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Journal articles on the topic 'Unbounded source'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Demir, Kaya, and Salih Ergün. "An Analysis of Deterministic Chaos as an Entropy Source for Random Number Generators." Entropy 20, no. 12 (2018): 957. http://dx.doi.org/10.3390/e20120957.

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This paper presents an analytical study on the use of deterministic chaos as an entropy source for the generation of random numbers. The chaotic signal generated by a phase-locked loop (PLL) device is investigated using numerical simulations. Depending on the system parameters, the chaos originating from the PLL device can be either bounded or unbounded in the phase direction. Bounded and unbounded chaos differs in terms of the flatness of the power spectrum associated with the chaotic signal. Random bits are generated by regular sampling of the signal from bounded and unbounded chaos. A white

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2

Natalini, R. "Unbounded solutions for conservation laws with source." Nonlinear Analysis: Theory, Methods & Applications 21, no. 5 (1993): 349–62. http://dx.doi.org/10.1016/0362-546x(93)90078-7.

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3

Cox, G., and R. Chitty. "Some Source-Dependent effects of unbounded fires." Combustion and Flame 60, no. 3 (1985): 219–32. http://dx.doi.org/10.1016/0010-2180(85)90027-6.

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4

ALEKSEEV, G. V. "Multidimensional inverse source problems of underwater acoustics." European Journal of Applied Mathematics 9, no. 6 (1998): 589–605. http://dx.doi.org/10.1017/s0956792598003611.

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We consider linear and nonlinear inverse source problems of sound radiation in an unbounded domain which models an oceanic waveguide. The method for analysing their solvability is based on analytical properties of generalized acoustic potentials and the theory of extremal problems.

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5

CONAND, NICOLE, and ALICIA DORNADIC. "The Ethnographer Unbounded: Considering open source in corporate environments." Ethnographic Praxis in Industry Conference Proceedings 2012, no. 1 (2012): 88–100. http://dx.doi.org/10.1111/j.1559-8918.2012.00011.x.

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6

SPEIRS, DAVID C., S. L. McCONVILLE, K. M. GILLESPIE, A. D. R. PHELPS, and K. RONALD. "Numerical simulations of unbounded cyclotron-maser emissions." Journal of Plasma Physics 79, no. 6 (2013): 999–1001. http://dx.doi.org/10.1017/s0022377813001141.

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AbstractNumerical simulations have been conducted to study the spatial growth rate and emission topology of the cyclotron-maser instability responsible for stellar/planetary auroral magnetospheric radio emission and intense non-thermal radio emission in other astrophysical contexts. These simulations were carried out in an unconstrained geometry, so that the conditions existing within the source region of some natural electron cyclotron masers could be more closely modelled. The results have significant bearing on the radiation propagation and coupling characteristics within the source region

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7

Wu, Zhen. "Fully coupled FBSDE with Brownian motion and Poisson process in stopping time duration." Journal of the Australian Mathematical Society 74, no. 2 (2003): 249–66. http://dx.doi.org/10.1017/s1446788700003281.

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AbstractWe first give the existence and uniqueness result and a comparison theorem for backward stochastic differential equations with Brownian motion and Poisson process as the noise source in stopping time (unbounded) duration. Then we obtain the existence and uniqueness result for fully coupled forward-backward stochastic differential equation with Brownian motion and Poisson process in stopping time (unbounded) duration. We also proved a comparison theorem for this kind of equation.

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8

Waxler, Roger M., Bin Liang, and Claus Hetzer. "Infrasound propagation from a vertically extended source." Journal of the Acoustical Society of America 153, no. 3_supplement (2023): A194. http://dx.doi.org/10.1121/10.0018635.

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The propagation of infrasound from a vertically extended source is investigated. The source is allowed to have azimuthal and vertical variation. The radial extent of the source is assumed to be small compared to an acoustic wavelength. No such assumption is made for the vertical extent. The problem is treated in cylindrical coordinates, as is appropriate for outdoor sound propagation, in a way analogous to the treatment of radiation from a compact source in unbounded three dimensional space. Several equivalent formulations will be presented along with example cases.

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9

Carrion, Philip, José Carcione, and Edson E. S. Sampaio. "Radiation patterns: Possibility for monitoring seismic sources." GEOPHYSICS 61, no. 1 (1996): 282–87. http://dx.doi.org/10.1190/1.1443950.

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Recent field measurements of the radiation in boreholes indicate that the radiation patterns of real seismic sources are not always in agreement with those corresponding to the point‐source excitation in unbounded homogeneous and isotropic acoustic or elastic media [we refer the reader to Aki and Richards (1980) for the basic discussion on the radiation patterns in homogeneous media]. This mismatch results from the fact that the point‐source radiation patterns corresponding to homogeneous media are too simplistic to satisfy any experiment in the more realistic Earth environment. A study of rad

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10

Pişkin, Erhan. "Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms." Advances in Mathematical Physics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/523254.

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We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense.

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11

Halilsoy, M., and A. Ovgun. "Particle Collision Near 1 + 1-Dimensional Horava-Lifshitz Black Hole and Naked Singularity." Advances in High Energy Physics 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/4383617.

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The unbounded center-of-mass (CM) energy of oppositely moving colliding particles near horizon emerges also in 1+1-dimensional Horava-Lifshitz gravity. This theory has imprints of renormalizable quantum gravity characteristics in accordance with the method of simple power counting. Surprisingly the result obtained is not valid for a 1-dimensional Compton-like process between an outgoing photon and an infalling massless/massive particle. It is possible to achieve unbounded CM energy due to collision between infalling photons and particles. The source of outgoing particles may be attributed to a

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12

Hofmann, Bernd, Peter Mathé, and Heinrich von Weizsäcker. "Regularization in Hilbert space under unbounded operators and general source conditions." Inverse Problems 25, no. 11 (2009): 115013. http://dx.doi.org/10.1088/0266-5611/25/11/115013.

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13

Rozanov, Yu A. "On Evolution of Random Fields with an Ultra Unbounded Stochastic Source." Theory of Probability & Its Applications 38, no. 2 (1994): 316–29. http://dx.doi.org/10.1137/1138028.

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14

Marklein, René, Karl J. Langenberg, and Torsten Kaczorowski. "Electromagnetic and elastodynamic point source excitation of unbounded homogeneous anisotropic media." Radio Science 31, no. 6 (1996): 1919–30. http://dx.doi.org/10.1029/96rs02155.

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15

Falconer, Kenneth J., Jiaxin Hu, and Yuhua Sun. "Inhomogeneous parabolic equations on unbounded metric measure spaces." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 5 (2012): 1003–25. http://dx.doi.org/10.1017/s0308210511000539.

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We study the inhomogeneous semilinear parabolic equationwith source term f independent of time and subject to f(x) ≥ 0 and with u(0, x) = φ(x) ≥ 0, for the very general setting of a metric measure space. By establishing Harnack-type inequalities in time t and some powerful estimates, we give sufficient conditions for non-existence, local existence and global existence of weak solutions, depending on the value of p relative to a critical exponent.

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16

Dhaliwal, Ranjit S., Samir R. Majumdar, and Jun Wang. "Thermoelastic waves in an infinite solid caused by a line heat source." International Journal of Mathematics and Mathematical Sciences 20, no. 2 (1997): 323–34. http://dx.doi.org/10.1155/s0161171297000434.

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The generalized thermoelasticity theory recently developed by Green and Naghdi is employed to investigate thermoelastic interactions caused by a continuous line heat source in a homogeneous isotropic unbounded solid. Hankel-Laplace transform technique is used to solve the problem. Explicit expressions, for stress and temperature fields, are obtained for small time approximation. Numerical values are displayed graphically. Our results show that this theory predicts an infinite speed for heat propagation in general, and includes the second sound phenomena as a special case.

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17

Hijden, J. H. M. T. "Radiation from an impulsive line source in an unbounded homogeneous anisotropic medium." Geophysical Journal International 91, no. 2 (1987): 355–72. http://dx.doi.org/10.1111/j.1365-246x.1987.tb05232.x.

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18

Tilgner, A. "Oscillatory shear layers in source driven flows in an unbounded rotating fluid." Physics of Fluids 12, no. 5 (2000): 1101–11. http://dx.doi.org/10.1063/1.870364.

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19

Chen, Zhiming, and Xueshuang Xiang. "A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain." SIAM Journal on Numerical Analysis 51, no. 4 (2013): 2331–56. http://dx.doi.org/10.1137/130917144.

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20

Krishnan, Gokul P., and David T. Leighton. "Diffusion from a point source in a time‐dependent unbounded extensional flow." Physics of Fluids A: Fluid Dynamics 4, no. 11 (1992): 2327–31. http://dx.doi.org/10.1063/1.858473.

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21

Povstenko, Yuriy, Martin Ostoja-Starzewski, and Tamara Kyrylych. "Telegraph equation in polar coordinates: Unbounded domain with moving time-harmonic source." International Journal of Heat and Mass Transfer 207 (June 2023): 124013. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2023.124013.

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22

Poletto, Flavio. "Energy balance of a drill-bit seismic source, part 1: Rotary energy and radiation properties." GEOPHYSICS 70, no. 2 (2005): T13—T28. http://dx.doi.org/10.1190/1.1897038.

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An issue in seismic-while-drilling (SWD) technology is to characterize the dynamic and radiation properties of the drill-bit source working under different operational conditions. The energy requirements, power losses, local crack effects, radiation, and near-field effects associated with rotary drilling are analyzed to quantify the waves produced by an SWD vertical force acting in bounded and unbounded media. Results are expressed in terms of a complex integrated impedance and the equations for rotary drilling. The calculations — extended to the waves in the drill string — are used in part 2

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23

CAULFIELD, C. P., and ANDREW W. WOODS. "Turbulent gravitational convection from a point source in a non-uniformly stratified environment." Journal of Fluid Mechanics 360 (April 10, 1998): 229–48. http://dx.doi.org/10.1017/s0022112098008623.

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We examine the turbulent gravitational convection which develops above a point source of buoyant fluid in a stably stratified environment in which the buoyancy frequency varies with height according to N2=N2s (z/zs)β. This generalizes the classical model of turbulent buoyant plumes rising through uniform and uniformly stratified environments originally developed by Morton et al. (1956). By analogy, the height of rise of a plume with initial buoyancy flux Fs has the form Hp= Apεp−1/2Fs1/4Ns−3/4hp (λ, β) where εp is the entrainment constant for plume motion, Ap is an O(1) constant, and the non-d

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24

Coco, Armando, Gilda Currenti, Ciro Del Negro, and Giovanni Russo. "A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology." Communications in Computational Physics 16, no. 4 (2014): 983–1009. http://dx.doi.org/10.4208/cicp.210713.010414a.

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AbstractWe propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded domains. The technique is based on a smooth coordinate transformation, which maps an unbounded domain into a unit square. Arbitrary geometries are defined by suitable level-set functions. The equations are discretized by classical nine-point stencil on interior points, while boundary conditions and high order reconstructions are used to define the field variables at ghost-points, which are grid nodes external to the domain with a

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25

Kaytmaz, Özlem. "The problem of determining source term in a kinetic equation in an unbounded domain." AIMS Mathematics 9, no. 4 (2024): 9184–94. http://dx.doi.org/10.3934/math.2024447.

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<abstract><p>In this paper, we deal with an inverse problem of determining the source function in a kinetic equation that is considered in an unbounded domain with Cauchy data. We prove the uniqueness of the solution of an inverse problem by means of a pointwise Carleman estimate. In recent years, kinetic equations have occurred in a variety of important fields and applications, such as aerospace engineering, semi-conductor technology, nuclear engineering, chemotaxis, and immunology.</p></abstract>

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26

Royer, Julien. "Semiclassical measure for the solution of the Helmholtz equation with an unbounded source." Asymptotic Analysis 91, no. 1 (2015): 11–32. http://dx.doi.org/10.3233/asy-141255.

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27

Hu, Guang-hui, Yavar Kian, and Yue Zhao. "Uniqueness to Some Inverse Source Problems for the Wave Equation in Unbounded Domains." Acta Mathematicae Applicatae Sinica, English Series 36, no. 1 (2019): 134–50. http://dx.doi.org/10.1007/s10255-020-0917-4.

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28

Ganapathy, R. "Weak Thermal Vortex Rings." Journal of Fluids Engineering 116, no. 1 (1994): 174–76. http://dx.doi.org/10.1115/1.2910233.

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A simple mathematical model is proposed and a similarity solution is obtained to study the behavior of very weak thermal vortex rings induced by a horizontal line source of thermal energy in an unbounded fluid. The temperature distribution is assumed to be unaffected by the fluid motion, and the Stokes flow approximation is invoked. Streamlines are computed to demonstrate the evolution of the flow field.

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29

SINAYOKO, SAMUEL, A. AGARWAL, and Z. HU. "Flow decomposition and aerodynamic sound generation." Journal of Fluid Mechanics 668 (December 3, 2010): 335–50. http://dx.doi.org/10.1017/s0022112010004672.

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An approximate decomposition of fluid-flow variables satisfying unbounded compressible Navier–Stokes equations into acoustically radiating and non-radiating components leads to well-defined source terms that can be identified as the physical sources of aerodynamic noise. We show that, by filtering the flow field by means of a linear convolution filter, it is possible to decompose the flow into non-radiating and radiating components. This is demonstrated on two different flows: one satisfying the linearised Euler equations and the other the Navier–Stokes equations. In the latter case, the corre

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30

Kahana, Adar, Eli Turkel, and Dan Givoli. "Convective Wave Equation and Time Reversal Process for Source Refocusing." Journal of Theoretical and Computational Acoustics 26, no. 02 (2018): 1850016. http://dx.doi.org/10.1142/s2591728518500160.

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The convective wave equation deals with wave propagation in a moving media. We focus on the underwater acoustic wave equation where the convective element is the flow of water inside a river, along its length. The main thrust of this paper is the ill-posed “refocusing” problem. The initial condition simulates an explosion in a small compact region and the response is recorded over time at several microphones. Having only partial and noisy information we expect that small perturbations will destroy the ability to recover the complete initial data. We use the time reversal (TR) technique to dete

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31

Palivos, Theodore, and Dimitrios Varvarigos. "POLLUTION ABATEMENT AS A SOURCE OF STABILIZATION AND LONG-RUN GROWTH." Macroeconomic Dynamics 21, no. 3 (2016): 644–76. http://dx.doi.org/10.1017/s1365100515000632.

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In a two-period overlapping-generations model with production, we consider the damaging impact of environmental degradation on health and consequently life expectancy. Despite the presence of social constant returns to capital, which would otherwise generate unbounded growth, when pollution is left unabated, the economy cannot achieve such a path. Instead, it converges either to a stationary level of capital per worker or to a cycle in which capital per worker oscillates permanently. The government's involvement in environmental preservation proves crucial for both short-term dynamics and long

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32

Hao, Xutong, Mingjun Zhou, and Xinxin Jing. "Asymptotic behavior of solutions to porous medium equations with boundary degeneracy." Electronic Journal of Differential Equations 2021, no. 01-104 (2021): 96. http://dx.doi.org/10.58997/ejde.2021.96.

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This article concerns the asymptotic behavior of solutions to a class of one-dimensional porous medium equations with boundary degeneracy on bounded and unbounded intervals. It is proved that the degree of degeneracy, the exponents of the nonlinear diffusion, and the nonlinear source affect the asymptotic behavior of solutions. It is shown that on a bounded interval, the problem admits both nontrivial global and blowing-up solutions if the degeneracy is not strong; while any nontrivial solution must blow up if the degeneracy is strong enough. For the problem on an unbounded interval, the blowi

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33

Cragg, Gordon M., and David J. Newman. "Biodiversity: A continuing source of novel drug leads." Pure and Applied Chemistry 77, no. 1 (2005): 7–24. http://dx.doi.org/10.1351/pac200577010007.

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Nature has been a source of medicinal agents for thousands of years and continues to be an abundant source of novel chemotypes and pharmacophores. With only 5 to 15 % of the approximately 250 000 species of higher plants systematically investigated, and the potential of the marine environment barely tapped, these areas will remain a rich source of novel bioactive compounds. Less than 1 % of bacterial and 5 % of fungal species are currently known, and the potential of novel microbial sources, particularly those found in extreme environments, seems unbounded. To these natural sources can be adde

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34

Zenkour, Ashraf M., Daoud S. Mashat, and Ashraf M. Allehaibi. "Thermoelastic Coupling Response of an Unbounded Solid with a Cylindrical Cavity Due to a Moving Heat Source." Mathematics 10, no. 1 (2021): 9. http://dx.doi.org/10.3390/math10010009.

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The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of

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35

Nam, Bui Duc, Bui Dai Nghia, and Nguyen Anh Tuan. "Mild solutions to Love-type equations on R^2." Electronic Journal of Differential Equations 2025, no. 01-?? (2025): 76. https://doi.org/10.58997/ejde.2025.76.

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In this article, we study a non-local Love problem on unbounded domains where the non-locality in the main equation is interpreted as a fractional Laplacian operator. With various assumptions on the initial conditions, we derive several estimates for mild solutions for the homogenous source scenario. For the nonlinear problem, we show the existence and uniqueness of a global mild solution. In two cases, we obtain convergence results. The first one states that the solution to the fractional Love equation converges to the mild solution of the fractional wave equation according to a cross-section

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36

Georgiev, Slavi, and Lubin Vulkov. "Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation." Applied Sciences 13, no. 7 (2023): 4536. http://dx.doi.org/10.3390/app13074536.

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In this paper, we suggest a method for recovering the unknown time-dependent strength of a contaminant concentration source from measurements of the concentration inside an unbounded domain. This problem is formulated as a Cauchy parabolic inverse problem. For its efficient numerical processing, the problem is solved by reduction of the Cauchy problem to a Dirichet one on a bounded domain using the method of the fundamental (potential) solutions in combination with an adjoint equation technique. A numerical solution to this approach is explained. Next, by choosing the source strength in the fo

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37

Simões, Inês, António Tadeu, and Nuno Simões. "Green’s Functions for Heat Conduction for Unbounded and Bounded Rectangular Spaces: Time and Frequency Domain Solutions." Journal of Applied Mathematics 2016 (2016): 1–22. http://dx.doi.org/10.1155/2016/6439710.

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This paper presents a set of fully analytical solutions, together with explicit expressions, in the time and frequency domain for the heat conduction response of homogeneous unbounded and of bounded rectangular spaces (three-, two-, and one-dimensional spaces) subjected to point, line, and plane heat diffusion sources. Particular attention is given to the case of spatially sinusoidal, harmonic line sources. In the literature this problem is often referred to as the two-and-a-half-dimensionalfundamental solutionor 2.5D Green’s functions. These equations are very useful for formulating three-dim

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38

Iranzo-Sánchez, Javier, Jorge Iranzo-Sánchez, Adrià Giménez, Jorge Civera, and Alfons Juan. "Segmentation-Free Streaming Machine Translation." Transactions of the Association for Computational Linguistics 12 (2024): 1104–21. http://dx.doi.org/10.1162/tacl_a_00691.

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Abstract Streaming Machine Translation (MT) is the task of translating an unbounded input text stream in real-time. The traditional cascade approach, which combines an Automatic Speech Recognition (ASR) and an MT system, relies on an intermediate segmentation step which splits the transcription stream into sentence-like units. However, the incorporation of a hard segmentation constrains the MT system and is a source of errors. This paper proposes a Segmentation-Free framework that enables the model to translate an unsegmented source stream by delaying the segmentation decision until after the

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39

Abbas, Ibrahim A. "Thermoelastic interactions in an isotropic unbounded medium due to moving heat source using GNIII model." Latin American Journal of Solids and Structures 12, no. 6 (2015): 1061–73. http://dx.doi.org/10.1590/1679-78251553.

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40

Xiang, Zhiming Chen and Xueshuang. "A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions." Numerical Mathematics: Theory, Methods and Applications 6, no. 3 (2013): 538–55. http://dx.doi.org/10.4208/nmtma.2013.1217nm.

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41

Hajarolasvadi, Setare, and Ahmed E. Elbanna. "A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities." Geophysical Journal International 211, no. 2 (2017): 851–64. http://dx.doi.org/10.1093/gji/ggx337.

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42

Abd-Alla, A. M. "On a generalized thermoelastic interaction in an unbounded body due to a line heat source." Applied Mathematics and Computation 100, no. 2-3 (1999): 285–95. http://dx.doi.org/10.1016/s0096-3003(98)00032-0.

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43

Lloyd, S. F., C. Jeong, H. N. Gharti, J. Vignola, and J. Tromp. "Spectral-Element Simulations of Acoustic Waves Induced by a Moving Underwater Source." Journal of Theoretical and Computational Acoustics 27, no. 03 (2019): 1850040. http://dx.doi.org/10.1142/s2591728518500408.

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In this study, we model acoustic waves induced by moving acoustic sources in three-dimensional (3D) underwater settings based on a spectral-element method (SEM). Numerical experiments are conducted using the SEM software package SPECFEM3D_Cartesian, which facilitates fluid–solid coupling and absorbing boundary conditions. Examples presented in this paper include an unbounded fluid truncated by using absorbing boundaries, and a shallow-water waveguide modeled as a fluid–solid coupled system based on domain decomposition. In the numerical experiments, the SEM-computed pressures match their analy

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44

Procopio, Giuseppe, and Massimiliano Giona. "Bitensorial formulation of the singularity method for Stokes flows." Mathematics in Engineering 5, no. 2 (2022): 1–34. http://dx.doi.org/10.3934/mine.2023046.

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<abstract><p>This paper develops the bitensorial formulation of the system of singularities associated with unbounded and bounded Stokes flows. The motivation for this extension is that Stokesian singularities and hydrodynamic fundamental solutions are multi-point functions, and bitensor calculus provides either the proper geometrical setting, in order to avoid inconsistencies and misunderstandings on the role of the different tensorial indices, or a way for compactly deriving hydrodynamic properties. A first relevant result is to provide a clear definition of the singularities (bo

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45

HOCKING, G. C., L. K. FORBES, and T. E. STOKES. "A NOTE ON STEADY FLOW INTO A SUBMERGED POINT SINK." ANZIAM Journal 56, no. 2 (2014): 150–59. http://dx.doi.org/10.1017/s1446181114000303.

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AbstractThe steady, axisymmetric flow induced by a point sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained, and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and, in fact, the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface.

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46

Jafarsadeghi-Pournaki, Ilgar, Ghader Rezazadeh, Mohammadreza Zamanzadeh, and Rasoul Shabani. "Parametric Thermally Induced Vibration of an Electrostatically Deflected FGM Micro-Beam." International Journal of Applied Mechanics 08, no. 08 (2016): 1650092. http://dx.doi.org/10.1142/s1758825116500927.

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The present paper deals with the study of nonlinear vibration of a functionally graded cantilever micro-beam imposed on a bias DC voltage and superimposed on a sinusoidal heat source. The governing equation of motion is derived extremizing the Lagrange’s equation and Hamilton’s principal under the assumption of Euler–Bernoulli beam theory. The thermo-elastic equation is obtained utilizing the first law of thermodynamics under the assumption of the classical Fourier heat conduction model. Due to the displacement dependency of the electrostatic force and time variability of the heat source, the

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47

Hussein, M. S., Daniel Lesnic, Vitaly L. Kamynin, and Andrey B. Kostin. "Direct and inverse source problems for degenerate parabolic equations." Journal of Inverse and Ill-posed Problems 28, no. 3 (2020): 425–48. http://dx.doi.org/10.1515/jiip-2019-0046.

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AbstractDegenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty,

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48

Kopylova, Vera G. "On the Solvability of the Identification Problem for a Source Function in a Quasilinear Parabolic System of Equations in Bounded and Unbounded Domains." Journal of Siberian Federal University. Mathematics & Physics 14, no. 4 (2001): 483–91. http://dx.doi.org/10.17516/1997-1397-2021-14-4-483-491.

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The paper considers the problem of identification for a source function in one of two equations of parabolic quasilinear system. The case of Cauchy data in an unbounded domain and the case of boundary conditions of the first kind in a rectangular domain are considered. The question of the existence and uniqueness of the solution is studied. The proof uses a differential level splitting method known as the weak approximation method. The solution is obtained on a small time interval in the class of sufficiently smooth bounded functions

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Baynes, Alexander B., and Oleg A. Godin. "A Semi-Analytic, Numerically Efficient Model for Low-Frequency Sound Scattering by an Infinite Cylinder Located Near a Boundary." Journal of Theoretical and Computational Acoustics 28, no. 04 (2020): 2050010. http://dx.doi.org/10.1142/s2591728520500103.

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Scattering of sound by a target can be described as a wave radiated by virtual point sources inside the target. In the Rayleigh scattering regime, the strength of the virtual sources can be calculated analytically. When a target is located close to the ocean surface or another reflecting boundary, reflections of the incident and single-scattered waves from the boundary lead to multiple scattering from the target, with the target being insonified by nearby virtual sources. At low frequencies and for shallow targets, the distance from a virtual source to the target is not necessarily large compa

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50

Adimurthi, Aekta Aggarwal, and G. D. Veerappa Gowda. "Godunov-Type Numerical Methods for a Model of Granular Flow on Open Tables with Walls." Communications in Computational Physics 20, no. 4 (2016): 1071–105. http://dx.doi.org/10.4208/cicp.290615.060516a.

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AbstractWe propose and analyse finite volume Godunov type methods based on discontinuous flux for a 2×2 system of non-linear partial differential equations proposed by Hadeler and Kuttler to model the dynamics of growing sandpiles generated by a vertical source on a flat bounded rectangular table. The problem considered here is the so-called partially open table problem where sand is blocked by a wall (of infinite height) on some part of the boundary of the table. The novelty here is the corresponding modification of boundary conditions for the standing and the rolling layers and generalizatio

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