Convergence (accounting), the goal of and work towards establishing a single set of accounting standards that will be used internationally
Digital convergence, the convergence of the information technology, telecommunications, consumer electronics, and entertainment industries into digital media conglomerates
Convergence (David Arkenstone and David Lanz album)
Convergence is an album by David Arkenstone and David Lanz, released in 1996. It is a compilation of tracks from Narada releases such as A Childhood Remembered and The Narada Wilderness Collection.
GSS Fall 2016 - Giovanni Gravina: An Introduction to Gamma-convergence
In this talk we will look at the so-called gamma-convergence, a notion of convergence for functionals which is particularly suited for problems in the calculus of variations. We'll start by motivating the definition and we'll prove properties of gamma-limits. Time permitting, we'll study the gamma-convergence of the Dirichlet energy on a perforated domain to investigate the behavior of solutions to Poisson's equation as the perforation vanishes.
published: 09 Nov 2016
Gamma Convergence (Lecture 2) by A K Nandakumaran
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous ...
published: 31 Dec 2019
Gamma Convergence | Lec#2 on Calculus of Variations | Shah Faisal | www.mathsvolunteers.com
Gamma Function and Convergence ||Maths for Graduates
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published: 19 Nov 2023
A Gamma-convergence result and an application to the Monge-Ampère gravitational model
Speaker: Luigi Ambrosio, Scuola Normale Superiore
2020 Fields Medal Symposium
http://www.fields.utoronto.ca/activities/20-21/fieldsmedalsym
Abstract: I illustrate a Gamma-convergence result for nonsmooth action functionals involving the minimal selection of the subdifferential of convex functions. The result has been motivated by the study of a discrete version of the MA gravitational model. Joint work with A.Baradat and Y.Brenier.
published: 20 Oct 2020
Matias Delgadino: Mean field limit by Gamma convergence
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory
Abstract: In this work we give a proof of the mean-field limit for λ-convex potentials using a purely variational viewpoint. We take advantage that all evolutions of the involved quantities can be written as gradient flows of functionals at different levels: in the set of symmetric probability measures on N variables and in the set of probability measures on probability measures. This basic fact allows us to rely on Γ-convergence tools for gradient flows to finish the proof by identifying the limits of the different terms in the Evolutionary Variational Inequalities (EVIs) associated to each gradient flow. The λ-convexity of the potentials is crucial to identify uniquely the limits and in order to derive...
published: 28 May 2019
Davini, C — Composite Thin Walled Beams by Γ-Convergence
Composite Thin Walled Beams by Γ-Convergence
Talk by Cesare Davini from the University of Udine during the 52nd Meeting of the Society for Natural Philosophy (SNP), which was held in the Pedro Calmon Room at the Praia Vermelha Campus of the Federal University of Rio de Janeiro from October 22 to 24, 2014.
published: 30 Oct 2015
Convergence of Gamma Function
Proof of the Convergence of the Gamma Function for all real x greater than 0.
published: 05 Feb 2024
MAT 2420 Lecture 20 10 31 2024
published: 04 Nov 2024
Gamma Convergence (Lecture 3) by Nandakumar
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous ...
In this talk we will look at the so-called gamma-convergence, a notion of convergence for functionals which is particularly suited for problems in the calculus ...
In this talk we will look at the so-called gamma-convergence, a notion of convergence for functionals which is particularly suited for problems in the calculus of variations. We'll start by motivating the definition and we'll prove properties of gamma-limits. Time permitting, we'll study the gamma-convergence of the Dirichlet energy on a perforated domain to investigate the behavior of solutions to Poisson's equation as the perforation vanishes.
In this talk we will look at the so-called gamma-convergence, a notion of convergence for functionals which is particularly suited for problems in the calculus of variations. We'll start by motivating the definition and we'll prove properties of gamma-limits. Time permitting, we'll study the gamma-convergence of the Dirichlet energy on a perforated domain to investigate the behavior of solutions to Poisson's equation as the perforation vanishes.
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 Augu...
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behavior of the material, which does not consist of microscopic heterogeneities and can be solved or computed.
Topics to be covered in the workshop include the following but not limited to:
1. Multi-scale problems in applications
2. Introduction to homogenization
3. Techniques in homogenization
4. Recent trends
Plan and Schedule of the Program:
In this discussion meeting, we go through several examples to understand the homogenization procedure in a general perspective together with applications. We also present various mathematical techniques available and some details about the techniques. A tutorial cum problem-solving session will also be conducted so that beginners can learn the material rigorously. In this way, we can train local and international junior students and researchers by equipping them with the theory and applications of multi-scale analysis and homogenization. Furthermore, the speakers will also discuss some ongoing current research and new problems which can foster mentoring or collaboration between students and experts on the area of analysis of multi-scale phenomena.
In addition to the basic material of homogenization, the speakers will be presenting the recent results in their area of expertise and this will be an opportunity for the youngsters to get into this beautiful area of research. Further, every day, we are planning to have a tutorial cum problem-solving session through which the beginners can learn the material in a better way. To make the tutorials/training sessions more effective, we may form small groups and each group may be asked to do some specific material that they can present on the last day. Each small group may be trained by one of the speakers who are available for the entire workshop,
The schedule mainly consists of 4, one-hour lectures per day and a Tutorial cum Problem-Solving Session of one and a half hours which can be extended according to the requirement of the participants.
CONTACT US: [email protected]
PROGRAM LINK: https://www.icts.res.in/program/math2019
Table of Contents (powered by https://videoken.com)
0:00:00 Gamma Convergence (Lecture 2)
0:03:50 Minimization problem
0:06:14 Alpha = inf F(y) [Minimal value; Minimal point; Minimal sequence]
0:09:16 Graphs
0:17:43 Coercine
0:22:45 Definition
0:25:53 Theorem: Assume F. X-is Coercine and lsc
0:29:38 Proof:
0:32:55 F is given by an integral functions
0:40:26 Problem Solution
0:46:54 Concept of derivative
0:57:04 Exercise: assume u E C2 (Omega)
1:01:56 Integral functions
1:04:34 Proposition: F is lsc in strong topology
1:10:27 Two other functions
1:13:33 Weak lower semi continuity
1:17:29 Homogenization
1:27:51 Next
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behavior of the material, which does not consist of microscopic heterogeneities and can be solved or computed.
Topics to be covered in the workshop include the following but not limited to:
1. Multi-scale problems in applications
2. Introduction to homogenization
3. Techniques in homogenization
4. Recent trends
Plan and Schedule of the Program:
In this discussion meeting, we go through several examples to understand the homogenization procedure in a general perspective together with applications. We also present various mathematical techniques available and some details about the techniques. A tutorial cum problem-solving session will also be conducted so that beginners can learn the material rigorously. In this way, we can train local and international junior students and researchers by equipping them with the theory and applications of multi-scale analysis and homogenization. Furthermore, the speakers will also discuss some ongoing current research and new problems which can foster mentoring or collaboration between students and experts on the area of analysis of multi-scale phenomena.
In addition to the basic material of homogenization, the speakers will be presenting the recent results in their area of expertise and this will be an opportunity for the youngsters to get into this beautiful area of research. Further, every day, we are planning to have a tutorial cum problem-solving session through which the beginners can learn the material in a better way. To make the tutorials/training sessions more effective, we may form small groups and each group may be asked to do some specific material that they can present on the last day. Each small group may be trained by one of the speakers who are available for the entire workshop,
The schedule mainly consists of 4, one-hour lectures per day and a Tutorial cum Problem-Solving Session of one and a half hours which can be extended according to the requirement of the participants.
CONTACT US: [email protected]
PROGRAM LINK: https://www.icts.res.in/program/math2019
Table of Contents (powered by https://videoken.com)
0:00:00 Gamma Convergence (Lecture 2)
0:03:50 Minimization problem
0:06:14 Alpha = inf F(y) [Minimal value; Minimal point; Minimal sequence]
0:09:16 Graphs
0:17:43 Coercine
0:22:45 Definition
0:25:53 Theorem: Assume F. X-is Coercine and lsc
0:29:38 Proof:
0:32:55 F is given by an integral functions
0:40:26 Problem Solution
0:46:54 Concept of derivative
0:57:04 Exercise: assume u E C2 (Omega)
1:01:56 Integral functions
1:04:34 Proposition: F is lsc in strong topology
1:10:27 Two other functions
1:13:33 Weak lower semi continuity
1:17:29 Homogenization
1:27:51 Next
This lecture was delivered on September 24, 2022 to audience of Maths Volunteers.
The Lecture include:
1. Recap of lecture#1 (Classical approach- based on solv...
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#RealAnalysishandwrittennotes
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Facebook
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For full Course click here:
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#RealAnalysishandwrittennotes
Whatsapp @9451434163 for more details.
or click below
Whatsapp
http://wa.me/+919451434163
Facebook
https://www.facebook.com/mathsforgraduates
Instagram
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Telegram
https://t.me/mathsforgraduates
For full Course click here:
https://www.youtube.com/playlist?list=PLbwJuBHc3YzUIgPk82CIm-doYjZa_SeKe
Speaker: Luigi Ambrosio, Scuola Normale Superiore
2020 Fields Medal Symposium
http://www.fields.utoronto.ca/activities/20-21/fieldsmedalsym
Abstract: I illust...
Speaker: Luigi Ambrosio, Scuola Normale Superiore
2020 Fields Medal Symposium
http://www.fields.utoronto.ca/activities/20-21/fieldsmedalsym
Abstract: I illustrate a Gamma-convergence result for nonsmooth action functionals involving the minimal selection of the subdifferential of convex functions. The result has been motivated by the study of a discrete version of the MA gravitational model. Joint work with A.Baradat and Y.Brenier.
Speaker: Luigi Ambrosio, Scuola Normale Superiore
2020 Fields Medal Symposium
http://www.fields.utoronto.ca/activities/20-21/fieldsmedalsym
Abstract: I illustrate a Gamma-convergence result for nonsmooth action functionals involving the minimal selection of the subdifferential of convex functions. The result has been motivated by the study of a discrete version of the MA gravitational model. Joint work with A.Baradat and Y.Brenier.
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory
Abstract: In this work we give a proof of the mean-field limit for ...
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory
Abstract: In this work we give a proof of the mean-field limit for λ-convex potentials using a purely variational viewpoint. We take advantage that all evolutions of the involved quantities can be written as gradient flows of functionals at different levels: in the set of symmetric probability measures on N variables and in the set of probability measures on probability measures. This basic fact allows us to rely on Γ-convergence tools for gradient flows to finish the proof by identifying the limits of the different terms in the Evolutionary Variational Inequalities (EVIs) associated to each gradient flow. The λ-convexity of the potentials is crucial to identify uniquely the limits and in order to derive the EVIs at each description level of the interacting particle system. This is joint work with J.A. Carrillo and G. Pavliotis.
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory
Abstract: In this work we give a proof of the mean-field limit for λ-convex potentials using a purely variational viewpoint. We take advantage that all evolutions of the involved quantities can be written as gradient flows of functionals at different levels: in the set of symmetric probability measures on N variables and in the set of probability measures on probability measures. This basic fact allows us to rely on Γ-convergence tools for gradient flows to finish the proof by identifying the limits of the different terms in the Evolutionary Variational Inequalities (EVIs) associated to each gradient flow. The λ-convexity of the potentials is crucial to identify uniquely the limits and in order to derive the EVIs at each description level of the interacting particle system. This is joint work with J.A. Carrillo and G. Pavliotis.
Composite Thin Walled Beams by Γ-Convergence
Talk by Cesare Davini from the University of Udine during the 52nd Meeting of the Society for Natural Philosophy (...
Composite Thin Walled Beams by Γ-Convergence
Talk by Cesare Davini from the University of Udine during the 52nd Meeting of the Society for Natural Philosophy (SNP), which was held in the Pedro Calmon Room at the Praia Vermelha Campus of the Federal University of Rio de Janeiro from October 22 to 24, 2014.
Composite Thin Walled Beams by Γ-Convergence
Talk by Cesare Davini from the University of Udine during the 52nd Meeting of the Society for Natural Philosophy (SNP), which was held in the Pedro Calmon Room at the Praia Vermelha Campus of the Federal University of Rio de Janeiro from October 22 to 24, 2014.
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 Augu...
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behavior of the material, which does not consist of microscopic heterogeneities and can be solved or computed.
Topics to be covered in the workshop include the following but not limited to:
1. Multi-scale problems in applications
2. Introduction to homogenization
3. Techniques in homogenization
4. Recent trends
Plan and Schedule of the Program:
In this discussion meeting, we go through several examples to understand the homogenization procedure in a general perspective together with applications. We also present various mathematical techniques available and some details about the techniques. A tutorial cum problem-solving session will also be conducted so that beginners can learn the material rigorously. In this way, we can train local and international junior students and researchers by equipping them with the theory and applications of multi-scale analysis and homogenization. Furthermore, the speakers will also discuss some ongoing current research and new problems which can foster mentoring or collaboration between students and experts on the area of analysis of multi-scale phenomena.
In addition to the basic material of homogenization, the speakers will be presenting the recent results in their area of expertise and this will be an opportunity for the youngsters to get into this beautiful area of research. Further, every day, we are planning to have a tutorial cum problem-solving session through which the beginners can learn the material in a better way. To make the tutorials/training sessions more effective, we may form small groups and each group may be asked to do some specific material that they can present on the last day. Each small group may be trained by one of the speakers who are available for the entire workshop,
The schedule mainly consists of 4, one-hour lectures per day and a Tutorial cum Problem-Solving Session of one and a half hours which can be extended according to the requirement of the participants.
CONTACT US: [email protected]
PROGRAM LINK: https://www.icts.res.in/program/math2019
Table of Contents (powered by https://videoken.com)
0:00:00 Gamma Convergence (Lecture 3)
0:03:09 Examples
0:09:43 Correct Function
0:11:40 Sketch the graph
0:18:16 Relaxation
0:22:40 Proposition: Arbitrary Sup (lower semi continuous) is lower semi continuous
0:30:05 Theorem:
0:36:38 Comparison with Continuity F
0:39:29 Theorem: Let F . X -R be Covicine
0:47:47 Assume f
0:50:19 First polar function
0:55:47 Def (Gamma - Convergence)
0:57:44 Comparison with point wise convergence
1:02:59 Exercise
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behavior of the material, which does not consist of microscopic heterogeneities and can be solved or computed.
Topics to be covered in the workshop include the following but not limited to:
1. Multi-scale problems in applications
2. Introduction to homogenization
3. Techniques in homogenization
4. Recent trends
Plan and Schedule of the Program:
In this discussion meeting, we go through several examples to understand the homogenization procedure in a general perspective together with applications. We also present various mathematical techniques available and some details about the techniques. A tutorial cum problem-solving session will also be conducted so that beginners can learn the material rigorously. In this way, we can train local and international junior students and researchers by equipping them with the theory and applications of multi-scale analysis and homogenization. Furthermore, the speakers will also discuss some ongoing current research and new problems which can foster mentoring or collaboration between students and experts on the area of analysis of multi-scale phenomena.
In addition to the basic material of homogenization, the speakers will be presenting the recent results in their area of expertise and this will be an opportunity for the youngsters to get into this beautiful area of research. Further, every day, we are planning to have a tutorial cum problem-solving session through which the beginners can learn the material in a better way. To make the tutorials/training sessions more effective, we may form small groups and each group may be asked to do some specific material that they can present on the last day. Each small group may be trained by one of the speakers who are available for the entire workshop,
The schedule mainly consists of 4, one-hour lectures per day and a Tutorial cum Problem-Solving Session of one and a half hours which can be extended according to the requirement of the participants.
CONTACT US: [email protected]
PROGRAM LINK: https://www.icts.res.in/program/math2019
Table of Contents (powered by https://videoken.com)
0:00:00 Gamma Convergence (Lecture 3)
0:03:09 Examples
0:09:43 Correct Function
0:11:40 Sketch the graph
0:18:16 Relaxation
0:22:40 Proposition: Arbitrary Sup (lower semi continuous) is lower semi continuous
0:30:05 Theorem:
0:36:38 Comparison with Continuity F
0:39:29 Theorem: Let F . X -R be Covicine
0:47:47 Assume f
0:50:19 First polar function
0:55:47 Def (Gamma - Convergence)
0:57:44 Comparison with point wise convergence
1:02:59 Exercise
In this talk we will look at the so-called gamma-convergence, a notion of convergence for functionals which is particularly suited for problems in the calculus of variations. We'll start by motivating the definition and we'll prove properties of gamma-limits. Time permitting, we'll study the gamma-convergence of the Dirichlet energy on a perforated domain to investigate the behavior of solutions to Poisson's equation as the perforation vanishes.
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behavior of the material, which does not consist of microscopic heterogeneities and can be solved or computed.
Topics to be covered in the workshop include the following but not limited to:
1. Multi-scale problems in applications
2. Introduction to homogenization
3. Techniques in homogenization
4. Recent trends
Plan and Schedule of the Program:
In this discussion meeting, we go through several examples to understand the homogenization procedure in a general perspective together with applications. We also present various mathematical techniques available and some details about the techniques. A tutorial cum problem-solving session will also be conducted so that beginners can learn the material rigorously. In this way, we can train local and international junior students and researchers by equipping them with the theory and applications of multi-scale analysis and homogenization. Furthermore, the speakers will also discuss some ongoing current research and new problems which can foster mentoring or collaboration between students and experts on the area of analysis of multi-scale phenomena.
In addition to the basic material of homogenization, the speakers will be presenting the recent results in their area of expertise and this will be an opportunity for the youngsters to get into this beautiful area of research. Further, every day, we are planning to have a tutorial cum problem-solving session through which the beginners can learn the material in a better way. To make the tutorials/training sessions more effective, we may form small groups and each group may be asked to do some specific material that they can present on the last day. Each small group may be trained by one of the speakers who are available for the entire workshop,
The schedule mainly consists of 4, one-hour lectures per day and a Tutorial cum Problem-Solving Session of one and a half hours which can be extended according to the requirement of the participants.
CONTACT US: [email protected]
PROGRAM LINK: https://www.icts.res.in/program/math2019
Table of Contents (powered by https://videoken.com)
0:00:00 Gamma Convergence (Lecture 2)
0:03:50 Minimization problem
0:06:14 Alpha = inf F(y) [Minimal value; Minimal point; Minimal sequence]
0:09:16 Graphs
0:17:43 Coercine
0:22:45 Definition
0:25:53 Theorem: Assume F. X-is Coercine and lsc
0:29:38 Proof:
0:32:55 F is given by an integral functions
0:40:26 Problem Solution
0:46:54 Concept of derivative
0:57:04 Exercise: assume u E C2 (Omega)
1:01:56 Integral functions
1:04:34 Proposition: F is lsc in strong topology
1:10:27 Two other functions
1:13:33 Weak lower semi continuity
1:17:29 Homogenization
1:27:51 Next
#RealAnalysishandwrittennotes
Whatsapp @9451434163 for more details.
or click below
Whatsapp
http://wa.me/+919451434163
Facebook
https://www.facebook.com/mathsforgraduates
Instagram
https://instagram.com/mathsforgraduates
Telegram
https://t.me/mathsforgraduates
For full Course click here:
https://www.youtube.com/playlist?list=PLbwJuBHc3YzUIgPk82CIm-doYjZa_SeKe
Speaker: Luigi Ambrosio, Scuola Normale Superiore
2020 Fields Medal Symposium
http://www.fields.utoronto.ca/activities/20-21/fieldsmedalsym
Abstract: I illustrate a Gamma-convergence result for nonsmooth action functionals involving the minimal selection of the subdifferential of convex functions. The result has been motivated by the study of a discrete version of the MA gravitational model. Joint work with A.Baradat and Y.Brenier.
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory
Abstract: In this work we give a proof of the mean-field limit for λ-convex potentials using a purely variational viewpoint. We take advantage that all evolutions of the involved quantities can be written as gradient flows of functionals at different levels: in the set of symmetric probability measures on N variables and in the set of probability measures on probability measures. This basic fact allows us to rely on Γ-convergence tools for gradient flows to finish the proof by identifying the limits of the different terms in the Evolutionary Variational Inequalities (EVIs) associated to each gradient flow. The λ-convexity of the potentials is crucial to identify uniquely the limits and in order to derive the EVIs at each description level of the interacting particle system. This is joint work with J.A. Carrillo and G. Pavliotis.
Composite Thin Walled Beams by Γ-Convergence
Talk by Cesare Davini from the University of Udine during the 52nd Meeting of the Society for Natural Philosophy (SNP), which was held in the Pedro Calmon Room at the Praia Vermelha Campus of the Federal University of Rio de Janeiro from October 22 to 24, 2014.
PROGRAM: MULTI-SCALE ANALYSIS AND THEORY OF HOMOGENIZATION
ORGANIZERS: Patrizia Donato, Editha Jose, Akambadath
Nandakumaran and Daniel Onofrei
DATE: 26 August 2019 to 06 September 2019
VENUE: Madhava Lecture Hall, ICTS, Bangalore
Homogenization is a mathematical procedure to understand the multi-scale analysis of various phenomena modeled by partial differential equations (PDEs). It is a relatively new area and has tremendous applications in various branches of engineering sciences like material science, porous media, the study of vibrations of thin structures, composite materials to name a few. Indeed, homogenization can be viewed as a process of understanding a heterogeneous media (where the heterogeneities are at the microscopic level like in composite materials) by a homogeneous media. Mathematically, homogenization deals with the study of asymptotic analysis of the solutions of PDEs by obtaining the equation satisfied by the limit. This limit equation will characterize the bulk or overall behavior of the material, which does not consist of microscopic heterogeneities and can be solved or computed.
Topics to be covered in the workshop include the following but not limited to:
1. Multi-scale problems in applications
2. Introduction to homogenization
3. Techniques in homogenization
4. Recent trends
Plan and Schedule of the Program:
In this discussion meeting, we go through several examples to understand the homogenization procedure in a general perspective together with applications. We also present various mathematical techniques available and some details about the techniques. A tutorial cum problem-solving session will also be conducted so that beginners can learn the material rigorously. In this way, we can train local and international junior students and researchers by equipping them with the theory and applications of multi-scale analysis and homogenization. Furthermore, the speakers will also discuss some ongoing current research and new problems which can foster mentoring or collaboration between students and experts on the area of analysis of multi-scale phenomena.
In addition to the basic material of homogenization, the speakers will be presenting the recent results in their area of expertise and this will be an opportunity for the youngsters to get into this beautiful area of research. Further, every day, we are planning to have a tutorial cum problem-solving session through which the beginners can learn the material in a better way. To make the tutorials/training sessions more effective, we may form small groups and each group may be asked to do some specific material that they can present on the last day. Each small group may be trained by one of the speakers who are available for the entire workshop,
The schedule mainly consists of 4, one-hour lectures per day and a Tutorial cum Problem-Solving Session of one and a half hours which can be extended according to the requirement of the participants.
CONTACT US: [email protected]
PROGRAM LINK: https://www.icts.res.in/program/math2019
Table of Contents (powered by https://videoken.com)
0:00:00 Gamma Convergence (Lecture 3)
0:03:09 Examples
0:09:43 Correct Function
0:11:40 Sketch the graph
0:18:16 Relaxation
0:22:40 Proposition: Arbitrary Sup (lower semi continuous) is lower semi continuous
0:30:05 Theorem:
0:36:38 Comparison with Continuity F
0:39:29 Theorem: Let F . X -R be Covicine
0:47:47 Assume f
0:50:19 First polar function
0:55:47 Def (Gamma - Convergence)
0:57:44 Comparison with point wise convergence
1:02:59 Exercise
Convergence (accounting), the goal of and work towards establishing a single set of accounting standards that will be used internationally
Digital convergence, the convergence of the information technology, telecommunications, consumer electronics, and entertainment industries into digital media conglomerates
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