The Ehrhart function for symbols and a generalization of Eulers - PowerPoint PPT Presentation

Dec 26, 2022 •329 likes •800 views

The Ehrhart function for symbols and a generalization of Eulers constant. Ehrhart from Euler- MacLaurin. Simple and non-simple polytopes. Non-simple Simple Some references for the exact Euler-MacLaurin formula in higher dimensions.

The Ehrhart function for symbols and a generalization of Euler’s constant.
Ehrhart from Euler- MacLaurin.
Simple and non-simple polytopes. Non-simple Simple
Some references for the exact Euler-MacLaurin formula in higher dimensions.
Regular polytopes.
Regular and non- regular polytopes.
The Khovanskii- Pukhlikov formula, 1.
The Khovanskii- Pukhlikov formula, 2, moving the facets.
The Khovanskii- Pukhlikov formula,3, the Todd operator.
The Khovanskii- Pukhlikov formula.
Symbols.
Polyhomogeneous symbols. n
The order of a symbol.
The Ehrhart formula.
The constant C .
Independence of regularization.
The polar decomposition theorem.
The construction in general.
Polar decomposition.
Using unweighted sums.
The Euler-MacLaurin formula with remainder.
A very rough outline of the proof.
The limiting form of the remainder.
Relation to Euler’s gamma.
Relation of C(s) to the zeta function.

Download Presentation

Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

function TT-Entails? ( KB , ) returns true or false symbols a list of the proposition

B.Y. Choueiry function TT-Entails? ( KB , ) returns true or false symbols a list of the proposition symbols in KB and return TT-Check-All ( KB , , symbols ,[ ]) function TT-Check-All ( KB , , symbols , model ) returns true

360 views • 3 slides

Generalized Ehrhart Polynomials Nan Li (MIT) with Sheng Chen (HIT) and Steven Sam (MIT) Aug 5,

Generalized Ehrhart Polynomials Nan Li (MIT) with Sheng Chen (HIT) and Steven Sam (MIT) Aug 5, 2010 Fpsac Outline Ehrhart Theorem Generalized Ehrhart polynomials by examples Main theorem in three equivalent versions Proof:

905 views • 33 slides

Theories 1 Definitions Definition A signature is a set of predicate and function symbols. A

First-order Predicate Logic Theories 1 Definitions Definition A signature is a set of predicate and function symbols. A -formula is a formula that contains only predicate and function symbols from . A -structure is a structure that

588 views • 10 slides

CS156: The Calculus of Signature T - set of constant, function, and predicate symbols

First-Order Theories I First-order theory T consists of CS156: The Calculus of Signature T - set of constant, function, and predicate symbols Computation Set of axioms A T - set of closed (no free variables) Zohar Manna T -formulae

217 views • 8 slides

ITERATED INTEGRALS, DEDEKIND SYMBOLS, AND ZETA POLYNOMIALS Yuri I. Manin 1 2 PLAN PART I:

ITERATED INTEGRALS, DEDEKIND SYMBOLS, AND ZETA POLYNOMIALS Yuri I. Manin 1 2 PLAN PART I: DEDEKIND SYMBOLS 1. CLASSICAL, GENERALIZED, AND NONCOMMUTATIVE DEDEKIND SYMBOLS 2. RECONSTRUCTION OF THE SYMBOL FROM ITS RECIPROCITY FUNCTION 3.

362 views • 25 slides

Ehrhart Positivity Federico Castillo University of California, Davis Joint work with Fu Liu

Ehrhart Positivity Federico Castillo University of California, Davis Joint work with Fu Liu December 15, 2016 Federico Castillo UC Davis Ehrhart Positivity Lattice points of a polytope A (convex) polytope is a bounded solution set of a

1.13k views • 100 slides

Gate Symbols OR NOR AND NAND INVERTER BUFFER Exercise :

Combinational Logic Gate Symbols OR NOR AND NAND INVERTER BUFFER Exercise : show that the equivalent gates do the same function Decoder Multiple-input/multiple-output device. Inputs ( n ) are

87 views • 6 slides

Introduction 1 st day Friederike Ehrhart, PhD Department of Bioinformatics-BiGCaT, Maastricht

Introduction 1 st day Friederike Ehrhart, PhD Department of Bioinformatics-BiGCaT, Maastricht University, The Netherlands BioSB course: Biological Network Analysis http://tinyurl.com/pl5yreh Amsterdam, 17-18 September 2015

504 views • 16 slides

Implementing Tangible Symbols for Every day Communication Anne M. Kuhlmeier, M.A., CCC/SLP, ATP

7/30/2013 Implementing Tangible Symbols for Every day Communication Anne M. Kuhlmeier, M.A., CCC/SLP, ATP annekuhlmeier@cableone.net Tangible Symbols How What Why Who WHAT: Tangible Symbols Rowland & Schwigert coined the term

123 views • 11 slides

Classification of Combinatorial Polynomials (in particular, Ehrhart Polynomials of Zonotopes)

Classification of Combinatorial Polynomials (in particular, Ehrhart Polynomials of Zonotopes) Matthias Beck San Francisco State University Katharina Jochemko Kungliga Tekniska H ogskolan Emily McCullough University of San Francisco

244 views • 20 slides

Foto: Michael Ehrhart MUSEUM FOR COMMUNICATION An exclusive and multifunctional location The

Foto: Michael Ehrhart MUSEUM FOR COMMUNICATION An exclusive and multifunctional location The Museum for Communication Berlin unites the past, present and future under one roof. Its permanent exhibition offers vivid insights into the origins,

790 views • 30 slides

Deep learning: Challenges in learning and generalization Tomas Mikolov, Facebook AI What is

Deep learning: Challenges in learning and generalization Tomas Mikolov, Facebook AI What is generalization? Memorization to remember all training examples (Universal Approximator) 2 + 3 = 5, 3 + 2 = 5, ... Generalization to

281 views • 14 slides

Beyond Picks theorem: Ehrhart polynomials and mixed volumes Kiran S. Kedlaya Department of

Beyond Picks theorem: Ehrhart polynomials and mixed volumes Kiran S. Kedlaya Department of Mathematics, University of California, San Diego kedlaya@ucsd.edu http://kskedlaya.org/slides/ PROMYS (virtual visit) July 8, 2020 Supported by NSF

1.08k views • 34 slides

Equational Logic A language L of algebras (or algebraic structures ) consists of a set F of

(LMCS, p. 133) III.1 Equational Logic A language L of algebras (or algebraic structures ) consists of a set F of function symbols f, g, h, a set C of constant symbols c, d, e, a set of variables x, y, z .

1.35k views • 105 slides

Ehrhart Quasi-polymomials of ClebschGordan Coefficients Tyrrell McAllister Univ. of

Ehrhart Quasi-polymomials of ClebschGordan Coefficients Tyrrell McAllister Univ. of California, Davis Joint Work with J. De Loera 25 Aug, 2005 Talk Outline 1. Lie algebras and their ClebschGordan coefficients 2. Polytopes for

586 views • 19 slides

$Discreet e Volume Computations \ for Polytopes: An Invitation to Ehrhart Theory Matthias Beck$

Discreet e Volume Computations \ for Polytopes: An Invitation to Ehrhart Theory Matthias Beck

Discreet e Volume Computations \ for Polytopes: An Invitation to Ehrhart Theory Matthias Beck San Francisco State University math.sfsu.edu/beck Meet my friends . . . If the solution set of a linear system of (in-)equalities is bounded, we

1.19k views • 80 slides

Morse Theory Roel Hospel Technische Universiteit Eindhoven roel.hospel@gmail.com May 24, 2018

Morse Theory Roel Hospel Technische Universiteit Eindhoven roel.hospel@gmail.com May 24, 2018 Roel Hospel (TU/e) Morse Theory May 24, 2018 1 / 29 Overview Why Morse Theory? 1 Manifolds 2 Smooth Functions 3 Morse Functions 4 The

441 views • 29 slides

Geometry and Topology Andrew Ranicki (a.ranicki@ed.ac.uk) substituting for Michael Weiss

1 Geometry and Topology Andrew Ranicki (a.ranicki@ed.ac.uk) substituting for Michael Weiss (m.weiss@maths.abdn.ac.uk) SMSTC Symposium, Perth, 10th October, 2007 2 Prerequisites A course in metric spaces or topological spaces (or both).

258 views • 12 slides

Color, Math, and Visualization Roxana Bujack Operated by Los Alamos National Security, LLC for

Color, Math, and Visualization Roxana Bujack Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA Author Text UNCLASSIFIED Color space is infinite dimensional image: wikimedia.org Roxana Bujack Title

1.5k views • 14 slides

Metric Spaces Definition If d is a metric on X , then the metric topology on X induced by d is

Metric Spaces Definition If d is a metric on X , then the metric topology on X induced by d is the topology generated by the basis = { B d ( X , ) : x X and > 0 } . The set X endowed with this topology is called the metric space (

52 views • 4 slides

9.1 Better numerical solutions than Eulers a lesson for MATH F302 Differential Equations Ed

9.1 Better numerical solutions than Eulers a lesson for MATH F302 Differential Equations Ed Bueler, Dept. of Mathematics and Statistics, UAF March 8, 2019 for textbook: D. Zill, A First Course in Differential Equations with Modeling

330 views • 20 slides

Initial-Value Problems for ODEs Eulers Method II: Error Bounds Numerical Analysis (9th

Initial-Value Problems for ODEs Eulers Method II: Error Bounds Numerical Analysis (9th Edition) R L Burden & J D Faires Beamer Presentation Slides prepared by John Carroll Dublin City University 2011 Brooks/Cole, Cengage Learning

890 views • 59 slides

Chapter 4: Higher-Order Differential Equations Part 1 Department of Electrical Engineering

Preliminary: Linear Equations Reduction of Order Homogeneous Linear Equations with Constant Coefficients Cauchy-Euler Equation Summary Chapter 4: Higher-Order Differential Equations Part 1 Department of Electrical Engineering National

833 views • 69 slides

Lecture 3.2: Equations with constant coefficients Matthew Macauley Department of Mathematical

Lecture 3.2: Equations with constant coefficients Matthew Macauley Department of Mathematical Sciences Clemson University http://www.math.clemson.edu/~macaule/ Math 2080, Differential Equations M. Macauley (Clemson) Lecture 3.2: Equations

103 views • 6 slides