The entropy-area spectrum of a black hole has been a long-standing and unsolved problem. Based on a recent methodology introduced by two of the authors, for the black hole radiation (Hawking effect) as tunneling effect, we obtain the entropy spectrum of a black hole. In Einstein’s gravity, we show that both entropy and area spectrum are evenly spaced. But in more general theories (like Einstein...

Convexity invariants like Caratheodory, Helly and Radon numbers are computed for triangle path convexity in graphs. Unlike minimal path convexities, the Helly and Radon numbers behave almost uniformly for triangle path convexity. c © 1999 Elsevier Science B.V. All rights reserved

This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group action, and therefore signature submanifold is a key for solving equivalence problems.

An algorithm is presented for automatically inferring loop invariants in separation logic for imperative list-processing programs. A prototype implementation for a C-like language is shown to be successful in generating loop invariants for a variety of sample programs. The programs, while relatively small, iteratively perform destructive heap operations and hence pose problems more than challen...

We advocate the usage of 3D Zernike invariants as descriptors for 3D shape retrieval. The basis polynomials of this representation facilitate computation of invariants under rotation, translation and scaling. Some theoretical results have already been summarized in the past from the aspect of pattern recognition and shape analysis. We provide practical analysis of these invariants along with al...

We investigate degeneracies of BPS states of D-branes on compact Calabi-Yau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial D-brane systems, and to clarify the subtle relation o...

It is well known that relations in the tautological ring of moduli spaces of pointed stable curves give partial differential equations for Gromov-Witten invariants of compact symplectic manifolds. These equations do not depend on the target symplectic manifolds and therefore are called universal equations for Gromov-Witten invariants. In the case that the quantum cohomology of the symplectic ma...

We present a method for generating linear invariants for large systems. The method performs forward propagation in an abstract domain consisting of arbitrary polyhedra of a predefined fixed shape. The basic operations on the domain like abstraction, intersection, join and inclusion tests are all posed as linear optimization queries, which can be solved efficiently by existing LP solvers. The nu...

In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and statitical independence of the constituent parts. An example of interacting Bernoulli units is used to illustrate the nature of these invariants. 1 Conditional exp...

We describe an abstract domain for representing useful invariants of heap-manipulating programs (in presence of recursive data structures and pointer arithmetic) written in languages like C or low-level code. This abstract domain allows representation of must and may equalities among pointer expressions. Pointer expressions contain existentially or universally quantified integer variables guard...