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Showing 1 to 20 of 201 for “"conjectures"”.
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Stark's conjectures
We give a slightly more general version of the Rubin-Stark conjecture, but show that in most cases it follows from the standard version. After covering the necessary background, we state the principal Stark conjecture and show that although the conjecture depends on a choice of a set of places and …
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Questions and conjectures about multinomial coefficients
The purpose of this thesis is to try to answer some of the questions in Dr. Bachman's paper "On Divisibility Properties of Certain Multinomial Coefficients". First we let {ai} be any sequence (finite or infinite) of positive integers such that i1ai ≤1 . It is clear that n!&sqbl0;na1 …
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New progress towards three open conjectures in geometric analysis
This thesis, like all of Gaul, is divided into three parts. In Chapter One, I study minimal surfaces in R⁴ with quadratic area growth. I give the first partial result towards a conjecture of Meeks and Wolf on asymptotic behavior of such surfaces at infinity. In particular, I prove that under mild …
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Numerical Tests of Two Conjectures in Fake Real Quadratic Orders
… behaves similarly to real quadratic orders. Two conjectures regarding fake real quadratic orders are discussed in the thesis. The first one is the Cohen-Lenstra heuristic. Our computation showed that for fixed p, the proportion of fake real quadratic orders for which the odd part of the class …
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Emerton-Gee Stacks, Serre Weights, and Breuil-Mézard Conjectures for GSp_4
We construct a moduli stack of rank 4 symplectic projective étale (phi,Gamma)-modules and prove its geometric properties for any prime p>2 and finite extension K/Q_p. When K/Q_p is unramified, we adapt the theory of local models recently developed by Le-Le Hung-Levin-Morra to study the geometry of …
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On conjectures related to character varieties of knots and Jones polynomials
It is well known that the Kauffman Bracket Skein Module of a knot complement K_q(S^3 \ K) is canonically a module over the Z_2-invariants of the quantum torus, A_q^{Z_2}, and this module determines the colored Jones polynomials J_n(K; q) of the knot K. Berest and Samuelson identified a conjecture …
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Rank constrained homotopies of matrices and the Blackadar-Handelman conjectures on C*-algebras
… n,k,l</em>))=0</p> <p>Blackadar-Handelman conjectures on <em>C</em>*-algebras:</p> <p>Let <em>DF</em>(<em>A</em>) denote the set of all dimension functions on a <em>C</em>*-algebra <em>A</em> and let <em>LDF</em>(<em>A</em>) be the set of all <em>s</em> ∈ <em>DF</em>(<em>A</em>) which are …
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
The conjecture of Birch and Swinnerton-Dyer is unquestionably one of the most important open problems in number theory today. Let $E$ be an elliptic curve defined over an imaginary quadratic field $K$ contained in $\mathbb{C}$, and suppose that $E$ has complex multiplication by the ring of integers …
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Multiple interactive competition among multiproduct firms: Theoretical and empirical analysis
… is represented by a set of price and product conjectures, which represents the firm's belief about rivals' responses against its decision changes. The U.S. automobile industry is used to examine the interaction. By estimating the competitive conjectures, diverse patterns of competition are …
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Dade's Conjecture for the McLaughlin Simple Group
… the first of what was to be a series of conjectures concerned with counting characters in the blocks of finite groups. Specifically, Dade's so-called Ordinary Conjecture asserts that if a finite group G has trivial p-core, and B is a p-block of G of positive defect, then the number k(B,d) …
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Dade's Conjecture for the McLaughlin Simple Group
… the first of what has to be a series of conjectures concerned with counting characters in the blocks of finite groups. Specifically, Dade's so-called Ordinary Conjecture asserts that if a finite group G has trivial p-core and B is a p-block of G of positive defect, then the number $k(B,\ …
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Explicit formulas for weighted orbital integrals for the inhomogeneous and semi-Lie arithmetic fundamental lemmas conjectured for the full spherical Hecke algebra
… trace formula approach to the Gan-Gross-Prasad conjectures, the arithmetic fundamental lemma was proposed by Wei Zhang and used in an approach to the arithmetic Gan-Gross-Prasad conjectures. The Jacquet-Rallis fundamental lemma was recently generalized by Spencer Leslie to a statement holding …
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A new structure on Khovanov's homology
The purpose of this thesis is proving conjectures in [1] on the Khovanov invariant. Khovanov invariant [6] is an invariant of (relatively) oriented links which is a cohomology theory over the cube of the resolutions of a link diagram. Khovanov invariant specializes to the Jones polynomial by taking …
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Intuicionistinis kontinuumas /
… intuitionistic continuum in order to prove their conjectures. This often philosophical activity is still carried out today because it is inherent in human beings to think and to seek to discover, while there may not be a single truth, as the phenomenon of the intuitionistic continuum shows. The …
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A study of circuit Complexity for Coherent States
… and collaborators proposed two holographic conjectures. The Complexity=Volume (CV) states that complexity of the boundary field theory is dual to the volume of a co dimension one maximal surface that extends to the boundary of the Ads space. Complexity=Action (CA) posits that complexity of …
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On Selmer groups and factoring p-adic L-functions
… Dasgupta's result is consistent with the main conjectures associated to the 4-dimensional representation (to which the 3-variable p-adic L-function is associated), the 3-dimensional representation (to which the 2-variable p-adic L-function is associated) and the 1-dimensional representation (to …
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Edge-colorings and flows in Class 2 graphs
… are strongly related to some outstanding open conjectures, such as the Cycle Double Cover Conjecture, the Berge-Fulkerson Conjecture, the Petersen Coloring Conjecture and the Tutte's 5-flow Conjecture. We obtain some new restrictions on the structure of a possible minimum counterexample to the …
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