20 research outputs found
Operational Methods in the Environment of a Computer Algebra System
This article presents the principal results of the doctoral thesis “Direct Operational Methods
in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of
mathematics and Informatics, BAS), successfully defended before the Specialised Academic
Council for Informatics and Mathematical Modelling on 23 March, 2009.The presented research is related to the operational calculus
approach and its representative applications. Operational methods are considered,
as well as their program implementation using the computer algebra
system Mathematica. The Heaviside algorithm for solving Cauchy’s problems
for linear ordinary differential equations with constant coefficients is
considered in the context of the Heaviside-Mikusinski operational calculus.
The program implementation of the algorithm is described and illustrative
examples are given. An extension of the Heaviside algorithm, developed by I. Dimovski and S. Grozdev, is used for finding periodic solutions of
linear ordinary differential equations with constant coefficients both in the
non-resonance and in the resonance cases. The features of its program implementation
are described and examples are given. An operational method
for solving local and nonlocal boundary value problems for some equations
of the mathematical physics (the heat equation, the wave equation and the
equation of a free supported beam) is developed and the capabilities of the
corresponding program packages for solving those problems are described.
A comparison with other methods for solving the same types of problems is
included and the advantages of the operational methods are marked
Подход на операционното смятане за получаване на периодични и средно-периодични решения на линейни обикновени диференциални уравнения с постоянни коефициенти
[Dimovski Ivan H.; Димовски Иван Х.]; [Spiridonova Margarita; Спиридонова МаргаритаAn approach to obtaining periodic and mean-periodic solutions of Linear Ordinary Dierential Equation (LODE) with constant coefficients is presented. The use of the Computer Algebra System (CAS) Mathematica for practical application of this approach is considered
International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts
The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of
Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the
International Conference on Mathematical Analysis and Applications in Science and Engineering –
ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days).
Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering,
industry, and technology, to discuss the development of new mathematical models, theories, and
applications that contribute to the advancement of scientific knowledge and practice. Authors proposed
research in topics including partial and ordinary differential equations, integer and fractional order
equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization,
control, probability, computational mathematics, amongst others.
The conference was designed to maximize the involvement of all participants and will present the state-of-
the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Continuous Measurement and Stochastic Methods in Quantum Optical Systems
This dissertation studies the statistics and modeling of a quantum system
probed by a coherent laser field. We focus on an ensemble of qubits
dispersively coupled to a traveling wave light field. The first research topic
explores the quantum measurement statistics of a quasi-monochromatic laser
probe. We identify the shortest timescale that successive measurements
approximately commute. Our model predicts that for a probe in the near
infrared, noncommuting measurement effects are apparent for subpicosecond
times.
The second dissertation topic attempts to find an approximation to a
conditional master equation, which maps identical product states to identical
product states. Through a technique known as projection filtering, we find such
a equation for an ensemble of qubits experiencing a diffusive measurement of a
collective angular momentum projection, and global rotations. We then test the
quality of the approximation through numerical simulations. In the presence of
strong randomized rotations, the approximation reproduces the exact expectation
values to within 95%.
The final topic applies the projection filter to the problem of state
reconstruction. We find an initial state estimate based on a single continuous
measurement of an identically prepared atomic ensemble. Given the ability to
make a continuous collective measurement and simultaneously applying time
varying controls, it is possible to find an accurate estimate given based upon
a single measurement realization. Here we explore the fundamental limits of
this protocol by studying an idealized model for pure qubits, which is limited
only by measurement backaction. Using the exact dynamics to produce simulated
measurements, we then numerically search for a maximum likelihood estimate
based on the approximate expression. Our estimation technique nearly achieves
an average fidelity bound set by an optimum POVM.Comment: PhD Dissertatio
Quantum Information Processing using the Power-of-SWAP
This project is a comprehensive investigation into the application of the exchange interaction,
particularly with the realization of the SWAP^1/n quantum operator, in quantum information
processing. We study the generation, characterization and application of entanglement in such
systems. Given the non-commutativity of neighbouring SWAP^1/n gates, the mathematical
study of combinations of these gates is an interesting avenue of research that we have
explored, though due to the exponential scaling of the complexity of the problem with the
number of qubits in the system, numerical techniques, though good for few-qubit systems, are
found to be inefficient for this research problem when we look at systems with higher number
of qubits. Since the group of SWAP^1/n operators is found to be isomorphic to the symmetric
group Sn, we employ group-theoretic methods to find the relevant invariant subspaces
and associated vector-states. Some interesting patterns of states are found including onedimensional invariant subspaces spanned by W-states and the Hamming-weight preserving
symmetry of the vectors spanning the various invariant subspaces. We also devise new
ways of characterizing entanglement and approach the separability problem by looking at
permutation symmetries of subsystems of quantum states. This idea is found to form a
bridge with the entanglement characterization tool of Peres-Horodecki’s Partial Positive
Transpose (PPT), for mixed quantum states. We also look at quantum information taskoriented ‘distance’ measures of entanglement, besides devising a new entanglement witness
in the ‘engle’. In terms of applications, we define five different formalisms for quantum
computing: the circuit-based model, the encoded qubit model, the cluster-state model,
functional quantum computation and the qudit-based model. Later in the thesis, we explore
the idea of quantum computing based on decoherence-free subspaces. We also investigate
ways of applying the SWAP^1/n in entanglement swapping for quantum repeaters, quantum
communication protocols and quantum memory.Trinity Barlow Scholarship by Trinity College (University of Cambridge), Nehru Bursary by Nehru Trust for Cambridge University, Hitachi CASE Grant by Hitachi-Cavendish Laboratory, Grants from Semiconductor Physics (SP) and Thin Film Magnetism (TFM) Groups, Cavendish Laboratory, University of Cambridg