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Showing 1 to 20 of 125 for “"Infinitesimal"”.
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Infinitesimal Probability Theory with Amalgamation
We introduce the notion of operator-valued infinitesimal independence for the free, Boolean, and monotone cases. We show that operator-valued infinitesimal free (respectively Boolean, monotone) independence is equivalent to the operator-valued free (respectively Boolean, monotone) independence over …
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Infinitesimal Models of Algebraic Theories
… always understood intuitively as spaces that are infinitesimally linear at each point, and thus infinitesimally affine when forgetting about the base point. The aim of this thesis is to develop a general theory of infinitesimal models of algebraic theories that provides us with a formalisation of …
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On the infinitesimal theory of Chow groups
… approach to this problem, focusing on the infinitesimal structure of the Chow groups near their identity elements. This method was adumbrated in recent work of Mark Green and Phillip Griffiths. Similar topics have been explored by Bloch, Stienstra, Hesselholt, Van der Kallen, and others. A …
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On unitary representations with regular infinitesimal character
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1986.
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Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis
… that nonstandard analysis (NSA) and smooth infinitesimal analysis (SIA) are alternatives to the standard approach to the calculus. In doing so, we outline the historical approaches to the calculus, the standard approach to the calculus, and two nonstandard approaches, namely NSA and SIA; we …
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Configuration Complexes and Tangential and Infinitesimal versions of Polylogarithmic Complexes
… in weight 2 and 3, and Cathelineau's infinitesimal polylogarithmic complexes as well as a tangential complex to the famous Bloch-Suslin complex (in weight 2) and to Goncharov's ``motivic`` complex (in weight 3), respectively, as proposed by Cathelineau [5]. Our main result is a …
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The affine Yangian of gl₁, and the infinitesimal Cherednik algebras
… of this thesis, we obtain some new results about infinitesimal Cherednik algebras. They have been introduced by Etingof-Gan-Ginzburg in [EGG] as appropriate analogues of the classical Cherednik algebras, corresponding to the reductive groups, rather than the finite ones. Our main result is the …
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The North Pole Problem and Recent Developments in Infinitesimal Free Probability
… state-of-the-art of the combinatorial theory of infinitesimal free probability, one of the principal extensions of free probability theory. We place particular focus on the recently developed theory of real infinitesimal free probability by Cébron and Mingo. We also briefly discuss (complex) …
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Local Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applications
In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space through studying a class of sets S which approximates A well in small balls. We …
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New symmetries from old: exploiting lie algebra structure to determine infinitesimal symmetries of differential equations
… find more symmetries of the system. A Lie (or infinitesimal) symmetry of a system of differential equations is a transformation of its dependent and independent variables, depending on continuous parameters, which maps any solution of the system to another solution of the same system. …
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Generic Reductions of an Integrable G-Structure and an Infinitesimal Version of Cartan-Sternberg Reduction
Given an integrable G-structure P and a closed subgroup H of G, we assign to each H-reduction of P a singular set in the base manifold. Our first main result is that generically, this singular set is a finite disjoint union of submanifolds (our theorem generalizes an unpublished result of L. …
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Semigroups of Composition Operators and the Cesaro Operator on H('p)(d) (Bergman Space, Infinitesimal Generator)
… functions mapping the unit disk into itself. The infinitesimal
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Computational Analysis of Elastic Moduli of Covalently Functionalized Carbon Nanomaterials, Infinitesimal Elastostatic Deformations of Doubly Curved Laminated Shells, and Curing of Laminates
We numerically analyze three mechanics problems described below. For each problem, the developed computational model is verified by comparing computed results for example problems with those available in the literature. Effective utilization of single wall carbon nanotubes (SWCNTs) and single layer …
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Connections on conformal blocks
… describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. This family of functors, parametrized by the Ran space of X, acts by averaging a quasi-coherent sheaf over infinitesimal modifications of G-bundles at prescribed points …
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Hyperreal structures arising from an infinite base logarithm
… presents new concepts in the use of infinite and infinitesimal numbers in real analysis. theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of "nonstandard analysis". paper begins with a short exposition of the construction of the …
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Invariantes integrales en grupos de Lie
… consiste en trasladar a izquierda una porción infinitesimal de curva (o n-superficies), consiguiendo que uno de los vértices coincida con el punto unidad del grupo base. El arco infinitesimal trasladado (o cada uno de los n arcos infinitesimales de la n-superficie trasladada), define un …
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Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation.
… non-classical method is utilized to find the <em>infinitesimal generator</em> and the <em>invariant surface condition</em> for the subgroup where the solutions for the desired PDE exist. Using the infinitesimal generator and the invariant surface condition, we reduce the PDE to a mildly nonlinear …
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The effect of shear on the stability and dynamic properties of elastic bodies
… major part of the study is the investigation of infinitesimal wave propagation within elastic material which has been subjected to a static pre-strain corresponding to simple shear. Initially we consider a prototype problem wherein the theory of incremental motions provides the mechanism for …
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On properties of linear control systems on Lie groups
… where the drift vector field X is an infinitesimal automorphism, u<sub>j</sub> are piecewise constant functions, and the control vectors Y<sub>j</sub> are left-invariant vector fields. Properties for the flow of the infinitesimal automorphism X and for the reachable set defined by …
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