application of second order differential equation in chemistry
Báo cáo hóa học: "Research Article Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation" potx
... Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988.16 D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics ... contraction mapping principleimplies thatAn0has a unique fixed point x∗ in CI,andsoA has a unique fixed pointx∗ in CI; by the definition of A, A has a unique fixed point x∗ in CI,thatis,x∗is ... solutions of nonlinear singular third -order two-point boundary value problem,”Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006.12 Y. Sun, “Positive solutions of...
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Báo cáo hóa học: " On a class of second-order nonlinear difference equation" potx
... kind of second- order rational difference equation. With the change of the initial values, we find thesuccessive lengths of positive and negative semicycles for oscillatory solutions of this equation, ... class of second- order nonlinear difference equation Li Dongsheng1*, Zou Shuliang1and Liao Maoxin2* Correspondence: lds1010@sina.com1School of Economics andManagement, University of SouthChina, ... of SouthChina, Hengyang, Hunan 421001,People’s Republic of ChinaFull list of author information isavailable at the end of the articleAbstract In this paper, we consider the rule of trajectory...
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báo cáo hóa học: " Study of the asymptotic eigenvalue distribution and trace formula of a second order operatordifferential equation" ppt
... 1. Hence, beginning with some k ,Equation 2.6 has exactly one positive root corresponding to the imaginary root of Equation 2.5.Now, find the asymptotic of the imaginary roots of Equation 2.5. ... numerator in the vicinity of zerois O(zν+1), and the order of its denominator is O(zν), the integral along the left part of contour vanishes. Now, consider the integrals along the remaining three ... vec tor functions with values in H (see [30], p. 57) that vanish in the vicinity of zero and are infinitely differentiable in the norm of H. Also, onD (L0)define theoperatorL0:L0Y...
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application of back-propagation neural network in data forec
... dataMIN_VAL: Min value of dataTFmax: Max of transformation functionTFmin: Min of transformation functionOV: Original Value Application Application TrainingTrainingTraining tunes a neural ... training, and testing. CONTENTCONTENTIntroductionIntroductionSteps in data forecasting modeling Steps in data forecasting modeling using neural networkusing neural networkDetermine ... employed in training the network. The test set, often includes 10% to 30% of training set, is used in testing the generalization. And the verification set is set balance between the needs of enough...
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quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order
... contains, in particular, the equation with principal part which coincides with the principal part of the equation of minimal surfaces (1.7.13). The latter is also contained in the thirdclass of equations ... satisfying (1.1) in SZ and coinciding with T on 852. While the admissiblestructure of linear elliptic equations is determined mainly by the condition of sufficient smoothness of the coefficients, in ... prioriestimate of maxnivul breaks down into two steps: 1) obtaining maxaalvul in terms of maxsljul, and 2) obtaining an estimate of maxr 1vul in terms of maxanlvul andmaxalul. The estimates of maxaulvul...
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Báo cáo toán học: " Lyapunov-type inequalities for a class of even-order differential equations" doc
... soon.Lyapunov-type inequalities for a class of even -order differential equationsJournal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5Qi-Ming Zhang (zhqm20082008@sina.com)Xiaofei ... below).For information about publishing your research in Journal of Inequalities and Applications go tohttp://www.journalofinequalitiesandapplications.com/authors/instructions/For information ... contributed to these interesting2 Lyapunov-type inequalities for a class of even -order differential equationsQi-Ming Zhang∗1and Xiaofei He21College of Science, Hunan University of Technology,...
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Báo cáo hóa học: " Infinitely many periodic solutions for some second-order differential systems with p(t)Laplacian" potx
... equations in ℝN. Nonlinear Anal. 59, 173–188(2004)19. Rabinowitz, PH: Minimax methods in critical point theory with applications to differential equations. In CBMS Reg ConfSer in Math, vol. 65,American ... W\Br2(0),whereBr2(0)is an open ball in W of radius r2centered at 0.Proof. The proof of Proposition 3.2 is the same as the proof of the condition (A2) in the proof of Theorem 3.1.We have proved ... . proof of Theorem 3.1, system (1.1) has infinite solutions {uk }in W1,p(t)Tfor ever y posi-tive integer k such that ||uk||đ +,ask đ ∞.TheproofofTheorem3.2iscomplete.Proof of Theorem...
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Báo cáo hóa học: " Global attractor of the extended FisherKolmogorov equation in Hk spaces" pot
... type equations. J DifferEqn. 184(1), 78–96 (2002). doi:10.1006/jdeq.2001.413512. Li, CY: Homoclinic orbits of two classes of fourth order semilinear differential equations with periodic nonlinearity. ... existence of global attractor for a class of infinite dimensional nonlinear dissipativedynamical systems. Chin Ann Math B. 26(3), 1–8 (2005)17. Temam, R: Infinite-Dimensional Dynamical Systems in ... PR China2College of Mathematics andSoftware Science, Sichuan Normal University, Chengdu, Sichuan 610066, PR ChinaCompeting interestsThe author declares that they have no competing interests.Received:...
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Báo cáo hóa học: " On the stability of an AQCQ-functional equation in random normed spaces" potx
... Journal of Inequalities and Applications 2011, 2011:34http://www.journalofinequalitiesandapplications.com/content/2011/1/34Page 8 of 12 4. Gajda, Z: On stability of additive mappings. Int J ... normed spaces.Journal of Inequalities and Applications 2011 2011:34.Park et al. Journal of Inequalities and Applications 2011, 2011:34http://www.journalofinequalitiesandapplications.com/content/2011/1/34Page ... equa-tion, Hyers-Ulam stability1. IntroductionThe stability problem of functional equations originated from a question of Ulam [1] in 1940, concerning the stability of group homomorphisms. Let (G1,·)beagroupandlet(G2,*,d)...
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Báo cáo hóa học: " Research Article Lagrangian Stability of a Class of Second-Order Periodic Systems" docx
... of Fx, t and ex, t,byasmall twist theorem of reversible mapping we obtain the existence of quasiperiodic solutions andboundedness of all the solutions.1. Introduction and Main Result In ... nite part of cylinder C S1ìR,whereS1 R/2Z,wedenoteby the class of Jordan curves in C that are homotopic to the circle r constant. The subclass of Γ composed of those curves lying in A will ... systems 1.9 to a form of small perturbation of integrable reversible system.Then a KAM Theorem f or reversible mapping can be applied to the Poincar´e mapping of thisnearly integrable reversible...
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báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... lj3.11are finite. Equation 3.10 is a inhomogeneous second- order linear difference equation; itssolution takes the form of a particular solution added to an arbitrary linear combination of solutions ... constant. Equation 4.14 is an inhomogeneous second- order linear difference equation; its solution takes theform of a particular solution added to an arbitrary linear combination of solutions ... Solutions of Second- order Linear Difference Equation II: the second case. In the rest of this paper, we would like to give an example to show how to use theresults of this paper to obtain error...
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báo cáo hóa học:" Research Article Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient" ppt
... k ≥ a In this case, completely analyzed in 1, any positive solution y is either decreasing oreventually increasing. We say that y is of class M in the first case, of class M− in the second one. ... 21ψj1hk∞jkhjGwj−1hk∞jkΔhjΔwj.3.16Solvability of this equation will be examined by means of the contraction mapping theorem in the Banach space of sequences converging towards zero. The following properties of hwill play ... solutions of 1.1 and D denote the set of allpositive dominant solutions of 1.1.FromTheorem 4.1, taking into account Theorem 3.1,the following characterization of recessive and dominant solution...
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báo cáo hóa học:" Research Article Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line" potx
... Differential Equations, vol. 23, pp. 979–987, 1987.4 C. P. Gupta, “Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation, ” Journal of Mathematical ... nonlinear second- order three-point boundary value problem,”Journal of Mathematical Analysis and Applications, vol. 296, no. 1, pp. 265–275, 2004.7 Y. Sun, “Positive solutions of nonlinear second- order ... results of 16, 17to some degree. The main tools used in this paper are Leray-Schauder nonlinear alternativeand the fixed point index theory.The rest of the paper is organized as follows. In Section...
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