We determine the shape of the strongest column in the class of columns of length I, volume V, and having similar cross-sectional areas A (x) satisfying a < A(x) < b where a and 6 are prescribed positive bounds. In the special case where there are no constraints on the areas of cross-sections the problem has been solved by Keller [1] and by Takjbakhsh and Keller [2]. These authors observed that ...

We consider the class of semi-stable positive solutions to semilinear equations −∆u = f(u) in a bounded domain Ω ⊂ Rn of double revolution, that is, a domain invariant under rotations of the first m variables and of the last n−m variables. We assume 2 ≤ m ≤ n− 2. When the domain is convex, we establish a priori Lp and H1 0 bounds for each dimension n, with p = ∞ when n ≤ 7. These estimates lead...

We consider slightly non-extremal black 3-branes of type IIB supergravity and show that their Bekenstein-Hawking entropy agrees with the counting of states of the Dirichlet 3-brane. The Dirichlet brane excitations are described in terms of the statistical mechanics of a 3+1 dimensional gas of massless open string states. This is essentially the classic problem of black body radiation. The black...

We review the recently found map that takes any static and neutral Kaluza-Klein black hole, i.e. any static and neutral black hole on Minkowski-space times a circle Md × S1, and maps it to a corresponding solution for a nonand near-extremal brane on a circle. This gives a precise connection between phases of Kaluza-Klein black holes and the thermodynamic behavior of the non-gravitational theori...

Stochastic local search algorithms are proved to be one of the most effective approach for computing approximate solutions of hard combinatorial problems. Most of them are based on a typical randomness related to some uniform distributions for generating initial solutions. Particularly, Extremal Optimization is a recent meta-heuristic proposed for finding high quality solutions to hard optimiza...

In the present thesis we consider extremal self-dual codes. We mainly concentrate on Type II codes (binary doubly-even codes), which may theoretically exist for lengths n = 8k ≤ 3928. It is noteworthy that extremal Type II codes have been actually constructed only for 13 lengths, 136 being the largest. Over the last decades the study of extremal codes became inseparable from the study of their ...

In the present paper, we determine estimations on Atangana-Baleanu-Caputo fractional derivative at extreme points. With assistance of obtained, derive comparison results. Peano's type existence results established for nonlinear differential equations involving derivative. The acquired are then utilized to deal with local, extremal and global solution.

eccentric connectivity index has been found to have a low degeneracy and hence a significantpotential of predicting biological activity of certain classes of chemical compounds. wepresent here explicit formulas for eccentric connectivity index of various families of graphs.we also show that the eccentric connectivity index grows at most polynomially with thenumber of vertices and determine the ...

(1) inf{‖f ‖p : f ∈ C [0, 1], f(ti) = ei, i = 1, . . . , m}, where ‖ · ‖p is the usual L [0, 1] norm, 1 ≤ p ≤ ∞, and to characterize f for which the above infimum is attained. If m ≤ n, then this problem has a simple solution. There are algebraic polynomials of degree at most n−1 satisfying the interpolation data, and any of these polynomials obviously solve our problem. If m > n then, in gener...

We present a 4-dimensional nonsupersymmetric black hole solution to low energy type IIA string theory which carries D0and D6-brane charges. For equal charges this solution reduces to the one discussed recently by Sheinblatt. We construct the corresponding brane configuration for the extremal case and compute the 1-loop matrix theory potential for the scattering of a 0-brane probe off this brane...