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Publications related to Operator Theory (1,329)
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Let us assume we are given a non-trivially projective, linearly free random variable ε. In [13], the authors address the existence of p-adic, super-composite ideals under the additional assumption that there exists a null, χ-commutative and generic class. We show that every singular, right-canonically canonical number is bounded and Grassmann. Here...
Article
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A growing interest in considering the “hybrid systems” of equations describing more complicated physical phenomena was observed throughout the last 10 years. We mean here, in particular, the so-called Navier–Stokes–Cahn–Hilliard equation, the Navier–Stokes–Poison equations, or the Cahn–Hilliard–Hele–Shaw equation. There are specific difficulties co...
Conference Paper
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The authors investigate the interested properties of certain subclasses of meromorphic functions in the punctured unit disks using a linear operator with a meromorphic function defined here through the Hadamard product (or convolution).
Conference Paper
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This work is concerned with the periodic solution of a p-Laplacian Allen-Cahn equation with nonlocal terms associated with Neumann boundary conditions. Namely, the topological degree theorem is applied to prove the existence of a limit point to the auxiliary problem, which is also considered a nontrivial nonnegative time-periodic solution of the ma...
Article
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Industrial pollution and over-exploitation of natural resources adversely affect the environment and are also a serious threat to society and economy development. At present, climate change, destruction of the ozone layer, water shortage, and sharp reduction of biodiversity have also become widespread environmental problems. Therefore, people have...
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We consider the family of $n$-tuples $P$ consisting of polynomials $P_1, \ldots, P_n$ with nonnegative coefficients such that $\partial_i P_j(0) = \delta_{i, j},$ $i, j=1, \ldots, n.$ With every such $P,$ we associate a Reinhardt domain $\triangle^{\!n}_{_P}$ to be called as the generalized Hartogs triangle. A basic family of these domains, where...
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The non-existence of a global solution in time plays an important role in PDE theory and its applications. In this paper we analyze and interpret unbounded solutions of a viscoelastic p(x)− Laplacian parabolic equation with logarithmic nonlinearity, which is the best way to establish non-existence of global solutions. Blow up is a phenomenon which...
Article
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In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information-theoretic divergences or distance me...
Article
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Background. The problem of aging in assessing and analyzing the durability of any living and technical systems has always been and remains a burning one, and medicine and technology in any foreseeable past have tried to find ways and means of solving it. However, no significant progress has yet been made. The most important thing in solving the pro...
Article
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The plasma modes are significantly influenced by the simple or/and molecular anions. The reciprocity of beam and tri-ion electron (TIE) plasmas is modeled by the kinetic theory. The set of Vlasov–Poisson equation is solved and decomposed by the Laguerre–Gaussian function under paraxial approximation. The beam plasma expedites unstable twisted modes...
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Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification and comparison. By viewing iterative algorithms as discrete-time dynamical systems, we leverage Koopman opera...
Article
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This paper introduces the recent developments in Renewable Energy Systems for building heating, cooling and electricity production with thermal energy storage. Due to the needed Clean Energy Transition in the many countries and regions and the goal of closing Net Zero Energy Buildings, it is crucial to provide efficient Renewable Energy Based heati...
Conference Paper
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This paper utilizes Koopman operator theory to generate robust optimal control laws for nonlinear systems with control-dependent noise. The Koopman operator is a theoretical, infinite-dimensional linear operator that characterizes the evolution of a nonlinear dynamical system in function space, i.e., the dynamics of a nonlinear system can be descri...
Article
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With the continuous development of society, information transmission can be seen everywhere, and various forms of visual communication with artistic design such as posters, periodicals, and electronic screens appear one after another. Visual communication is the effective communication of information through various visual elements. Visual communic...
Conference Paper
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A framework is presented where a nonlinear dynamical system is transformed into a higher-dimensional bilinear system using the Koopman operator theory. The nonlinear dynamics are projected onto a set of orthogonal polynomials via the Galerkin method to obtain the evolution of the eigenfunctions, so that the time evolution of any observable is descr...
Article
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Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two infinite series. This new representation, evaluated at integer values of the argument, produces results that...
Article
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Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models which can accommodate non-normalizable form factors, provided that they satisfy a weaker growth cons...
Preprint
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We provide a short proof for the twisted multiplicativity property of the operator-valued S-transform. This is my contribution to the topical collection ''Multivariable Operator Theory. The J\"org Eschmeier Memorial'' of Complex Analysis and Operator Theory.
Book
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The aim of this conference is to exchange ideas, discuss developments in mathematics, develop collaborations and interact with professionals and researchers from all over the world about some of the following interesting topics: Functional Analysis, Approximation Theory, Real Analysis, Complex Analysis, Harmonic and non-Harmonic Analysis, Applied A...
Article
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The Laplace–de Rham operator acting on a one-form a: □ a in [Formula: see text] or [Formula: see text] spaces is restricted to n-dimensional pseudo-spheres. This includes, in particular, the n-dimensional de Sitter and anti-de Sitter space-times. The restriction is designed to extract the corresponding n-dimensional Laplace–de Rham operator acting...
Article
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In this work, we present a systematic procedure to build phase diagrams for chemically relevant properties by the use of a semi-supervised machine learning technique called uncertainty sampling. Concretely, we focus on ground state spin multiplicity and chemical bonding properties. As a first step, we have obtained single-eutectic-point-containing...
Article
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We study recurrence coefficients of semi-classical Laguerre orthogonal polynomials and the associated Hankel determinant generated by a semi-classical Laguerre weight [Formula: see text]. If t = 0, it is reduced to the classical Laguerre weight. For t > 0, this weight tends to zero faster than the classical Laguerre weight as x → ∞. In the finite n...
Article
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In this paper, we consider the gaps λ 2n (q)−λ 1 (q) for the Dirichlet eigenvalues {λ m (q)} of Sturm-Liouville operators with potentials q on the unit interval. By merely assuming that potentials q have the L 1 norm r, we will explicitly give the solutions to the maximization problems of λ 2n (q) − λ 1 (q), where n is arbitrary. As a consequence,...
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Soft grippers are gaining momentum across applications due to their flexibility and dexterity. However, the infinite-dimensionality and non-linearity associated with soft robots challenge modeling and closed-loop control of soft grippers to perform grasping tasks. To solve this problem, data-driven methods have been proposed. Most data-driven metho...
Article
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Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in the [Formula: see text] lattice, we depart from the well-known Araki–Evans [Formula: see text] index for quasi-free fermion states and rewrite it in terms of states rather than in terms of basis projections. Furthermore, we reformulate results that relate eq...
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The goal of this paper is to study the noncommutative polydomains and their universal operator models generated by admissible k-tuples of formal power series in several noncommuting indeterminates. Several aspects of the multi-variable operator theory of these polydomains and their universal models are discussed in connection with the noncommutativ...
Book
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This book contains hundreds of counterexamples in operator theory (in the context of bounded and unbounded operators). Here are some other features of this manuscript: • It covers many topics in operator theory (bounded and unbounded operators). • Half of it is devoted to solved problems about unbounded linear operators. • It contains over 500 cou...
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We compare initial value and eigenvalue problems for two-dimensional perturbations of the inviscid shear flow in a channel. Singular solutions, known in plasma physics as van Kampen (vK) modes, are constructed. They form a complete set of eigenfunctions for decomposition of any initial perturbation for stable wavy perturbations. A pair of discrete...
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In this work, we present a one-step second-order converger for state-specific (SS) and state-averaged (SA) complete active space self-consistent field(CASSCF) wave functions. Robust convergence is achieved through step restrictions using a trust-region augmented Hessian (TRAH) algorithm. To avoid numerical instabilities, an exponential parametrizat...
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In this paper, the newly developed fractal-fractional differential and integral operators are used to analyze the dynamics of chaotic system based on image encryption. The problem is modeled in terms of classical order nonlinear, coupled ordinary differential equations that are then generalized through fractal-fractional differential operator of Mi...
Poster
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The Department of Mathematics Education at Tishk International University invites you to an International Workshop titled, 1st International Workshop on Global Contributions to Mathematical Sciences; themed “Operator theory and its interdisciplinary applications.” The workshop on Global Contributions to Mathematical Sciences is the maiden internat...
Article
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Single-mode equivalent space-time representations of the acoustic wave propagating in a Biot poroelastic medium have previously been found only for asymptotic cases: In the low frequency regime, where the viscous skin depth is greater than the characteristic pore size, the time domain equivalent is represented with integer order temporal and spatia...
Conference Paper
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The future Air Traffic Management will be conducted in an environment of significant and continued advances in ground and airborne technologies. The new avionics that will equip the future aircrafts will enhance their flight capabilities and multiple-option forms of efficient and environmentally friendly free-flight, as well as the capability for s...
Preprint
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We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces $\ell_1$ and $\ell_{\infty}$. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms $\ell_1$ or $\ell_{\infty}$. In analogy with their Euclidean counterparts, mappings which are monotone with res...
Article
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The theoretical framework for the uncertainty relation of Hermitian operators is perfect and has been applied in many fields. At the same time, non-Hermitian operators are also widely used in some other fields. However, the uncertainty relation of non-Hermitian operators remains to be explored. K.W. Bong and his co-workers proposed the theory of un...
Preprint
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In this article, the author attempts to shed light on density operators behind product operators; one may be able to understand how the product operators can describe the rotation of magnetizations. Furthermore, the author will explain the product operator theory extended to be applicable to strongly-coupled spin systems in solution-state and solid...
Article
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We prove the analogue of the strong Szegő limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk (Physica A 144:44–104, 1987) for the next-to-diagonal correlations ⟨σ0,0σN-1,N⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsf...
Conference Paper
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Abstract. The incidence of heart disease is increasing every year. One of the preventive actions is through early detection of the disease to take further action. Computer-Aided Diagnosis (CAD) helps doctors and cardiologists detect heart abnormalities seen in non-contrast cardiac CT images faster than manual detection. This study aims to detect th...
Poster
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5th International Conference on Mathematical Advances and Applications (ICOMAA-2022) aims to present research, exchange ideas, discuss developments in mathematics, develop collaborations and interact with professionals and researchers from all over the world. Participants are invited to submit one-page summaries of their work, with some of the fol...
Article
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In this paper, we consider a one-dimensional model of ferromagnetic rings, taking into account curvature and anisotropy effects. We describe relevant stationary configurations of the magnetization and we investigate their stability in the Liapunov sense.
Article
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The author attempts to shed light on density operators behind product operators; one may be able to understand the concept of coherences and thereby learn how the product operators can describe the rotations of magnetizations, for example. The author explains the product operator theory extended to be applicable to strongly-coupled spin systems in...
Article
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Volumetric wave-based simulation methods for room and virtual acoustics, such as the finite difference time domain method, are computationally intensive; for large volumes, operation over a regular grid is desirable for the sake of efficiency. In coping with realistic irregular geometries (such as enclosures or scattering objects), form-fitting mes...
Article
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The design of optimal Magnetic Resonance Imaging (MRI) coils is modeled as a minimum-norm problem (MNP), that is, as an optimization problem of the form $\min_{x\in\mathcal{R}}\|x\|$ min x ∈ R ∥ x ∥ , where $\mathcal{R}$ R is a closed and convex subset of a normed space X . This manuscript is aimed at revisiting MNPs from the perspective of Functio...
Article
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Using the one-dimensional potential well with realistic parameters for atomic nuclei, we illustrate the movement of the poles of the S-matrix and the transmission coefficient when the well supports an anti-bound state. We calculate the phase shift of the atomic nuclei 5 He using the three-dimensional potential well and compare it with the experimen...
Article
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In this paper, we have illustrated the construction of a real structure on a fuzzy sphere S*2 in its spin-1/2 representation. Considering the SU(2) covariant Dirac and chirality operator on S*2 given by U. C. Watamura and Watamura [Commun. Math. Phys. 183, 365–382 (1997) and Commun. Math. Phys. 212, 395–413 (2000)], we have shown that the real stru...
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We undertake a reconstruction of the epistemic significance of research on operational theories in quantum foundations. We suggest that the space of operational theories is analogous to the space of possible worlds employed in the possible world semantics for modal logic, so research of this sort can be understood as probing modal structure. Thus w...
Article
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First, a family of quadratic displacement operators based on group Fourier Transform has been proposed for joint distribution analysis. Second, considering the quadratic displacement operators, a novel millimeter-wave massive MIMO channel tracking has been proposed in Time-Angle (TA) plane. Due to a poor scattering environment, millimeter-wave comm...
Article
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This is a review of Kusraev, A. G.; Kutateladze, S. S. Boolean valued analysis: background and results. (English) Zbl 07437842 Kusraev, Anatoly G. (ed.) et al., Operator theory and differential equations. Selected papers based on the presentations at the 15th conference on order analysis and related problems of mathematical modeling, Vladikavkaz,...
Article
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Sensory deprivation has long been known to cause hallucinations or “phantom” sensations, the most common of which is tinnitus induced by hearing loss, affecting 10–20% of the population. An observable hearing loss, causing auditory sensory deprivation over a band of frequencies, is present in over 90% of people with tinnitus. Existing plasticity-ba...
Article
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Compared with macroscopic conservation law for the solution of the derivative nonlinear Schrödinger equation (DNLS) with small mass in Klaus and Schippa (A priori estimates for the derivative nonlinear Schrödinger equation. Accepted by Funkcial. Ekvac), we show the corresponding microscopic conservation laws for the Schwartz solutions of DNLS with...
Article
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In this work, we introduce a novel data-driven formulation, the Koopman-Linearly Time-Invariant (Koopman-LTI) analysis, for analyzing Fluid-Structure Interactions (FSI). An implementation of the Koopman-LTI on a subcritical free-shear flow over a prism at Re = 22 000 corroborated a configuration-wise universal Koopman system, which approximated the...
Article
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The zeta functions for the Schrödinger equation with a triangular potential are investigated. Values of the zeta functions are computed using both the Weierstrass factorization theorem and analytic continuation via contour integration. The results were found to be consistent where the domains of the two methods overlap. Analytic continuation is use...
Article
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In this manuscript, by using weakly Picard operators we investigate the Ulam type stability of fractional q -difference An illustrative example is given in the last section.
Preprint
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The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a finite-dimensional nonlinear system to an infinite-dimensional function space where the evolution of the origi...
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This paper investigates the application of the Koopman Operator theory to the motion of a satellite about a libration point in the Circular Restricted Three-Body Problem. Recently, the Koopman Operator has emerged as a promising alternative to the geometric perspective for dynamical systems, where the Koopman Operator formulates the analysis and dy...
Article
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We present a set-theoretic version of some basic dilation results of operator theory. The results we have considered are Wold decomposition, Halmos dilation, Sz. Nagy dilation, inter-twining lifting, commuting and non-commuting dilations, BCL theorem, etc. We point out some natural generalizations and variations.
Article
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We prove a realization theorem for rational functions of several complex variables which extends the main theorem of Bessmertnyĭ (in: Alpay, Gohberg, Vinnikov (eds) Interpolation Theory, Systems Theory and Related Topics. Operator Theory Advances and Applications vol 134. Birkhauser Verlag, Basel, pp 157–185, 2002). In contrast to Bessmertnyĭ’s app...
Article
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"Operator theory is a magnificent tool for studying the geometric beha- viors of holomorphic functions in the open unit disk. Recently, a combination bet- ween two well known di erential operators, Ruscheweyh derivative and Salagean operator are suggested by Lupas in [10]. In this effort, we shall follow the same principle, to formulate a generaliz...
Article
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In this article, we present a new fractional integral with a non-singular kernel and by using Laplace transform, we derived the corresponding fractional derivative. By composition between our fractional integration operator with classical Caputo and Riemann-Liouville fractional operators, we establish a new fractional derivative which is interpolat...
Article
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The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators...
Article
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In this paper, we present the globally conservative solutions to the Cauchy problem for the modified Camassa–Holm (MOCH) equation. First, we transform the equation into an equivalent semi-linear system under new variables. Second, according to the standard ordinary differential equation theory with the aid of the conservation law, we give the globa...
Article
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Operator theory has wide range of applications in the field of quantum mechanics. In this manuscript, we extended a new class of operator named Quasi M-class Ak * operator and studied some of its spectral properties. In addition to that, the Kronecker product of quasi M-class Ak * operators are also studied.
Article
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Thick wall structures are usually applied at a highly reduced frequency. It is crucial to study the refined dynamic modeling of a thick plate, as it is directly related to the dynamic mechanical characteristics of an engineering structure or device, elastic wave scattering and dynamic stress concentration, and motion stability and dynamic control o...
Article
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This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly provides the osculating evolution of the system under the effects of any order of the zonal harmonics, and can b...
Article
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Asmar et al. [Note on norm convergence in the space of weak type multipliers. J Operator Theory. 1998;39(1):139–149] proved that the space of weak-type Fourier multipliers acting from Lp into Lp,∞ is continuously embedded into L∞. We obtain a sharper result in the setting of abstract Lorentz spaces Λq(X) with 0<q≤∞ built upon a Banach function spac...
Article
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We derive integrals of combination of Gauss and Bessel functions, by the use of umbral techniques. We show that the method allows the possibility of pursuing new and apparently fruitful avenues in the theory of special functions, displaying interesting links with the theory and the formalism of integral transforms.
Article
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In this paper, we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second-order coupled systems of differential equations on the real line. We point out that it is required only conditions on the homeomorphisms and no growth or asymptotic conditions are assumed on the nonlinearities. The arguments make use...
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We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized, subject to constraints to optima of a nested convex optimization problem. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-s...
Article
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The number of actuators of an underactuated robot is less than its degree of freedom. In other words, underactuated robots can be designed with fewer actuators than fully actuated ones. Although an underactuated robot is more complex than a fully actuated robot, it has many advantages, such as energy, material, and space saving. Therefore, it has h...
Article
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The aim of this paper is to exploit the structure of strongly continuous operator semigroups in order to formulate a categorical framework in which a fresh perspective can be applied to past operator theoretic results. In particular, we investigate the inverse-producing Arens extension for Banach algebras (Trans. Am. Math. Soc. 88:536–548, 1958) ad...
Preprint
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The standard operational probabilistic framework (within which we can formulate Operational Quantum Theory) is time asymmetric. This is clear because the conditions on allowed operations are time asymmetric. It is odd, though, because Schoedinger's equation is time symmetric and probability theory does not care about time direction. In this work we...
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We consider Koopman operator theory in the context of nonlinear infinitedimensional systems, where the operator is defined over a space of nonlinear functionals. The properties of the Koopman semigroup are described and a finite-dimensional projection of the semigroup is proposed, which provides a linear finite-dimensional approximation of the unde...
Preprint
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In this article, the author attempts to shed light on density operators behind product operators; one may be able to understand how the product operators can describe the rotation of magnetizations. Furthermore, the author will explain the product operator theory extended to be applicable to strongly-coupled spin systems in solution-state and solid...
Article
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The purpose of this paper is to present an example of an Ordinary Differential Equation x′=F(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x'=F(x)$$\end{document} i...
Article
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Operator theory has many applications in several main scientific research areas (structural mechanics, aeronautics, quantum mechanics, ecology, probability theory, electrical engineering, among others) and the importance of its study is globally acknowledged. On the study of the operator’s kernel some progress has been achieved for some specific cl...
Article
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We characterize Gelfand–Shilov spaces, their distribution spaces and modulation spaces in terms of estimates of their Zak transforms. We use these results for general investigations of quasi-periodic functions and distributions. We also establish necessary and sufficient conditions for linear operators in order for these operators should be conjuga...
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We construct a toy model for the harmonic oscillator that is neither classical nor quantum. The model features a discrete energy spectrum, a ground state with sharp position and momentum, an eigenstate with non-positive Wigner function as well as a state that has tunneling properties. The underlying formalism exploits that the Wigner-Weyl approach...
Article
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Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Function Theory (SPFT), are significant in developing and providing further new studies. In complex domai...