In this paper, binary extremal self-dual codes of length 48 and extremal unimodular lattices in dimension 48 are studied through their shadows and neighbors. We relate an extremal singly even self-dual [48, 24, 10] code whose shadow has minimum weight 4 to an extremal doubly even selfdual [48, 24, 12] code. It is also shown that an extremal odd unimodular lattice in dimension 48 whose shadow ha...

As in the grand canonical treatment of Reissner-Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.

Since then, many extremal problems for the class ~ and related classes have been considered ([1], [2], [4] to [9]). In many of these extremal problems, the extremal function is symmetric with respect to the real axis; or if an extremal function is not unique, there exists a symmetric extremal function [7]. This leads us to consider the compact subclass of functions whose image is symmetric with...

in this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities  have been proved for an ivp of first order hybrid  random differential equations with the linear perturbation of second type. a comparison theorem is proved and  applied to prove the uniqueness of random solution for the considered perturbed random differential equ...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

We give several pieces of evidence to show that extremal black holes cannot be obtained as limits of non-extremal black holes. We review arguments in the literature showing that the entropy of extremal black holes is zero, while that of near-extremal ones obey the Bekenstein-Hawking formula. However, from the counting of degeneracy of quantum (BPS) states of string theory the entropy of extrema...

We define the extremal length of vector measures. We show the reciprocal relation between extremal distance and extremal width of vector measures.

We consider the one-loop corrected geometry and thermodynamics of a rotating BTZ black hole by way of a dimensionally reduced dilaton model. The analysis begins with a comprehensive study of the non-extremal solution after which two different methods are invoked to study the extremal case. The first approach considers the extremal limit of the non-extremal calculations, whereas the second treat...

The lexicographical order ᏸ on a sequence space ᐄ n ϭ ͕ 0 , 1 ,. .. , ␣ ͖ n , defined by x n Ͻ ᏸ y n if f there exists a t such that x t Ͻ y t and x s ϭ y s for s Ͻ t , is one of the most important and frequently encountered orders in combinatorial extremal theory. An early result in this area , Harper's solution of an edge-isoperimetric problem (EIP) in binary Hamming space ([13]) (generalized i...

Let X be a compact Riemann surface of genus ≥ 2 of constant negative curvature −1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an extremal surface. This paper gives formulas enumerating extremal surfaces of genus ≥ 4 up to isometry. We show also that the isometry group of an extremal surface is always cyclic o...