Seminars 2017-2018

 

Drakhlin’s seminar on

Functional Differential Equations

Jule 18 , 2018, Wednesday

Speaker: Yochay Jerby,

individual researcher

Title:

On the monotonicity of the Riemann Zeta function

Abstract:

The Riemann zeta function is of central importance – both due to its relations to the study of prime numbers and the fact that it is the basic model for L-functions in general. In the early 70’s of the previous century R. Spira started a pioneering investigation of zeta using computer (a room sized IBM 7040). One of the properties discovered by Spira is a left monotonicty property – which is equivalent to the Riemann hypothesis. In this talk I would discuss new results about zetasuch as the existence of the core function C(z) and spectrum, and their relations to monotonicity. The talk would be self-contained, assuming no previous knowledge on number theory and zeta.

Drakhlin’s seminar on

Functional Differential Equations

June 17 , 2018, Wednesday

Speaker: Prof Alex Iosevich,

University of Rochester

Title:

The Fuglede conjecture and geometric combinatorics

Abstract:

In 1974 Fuglede conjectured that if  is a bounded domain in  , then  possesses an orthogonal basis of exponentials if and only if  tiles  by translation. He also formulated this conjecture in the wider setting of locally compact abelian groups. Even though the conjecture died a rather miserable death at the hands of Terry Tao in 2003, it led to and continues to inspire some very interesting mathematics. We are going to describe the problem and some of the recent developments, with emphasis on the interaction between analytic, algebraic and combinatorial techniques.

Drakhlin’s seminar on

Functional Differential Equations

June13 , 2018, Wednesday

Speaker: Prof. Barry Martin Simon

https://www.wikiwand.com/en/Barry_Simon

Title:

Tales of Our Forefathers

Abstract:

This is not a mathematics talk but it is a talk for mathematicians. Too

often, we think of historical mathematicians as only names assigned to theorems.

With vignettes and anecdotes, I’ll convince you they were also human beings and that,

as the Chinese say,”May you live in interesting times” really is a curse

Drakhlin’s seminar on

Functional Differential Equations

May 16 , 2018, Wednesday

Speaker: Dr. Itzhak Fouxon

Hebrew University of Jerusalem, Department of Earth Sciences

Title:

Flow description of motion of inertial particles in turbulence

Abstract:

In this talk we will consider the description of motion of inertial particles in turbulent or chaotic flow with the help of a smooth spatial vector flow. The law of motion prescribes uniqueness of trajectories in the phase space and not the real space, however we demonstrate that the reduction is possible in some limits. This includes the case of water droplets in warm clouds relevant for rain formation problem. The flow obeys a partial differential equation that can produce finite time blow up. The theory presented is confirmed with direct numerical simulations of the motion of particles in the turbulent flow governed by the Navier-Stokes equations.

Drakhlin’s seminar on

Functional Differential Equations

May 5 , 2018, Wednesday

Speaker: Raichik Vladimir

Title:

The Sturm Separation Theorem for Impulsive Delay Differential Equations

Abstract:

The Sturm Separation Theorem for Impulsive Delay

Di_erential Equations

Alexander Domoshnitsky and Vladimir Raichik

Ariel University, Israel

Wronskian is one of the classical objects in the theory of ordinary di_eren-

tial equations. Properties of Wronskian lead to important conclusions on

behavior of solutions of delay equations.

For instance, non-vanishing Wronskian ensures validity of Sturms separa-

tion theorem(between two adjacent zeros of a solution there is one and only

one zero of every other nontrivial linearly independent solution) for delay

equations.

We propose the Sturm separation theorem in case of impulsive delay di_er-

ential equations and obtain assertions about its validity for impulsive delay

di_erential equations.

Drakhlin’s seminar on

Functional Differential Equations

May 2 , 2018, Wednesday

Speaker: Julia Mizgireva,

Title:

Sign-constancy of Green’s Functions for Boundary Value Problems with Second-order Impulsive Functional Differential Equation

Drakhlin’s seminar on

Functional Differential Equations

February 14, 2018, Wednesday

Speaker: Prof. Vedeneev,

Associate Professor of Department of Hydromechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University,

Head of Lab of Experimental Hydromechanics, Institute of Mechanics,   Lomonosov Moscow State University.

Title:

“Development of nonlinear oscillations in a single mode panel flutter”

Abstract:

The loss of stability and intensive vibrations of aircraft skin panels  caused by aeroelastic interaction with the air flow is a well known phenomenon in aviation called “panel flutter”. There exist two types of panel flutter: a coupled-mode and a single-mode flutter. A coupled-mode flutter was studied in detail in the 1950-1970th in linear and nonlinear formulations; it leads to the occurrence of a single stable limit cycle. Single-mode flutter was investigated in a linear formulation only a few years ago. Its nonlinear development turns out to be much more interesting than the development of coupled-mode flutter.

The study consists of two parts, analytical and numerical. In the first part, the Bubnov-Galerkin and harmonic balance methods are used to obtain a system of equations for the amplitudes, which describes the limiting cycles. The solutions of this system are investigated analytically. It is shown that with a small penetration into the flutter region, a single stable limit cycle exists. With further deepening, there appears an internal fractional resonance between the growing and damped modes, leading to the birth of a resonance limit cycle. Further, other non-resonant and resonant limit cycles appear, in which several modes participate. A possibility of co-existence of stable limit cycles, resonant and non-resonant that involve oscillations in the same modes, is proved.

The second part of the talk is devoted to the study of nonlinear oscillations using direct numerical simulation. The calculation is conducted in FlowVision (air flow simulations) and Abaqus (plate motion simulation). We study the development of a small perturbation of a plate introduced at t=0 up to the formation of limit cycle oscillations. The amplitudes of the oscillations are found, and it is shown that the amplitude growth when deepening into the flutter region occurs much faster for a single-mode than for a coupled-mode flutter. A region of Mach numbers (quite remote from the stability boundary) is found, where there is a transition from the limit cycle to non-periodic oscillations. With a further increase in the Mach number, a return to periodic oscillations, and then to a stable state occurs. At much higher Mach numbers, a flutter appears again, but of a coupled-mode type. Correlation between analytical and numerical results is discussed.

Drakhlin’s seminar on

Functional Differential Equations

January 10, 2018, Wednesday

Speaker: Professor Yossi Pinhasi, Ariel University

Title:

Topics for possible collaboration between Departments of Electrical Engineering and Mathematics.

Drakhlin’s seminar on

Functional Differential Equations

January 3, 2018, Wednesday

Speaker: Professor Yossi Pinhasi, Ariel University

Title:

Topics for possible collaboration between Departments of Electrical Engineering and Mathematics.

Drakhlin’s seminar on

Functional Differential Equations

December 20, 2017, Wednesday

Speaker: Professor Yossi Pinhasi, Ariel University

Title:

Topics for possible collaboration between Departments of Electrical Engineering and Mathematics.

Drakhlin’s seminar on

Functional Differential Equations

December 6, 2017, Wednesday

Speaker: Yakov Mordehay

Department of Mathematics, Bar Ilan University

Title:

Local Solutions to the Vlasov equation in integral form

Drakhlin’s seminar on

Functional Differential Equations

November 15, 2017, Wednesday

Speaker: Ivan Egoshin

postgraduate student, Mari State University, Yoshkar-Ola, Russia

Title:

Signal Detection and Extraction of Radiophysics Sounding of Ionosphere A Segmentation Approach for Mammographic Images and Its Clinical Value

Drakhlin’s seminar on

Functional Differential Equations

November 8, 2017, Wednesday

Speaker: Dr. Alex Axelrod

Title:

Structure Vacuum Hypothesis

Drakhlin’s seminar on

Functional Differential Equations

November 1, 2017, Wednesday

Speaker: Dr. Alex Axelrod

Title:

Structure Vacuum Hypothesis

Drakhlin’s seminar on

Functional Differential Equations

August 17, 2017, Thursday

August 30, 2017, Wednesday

Speaker:

Professor Irina Astashova, Lomonosov Moscow State University

Title: 1. On Kondratiev’s results in ordinary differential equations and its advancements.

2. On methods of studying asymptotic properties to Emden-Fowler type higher-order differential equations.

Drakhlin’s seminar on

Functional Differential Equations

June 14, 2017, Wednesday

Speaker:

Professor Richard Schoen Winner of Wolf Prize in Mathematics – 2017

The jury panel of the 2017 Wolf Prize in Mathematics  has unanimously decided to award the prize to Professor Charles Fefferman & professor Richard Schoen. For their striking contributions to analysis and geometry.

Richard Schoen has been a pioneer and a driving force in geometric analysis.

His work on the regularity of harmonic maps and minimal surfaces had a lasting impact on the field. His solution of the Yamabe problem is based on the discovery of a deep connection to general relativity. Through his work on geometric analysis Schoen has contributed greatly to our understanding of the interrelation between partial differential equations and differential geometry. Many of the techniques he developed continue to influence the advance of non-linear analysis.

Title: The problem of gravitational mass

Abstract: Einstein’s equations of general relativity describe gravity in terms of

spacetime curvature and, as such, is a purely geometric theory. One of the

difficulties with the theory is that there is no point-wise mass or energy density

which can be assigned to the gravitational field. There are notions of total

mass for isolated systems based on the natural mass parameter which arises

in the Schwarzschild solution, and there are some notions of quasi-local mass

which assign a mass content to a finite spatial region in spacetime. In this

talk we will give a general discussion of this topic and describe the positive mass

theorem. The problem can be posed in any dimension and is of importance

in differential geometry as well as physics. It has only recently been solved in

all cases, and we will describe some of the issues which arise in high dimensional

cases.

Drakhlin’s seminar on

Functional Differential Equations

May 3, 2017, Wednesday

Speaker: Dr. Arkady Beriozkin (Civil Engineering, Ariel University)

Title:

A Novel Approach to the Problem of Optimization of the Kernel Function of a Predictive Integral Operator

Summary:

In this companion study an integral predictive operator, of the Fredholm type, that reflects an inter-functional regularity existing between two families of functions, A and B, is developed. The optimization procedure, based on a limited set of N known pairs of functions from families A and B, consists of four stages: (i) obtainment of the tentative operator that exactly reproduces each function of set B from its corresponding source function of set A (source functions); (ii) determination of the optimal sample of the basis polynomials constituting the kernel function; (iii) determination of the representative set of pairs of functions of A and of B, by detecting and excluding of irregular pairs; and (iv) approximation of the optimal operator vs. representative set of known pairs of functions of A and B. When the operator is fully developed, a statistical closeness of the considered interfunctional relationship is evaluated.

The optimal operator is developed to satisfy two opposite conditions: (1) on the one hand the optimal operator should be as accurate as possible in reproducing the functions of family B from their corresponding functions of family A, for the known pairs used in kernel approximation; and (2) on the other hand the optimal operator should be “numerically stable”, i.e. should not vary distinctly as a result of exclusion of any one pair from the above limited set of N known pairs of functions used for kernel derivation. The obtained operator will serve as a reliable predictive tool for forecasting the desired, initially unknown, function of family B from the corresponding known function of family A, in case where this pair was not used in optimization. The physically inverse problem is solved iteratively as finding a fixed point of a contracting mapping, based on the developed operator. An important advantage of the proposed approach is a possibility of permanent updating the operator using newly incoming measured data, what enhances its trustworthiness.

Drakhlin’s seminar on

Functional Differential Equations

April 26, 2017, Wednesday

Speaker: Dr. Arkady Beriozkin (Civil Engineering, Ariel University)

Title:

Developing a Universal Predictive Operator for Description of “Capillary Pressure – Water Content” Hysteresis Loop in Porous Media

Drakhlin’s seminar on

Functional Differential Equations

March 22, 2017, Wednesday

Speaker: Guy Landesman

Bar-Ilan University

Title:

Drakhlin’s seminar on

Functional Differential Equations

March 8, 2017, Wednesday

Speaker: Dr. Zoya Arav

Bar-Ilan University

Title:

Livsic-Brodskii nodes with Strongly Regular characteristic matrix functions.

Drakhlin’s seminar on

Functional Differential Equations

March 1, 2017, Wednesday

Speaker: Guy Landesman

Bar-Ilan University

Title:

Drakhlin’s seminar on

Functional Differential Equations

January 18, 2017, Wednesday

Speaker: Dr. Alexander Rasin

Title: B\”acklund Transformations for the Boussinesq Equation and Merging Solitons

Abstract:

The B\”acklund transformation (BT) for the “good” Boussinesq equation and its

superposition principles are presented and applied. Unlike many other standard integrable

equations, the Boussinesq equation does not have a strictly algebraic superposition principle

for 2 BTs, but it does for 3. We present associated lattice systems.

Applying the BT to the trivial solution generates standard solitons but also what we

call “merging solitons” — solutions in which two solitary waves (with related speeds)

merge into a single one. We use the superposition principles to generate a variety of interesting solutions,

including superpositions of a merging soliton with $1$ or $2$ regular solitons, and solutions that

develop a singularity in finite time which then disappears at some later finite time. We prove a

Wronskian formula for the solutions obtained by applying a general sequence of BTs on the trivial solution.

Finally, we show how to obtain the standard conserved quantities of the Boussinesq equation from the BT, and

how the hierarchy of local symmetries follows in a simple manner from the superposition principle for 3 Bts.

Drakhlin’s seminar on

Functional Differential Equations

December 21, 2016, Wednesday

Speaker: Dr. Arkady Kossishvili

מודל עבודת N-פול בתנאי תחרות חופשית (ללא התערבות  שרירותית של ממשלה).

מטרת העבודה: חלוקת רווח בין N-פול לבין ממשלה על סמך קריטריון אובייקטיבי (ראה למטה). או, במילים אחרות חישוב

                      פונקציה G(N), כאשר:  N- כמות חברות תחרותיות ב- N-פול

                                                     ו- G- חלק של רווח שיישאר לחברה

הקריטריון-  א)  כל חברה תחרותית עובדת באופן אופטימלי- ז.א. כמות יחידות ייצור x=x* כך שרווח החברה f(x*)=Max

                ב) רווח ממשלה הוא מקסימלי בתאי שמתקיים סעיף א.”

Drakhlin’s seminar on

Functional Differential Equations

December 14, 2016, Wednesday

Speaker: Doctor Oleg Kupervasser

Title: Methods of visual navigation for drones and ground robots

Abstract: “The topic of the lecture is methods of vision-based navigation for drones and ground robots. The visual navigation of robots is based on the same principles that human visual navigation. The three main methods for visual navigation exist: navigation without any data about terrarium, navigation according digital terrarium map, navigation according previously made photos (videos) of terrarium. These methods are used for autonomous flight over equidistant heights, coming back according stored images, landing and take-off. New patented methods for the visual navigation of ground robots (lawnmowers) will be reported.  The lecturer started his investigation in visual navigation in Technion (Computer Science Department) and now starts new project with Chinese company Avisi. This project will continue during 5 years. ”

Drakhlin’s seminar on

Functional Differential Equations

2.11.2016, Wednesday

Speaker: Baruch Cahlon and Darrell Schmidt

Title: “On Neutral First Order Delay Differential Equations With Commensurate Delays”

Department of Mathematics and Statistics

Oakland University

Rochester, MI 48309-4401, USA

Drakhlin’s seminar on

Functional Differential Equations

September 28, 2016, Wednesday

Speaker: Prof. Irina Astashova

(Department of Differential Equations, Lomonosov Moscow State University)

Tittle:   1.   On One Model of Temperature Control In Hothouses

(Joint work with A.Filinovskiy and D.Lashin)

We study the problem of control over the temperature

conditions in industrial hothouses. We consider a model

based on the one-dimensional parabolic equation on a bounded

interval with quadratic cost functional, prove the existence and

the uniqueness of a control function from a prescribed set, and

study the structure of the set of accessible temperature functions.

2.  On qualitative properties of oscillatory solutions to a higher-order nonlinear differential equations.

New results on qualitative properties of oscillatory solutions to higher

order differential equations with power regular and singular nonlinearity

will be presented.

Drakhlin’s seminar on

Functional Differential Equations

21.09. 16, Wednesday

Speaker: Prof Sumio Yamada, Gakushuin, Tokyo

Title: On 4+1 stationary solutions to the Einstein equation with non-spherical blackhole horizons

Abstract: In the last 15 years, there has been much progress on higher dimensional solutions to the Einstein equation, much of it from the physics community.  They are particularly interesting as, unlike 4 dimensional spacetimes, the horizon is no longer restricted to begin diffeomorphic to the sphere, as demonstrated by the celebrated black ring solution of Emparan and Reall.  Using the Weyl-Papapetrou coordinates and harmonic map,  we show the existence of stationary solutions to the 5 dimensional vacuum Einstein equation, which are bi-axisymmetric solutions with lens space horizons.  This is a joint project with Marcus Khuri and Gilbert Weinstein

Drakhlin’s seminar on

Functional Differential Equations

Monday, September 5, 2016

The lecturer: Professor Angela Slavova, Head

Department of Differential Equations and Mathematical Physics

Institute of Mathematics of Bulgarian Academy of Science

Sofia, Bulgaria

The title:

Studying new nonlinear wave phenomena described by mathematical physics equations

 

In this talk we shall present some new waves phenomena. We shall consider several classes of PDEs of mathematical physics having different types of singularities.

First, we shall study compact traveling waves and peakon solutions of Camassa-Holm type of equations. Then we shall investigate viscoelastic generalization of the Burger’s equation. Two-component Camassa-Holm type system will be considered. Finally traveling wave solutions of special type of third order nonlinear PDE will be delivered. Interaction of fluxons will be presented via CNN approach.

Drakhlin’s seminar on

Functional Differential Equations

June 22, 2016, Wednesday

Speaker: Doctor Felix Polyakov

(Department of Mathematics, Bar Ilan University)

Title: Bond options and swaptions pricing: a computational investigation of volatility inference

Abstract: Derivative pricing is especially challenging in novel and illiquid markets where pricing relies greatly on assumptions and models rather than on known flow of market prices. In the novel market of shekel bond options the estimate of implied volatility could be based on the information about other – more liquid – financial instruments in the market. Here I show relevance but not equivalence of the information about volatility of swap rates (swaptions market) to volatility of bond prices (bond options market). An approximation of bond price implied volatility based on known yield implied volatility may be potentially useful in pricing bond options. Numerical simulations and analysis of historical data have been employed to examine accuracy of approximating bond price implied volatility with yield implied volatility.

Drakhlin’s seminar on

Functional Differential Equations

Jule 18 , 2018, Wednesday

Speaker: Yochay Jerby,

individual researcher

Title:

On the monotonicity of the Riemann Zeta function

Abstract:

The Riemann zeta function is of central importance – both due to its relations to the study of prime numbers and the fact that it is the basic model for L-functions in general. In the early 70’s of the previous century R. Spira started a pioneering investigation of zeta using computer (a room sized IBM 7040). One of the properties discovered by Spira is a left monotonicty property – which is equivalent to the Riemann hypothesis. In this talk I would discuss new results about zetasuch as the existence of the core function C(z) and spectrum, and their relations to monotonicity. The talk would be self-contained, assuming no previous knowledge on number theory and zeta.

Drakhlin’s seminar on

Functional Differential Equations

June 17 , 2018, Wednesday

Speaker: Prof Alex Iosevich,

University of Rochester

Title:

The Fuglede conjecture and geometric combinatorics

Abstract:

In 1974 Fuglede conjectured that if  is a bounded domain in  , then  possesses an orthogonal basis of exponentials if and only if  tiles  by translation. He also formulated this conjecture in the wider setting of locally compact abelian groups. Even though the conjecture died a rather miserable death at the hands of Terry Tao in 2003, it led to and continues to inspire some very interesting mathematics. We are going to describe the problem and some of the recent developments, with emphasis on the interaction between analytic, algebraic and combinatorial techniques.

Drakhlin’s seminar on

Functional Differential Equations

June13 , 2018, Wednesday

Speaker: Prof. Barry Martin Simon

https://www.wikiwand.com/en/Barry_Simon

Title:

Tales of Our Forefathers

Abstract:

This is not a mathematics talk but it is a talk for mathematicians. Too

often, we think of historical mathematicians as only names assigned to theorems.

With vignettes and anecdotes, I’ll convince you they were also human beings and that,

as the Chinese say,”May you live in interesting times” really is a curse

Drakhlin’s seminar on

Functional Differential Equations

May 16 , 2018, Wednesday

Speaker: Dr. Itzhak Fouxon

Hebrew University of Jerusalem, Department of Earth Sciences

Title:

Flow description of motion of inertial particles in turbulence

Abstract:

In this talk we will consider the description of motion of inertial particles in turbulent or chaotic flow with the help of a smooth spatial vector flow. The law of motion prescribes uniqueness of trajectories in the phase space and not the real space, however we demonstrate that the reduction is possible in some limits. This includes the case of water droplets in warm clouds relevant for rain formation problem. The flow obeys a partial differential equation that can produce finite time blow up. The theory presented is confirmed with direct numerical simulations of the motion of particles in the turbulent flow governed by the Navier-Stokes equations.

Drakhlin’s seminar on

Functional Differential Equations

May 5 , 2018, Wednesday

Speaker: Raichik Vladimir

Title:

The Sturm Separation Theorem for Impulsive Delay Differential Equations

Abstract:

The Sturm Separation Theorem for Impulsive Delay

Di_erential Equations

Alexander Domoshnitsky and Vladimir Raichik

Ariel University, Israel

Wronskian is one of the classical objects in the theory of ordinary di_eren-

tial equations. Properties of Wronskian lead to important conclusions on

behavior of solutions of delay equations.

For instance, non-vanishing Wronskian ensures validity of Sturms separa-

tion theorem(between two adjacent zeros of a solution there is one and only

one zero of every other nontrivial linearly independent solution) for delay

equations.

We propose the Sturm separation theorem in case of impulsive delay di_er-

ential equations and obtain assertions about its validity for impulsive delay

di_erential equations.

Drakhlin’s seminar on

Functional Differential Equations

May 2 , 2018, Wednesday

Speaker: Julia Mizgireva,

Title:

Sign-constancy of Green’s Functions for Boundary Value Problems with Second-order Impulsive Functional Differential Equation

Drakhlin’s seminar on

Functional Differential Equations

February 14, 2018, Wednesday

Speaker: Prof. Vedeneev,

Associate Professor of Department of Hydromechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University,

Head of Lab of Experimental Hydromechanics, Institute of Mechanics,   Lomonosov Moscow State University.

Title:

“Development of nonlinear oscillations in a single mode panel flutter”

Abstract:

The loss of stability and intensive vibrations of aircraft skin panels  caused by aeroelastic interaction with the air flow is a well known phenomenon in aviation called “panel flutter”. There exist two types of panel flutter: a coupled-mode and a single-mode flutter. A coupled-mode flutter was studied in detail in the 1950-1970th in linear and nonlinear formulations; it leads to the occurrence of a single stable limit cycle. Single-mode flutter was investigated in a linear formulation only a few years ago. Its nonlinear development turns out to be much more interesting than the development of coupled-mode flutter.

The study consists of two parts, analytical and numerical. In the first part, the Bubnov-Galerkin and harmonic balance methods are used to obtain a system of equations for the amplitudes, which describes the limiting cycles. The solutions of this system are investigated analytically. It is shown that with a small penetration into the flutter region, a single stable limit cycle exists. With further deepening, there appears an internal fractional resonance between the growing and damped modes, leading to the birth of a resonance limit cycle. Further, other non-resonant and resonant limit cycles appear, in which several modes participate. A possibility of co-existence of stable limit cycles, resonant and non-resonant that involve oscillations in the same modes, is proved.

The second part of the talk is devoted to the study of nonlinear oscillations using direct numerical simulation. The calculation is conducted in FlowVision (air flow simulations) and Abaqus (plate motion simulation). We study the development of a small perturbation of a plate introduced at t=0 up to the formation of limit cycle oscillations. The amplitudes of the oscillations are found, and it is shown that the amplitude growth when deepening into the flutter region occurs much faster for a single-mode than for a coupled-mode flutter. A region of Mach numbers (quite remote from the stability boundary) is found, where there is a transition from the limit cycle to non-periodic oscillations. With a further increase in the Mach number, a return to periodic oscillations, and then to a stable state occurs. At much higher Mach numbers, a flutter appears again, but of a coupled-mode type. Correlation between analytical and numerical results is discussed.

Drakhlin’s seminar on

Functional Differential Equations

January 10, 2018, Wednesday

Speaker: Professor Yossi Pinhasi, Ariel University

Title:

Topics for possible collaboration between Departments of Electrical Engineering and Mathematics.

Drakhlin’s seminar on

Functional Differential Equations

January 3, 2018, Wednesday

Speaker: Professor Yossi Pinhasi, Ariel University

Title:

Topics for possible collaboration between Departments of Electrical Engineering and Mathematics.

Drakhlin’s seminar on

Functional Differential Equations

December 20, 2017, Wednesday

Speaker: Professor Yossi Pinhasi, Ariel University

Title:

Topics for possible collaboration between Departments of Electrical Engineering and Mathematics.

Drakhlin’s seminar on

Functional Differential Equations

December 6, 2017, Wednesday

Speaker: Yakov Mordehay

Department of Mathematics, Bar Ilan University

Title:

Local Solutions to the Vlasov equation in integral form

Drakhlin’s seminar on

Functional Differential Equations

November 15, 2017, Wednesday

Speaker: Ivan Egoshin

postgraduate student, Mari State University, Yoshkar-Ola, Russia

Title:

Signal Detection and Extraction of Radiophysics Sounding of Ionosphere A Segmentation Approach for Mammographic Images and Its Clinical Value

Drakhlin’s seminar on

Functional Differential Equations

November 8, 2017, Wednesday

Speaker: Dr. Alex Axelrod

Title:

Structure Vacuum Hypothesis

Drakhlin’s seminar on

Functional Differential Equations

November 1, 2017, Wednesday

Speaker: Dr. Alex Axelrod

Title:

Structure Vacuum Hypothesis

Drakhlin’s seminar on

Functional Differential Equations

August 17, 2017, Thursday

August 30, 2017, Wednesday

Speaker:

Professor Irina Astashova, Lomonosov Moscow State University

Title: 1. On Kondratiev’s results in ordinary differential equations and its advancements.

2. On methods of studying asymptotic properties to Emden-Fowler type higher-order differential equations.

Drakhlin’s seminar on

Functional Differential Equations

June 14, 2017, Wednesday

Speaker:

Professor Richard Schoen Winner of Wolf Prize in Mathematics – 2017

The jury panel of the 2017 Wolf Prize in Mathematics  has unanimously decided to award the prize to Professor Charles Fefferman & professor Richard Schoen. For their striking contributions to analysis and geometry.

Richard Schoen has been a pioneer and a driving force in geometric analysis.

His work on the regularity of harmonic maps and minimal surfaces had a lasting impact on the field. His solution of the Yamabe problem is based on the discovery of a deep connection to general relativity. Through his work on geometric analysis Schoen has contributed greatly to our understanding of the interrelation between partial differential equations and differential geometry. Many of the techniques he developed continue to influence the advance of non-linear analysis.

Title: The problem of gravitational mass

Abstract: Einstein’s equations of general relativity describe gravity in terms of

spacetime curvature and, as such, is a purely geometric theory. One of the

difficulties with the theory is that there is no point-wise mass or energy density

which can be assigned to the gravitational field. There are notions of total

mass for isolated systems based on the natural mass parameter which arises

in the Schwarzschild solution, and there are some notions of quasi-local mass

which assign a mass content to a finite spatial region in spacetime. In this

talk we will give a general discussion of this topic and describe the positive mass

theorem. The problem can be posed in any dimension and is of importance

in differential geometry as well as physics. It has only recently been solved in

all cases, and we will describe some of the issues which arise in high dimensional

cases.

Drakhlin’s seminar on

Functional Differential Equations

May 3, 2017, Wednesday

Speaker: Dr. Arkady Beriozkin (Civil Engineering, Ariel University)

Title:

A Novel Approach to the Problem of Optimization of the Kernel Function of a Predictive Integral Operator

Summary:

In this companion study an integral predictive operator, of the Fredholm type, that reflects an inter-functional regularity existing between two families of functions, A and B, is developed. The optimization procedure, based on a limited set of N known pairs of functions from families A and B, consists of four stages: (i) obtainment of the tentative operator that exactly reproduces each function of set B from its corresponding source function of set A (source functions); (ii) determination of the optimal sample of the basis polynomials constituting the kernel function; (iii) determination of the representative set of pairs of functions of A and of B, by detecting and excluding of irregular pairs; and (iv) approximation of the optimal operator vs. representative set of known pairs of functions of A and B. When the operator is fully developed, a statistical closeness of the considered interfunctional relationship is evaluated.

The optimal operator is developed to satisfy two opposite conditions: (1) on the one hand the optimal operator should be as accurate as possible in reproducing the functions of family B from their corresponding functions of family A, for the known pairs used in kernel approximation; and (2) on the other hand the optimal operator should be “numerically stable”, i.e. should not vary distinctly as a result of exclusion of any one pair from the above limited set of N known pairs of functions used for kernel derivation. The obtained operator will serve as a reliable predictive tool for forecasting the desired, initially unknown, function of family B from the corresponding known function of family A, in case where this pair was not used in optimization. The physically inverse problem is solved iteratively as finding a fixed point of a contracting mapping, based on the developed operator. An important advantage of the proposed approach is a possibility of permanent updating the operator using newly incoming measured data, what enhances its trustworthiness.

Drakhlin’s seminar on

Functional Differential Equations

April 26, 2017, Wednesday

Speaker: Dr. Arkady Beriozkin (Civil Engineering, Ariel University)

Title:

Developing a Universal Predictive Operator for Description of “Capillary Pressure – Water Content” Hysteresis Loop in Porous Media

Drakhlin’s seminar on

Functional Differential Equations

March 22, 2017, Wednesday

Speaker: Guy Landesman

Bar-Ilan University

Title:

Drakhlin’s seminar on

Functional Differential Equations

March 8, 2017, Wednesday

Speaker: Dr. Zoya Arav

Bar-Ilan University

Title:

Livsic-Brodskii nodes with Strongly Regular characteristic matrix functions.

Drakhlin’s seminar on

Functional Differential Equations

March 1, 2017, Wednesday

Speaker: Guy Landesman

Bar-Ilan University

Title:

Drakhlin’s seminar on

Functional Differential Equations

January 18, 2017, Wednesday

Speaker: Dr. Alexander Rasin

Title: B\”acklund Transformations for the Boussinesq Equation and Merging Solitons

Abstract:

The B\”acklund transformation (BT) for the “good” Boussinesq equation and its

superposition principles are presented and applied. Unlike many other standard integrable

equations, the Boussinesq equation does not have a strictly algebraic superposition principle

for 2 BTs, but it does for 3. We present associated lattice systems.

Applying the BT to the trivial solution generates standard solitons but also what we

call “merging solitons” — solutions in which two solitary waves (with related speeds)

merge into a single one. We use the superposition principles to generate a variety of interesting solutions,

including superpositions of a merging soliton with $1$ or $2$ regular solitons, and solutions that

develop a singularity in finite time which then disappears at some later finite time. We prove a

Wronskian formula for the solutions obtained by applying a general sequence of BTs on the trivial solution.

Finally, we show how to obtain the standard conserved quantities of the Boussinesq equation from the BT, and

how the hierarchy of local symmetries follows in a simple manner from the superposition principle for 3 Bts.

Drakhlin’s seminar on

Functional Differential Equations

December 21, 2016, Wednesday

Speaker: Dr. Arkady Kossishvili

מודל עבודת N-פול בתנאי תחרות חופשית (ללא התערבות  שרירותית של ממשלה).

מטרת העבודה: חלוקת רווח בין N-פול לבין ממשלה על סמך קריטריון אובייקטיבי (ראה למטה). או, במילים אחרות חישוב

                      פונקציה G(N), כאשר:  N- כמות חברות תחרותיות ב- N-פול

                                                     ו- G- חלק של רווח שיישאר לחברה

הקריטריון-  א)  כל חברה תחרותית עובדת באופן אופטימלי- ז.א. כמות יחידות ייצור x=x* כך שרווח החברה f(x*)=Max

                ב) רווח ממשלה הוא מקסימלי בתאי שמתקיים סעיף א.”

Drakhlin’s seminar on

Functional Differential Equations

December 14, 2016, Wednesday

Speaker: Doctor Oleg Kupervasser

Title: Methods of visual navigation for drones and ground robots

Abstract: “The topic of the lecture is methods of vision-based navigation for drones and ground robots. The visual navigation of robots is based on the same principles that human visual navigation. The three main methods for visual navigation exist: navigation without any data about terrarium, navigation according digital terrarium map, navigation according previously made photos (videos) of terrarium. These methods are used for autonomous flight over equidistant heights, coming back according stored images, landing and take-off. New patented methods for the visual navigation of ground robots (lawnmowers) will be reported.  The lecturer started his investigation in visual navigation in Technion (Computer Science Department) and now starts new project with Chinese company Avisi. This project will continue during 5 years. ”

Drakhlin’s seminar on

Functional Differential Equations

2.11.2016, Wednesday

Speaker: Baruch Cahlon and Darrell Schmidt

Title: “On Neutral First Order Delay Differential Equations With Commensurate Delays”

Department of Mathematics and Statistics

Oakland University

Rochester, MI 48309-4401, USA

Drakhlin’s seminar on

Functional Differential Equations

September 28, 2016, Wednesday

Speaker: Prof. Irina Astashova

(Department of Differential Equations, Lomonosov Moscow State University)

Tittle:   1.   On One Model of Temperature Control In Hothouses

(Joint work with A.Filinovskiy and D.Lashin)

We study the problem of control over the temperature

conditions in industrial hothouses. We consider a model

based on the one-dimensional parabolic equation on a bounded

interval with quadratic cost functional, prove the existence and

the uniqueness of a control function from a prescribed set, and

study the structure of the set of accessible temperature functions.

2.  On qualitative properties of oscillatory solutions to a higher-order nonlinear differential equations.

New results on qualitative properties of oscillatory solutions to higher

order differential equations with power regular and singular nonlinearity

will be presented.

Drakhlin’s seminar on

Functional Differential Equations

21.09. 16, Wednesday

Speaker: Prof Sumio Yamada, Gakushuin, Tokyo

Title: On 4+1 stationary solutions to the Einstein equation with non-spherical blackhole horizons

Abstract: In the last 15 years, there has been much progress on higher dimensional solutions to the Einstein equation, much of it from the physics community.  They are particularly interesting as, unlike 4 dimensional spacetimes, the horizon is no longer restricted to begin diffeomorphic to the sphere, as demonstrated by the celebrated black ring solution of Emparan and Reall.  Using the Weyl-Papapetrou coordinates and harmonic map,  we show the existence of stationary solutions to the 5 dimensional vacuum Einstein equation, which are bi-axisymmetric solutions with lens space horizons.  This is a joint project with Marcus Khuri and Gilbert Weinstein

Drakhlin’s seminar on

Functional Differential Equations

Monday, September 5, 2016

The lecturer: Professor Angela Slavova, Head

Department of Differential Equations and Mathematical Physics

Institute of Mathematics of Bulgarian Academy of Science

Sofia, Bulgaria

The title:

Studying new nonlinear wave phenomena described by mathematical physics equations

 

In this talk we shall present some new waves phenomena. We shall consider several classes of PDEs of mathematical physics having different types of singularities.

First, we shall study compact traveling waves and peakon solutions of Camassa-Holm type of equations. Then we shall investigate viscoelastic generalization of the Burger’s equation. Two-component Camassa-Holm type system will be considered. Finally traveling wave solutions of special type of third order nonlinear PDE will be delivered. Interaction of fluxons will be presented via CNN approach.

Drakhlin’s seminar on

Functional Differential Equations

June 22, 2016, Wednesday

Speaker: Doctor Felix Polyakov

(Department of Mathematics, Bar Ilan University)

Title: Bond options and swaptions pricing: a computational investigation of volatility inference

Abstract: Derivative pricing is especially challenging in novel and illiquid markets where pricing relies greatly on assumptions and models rather than on known flow of market prices. In the novel market of shekel bond options the estimate of implied volatility could be based on the information about other – more liquid – financial instruments in the market. Here I show relevance but not equivalence of the information about volatility of swap rates (swaptions market) to volatility of bond prices (bond options market). An approximation of bond price implied volatility based on known yield implied volatility may be potentially useful in pricing bond options. Numerical simulations and analysis of historical data have been employed to examine accuracy of approximating bond price implied volatility with yield implied volatility.