Gotowe bibliografie tematyczne / Non-solvable system of equations

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Gotowa bibliografia na temat „Non-solvable system of equations”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 22 czerwca 2025

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Artykuły w czasopismach na temat "Non-solvable system of equations"

KARA, MERVE, and YASIN YAZLIK. "ON A SOLVABLE SYSTEM OF NON-LINEAR DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS." Journal of Science and Arts 21, no. 1 (2021): 145–62. http://dx.doi.org/10.46939/j.sci.arts-21.1-a13.

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In this paper, we show that the system of difference equations can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system.

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Stević, Stevo, Bratislav Iricanin, and Witold Kosmala. "Symmetric nonlinear solvable system of difference equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 49 (2024): 1–16. http://dx.doi.org/10.14232/ejqtde.2024.1.49.

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We show the theoretical solvability of the system of difference equations x n + k = y n + l y n − c d y n + l + y n − c − d , y n + k = x n + l x n − c d x n + l + x n − c − d , n ∈ N 0 , where k ∈ N , l ∈ N 0 , l < k , c , d ∈ C and x j , y j ∈ C , j = 0 , k − 1 ¯ . For several special cases of the system, we give some detailed explanations on how some formulas for their general solutions can be found in closed form, that is, we show their practical solvability. To do this, among other things, we use the theory of homogeneous linear difference equations with constant coefficients and the product-type difference equations with integer exponents, which are theoretically solvable.

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Bombelli, L., W. E. Couch, and R. J. Torrence. "Solvable systems of wave equations and non-Abelian Toda lattices." Journal of Physics A: Mathematical and General 25, no. 5 (1992): 1309–27. http://dx.doi.org/10.1088/0305-4470/25/5/032.

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Stanzhytskyi, O. M., R. E. Uteshova, M. Mukash, and V. V. Mogylova. "Application of the method of averaging to boundary value problems for differential equations with non-fixed moments of impulse." Carpathian Mathematical Publications 14, no. 2 (2022): 304–26. http://dx.doi.org/10.15330/cmp.14.2.304-326.

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The method of averaging is applied to study the existence of solutions of boundary value problems for systems of differential equations with non-fixed moments of impulse action. It is shown that if an averaged boundary value problem has a solution, then the original problem is solvable as well. Here the averaged problem for the impulsive system is a simpler problem of ordinary differential equations.

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Stević, Stevo, Josef Diblík, Bratislav Iričanin, and Zdeněk Šmarda. "On a solvable system of rational difference equations." Journal of Difference Equations and Applications 20, no. 5-6 (2013): 811–25. http://dx.doi.org/10.1080/10236198.2013.817573.

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Stević, Stevo. "On a solvable rational system of difference equations." Applied Mathematics and Computation 219, no. 6 (2012): 2896–908. http://dx.doi.org/10.1016/j.amc.2012.09.012.

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Zhu, Changrong. "From homoclinics to quasi-periodic solutions for ordinary differential equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 5 (2015): 1091–114. http://dx.doi.org/10.1017/s0308210515000189.

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We consider the quasi-periodic solutions bifurcated from a degenerate homoclinic solution. Assume that the unperturbed system has a homoclinic solution and a hyperbolic fixed point. The bifurcation function for the existence of a quasi-periodic solution of the perturbed system is obtained by functional analysis methods. The zeros of the bifurcation function correspond to the existence of the quasi-periodic solution at the non-zero parameter values. Some solvable conditions of the bifurcation equations are investigated. Two examples are given to illustrate the results.

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Kara, Merve, and Yasin Yazlik. "Solvable three-dimensional system of higher-order nonlinear difference equations." Filomat 36, no. 10 (2022): 3449–69. http://dx.doi.org/10.2298/fil2210449k.

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In this work, we indicate three-dimensional system of difference equations xn = ayn?k + dyn?kxn?k?l/?bxn?k?l+?czn?l, yn = ?zn?k + ?zn?kyn?k?l/??yn?k?l + ??xn?l, zn = exn?k + hxn?kzn?k?l/?fzn?k?l +?g?yn?l , n ? N0, where k and l are positive integers, the parameters a,?b, ?c, d, ?, ??, ??, ?, e, ?f ,?g, h and the initial values x?j, y?j, z?j j = ?1,k+l, are non-zero real numbers, can be solved in closed form. In addition, we obtain explicit formulas for the well-defined solutions of the aforementioned system for the case l = 1. Also, the set of undefinable solutions of the system is found. Finally, an application about a three-dimensional system of difference equations is given.

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Pinar, Zehra. "The symmetry analysis of electrostatic micro-electromechanical system (MEMS)." Modern Physics Letters B 34, no. 18 (2020): 2050199. http://dx.doi.org/10.1142/s0217984920501997.

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The model of electrostatic Micro-Electromechanical System (MEMS) is considered without/with an external pressure. The model represents nonlinear elliptic or parabolic problem due to the steady or non-steady state problem, respectively. To obtain exact solutions in an explicit form, the symmetry analysis is considered. With symmetries, the transformations are obtained and by means of these transformations, solvable equations are hold. The obtained results have a major role in the literature so that the considered equation is seen in a large-scale applications.

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Tarasov, Vasily E. "General Non-Markovian Quantum Dynamics." Entropy 23, no. 8 (2021): 1006. http://dx.doi.org/10.3390/e23081006.

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A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus. In the proposed approach, the non-locality in time is represented by operator kernels of the Sonin type. A wide class of the exactly solvable models of non-Markovian quantum dynamics is suggested. These models describe open (non-Hamiltonian) quantum systems with general form of nonlocality in time. To describe these systems, the Lindblad equations for quantum observable and states are generalized by taking into account a general form of nonlocality. The non-Markovian quantum dynamics is described by using integro-differential equations with general fractional derivatives and integrals with respect to time. The exact solutions of these equations are derived by using the operational calculus that is proposed by Yu. Luchko for general fractional differential equations. Properties of bi-positivity, complete positivity, dissipativity, and generalized dissipativity in general non-Markovian quantum dynamics are discussed. Examples of a quantum oscillator and two-level quantum system with a general form of nonlocality in time are suggested.

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Rozprawy doktorskie na temat "Non-solvable system of equations"

Lee, Hwasung. "Strominger's system on non-Kähler hermitian manifolds." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef.

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In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds M with c₁(M) = 0. These manifolds are more general than balanced hermitian manifolds with holomorphically trivial canonical bundles. We will then consider explicit examples when M can be realized as a principal torus fibration over a Kähler surface S. We will solve the Strominger system on such construction which also includes manifolds of topology (k−1)(S²×S⁴)#k(S³×S³). We will investigate the anomaly cancellation condition on the principal torus fibration M. The anomaly cancellation condition reduces to a complex Monge-Ampère-type PDE, and we will prove existence of solution following Yau’s proof of the Calabi-conjecture [Yau78], and Fu and Yau’s analysis [FY08]. Finally, we will discuss the physical aspects of our work. We will discuss the Strominger system using α'-expansion and present a solution up to (α')¹-order. In the α'-expansion approach on a principal torus fibration, we will show that solving the anomaly cancellation condition in topology is necessary and sufficient to solving it analytically. We will discuss the potential problems with α'-expansion approach and consider the full Strominger system with the Hull connection. We will show that the α'-expansion does not correctly capture the behaviour of the solution even up to (α')¹-order and should be used with caution.

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Voldman, Aleksandr. "Topological classification of non-degenerate quadratic system." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1192.

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Chow, Tanya L. M., of Western Sydney Macarthur University, and Faculty of Business and Technology. "Systems of partial differential equations and group methods." THESIS_FBT_XXX_Chow_T.xml, 1996. http://handle.uws.edu.au:8081/1959.7/43.

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This thesis is concerned with the derivation of similarity solutions for one-dimensional coupled systems of reaction - diffusion equations, a semi-linear system and a one-dimensional tripled system. The first area of research in this thesis involves a coupled system of diffusion equations for the existence of two distinct families of diffusion paths. Constructing one-parameter transformation groups preserving the invariance of this system of equations enables similarity solutions for this coupled system to be derived via the classical and non-classical procedures. This system of equation is the uncoupled in the hope of recovering further similarity solutions for the system. Once again, one-parameter groups leaving the uncoupled system invariant are obtained, enabling similarity solutions for the system to be elicited. A one-dimensional pattern formation in a model of burning forms the next component of this thesis. The primary focus of this area is the determination of similarity solutions for this reaction - diffusion system by means of one-parameter transformation group methods. Consequently, similarity solutions which are a generalisation of the solutions of the one-dimensional steady equations derived by Forbes are deduced. Attention in this thesis is then directed toward a semi-linear coupled system representing a predator - prey relationship. Two approaches to solving this system are made using the classical procedure, leading to one-parameter transformation groups which are instrumental in elicting the general similarity solution for this system. A triple system of equations representing a one-dimensional case of diffusion in the presence of three diffusion paths constitutes the next theme of this thesis. In association with the classical and non-classical procedures, the derivation of one-parameter transformation groups leaving this system invariant enables similarity solutions for this system to be deduced. The final strand of this thesis involves a one- dimensional case of the general linear system of coupled diffusion equations with cross-effects for which one-parameter transformation group methods are once more employed. The one-parameter groups constructed for this system prove instrumental in enabling the attainment of similarity solutions for this system to be accomplished Faculty of Business and Technology

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Ikeda, Tatsushi. "Quantum Hierarchical Fokker-Planck and Smoluchowski Equations: Application to Non-Adiabatic Transition and Non-Linear Optical Response." Kyoto University, 2019. http://hdl.handle.net/2433/242623.

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Post, Katharina. "A System of Non-linear Partial Differential Equations Modeling Chemotaxis with Sensitivity Functions." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 1999. http://dx.doi.org/10.18452/14365.

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Wir betrachten ein System nichtlinearer parabolischer partieller Differentialgleichungen zur Modellierung des biologischen Phänomens Chemotaxis, das unter anderem in Aggregationsprozessen in Lebenszyklen bestimmter Einzeller eine wichtige Rolle spielt. Unser Chemotaxismodell benutzt Sensitivitäts funktionen, die die vorkommenden biologischen Prozesse genauer spezifizieren. Trotz der durch die Sensitivitätsfunktionen eingebrachten, zusätzlichen Nichtlinearitäten in den Gleichungen erhalten wir zeitlich globale Existenz von Lösungen für verschiedene biologisch realistische Klassen von Sensitivitätsfunktionen und können unter unterschiedlichen Bedingungen an die Systemdaten Konvergenz der Lösungen zu trivialen und nicht-trivialen stationären Punkten beweisen. We consider a system of non-linear parabolic partial differential equations modeling chemotaxis, a biological phenomenon which plays a crucial role in aggregation processes in the life cycle of certain unicellular organisms. Our chemotaxis model introduces sensitivity functions which help describe the biological processes more accurately. In spite of the additional non-linearities introduced by the sensitivity functions into the equations, we obtain global existence of solutions for different classes of biologically realistic sensitivity functions and can prove convergence of the solutions to trivial and non-trivial steady states.

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Di, Cosmo Jonathan. "Nonlinear Schrödinger equation and Schrödinger-Poisson system in the semiclassical limit." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209863.

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The nonlinear Schrödinger equation appears in different fields of physics, for example in the theory of Bose-Einstein condensates or in wave propagation models. From a mathematical point of view, the study of this equation is interesting and delicate, notably because it can have a very rich set of solutions with various behaviours.In this thesis, we have been interested in standing waves, which satisfy an elliptic partial differential equation. When this equation is seen as a singularly perturbed problem, its solutions concentrate, in the sense that they converge uniformly to zero outside some concentration set, while they remain positive on this set.We have obtained three kind of new results. Firstly, under symmetry assumptions, we have found solutions concentrating on a sphere. Secondly, we have obtained the same type of solutions for the Schrödinger-Poisson system. The method consists in applying the mountain pass theorem to a penalized problem. Thirdly, we have proved the existence of solutions of the nonlinear Schrödinger equation concentrating at a local maximum of the potential. These solutions are found by a more general minimax principle. Our results are characterized by very weak assumptions on the potential./L'équation de Schrödinger non-linéaire apparaît dans différents domaines de la physique, par exemple dans la théorie des condensats de Bose-Einstein ou dans des modèles de propagation d'ondes. D'un point de vue mathématique, l'étude de cette équation est intéressante et délicate, notamment parce qu'elle peut posséder un ensemble très riche de solutions avec des comportements variés. Dans cette thèse ,nous nous sommes intéressés aux ondes stationnaires, qui satisfont une équation aux dérivées partielles elliptique. Lorsque cette équation est vue comme un problème de perturbations singulières, ses solutions se concentrent, dans le sens où elles tendent uniformément vers zéro en dehors d'un certain ensemble de concentration, tout en restant positives sur cet ensemble. Nous avons obtenu trois types de résultats nouveaux. Premièrement, sous des hypothèses de symétrie, nous avons trouvé des solutions qui se concentrent sur une sphère. Deuxièmement, nous avons obtenu le même type de solutions pour le système de Schrödinger-Poisson. La méthode consiste à appliquer le théorème du col à un problème pénalisé. Troisièmement, nous avons démontré l'existence de solutions de l'équation de Schrödinger non-linéaire qui se concentrent en un maximum local du potentiel. Ces solutions sont obtenues par un principe de minimax plus général. Nos résultats se caractérisent par des hypothèses très faibles sur le potentiel. Doctorat en sciences, Spécialisation mathématiques info:eu-repo/semantics/nonPublished

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Svedberg, Christopher. "Future stability of the Einstein-Maxwell-Scalar field system and non-linear wave equations coupled to generalized massive-massless Vlasov equations." Doctoral thesis, KTH, Matematik (Avd.), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-93891.

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This thesis consists of two articles related to mathematical relativity theory. In the first article we prove future stability of certain spatially homogeneous solutionsto Einstein’s field equations. The matter model is assumed to consist of an electromagnetic field and a scalar field with a potential creating an accelerated expansion. Beside this, more general properties concerning Einstein’s field equation coupled to a scalar field and an electromagnetic field are settled. The most important of these questions are the existence of a maximal globally hyperbolic development and the Cauchy stability of solutions to the initial value problem. In the second article we consider Einstein’s field equations where the matter model consists of two momentum distribution functions. The first momentum distribution function represents massive matter, for instance galactic dust, and the second represents massless matter, for instance radiation. Furthermore, we require that each of the momentum distribution functions shall satisfy the Vlasov equation. This means that the momentum distribution functions represent collisionless matter. If Einstein’s field equations with such a matter model is expressed in coordinates and if certain gauges are fixed we get a system of integro-partial differential equations we shall call non-linear wave equations coupled to generalized massive-massless Vlasov equations. In the second article we prove that the initial value problem associated to this kind of equations has a unique local solution. QC 20120503

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Talib, Ahmed Abedelhussain. "Optimal system of subalgebras and invariant solutions for a nonlinear wave equation." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-2675.

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This thesis is devoted to use Lie group analysis to obtain all invariant solutions by constructing optimal system of one-dimensional subalgebras of the Lie algebra L5 for a nonlinear wave equation. I will show how the given symmetries ( Eq.2) are admitted by using partial differential equation (Eq.1), In addition to obtain the commutator table by using the same given symmetries. Subsequently, I calculate the transformations of the generators with the Lie algebra L5, which provide the 5-parameter group of linear transformations for the operators. Finally, I construct the invariant solutions for each member of the optimal system.

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Leto, Jonathan. "SOLITARY WAVE FAMILIES IN TWO NON-INTEGRABLE MODELS USING REVERSIBLE SYSTEMS THEORY." Master's thesis, University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3504.

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In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions of both models here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves for each model, we find a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. For the microstructure equation, the new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new. Directions for future work, including the dynamics of each family of solitary waves using exponential asymptotics techniques, are also mentioned. M.S. Department of Mathematics Sciences Mathematical Science MS

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Chow, Tanya L. M. "Systems of partial differential equations and group methods." Thesis, [Campbelltown, N.S.W. : The Author], 1996. http://handle.uws.edu.au:8081/1959.7/43.

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Książki na temat "Non-solvable system of equations"

Vidyasagar, M. Non-linear systems analysis. 2nd ed. Prentice-Hall International (UK), 1993.

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Kaikko, Juha. Performance prediction of gas turbines by solving a system of non-linear equations. Lappeenranta University of Technology, 1998.

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Burns, John. On non-convergence of adjoint semigroups for control systems with delays. ICASE, 1987.

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Burns, John. On non-convergence of adjoint semigroups for control systems with delays. National Aeronautics and Space Administration, Langley Research Center, 1987.

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Burns, John. On non-convergence of adjoint semigroups for control systems with delays. National Aeronautics and Space Administration, Langley Research Center, 1987.

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Verhulst, Ferdinand. Nonlinear differential equations and dynamical systems. Springer-Verlag, 1990.

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Kikuchi, Tetsuya. Studies on commuting difference systems arising from solvable lattice models. Tohoku University, 2000.

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Grusa, Karl-Ulrich. Mathematical analysis of nonlinear dynamic processes: An introduction to processes governed by partial differential equations. Longman Scientific & Technical, 1988.

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V, Uspenskiĭ S., ed. Partial differential equations and systems not solvable with respect to the highest-order derivative. Marcel Dekker, 2003.

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Braga da Costa Campos, Luis Manuel. Non-Linear Differential Equations and Dynamical Systems. Edited by L. M. B. C. Campos. CRC Press, 2019. http://dx.doi.org/10.1201/9780429028991.

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Części książek na temat "Non-solvable system of equations"

Kim, Tujin, and Daomin Cao. "The Non-steady Boussinesq System." In Equations of Motion for Incompressible Viscous Fluids. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78659-5_8.

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Kim, Tujin, and Daomin Cao. "The Non-steady Navier-Stokes System." In Equations of Motion for Incompressible Viscous Fluids. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78659-5_4.

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Winkler, Henrik, and Harald Woracek. "Reparametrizations of Non Trace-normed Hamiltonians." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_40.

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Kavallaris, Nikos I., and Takashi Suzuki. "Gierer–Meinhardt System." In Non-Local Partial Differential Equations for Engineering and Biology. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67944-0_5.

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Horgmo Jæger, Karoline, and Aslak Tveito. "Re-Introducing the Cell: The Extracellular-Membrane-Intracellular (EMI) Model." In Differential Equations for Studies in Computational Electrophysiology. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_11.

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AbstractAs mentioned earlier, the bidomain system is currently the standard mathematical model of cardiac electrophysiology. This system is nowroutinely solved and provides valuable insights into the conduction of electrical signals in cardiac tissue. However, the model has one glaring limitation: The cardiomyocyte is nowhere to be found in the model, since the extracellular space, the intracellular space and the cell membrane are all assumed to be everywhere in the computational domain. The cell was lost in homogenization! There is a tremendous advantage to this because the model becomes much simpler and thus solvable for the whole human heart. And it works! But the downside is of course that the cell is the essential building block of the tissue and leaving it out of the model has consequences. For instance, it becomes impossible to investigate the detailed dynamics of the electrochemical processes in the vicinity of a small collection of cells.

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Colombo, Maria. "The semigeostrophic system." In Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations. Scuola Normale Superiore, 2017. http://dx.doi.org/10.1007/978-88-7642-607-0_9.

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Bagarello, Fabio, and Miloslav Znojil. "The Dynamical Problem for a Non Self-adjoint Hamiltonian." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_6.

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Colombo, Maria. "The Vlasov-Poisson system." In Flows of Non-smooth Vector Fields and Degenerate Elliptic Equations. Scuola Normale Superiore, 2017. http://dx.doi.org/10.1007/978-88-7642-607-0_8.

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Hanzon, Bernard, and Finbarr Holland. "Non-negativity Analysis for Exponential-Polynomial-Trigonometric Functions on [0,∞)." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_21.

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Bart, Harm, Torsten Ehrhardt, and Bernd Silbermann. "Families of Homomorphisms in Non-commutative Gelfand Theory: Comparisons and Examples." In Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0297-0_8.

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Streszczenia konferencji na temat "Non-solvable system of equations"

Allan, Douglas A., Anca Ostace, Andrew Lee, et al. "Jacobian-based Model Diagnostics and Application to Equation Oriented Modeling of a Carbon Capture System." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.160262.

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Equation-oriented (EO) modeling has the potential to enable the effective design and optimization of the operation of advanced energy systems. However, advanced modeling of energy systems results in a large number of variables and non-linear equations, and it can be difficult to search through these to identify the culprit(s) responsible for convergence issues. The Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES-IP) contains a tool to identify poorly scaled constraints and variables by searching for rows and columns of the Jacobian matrix with small L2-norms so they can be rescaled. A further singular value decomposition can be performed to identify degenerate sets of equations and remaining scaling issues. This work presents an EO model of a flowsheet developed for post-combustion carbon capture using a monoethanolamine (MEA) solvent system as a case study. The IDAES diagnostics tools were successfully applied to this flowsheet to identify problems to improve model robustness and enable the optimization of process design and operating conditions of a carbon capture system.

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Elperin, Tov, Andrew Fominykh, and Boris Krasovitov. "Simultaneous Heat and Mass Transfer During Evaporation/Condensation on the Surface of a Stagnant Droplet in the Presence of Inert Admixtures Containing Non-Condensable Solvable Gas." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72493.

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In this study we investigated numerically simultaneous heat and mass transfer during evaporation/condensation on the surface of a stagnant droplet in the presence of inert admixtures containing non-condensable solvable gas. The performed analysis is pertinent to slow droplet evaporation/condensation when Mach number is small (M≪1). The system of transient conjugate nonlinear energy and mass conservation equations was solved using anelastic approximation. Transport coefficients of the gaseous phase were calculated as functions of temperature and concentrations of gaseous species. Thermophysical properties of the liquid phase are assumed to be constant. Using the material balance at the droplet surface we obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account the effect of solvable gas absorption at the gas-liquid interface. We derived also boundary conditions at gas-liquid interface taking into account the effect of gas absorption. The governing equations were solved using a method of lines. Numerical calculations showed essential change of the rates of heat and mass transfer in water droplet-air-water vapor system under the influence of solvable species in a gaseous phase. Consequently, the use of additives of solvable noncondensable gases to enhance the rate of heat and mass transfer in dispersed systems allows to increase the efficiency and reduce the size of gas-liquid contactors.

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Elperin, Tov, Andrew Fominykh, and Boris Krasovitov. "Modeling of Simultaneous Gas Absorption and Evaporation of Large Droplet." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79924.

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Brill, Michael H. "Direct linear transformation methods of triangulating from optical and SAR images." In OSA Annual Meeting. Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.fq9.

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Given an optical photograph with images of six control points (whose three-space coordinates are known), and the two image coordinates of an unknown ground point, it is possible to determine the equation of the line of sight from the camera station to the unknown point via a direct linear transformation (DLT) approach.1 To do this requires writing the projective equations for the control points in a form that is linear in the unknowns containing camera position, orientation, and (assumed affine) film distortions. These equations are written so each image coordinate of each control point appears in only one equation. The result is a linear system solvable for eleven camera variables, which can then be used with the unknown-point image coordinates to determine the line of sight. In the spotlight mode of synthetic-aperture radar (SAR), similar DLT equations are developed to determine the projection circle which is the intersection of the isorange sphere and iso-Doppler cone for a reflecting point. To avoid singularity, the Doppler equations are used to eliminate one image coordinate of each control point in the range equations, where that coordinate appears to the first power. The result is a linear system solvable for thirteen camera variables, which can then be used to determine the projection circle for an unknown ground point. Eight control points are needed for solution. Given optical and SAR images of a ground point, it is now possible to triangulate by intersecting two optical lines of sight, two SAR projection circles, or a line of sight and a projection circle, depending on the available imagery.

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Young, Robin. "The p-system II: The vacuum." In Evolution Equations Propagation Phenomena - Global Existence - Influence of Non-Linearities. Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc60-0-19.

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Chen, Shuxing. "Formation and development of global shock for p-system." In Evolution Equations Propagation Phenomena - Global Existence - Influence of Non-Linearities. Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc60-0-14.

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Pawłow, Irena, and Antoni Żochowski. "Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems." In Evolution Equations Propagation Phenomena - Global Existence - Influence of Non-Linearities. Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc60-0-25.

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Dhingra, A. K., A. N. Almadi, and D. Kohli. "A Framework for Closed-Form Displacement Analysis of 10-Link 1-DOF Mechanisms." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5885.

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Abstract This paper presents a closed-form approach, based on the theory of resultants, to the displacement analysis problem of planar 10-link 1-DOF mechanisms. Since each 10-link mechanism has 4 independent loops, its displacement analysis problem can be written as a system of 4 reduced loop-closure equations in 4 unknowns. This system of 4 reduced loop closure equations, for all non-trivial mechanisms resulting from 230 10-link kinematic chains, can be classified into 22 distinct structures. Using the successive and repeated elimination procedures presented herein, it is shown how each of these structures can be reduced into a univariate polynomial devoid of any extraneous roots. This univariate polynomial corresponds to the input-output (I/O) polynomial of the mechanism. Based on the results presented, it can be seen that the displacement analysis problem for all 10-link 1-DOF mechanisms is completely solvable, in closed-form, devoid of any extraneous roots.

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PETZELTOVÁ, H. "CONVERGENCE OF SOLUTIONS OF A NON-LOCAL PHASE-FIELD SYSTEM WITH MEMORY." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0110.

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Joshi, Gopesh, and M. Bala Krishna. "Solving system of non-linear equations using Genetic Algorithm." In 2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI). IEEE, 2014. http://dx.doi.org/10.1109/icacci.2014.6968423.

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Raporty organizacyjne na temat "Non-solvable system of equations"

McDougall, Robert. A New Regional Household Demand System for GTAP. GTAP Working Paper, 2000. http://dx.doi.org/10.21642/gtap.wp14.

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The GTAP final demand system has some known defects: the computation of the equivalent variation is not exact; with non-standard demand parameters, the equivalent variation may be grossly in error; the decomposition of the equivalent variation contains a nuisance term. We find a further defect, that the upper-level demand equations are invalid. We revise the model to remove these defects.

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McDougall, Robert. A New Regional Household Demand System for GTAP. GTAP Technical Paper, 2002. http://dx.doi.org/10.21642/gtap.tp20.

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The GTAP model, versions 4.1 and lower, suffers from some defects in the implementation of the regional household demand system. Most seriously, the upper level of the demand system assumes that each regional household faces a fixed price for utility from private consumption. But with a private consumption demand system of the CDE form, the price of utility from private consumption depends on the level of private consumption expenditure. With no fixed price for utility from private consumption, the familiar Cobb-Douglas demand system does not apply. Accordingly, the upper-level demand equations are in error. Furthermore, utility and equivalent variation are wrongly computed in simulations with non-standard settings for the CDE expansion parameters. Even with the standard settings, in multi-step simulations the utility and equivalent variation computations are inexact. The welfare decomposition inherits the defects of the equivalent variation computation. In removing these defects we revise in passing some minor misfeatures of the old treatment: Firstly, we treat the entire final demand system as the demand system of a representative household, rather than a conglomeration of representative and region-wide demand systems (subsection 2.6). Secondly, we provide a new facility for shifting the allocation of regional income exogenously by modifying rather than overriding the final demand system (subsection 2.14). Finally, we eliminate an uninterpretable \nuisance term" from the decomposition of equivalent variation (subsection 4.3).

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Peterson, Warren. PR-663-19600-Z01 Develop Guidance for Calculation of HCDP in Pipelines. Pipeline Research Council International, Inc. (PRCI), 2020. http://dx.doi.org/10.55274/r0011659.

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To maintain the integrity and reliability of natural gas transportation systems, system operators ensure that products in transit remain in the gas phase under foreseeable operating conditions. Compliance with pipeline hydrocarbon dew point (HCDP) specifications are demonstrated though in-situ testing or predictive models based on Equations of State (EOS) calculations. Numerical prediction of HCDP is a product of contributing elements, including gas chromatography, calibration gas quality, thermophysical science and the experimental data that underpins equations of state. Some hydrocarbon mixtures, such as those from non-traditional gas supplies, are more difficult to sample and assess than others. The methods described in this paper and accompanying spreadsheet examples are designed to assist persons in making technically defendable decisions with respect to predictive methods and the operational impacts of liquid dropout. The primary focus of this work is to connect the over-all performance of HCDP prediction to its operational implications. The secondary objective of the work is to provide tools for assessing the potential benefit from using C9+ versus C6+ gas chromatographs.

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Pasupuleti, Murali Krishna. Mathematical Modeling for Machine Learning: Theory, Simulation, and Scientific Computing. National Education Services, 2025. https://doi.org/10.62311/nesx/rriv125.

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Abstract Mathematical modeling serves as a fundamental framework for advancing machine learning (ML) and artificial intelligence (AI) by integrating theoretical, computational, and simulation-based approaches. This research explores how numerical optimization, differential equations, variational inference, and scientific computing contribute to the development of scalable, interpretable, and efficient AI systems. Key topics include convex and non-convex optimization, physics-informed machine learning (PIML), partial differential equation (PDE)-constrained AI, and Bayesian modeling for uncertainty quantification. By leveraging finite element methods (FEM), computational fluid dynamics (CFD), and reinforcement learning (RL), this study demonstrates how mathematical modeling enhances AI-driven scientific discovery, engineering simulations, climate modeling, and drug discovery. The findings highlight the importance of high-performance computing (HPC), parallelized ML training, and hybrid AI approaches that integrate data-driven and model-based learning for solving complex real-world problems. Keywords Mathematical modeling, machine learning, scientific computing, numerical optimization, differential equations, PDE-constrained AI, variational inference, Bayesian modeling, convex optimization, non-convex optimization, reinforcement learning, high-performance computing, hybrid AI, physics-informed machine learning, finite element methods, computational fluid dynamics, uncertainty quantification, simulation-based AI, interpretable AI, scalable AI.

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Lubowa, Nasser, Zita Ekeocha, Stephen Robert Byrn, and Kari L. Clase. Pharmaceutical Industry in Uganda: A Review of the Common GMP Non-conformances during Regulatory Inspections. Purdue University, 2021. http://dx.doi.org/10.5703/1288284317442.

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The prevalence of substandard medicines in Africa is high but not well documented. Low and Middle-Income Countries (LMICs) are likely to face considerable challenges with substandard medications. Africa faces inadequate drug regulatory practices, and in general, compliance with Good Manufacturing Practices (GMP) in most of the pharmaceutical industries is lacking. The majority of pharmaceutical manufacturers in developing countries are often overwhelmed by the GMP requirements and therefore are unable to operate in line with internationally acceptable standards. Non-conformances observed during regulatory inspections provide the status of the compliance to GMP requirements. The study aimed to identify the GMP non-conformances during regulatory inspections and gaps in the production of pharmaceuticals locally manufactured in Uganda by review of the available 50 GMP reports of 21 local pharmaceutical companies in Uganda from 2016. The binary logistic generalized estimating equations (GEE) model was applied to estimate the association between odds of a company failing to comply with the GMP requirements and non-conformances under each GMP inspection parameter. Analysis using dummy estimation to linear regression included determination of the relationship that existed between the selected variables (GMP inspection parameters) and the production capacity of the local pharmaceutical industry. Oral liquids, external liquid preparations, powders, creams, and ointments were the main categories of products manufactured locally. The results indicated that 86% of the non-conformances were major, 11% were minor, and 3% critical. The majority of the non-conformances were related to production (30.1%), documentation (24.5%), and quality control (17.6%). Regression results indicated that for every non-conformance under premises, equipment, and utilities, there was a 7-fold likelihood of the manufacturer failing to comply with the GMP standards (aOR=6.81, P=0.001). The results showed that major non-conformances were significantly higher in industries of small scale (B=6.77, P=0.02) and medium scale (B=8.40, P=0.04), as compared to those of large scale. This study highlights the failures in quality assurance systems and stagnated GMP improvements in these industries that need to be addressed by the manufacturers with support from the regulator. The addition of risk assessment to critical production and quality control operations and establishment of appropriate corrective and preventive actions as part of quality management systems are required to ensure that quality pharmaceuticals are manufactured locally.

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Warrick, Arthur W., Gideon Oron, Mary M. Poulton, Rony Wallach, and Alex Furman. Multi-Dimensional Infiltration and Distribution of Water of Different Qualities and Solutes Related Through Artificial Neural Networks. United States Department of Agriculture, 2009. http://dx.doi.org/10.32747/2009.7695865.bard.

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The project exploits the use of Artificial Neural Networks (ANN) to describe infiltration, water, and solute distribution in the soil during irrigation. It provides a method of simulating water and solute movement in the subsurface which, in principle, is different and has some advantages over the more common approach of numerical modeling of flow and transport equations. The five objectives were (i) Numerically develop a database for the prediction of water and solute distribution for irrigation; (ii) Develop predictive models using ANN; (iii) Develop an experimental (laboratory) database of water distribution with time; within a transparent flow cell by high resolution CCD video camera; (iv) Conduct field studies to provide basic data for developing and testing the ANN; and (v) Investigate the inclusion of water quality [salinity and organic matter (OM)] in an ANN model used for predicting infiltration and subsurface water distribution. A major accomplishment was the successful use of Moment Analysis (MA) to characterize “plumes of water” applied by various types of irrigation (including drip and gravity sources). The general idea is to describe the subsurface water patterns statistically in terms of only a few (often 3) parameters which can then be predicted by the ANN. It was shown that ellipses (in two dimensions) or ellipsoids (in three dimensions) can be depicted about the center of the plume. Any fraction of water added can be related to a ‘‘probability’’ curve relating the size of the ellipse (or ellipsoid) that contains that amount of water. The initial test of an ANN to predict the moments (and hence the water plume) was with numerically generated data for infiltration from surface and subsurface drip line and point sources in three contrasting soils. The underlying dataset consisted of 1,684,500 vectors (5 soils×5 discharge rates×3 initial conditions×1,123 nodes×20 print times) where each vector had eleven elements consisting of initial water content, hydraulic properties of the soil, flow rate, time and space coordinates. The output is an estimate of subsurface water distribution for essentially any soil property, initial condition or flow rate from a drip source. Following the formal development of the ANN, we have prepared a “user-friendly” version in a spreadsheet environment (in “Excel”). The input data are selected from appropriate values and the output is instantaneous resulting in a picture of the resulting water plume. The MA has also proven valuable, on its own merit, in the description of the flow in soil under laboratory conditions for both wettable and repellant soils. This includes non-Darcian flow examples and redistribution and well as infiltration. Field experiments were conducted in different agricultural fields and various water qualities in Israel. The obtained results will be the basis for the further ANN models development. Regions of high repellence were identified primarily under the canopy of various orchard crops, including citrus and persimmons. Also, increasing OM in the applied water lead to greater repellency. Major scientific implications are that the ANN offers an alternative to conventional flow and transport modeling and that MA is a powerful technique for describing the subsurface water distributions for normal (wettable) and repellant soil. Implications of the field measurements point to the special role of OM in affecting wettability, both from the irrigation water and from soil accumulation below canopies. Implications for agriculture are that a modified approach for drip system design should be adopted for open area crops and orchards, and taking into account the OM components both in the soil and in the applied waters.

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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.

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