It is shown that a locally Lipschitz function is approximately convex if, and only if, its Clarke subdifferential is a submonotone operator. Consequently, in finite dimensions, the class of locally Lipschitz approximately convex functions coincides with the class of lower-C functions. Directional approximate convexity is introduced and shown to be a natural extension of the class of lower-C fun...

We study mainly the class (GC) of all real Banach spaces X such that the set E f (a) of the minimizers of the function X 3 x 7 ! f(kx ? a 1 k;: : : ; kx ? a N k) is nonempty whenever N is a positive integer, a 2 X N , and f is a continuous monotone coercive function on 0;+1 N. For particular choices of f, the set E f (a) coincides with the set of Chebyshev centers of the set fa i : i = 1;: :: ;...

Background: There is a general deterioration in sperm quality depending on time postmortem. Refrigeration of the epididymes down to around 5°C is the best strategy to lower this damage and there are many dissim ilarities between species, possibly due to differences on cold shock endurance of epididymal sperm. Our objective was to determine the effect of 5°C and 37°C on goat epididymal sperms mo...

Data Types.Abstract data types represent the inter-face to more than one implementation of a common' usuallycomplicated concept. Because an abstract data$pe is abaseclass to more than one derived class, it must contain at leastone pure virtual function. Objects of this type can only becreated through derivation in which the pure virtual functionimplementation is fill...

BACKGROUND Few data are available on the safety and efficacy of sorafenib in patients with multifocal hepatocellular carcinoma (HCC) and advanced liver cirrhosis. METHODS Between May 2006 and December 2007, we treated 59 patients (Child-Pugh class A/B/C, 26/23/10) with unresectable HCC with sorafenib (daily target dose, 400 mg twice daily). Data were collected retrospectively. Survival curves...

In the paper, we present sufficient conditions of boundedness L-index in joint variables for a sum entire functions, where L : C n → R + is continuous function, R+ = (0, +∞). They are applicable to very wide class functions because every function F with bounded multiplicities zero points there exists positive such that has variables. Our propositions generalizations Pugh’s result obtained one v...

Stack allocation and first-class functions don’t naturally mix together. In this paper we show that a type and effect system can be the detergent that helps these features form a nice emulsion. Our interest in this problem comes from our work on the Chapel language, but this problem is also relevant to lambda expressions in C++ and blocks in Objective C. The difficulty in mixing first-class fun...

In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

For (c,,..., c„) in C, let C(cx,..., c„) denote the class of functions/(z) = 1 + cxz + ■ ■ • + cnz" + 2*>_„+ia*z* which are analytic and satisfy Re/(z) > 0 in the unit disc. The unique function of least H2 norm in C(cx,. .., c„) is explicitly determined. In this paper we consider a minimal interpolation problem at the origin, for the class H2 n C, where H2 denotes the well-known Hardy space for...

in this paper we define the removable cycle that, if $im$ is a class of graphs, $gin im$, the cycle $c$ in $g$ is called removable if $g-e(c)in im$. the removable cycles in eulerian graphs have been studied. we characterize eulerian graphs which contain two edge-disjoint removable cycles, and the necessary and sufficient conditions for eulerian graph to have removable cycles h...