On some reconstruction problems

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

On some factorization problems

We consider three notions of factorization arising in different frameworks: factorizing languages, factorization of the natural numbers, factorizing codes. A language X ⊆ A∗ is called factorizing if there exists a language Y ⊆ A∗ such that XY = A∗ and the product is unambiguous. This is a decidable property for recognizable languages X . If we consider the particular case of unary alphabets, we...

Kocay's Lemma, Whitney's Theorem, and some Polynomial Invariant Reconstruction Problems

Given a graph G, an incidence matrix N (G) is defined on the set of distinct isomorphism types of induced subgraphs of G. It is proved that Ulam’s conjecture is true if and only if the N -matrix is a complete graph invariant. Several invariants of a graph are then shown to be reconstructible from its N -matrix. The invariants include the characteristic polynomial, the rank polynomial, the numbe...

Commcnts on Some Problems

Sparse Acquisition and Reconstruction for some Computer Vision Problems

Title of dissertation: SPARSE ACQUISITION AND RECONSTRUCTION FOR SOME COMPUTER VISION PROBLEMS Nagilla Dikpal Reddy, Doctor of Philosophy, 2011 Dissertation directed by: Professor Rama Chellappa Department of Electrical and Computer Engineering Sparse representation, acquisition and reconstruction of signals guided by theory of Compressive Sensing (CS) has become an active research research top...