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. |