Hörmander’S L2 -Method, ∂-Problem And Polyanalytic Function Theory In One Complex Variable, 2023 Chapman University
Hörmander’S L2 -Method, ∂-Problem And Polyanalytic Function Theory In One Complex Variable, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we consider the classical ∂-problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of polyanalytic functions in order to construct particular solutions of this problem and obtain new Hörmander type estimates using suitable powers of the Cauchy-Riemann operator. We also compute particular solutions of the ∂-problem for specific polyanalytic data such as the Itô complex Hermite polynomials and polyanalytic Fock kernels.
Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, 2023 Louisiana State University and Agricultural and Mechanical College
Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh
LSU Doctoral Dissertations
In this thesis we consider the Toeplitz operators on the weighted Bergman spaces and their analytic continuation. We proved the commutativity of the $C^*-$algebras generated by the analytic continuation of Toeplitz operators with special class of symbols that are invariant under suitable subgroups of $SU(n,1)$, and we showed that commutative $C^*-$algebras with symbols invariant under compact subgroups of $SU(n,1)$ are completely characterized in terms of restriction to multiplicity free representations. Moreover, we extended the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of the universal covering group $\widetilde{SU(n,1)}$, and we obtained the generalized Segal-Bargmann transform, where …
Modelling Illiquid Stocks Using Quantum Stochastic Calculus, 2023 Memorial University of Newfoundland, St Johns, NL A1C 5S7, Canada
Modelling Illiquid Stocks Using Quantum Stochastic Calculus, Will Hicks
Journal of Stochastic Analysis
No abstract provided.
Integration Of The Negative Order Korteweg-De Vries Equation With Self-Consistent Source, 2023 Comenius University in Bratislava, Bratislava, Slovakia
Integration Of The Negative Order Korteweg-De Vries Equation With Self-Consistent Source, Michal Fečkan, Gayrat Urazboev, Iroda Baltaeva, Oxunjon Ismoilov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper, we show that the negative-order Korteweg-de Vries equation with a self-consistent source can be solved by the inverse scattering method. The evolution of the spectral data of the Sturm-Liouville operator with the potential associated with the solution of the negative order Korteweg-de Vries equation with a self-consistent source is determined. The results obtained make it possible to apply the method of the inverse scattering problem to solve the problem under consideration.
Some Properties Of The Quartic Numerical Range For 4x4 Operator Matrices, 2023 Bukhara State University
Some Properties Of The Quartic Numerical Range For 4x4 Operator Matrices, Hakimboy Latipov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In the present paper we consider self-adjoint 4x4 operator matrices A. For some special cases the alternative formulas for the calculating the quartic numerical range of 4x4 operator matrices A are derived. Using the obtained alternative formula for the quartic numerical range of A we estimate the lower and upper bound of A.
Inverse Source Problem For The Heat Equation On A Metric Star Graph With Integral Over-Determination Condition, 2023 National University of Uzbekistan, Tashkent, Uzbekistan; V.I.Romanovskiy Institute of Mathematics, Tashkent, Uzbekistan
Inverse Source Problem For The Heat Equation On A Metric Star Graph With Integral Over-Determination Condition, Zarif Sobirov, Ariuxan Turemuratova
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this work we investigated an initial boundary value problem for the heat equation on a metric star graph in Sobolev space. The existence and uniqueness of the generalized solution are proved with the classical functional method based on a priori estimates. Also, we considered the inverse source problem with the integral over-determination condition. We reduced the inverse problem to the operator-based equation and proved that the corresponding resolvent operator is well-defined.
A Characterization Of Approximately Inner Automorphisms Of Aw*-Factor Of Type Ii1, 2023 National University of Uzbekistan, Tashkent, Uzbekistan
A Characterization Of Approximately Inner Automorphisms Of Aw*-Factor Of Type Ii1, Dmitriy Kim
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
Approximately inner *-automorphisms of AW*-algebra of type II1 are considered. Faithful normalized quasitraces of AW*-algebras are studied and the inequality connecting ||.||1 and ||.||2 norms generated by quasitrace is obtained. It is showed the characterization of approximately inner *-automorphisms of AW*-algebra of type II1.
On Generalizations Of The Upper Half Plane In A Multidimensional Complex Space, 2023 Karakalpak state university, Nukus, Uzbekistan
On Generalizations Of The Upper Half Plane In A Multidimensional Complex Space, Bukharbay Kurbanov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
The paper considers an unbounded realization of a polydisk and a unit ball: the group of holomorphic automorphisms is described, and the Cauchy-Szego and Poisson kernels are calculated explicitly.
On The Negative Order Loaded Modified Korteweg–De Vries Equation, 2023 Anand International College of Engineering, India
On The Negative Order Loaded Modified Korteweg–De Vries Equation, Praveen Agarwal, Bakhrom Abdullaev, Iroda Baltaeva, Shoira Atanazarova
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this study, we establish the integration of the negative order loaded modified Korteweg-de Vries equation using the inverse scattering transform method. The main result is included in deriving the evolution equations for scattering data of the Dirac operator which is associated with the considered problem. Moreover, it was described the process of the construction of one-soliton solution of the negative order loaded modified Korteweg-de Vries equation.
Symmetric Functions Algebras I: Introduction And Basic Features, 2023 Southern Illinois University, Carbondale, Illinois 62901, USA
Symmetric Functions Algebras I: Introduction And Basic Features, Philip Feinsilver
Journal of Stochastic Analysis
No abstract provided.
Random Variables With Overlapping Number And Weyl Algebras I, 2023 Missouri State University, Springfield, MO 65897, U.S.A.
Random Variables With Overlapping Number And Weyl Algebras I, Ruma Dutta, Gabriela Popa, Aurel Stan
Journal of Stochastic Analysis
No abstract provided.
Pricing Multi-Asset Contingent Claims In A Multi-Dimensional Binomial Market, 2023 University of Aberdeen, AB24 3UE Aberdeen, Scotland, UK
Pricing Multi-Asset Contingent Claims In A Multi-Dimensional Binomial Market, Jarek Kedra, Assaf Libman, Victoria Steblovskaya
Journal of Stochastic Analysis
No abstract provided.
The Malliavin-Stein Method For Normal Random Walks With Dependent Increments, 2023 University Melbourne, Parkville VIC 3010, Australia
The Malliavin-Stein Method For Normal Random Walks With Dependent Increments, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi
Journal of Stochastic Analysis
No abstract provided.
Asymptotic Behaviour Of Hyperbolic Partial Differential Equations, 2023 University of Kentucky
Asymptotic Behaviour Of Hyperbolic Partial Differential Equations, Shi-Zhuo Looi
Theses and Dissertations--Mathematics
We investigate the asymptotic behaviour of solutions to a range of linear and nonlinear hyperbolic equations on asymptotically flat spacetimes. We develop a comprehensive framework for the analysis of pointwise decay of linear and nonlinear wave equations on asymptotically flat manifolds of three space dimensions that are allowed to be time-varying or nonstationary, including quasilinear wave equations. The Minkowski space and time-varying perturbations thereof are included among these spacetimes. A result on scattering for a nonlinear wave equation with finite-energy solutions on nonstationary spacetimes is presented. This work was motivated in part by the investigation of more precise asymptotic behaviour …
A Scattering Result For The Fifth-Order Kp-Ii Equation, 2023 University of Kentucky
A Scattering Result For The Fifth-Order Kp-Ii Equation, Camille Schuetz
Theses and Dissertations--Mathematics
We will prove scattering for the fifth-order Kadomtsev-Petviashvilli II (fifth-order KP-II) equation. The fifth-order KP-II equation is an example of a nonlinear dispersive equation which takes the form $u_t=Lu + NL(u)$ where $L$ is a linear differential operator and $NL$ is a nonlinear operator. One looks for solutions $u(t)$ in a space $C(\R,X)$ where $X$ is a Banach space. For a nonlinear dispersive differential equation, the associated linear problem is $v_t=Lv$. A solution $u(t)$ of the nonlinear equation is said to scatter if as $t \to \infty$, the solution $u(t)$ approaches a solution $v(t)$ to the linear problem in the …
Graphs, Adjacency Matrices, And Corresponding Functions, 2023 Bucknell University
Graphs, Adjacency Matrices, And Corresponding Functions, Yang Hong
Honors Theses
Stable polynomials, in the context of this research, are two-variable polynomials like $p(z_1,z_2) = 2 - z_1 - z_2$ that are guaranteed to be non-zero if both input variables have an absolute value less than one in the complex plane. Stable polynomials are used in a variety of mathematical fields, thus finding ways to construct stable polynomials is valuable. An important property of these polynomials is whether they have boundary zeros, which are points in the complex plane where the polynomial equals zero and both variables have an absolute value of 1. Overall, it is challenging to find stable polynomials …
Peer-To-Peer Energy Trading In Smart Residential Environment With User Behavioral Modeling, 2023 University of Kentucky
Peer-To-Peer Energy Trading In Smart Residential Environment With User Behavioral Modeling, Ashutosh Timilsina
Theses and Dissertations--Computer Science
Electric power systems are transforming from a centralized unidirectional market to a decentralized open market. With this shift, the end-users have the possibility to actively participate in local energy exchanges, with or without the involvement of the main grid. Rapidly reducing prices for Renewable Energy Technologies (RETs), supported by their ease of installation and operation, with the facilitation of Electric Vehicles (EV) and Smart Grid (SG) technologies to make bidirectional flow of energy possible, has contributed to this changing landscape in the distribution side of the traditional power grid.
Trading energy among users in a decentralized fashion has been referred …
An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, 2023 Old Dominion University
An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu
OUR Journal: ODU Undergraduate Research Journal
This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …
Finite Matroidal Spaces And Matrological Spaces, 2023 West Virginia University
Finite Matroidal Spaces And Matrological Spaces, Ziyad M. Hamad
Graduate Theses, Dissertations, and Problem Reports
The purpose of this thesis is to present new different spaces as attempts to generalize the concept of topological vector spaces. A topological vector space, a well-known concept in mathematics, is a vector space over a field \mathbb{F} with a topology that makes the addition and scalar multiplication operations of the vector space continuous functions. The field \mathbb{F} is usually \mathbb{R} or \mathbb{C} with their standard topologies. Since every vector space is a finitary matroid, we define two spaces called finite matroidal spaces and matrological spaces by replacing the linear structure of the topological vector space with a finitary matroidal …
Stochastic Optimization To Reduce Aircraft Taxi-In Time At Igia, New Delhi, 2023 Brainware University, Kolkata
Stochastic Optimization To Reduce Aircraft Taxi-In Time At Igia, New Delhi, Rajib Das, Saileswar Ghosh, Rajendra Desai, Pijus Kanti Bhuin, Stuti Agarwal
International Journal of Aviation, Aeronautics, and Aerospace
Since there is an uncertainty in the arrival times of flights, pre-scheduled allocation of runways and stands and the subsequent first-come-first-served treatment results in a sub-optimal allocation of runways and stands, this is the prime reason for the unusual delays in taxi-in times at IGIA, New Delhi.
We simulated the arrival pattern of aircraft and utilized stochastic optimization to arrive at the best runway-stands allocation for a day. Optimization is done using a GRG Non-Linear algorithm in the Frontline Systems Analytic Solver platform. We applied this model to eight representative scenarios of two different days. Our results show that without …