordal perfect total split line dually graphs. We give equations to compute numbers show that {k}-clique is polynomial-time solvable graphs whose equal thei...

We show that for any nontrivial knot K and any natural number n there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot.

The mechanisms of water and ion transport in ascending and descending rat colon were compared using an everted open mucosal sac preparation. Net water flux, measured gravimetrically, was similar in both segments (15.3 plus or minus 1.2 and 13.7 plus or minus 1.3mul h(-1) mg(-1), NS). Net catonic flux J(Na+K),net anionic flux J(Cl-HCO3), and net solute flux Josm were also similar; but the const...