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Relevant bibliographies by topics / Algebras, Linear. Integral equations

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Academic literature on the topic 'Algebras, Linear. Integral equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 February 2022

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Journal articles on the topic "Algebras, Linear. Integral equations"

1

Kalitvin, A. S., and V. A. Kalitvin. "Linear Operators and Equations with Partial Integrals." Contemporary Mathematics. Fundamental Directions 65, no. 3 (2019): 390–433. http://dx.doi.org/10.22363/2413-3639-2019-65-3-390-433.

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We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, and spaces of continuous functions. We study the action, regularity, duality, algebras, Fredholm properties, invertibility, and spectral properties of such operators. We describe principal properties of linear equations with partial integrals. We show that such equations are essentially diﬀerent compared to usual integral equations. We obtain conditions for the Fredholm alternative, conditions for zero spectral radius of the Volterra operator with partial integrals, and constru

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CARIÑENA, JOSÉ F., KURUSCH EBRAHIMI-FARD, HÉCTOR FIGUEROA, and JOSÉ M. GRACIA-BOND. "HOPF ALGEBRAS IN DYNAMICAL SYSTEMS THEORY." International Journal of Geometric Methods in Modern Physics 04, no. 04 (2007): 577–646. http://dx.doi.org/10.1142/s0219887807002211.

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The theory of exact and of approximate solutions for non-autonomous linear differential equations forms a wide field with strong ties to physics and applied problems. This paper is meant as a stepping stone for an exploration of this long-established theme, through the tinted glasses of a (Hopf and Rota–Baxter) algebraic point of view. By reviewing, reformulating and strengthening known results, we give evidence for the claim that the use of Hopf algebra allows for a refined analysis of differential equations. We revisit the renowned Campbell–Baker–Hausdorff–Dynkin formula by the modern approa

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S., F., and Rainer Kress. "Linear Integral Equations." Mathematics of Computation 56, no. 193 (1991): 379. http://dx.doi.org/10.2307/2008551.

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Huffman, Jason P., and Henry E. Heatherly. "Convolution algebras arising from Sturm-Liouville transforms and applications." International Journal of Mathematics and Mathematical Sciences 27, no. 4 (2001): 221–28. http://dx.doi.org/10.1155/s0161171201010584.

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A regular Sturm-Liouville eigenvalue problem gives rise to a related linear integral transform. Churchill has shown how such an integral transform yields, under certain circumstances, a generalized convolution operation. In this paper, we study the properties of convolution algebras arising in this fashion from a regular Sturm-Liouville problem. We give applications of these convolution algebras for solving certain differential and integral equations, and we outline an operational calculus for classes of such equations.

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Garetto, Claudia, and Michael Oberguggenberger. "Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities." Proceedings of the Edinburgh Mathematical Society 57, no. 2 (2013): 426–63. http://dx.doi.org/10.1017/s0013091513000424.

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AbstractThis paper addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalized functions. We employ the recently developed theory of generalized Fourier integral operators to construct parametrices for the solutions and to describe propagation of singularities in this setting. As required tools, the construction of generalized solutions to eikonal and transport equations is given and results on the microlocal regularity of the kernels of generalized Fourier integral oper

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Mahomed, K. S., and E. Momoniat. "Characterization of Symmetry Properties of First Integrals for Submaximal Linearizable Third-Order ODEs." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/214872.

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The relationship between first integrals of submaximal linearizable third-order ordinary differential equations (ODEs) and their symmetries is investigated. We obtain the classifying relations between the symmetries and the first integral for submaximal cases of linear third-order ODEs. It is known that the maximum Lie algebra of the first integral is achieved for the simplest equation and is four-dimensional. We show that for the other two classes they are not unique. We also obtain counting theorems of the symmetry properties of the first integrals for these classes of linear third-order ODE

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Chill, Ralph, and Jan Pr�ss. "Asymptotic behaviour of linear evolutionary integral equations." Integral Equations and Operator Theory 39, no. 2 (2001): 193–213. http://dx.doi.org/10.1007/bf01195817.

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ĐAPIĆ, N., M. KUNZINGER, and S. PILIPOVIĆ. "SYMMETRY GROUP ANALYSIS OF WEAK SOLUTIONS." Proceedings of the London Mathematical Society 84, no. 3 (2002): 686–710. http://dx.doi.org/10.1112/s0024611502013436.

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Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and non-linear) partial differential equations, where the term `weak solution' comprises the following settings: distributional solutions; solutions in generalized function algebras; solutions in the sense of association (corresponding to a number of weak or integral solution concepts in classical analysis). Factorization properties and infinitesimal criteria that allow the treatment of all three settings simultaneously are developed, thereby unifying and extending previous work in this area.2000

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van der Houwen, P. J., and H. J. J. te Riele. "Linear multistep methods for Volterra integral and integro-differential equations." Mathematics of Computation 45, no. 172 (1985): 439. http://dx.doi.org/10.1090/s0025-5718-1985-0804934-5.

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K. Eshkuvatov, Z., M. Kammuji, Bachok M. Taib, and N. M. A. Nik Long. "Effective approximation method for solving linear Fredholm-Volterra integral equations." Numerical Algebra, Control & Optimization 7, no. 1 (2017): 77–88. http://dx.doi.org/10.3934/naco.2017004.

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Dissertations / Theses on the topic "Algebras, Linear. Integral equations"

1

Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear." Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.

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Doutoramento em Matemática<br>Nesta tese de Doutoramento desenvolve-se principalmente uma abordagem algébrica à teoria de sistemas de controlo não lineares. No entanto, outros tópicos são também estudados. Os tópicos tratados são os seguidamente enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres, estabilidade de um sistema de corpos rolantes, algoritmos para aritmética digital, e equações integrais de Fredholm não lineares. No primeiro e principal tópico estudam-se representações para as soluções de sistemas de controlo lineares no controlo. As suas trajetórias

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Altassan, Alaa Abdullah. "Linear equations over free Lie algebras." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/linear-equations-over-free-liealgebras(6e29b286-1869-4207-b054-8baab98e70df).html.

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In this thesis, we study equations of the form $[x_1,u_1]+[x_2, u_2]+\ldots+[x_k,u_k]=0$ over a free Lie algebra $L$, where $k>1$ and the coefficients $u_1, u_2, \ldots,u_k$ belong to $L$. The starting point of this research is a paper [22], in which the authors embarked on a systematic study of very concrete linear equations over free Lie algebras. They focused on the given equations in the case where $k=2$. We generalise and develop a number of the results on equations with two variables to equations with an arbitrary number of indeterminates. Most of the results refer to the case where the

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Wilkerson, Owen Tanner. "Fast, Sparse Matrix Factorization and Matrix Algebra via Random Sampling for Integral Equation Formulations in Electromagnetics." UKnowledge, 2019. https://uknowledge.uky.edu/ece_etds/147.

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Many systems designed by electrical & computer engineers rely on electromagnetic (EM) signals to transmit, receive, and extract either information or energy. In many cases, these systems are large and complex. Their accurate, cost-effective design requires high-fidelity computer modeling of the underlying EM field/material interaction problem in order to find a design with acceptable system performance. This modeling is accomplished by projecting the governing Maxwell equations onto finite dimensional subspaces, which results in a large matrix equation representation (Zx = b) of the EM problem

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Fan, Ka-wing. "Prime solutions in arithmetic progressions of some quadratic equations and linear equations /." Hong Kong : University of HOng Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B23540308.

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Porter, Annabelle Louise. "The evolution of equation-solving: Linear, quadratic, and cubic." CSUSB ScholarWorks, 2006. https://scholarworks.lib.csusb.edu/etd-project/3069.

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This paper is intended as a professional developmental tool to help secondary algebra teachers understand the concepts underlying the algorithms we use, how these algorithms developed, and why they work. It uses a historical perspective to highlight many of the concepts underlying modern equation solving.

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Kong, Yafang, and 孔亚方. "On linear equations in primes and powers of two." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.

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It is known that the binary Goldbach problem is one of the open problems on linear equations in primes, and it has the Goldbach-Linnik problem, that is, representation of an even integer in the form of two odd primes and powers of two, as its approximate problem. The theme of my research is on linear equations in primes and powers of two. Precisely, there are two cases: one pair of linear equations in primes and powers of two, and one class of pairs of linear equations in primes and powers of two, in this thesis. In 2002, D.R. Heath-Brown and P.C. Puchta obtained that every sufficiently lar

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Muiños, Bellester Ferran. "The equations of Rees algebras of ideals of almost-linear type." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/130901.

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L’àlgebra de Rees R(I) d’un ideal I d’un anell Noetherià local R juga un paper molt important en àlgebra commutativa i geometria algebraica, perquè Proj(R(I)) és l’explosió (blowup) de l’esquema afí Spec(R) al llarg del subesquema Spec(R/I). Fins avui dia, el problema de descriure les equacions de l’àlgebra de Rees d’ideals, així com altres àlgebres relacionades, com ara l’anell graduat associat G(I) o el con de la fibra F(I), s’ha mostrat molt rellevant per tal de comprendre els fenòmens que envolten aquestes àlgebres. Les equacions de l’àlgebra de Rees R(I) són definibles com els elements

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樊家榮 and Ka-wing Fan. "Prime solutions in arithmetic progressions of some quadratic equationsand linear equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31225962.

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Goh, K. H. M. "Numerical solution of quadratically non-linear boundary value problems using integral equation techniques : with applications to nozzle and wall flows /." Title page, contents and summary only, 1986. http://web4.library.adelaide.edu.au/theses/09PH/09phg614.pdf.

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Pipkins, Daniel Scott. "Non-linear analysis of (i) wave propagation using transform methods and (ii) plates and shells using integral equations." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/20052.

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Books on the topic "Algebras, Linear. Integral equations"

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Diophantine equations and power integral bases: New computational methods. Birkhäuser, 2002.

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Linear integral equations. Springer-Verlag, 1989.

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Lovitt, William Vernon. Linear integral equations. Dover Publications, 2005.

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Kress, Rainer. Linear Integral Equations. Springer Berlin Heidelberg, 1989.

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Kress, Rainer. Linear Integral Equations. Springer New York, 1999.

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Kress, Rainer. Linear Integral Equations. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4614-9593-2.

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Kanwal, Ram P. Linear Integral Equations. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6012-1.

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Kress, Rainer. Linear Integral Equations. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3.

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Kress, Rainer. Linear Integral Equations. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4.

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Kanwal, Ram P. Linear Integral Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0765-8.

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Book chapters on the topic "Algebras, Linear. Integral equations"

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Ganzha, Elena I. "Intertwining Laplace Transformations of Linear Partial Differential Equations." In Algebraic and Algorithmic Aspects of Differential and Integral Operators. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54479-8_4.

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Eichenherr, H., H. J. de Vega, and J. M. Maillet. "Yang-Baxter charge algebras in integrable classical and quantum field theorie." In Non-Linear Equations in Classical and Quantum Field Theory. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/3-540-15213-x_79.

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Dzyadyk, V. K. "Approximative-Iterative Method for Solving Non-Linear Differential and Integral Equations." In Algebraic and Geometric Methods in Mathematical Physics. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-0693-3_23.

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Bronshtein, I. N., K. A. Semendyayev, Gerhard Musiol, and Heiner Mühlig. "Linear Integral Equations." In Handbook of Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46221-8_11.

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Prössdorf, S. "Linear Integral Equations." In Analysis IV. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58175-5_1.

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Bronshtein, Ilja N., Konstantin A. Semendyayev, Gerhard Musiol, and Heiner Muehlig. "Linear Integral Equations." In Handbook of Mathematics. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05382-9_11.

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Kress, Rainer. "Singular Integral Equations." In Linear Integral Equations. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4_7.

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Kanwal, Ram P. "Singular Integral Equations." In Linear Integral Equations. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-6012-1_8.

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Kress, Rainer. "Singular Integral Equations." In Linear Integral Equations. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_7.

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Kanwal, Ram P. "Singular Integral Equations." In Linear Integral Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0765-8_8.

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Conference papers on the topic "Algebras, Linear. Integral equations"

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Spanos, Pol D., and Scott M. Miller. "Hilbert Transform Generalization of a Classical Random Vibration Integral." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0046.

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Abstract Integrals which represent the spectral moments of the stationary response of a linear, time-invariant system under random excitation are considered. It is shown that these integrals can be determined through the solution of linear algebraic equations. These equations are derived by considering differential equations for both the autocorrelation function of the system response and its Hilbert transform. The method can be applied to determine both even order and odd order spectral moments. Furthermore, it provides a potent generalization of a classical formula used in control engineerin

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Huo, Y., B. Q. Li, and R. Akarapu. "A Finite Element-Boundary Integral Method for 3-D Electromagnetic Heating Analysis." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56392.

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A three-dimensional finite element-boundary integral formulation is presented for the analysis of the electric and magnetic field distribution, power absorption and the temperature distribution in electrically conduction and dielectric materials. For large-scale electromagnetic-thermal materials processing system analyses, the hybrid finite/boundary method represents an optimal approach. To further improve the efficiency, the present formulation also incorporates various efficient solvers designed specifically for the solution of large sparse systems of linear algebraic equations. The resultin

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Makaryan, Vahagn, Michael Sutton, Tatevik Yeghiazaryan, Davresh Hasanyan, and Xiaomin Deng. "Cracked Elastic Layer Under a Compressive Mechanical Load." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-11967.

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In the present work, the problem of an elastic layer weakened by a finite penny shaped crack parallel to a layer’s surface that is loaded in compression is considered. Assuming that the surfaces of the crack have frictional slipping contact, Henkel and Legendre integral transformation techniques are employed to formulate solutions in the form of an infinite system of linear algebraic equations. The regularity of the equations is established and closed-form solutions are obtained for stresses and strains. Assuming shear stress on the crack surfaces is linearly distributed, numerical results sho

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Agrawal, Om P. "A Numerical Scheme and an Error Analysis for a Class of Fractional Optimal Control Problems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87367.

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There has been a growing interest in recent years in the area of Fractional Optimal Control (FOC). In this paper, we present a formulation for a class of FOC problems, in which a performance index is defined as an integral of a quadratic function of the state and the control variables, and a dynamic constraint is defined as a Fractional Differential Equation (FDE) linear in both the state and the control variables. The fractional derivative is defined in the Caputo sense. In this formulation, the FOC problem is reduced to a Fractional Variational Problem (FVP), and the necessary differential e

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Tangpong, X. W., and Om P. Agrawal. "Fractional Optimal Control of Distributed Systems." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43046.

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This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a Fractional Optimal Control Problem (FOCP) is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE). The scheme presented rely on reducing the equations for distributed system into a set of equations that have no space parameter. Several strategies are pointed out for this t

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Ye, Honglin, and Robert M. Corless. "Solving linear integral equations in Maple." In Papers from the international symposium. ACM Press, 1992. http://dx.doi.org/10.1145/143242.143279.

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Agrawal, Om P. "Fractional Optimal Control of a Distributed System Using Eigenfunctions." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35921.

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This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a FOCP is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equations (PFDEs). Eigenfunctions are used to eliminate the space parameter, and to define the problem in terms of a set of state and control variables. This leads to a multi FOCP in which each FOCP could be solved independently

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Uslenghi, Piergiorgio L. E. "Frequency-domain Integral Equations in Linear Electrodynamics." In 2007 International Conference on Electromagnetics in Advanced Applications. IEEE, 2007. http://dx.doi.org/10.1109/iceaa.2007.4387387.

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Crosa, G., F. Pittaluga, A. Trucco Martinengo, F. Beltrami, A. Torelli, and F. Traverso. "Heavy-Duty Gas Turbine Plant Aerothermodynamic Simulation Using Simulink." In ASME 1996 Turbo Asia Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-ta-022.

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This paper presents a physical simulator for predicting the off-design and dynamic behaviour of a single shaft heavy-duty gas turbine plant, suitable for gas-steam combined cycles. The mathematical model, which is non linear and based on the lumped parameter approach, is described by a set of first-order differential and algebraic equations. The plant components are described adding to their steady state characteristics the dynamic equations of mass, momentum and energy balances. The state variables are mass flow rates, static pressures, static temperatures of the fluid, wall temperatures and

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ERBE, LYNN, ALLAN PETERSON, and PAVEL ŘEHÁK. "INTEGRAL COMPARISON THEOREMS FOR SECOND ORDER LINEAR DYNAMIC EQUATIONS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770752_0042.

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