Let G = (V, E) be a graph. For any real valued function 1 : V --+ R and S ~ V, let 1 (S) = L:UES 1 ( u). The weight of 1 is defined as I(V). We will also denote I(N[v]) by I[v]' where v E V. A minus k-subdominating function (k8F) for G is defined in [1] as a function 1 : V --+ {-I, 0, I} such that I[v] 2:: 1 for at least k vertices of G. The minus k-subdomination number of a graph G, denoted by...

In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...

Fluxes of ions and water across the short-circuited, excised bullfrog lung were determined by radioisotope techniques. The unidirectional flows of Na+, K+, Ca++, TcO4 minus, HCO3 minus, gluconate, rho-aminohippurate, dinitrophenolate, SO4 equal to, and water were symmetrical. Both HCO3 minus fluxes were reduced by acetazolamide. In contrast, Cl minus, Br minus I minus, and SCN minus movement fr...

Plasma and urine concentrations of Na+, K+, and urea were examined in hibernating, hypothermic, and normothermic hamsters. Plasma Na+ and K+ appear unaffected by 48 h of hypothermia (T-re 7 degrees C); however, plasma Na+ increased (P smaller than 0.05) from control values of 125.8 plus or minus 10.2 to 173 plus or minus 9.2 meg/liter in hibernators. Plasma K+ of the hibernator increased to 9.6...

We develop the plus/minus p-Selmer group theory and plus/minus padic L-function theory for an elliptic curve E with complex multiplication over an abelian extension F of the imaginary quadratic field K given by the complex multiplication of E when p is a prime inert over K/Q (i.e. supersingular). As a result, we prove that the characteristic ideal of the Pontryagin dual of the plus/minus p-Selm...

The mitotic spindle is made of microtubules (MTs) nucleated through different pathways involving the centrosomes, the chromosomes or the walls of pre-existing MTs. MCRS1 is a RanGTP target that specifically associates with the chromosome-driven MTs protecting them from MT depolymerases. MCRS1 is also needed for the control of kinetochore fiber (K-fiber) MT minus-ends dynamics in metaphase. Here...

A function f : V (G) → {+1,−1} defined on the vertices of a graph G is a signed dominating function if for any vertex v the sum of function values over its closed neighborhood is at least 1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. By simply changing “{+1,−1}” in the above definition to “{+1, 0,−1}”, we can define the minus dominating f...