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Showing 1 to 20 of 489 for “"Regularity"”.
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Regularity theory for nonlocal equations
… is primarily concerned with proving Sobolev regularity results of Calderón-Zygmund-type for nonlinear nonlocal equations with possibly very irregular coefficients of VMO-type or even coefficients that are merely small in BMO. In particular, such coefficients might be discontinuous.<br /><br …
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Arithmetic regularity lemmas and applications
… investigates various aspects of arithmetic regularity lemmas in the context of vector spaces over finite fields of prime characteristic. Chapter 1 obtains a generalisation of the induced arithmetic removal lemma of Bhattacharyya, Fischer, and Lovett [6] for translation-invariant arithmetic …
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Sparse regularity and relative Szemerédi theorems
… the sparse setting. First, we consider Szemerédi regularity lemma, a fundamental tool in extremal combinatorics. The regularity method, in its original form, is effective only for dense graphs. It has been a long standing problem to extend the regularity method to sparse graphs. We solve this …
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Party Regularity in the Sixty-Third Congress
Made available in DSpace on 2014-12-05T17:25:40Z (GMT). No. of bitstreams: 1 0003147.pdf: 25149425 bytes, checksum: a1d5dff2011993b207fd88d40fb09d70 (MD5) Previous issue date: 1951
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The influence of statistical regularity on perception
… builds a representation of statistical regularity of the environment into the brain and that the brain takes advantage of these learned representations when attempting to make sense of incoming stimuli. Experiment 1 replicates and expands upon previous research showing that statistically …
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Fine regularity properties of SLE_4 and SLE_8
The Schramm-Loewner evolution (SLE$_{\kappa}$) is a one parameter family ($\kappa$>0) of curves which connect two boundary points of a simply connected domain. It was introduced by Schramm in 1999 as a candidate to describe the scaling limits of the interfaces in statistical mechanics models on …
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Regularity and removal lemmas and their applications
In this thesis, we analyze the regularity method pioneered by Szemerédi, and also discuss one of its prevalent applications, the removal lemma. First, we prove a new lower bound on the number of parts required in a version of Szemerédi's regularity lemma, determining the order of the tower height …
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STRICT REGULARITY OF POSITIVE DEFINITE TERNARY QUADRATIC FORMS
… and lattices that are candidates for strict regularity. An integer that is primitively represented by a genus, but not by some specific form in that genus, is called a primitive exception for that form. So, the strictly regular forms are those forms for which there are no primitive exceptions. …
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Schauder Regularity Theory for Degenerate and Singular PDEs
L'abstract è presente nell'allegato / the abstract is in the attachment
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Local Regularity of the Complex Monge-Ampere Equation
… account of the current development in the local regularity theory of the complex Monge-Ampere equation through the modern fully-nonlinear PDE point of view. We have apply the modern elliptic techniques to establish new local regularity results. These includes: regularity of small perturbed …
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Regularity results for some elliptic and parabolic problems
The present thesis deals with the regularity of solutions to nonlinear partial differential equations of elliptic and parabolic type, and it collects some results obtained during the last three years under the supervision of Prof. Ugo Gianazza The first part concernes the study of singular porous …
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The regularity method in directed graphs and hypergraphs
In recent years the regularity method has been used to tackle many embedding problems in extremal graph theory. This thesis demonstrates and develops three different techniques which can be used in conjunction with the regularity method to solve such problems. These methods enable us to prove an …
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Abstract Density Theorems Under Hypothesis of Mean Regularity
Made available in DSpace on 2014-12-09T22:17:12Z (GMT). No. of bitstreams: 1 6408374.pdf: 757782 bytes, checksum: 518bec56a12cb8f39496ae9e14d81090 (MD5) Previous issue date: 1964
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Regularity and boundary variations for the Neumann problem
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Three applications of the regularity method in combinatorics
Szemerédi’s regularity lemma is one of the central tools in extremal graph theory and additive combinatorics. We present three versions of this lemma tailored for three applications. The first application considered is the graph removal lemma, which states that for any graph 𝐻 on 𝑘 vertices and all …
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Regularity-Preserving Terrain Simplification For Faster Line-of-Sight
… exist for regular terrain models, we introduce regularity-preserving terrain simplification methods based on reverse subdivision and examine their effect on query accuracy. Furthermore, we develop a novel feature preserving reverse subdivision scheme that attempts to improve query accuracy over …
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On regularity for integral currents - the smooth approximation of cycles
This thesis is devoted to the study of regularity properties of generalized surfaces in the Plateau problem. The first part of the thesis focuses on the regularity theory for Federer-Fleming integral currents, proving that every integral cycle can be approximated by a smooth submanifold up to a …
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Global Regularity for Euler Vortex Patch in Bounded Smooth Domains
… enough initially. In bounded domains, the regularity theory for patch solutions is less complete. In this thesis, I study the Euler vortex patch in a general smooth bounded domain. I prove global in time regularity by providing the upper bound of the growth on curvature of the patch …
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