equations helmholtz equations electromagnetic potentials and green s functions
báo cáo hóa học:" Research Article Solutions and Green’s Functions for Boundary Value Problems of Second-Order Four-Point Functional Difference Equations" ppt
... respectively Thus, 1,T 3.14 It follows from the definition of K that T Φy t G1 t, s r s f s, ys t∈ 1,T t∈ 1,T ≥m us s T r s f s, ys us s ≥ ≥ which implies that Φ K ⊂ K m T Ms max G1 t, s 1 s, t≤T ... 1 s, t≤T r s f s, ys T m max G1 t, s r s f s, ys M t∈ 1,T s m Φy , M us us 3.15 Boundary Value Problems 13 Lemma 3.4 Suppose that (H1 ) holds Then Φ : K → K is completely continuous We assume that ... equations Here this condition connects the history u0 with the single u η This is suggested by the well-posedness of BVP 1.9 , since the function f depends on the term ut i.e., past values of u As...
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Source investigation of a small event using empirical Green’s functions and simulated annealing ppt
... events and likeness of focal mechanisms the northern side leads us to consider the August 16 event as a possible empirical A seismic network was deployed in 1991 July and August, Green' s function ... to use empirical Green' s ively (see Fig 3) Seismograms of both events recorded by the functions to model path effects on seismograms We defined three stations are shown in Fig The study is mainly ... quantities estimated by our analysis Results for stress drop, total active arca and avcrage total slip are shown in Table for the two possible fault planes and two different rise times The values are...
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Báo cáo hóa học: " Singular integrals of the compositions of LaplaceBeltrami and Green’s operators" potx
... operators] The differential forms can be used to describe various systems of PDEs and to express different geometric structures on manifolds For instance, some kinds of differential forms are often ... λ /s m |x − xB | ) dx⎠ σB ⎞1 /s ⎛ ⎛ −λ /s s ≤⎝ (|u||x − xB | σB ⎛ ≤⎝ ) dx⎠ ⎝ ⎞1 /s (|x − xB σB |u| |x − xB | dx⎠ C5 (σ rB ) −λ s σB ⎛ ≤ C6 ⎝ σB ⎞ s m ms ms |λ /s ) s m dx⎠ (2:8) λ /s+ n (s m)/ms ⎞1 /s ... n−αβ+λβ+ nβ (s m) m 1/ s 1/ s ⎞1 /s |u| |x − xB | dx⎠ −λ s σB ⎞1 /s |u| |x − xB | dx⎠ , −λ s σB thus is, ⎛ ⎝ Dδ ⎛ ⎞1 /s | G(u) |s dx⎠ ≤ C10 ⎝ d(x, ∂M)α σB ⎞1 /s |u |s dx⎠ |x − xB |λ (2:10) 1 /s s | G(u)|...
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Green’s Functions in Physics Version 1 pdf
... shall see (in chapter 3) that the Green s function corresponds to an impulsive force and is represented by a complete set of functions Consider N mass points of mass mi attached to a massless string, ... CHAPTER GREEN S IDENTITIES Physical Interpretations of the G.I .s sec2.4 Certain qualities of the Green s Identities correspond to physical situations and constraints 2.4.1 The Physics of Green s 2nd ... conditions first two in chapter Jan p3.3 pr:sbc1 cases will ensure that the right-hand side of Green s second identity (introduced in chapter 2) vanishes This is necessary for a physical system 1.4 SPECIAL...
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fulling. green's functions, heat kernels, kasimir effect
... 1) ass Γ (s + 1) (21) Eq (18) corresponds to ∞ T (t) ≡ e−ωt dµ ∼ ∞ es t−m +s + s= 0 ∞ fs t−m +s ln t, (22) s= m+1 s m odd where es and fs are related to css and dss in much the same way as bs is related ... ω), s= m+1 s m odd (18) where • c s = constant × a s if s ≤ m or s − m is even; • c s is undetermined by a s if s > m and s − m is odd; • d s = constant × a s if s > m and s − m is odd The constants ... differential equations or operators in Hilbert space They are instances of some classical theory on the summability of infinite series and integrals, developed circa 1915 9,10 Spectral Densities The Green...
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Báo cáo hóa học: " Local stability of the Pexiderized Cauchy and Jensen’s equations in fuzzy spaces" pptx
... Fuzzy Sets Syst 159, 730–738 (2008) doi:10.1016/j.fss.2007.07.011 Mirmostafee, AK, Moslehian, MS: Fuzzy versions of Hyers-Ulam-Rassias theorem Fuzzy Sets Syst 159, 720–729 (2008) doi:10.1016/j.fss.2007.09.016 ... Trans Am Math Soc 347, 3111–3119 (1995) doi:10.2307/2154775 Hyers, DH, Isac, G, Rassias, ThM: Stability of Functional Equations in Several Variables Birkhäuser, Basel (1998) Hyers, DH, Isac, ... Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality Math Inequal Appl 4, 93–118 (2001) Jung, S- M: Hyers-Ulam-Rassias stability of Jensen s equation and its application Proc Am Math Soc...
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CHAPTER 10: TIME-VARYING FIELDS AND MAXWELL''''S EQUATIONS pot
... Contents | TIME-VARYING FIELDS AND MAXWELL 'S EQUATIONS We now wish to define suitable time-varying potentials which are consistent with the above expressions when only static charges and direct ... over identical surfaces The surfaces are perfectly general and may be chosen as differentials,
r  E Á dS À @B Á dS @t and rÂEÀ @B @t
6 This is one of Maxwell 's four equations as written in ... Á We should first look at the point form of Ampere 's circuital law as it applies to steady magnetic fields, rÂEÀ | v v This is discussed in several of the references listed in the Suggested...
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Đề tài " Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers " pdf
... follows Section is devoted to a survey of previous results Sections and are concerned with useful preliminaries Steps (i) and (ii) are treated in Sections and 6, respectively Sections and are ... present a brief survey of known results in Section The main steps in the proofs of Theorems and are as follows: (i) We associate Frey curves to putative solutions of the equations Fn = y p and ... Classically, we first use estimates for linear forms in logarithms in order to bound the exponent p, and then we use a sieve Equations (2) and (4) yield linear forms in three logarithms, and thus...
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The nonlinear schroedinger equations self focusing and wave collapse catherine sulem , pierre louis sulem
... le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p ... le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p ... le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p le io g z Ps z z Pf r p...
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equations of state and pvt analysis tarek ahmed
... values Source: GSPA Engineers Data Book, 10th ed Tulsa, OK: Gas Processors Suppliers Association, 1987 Courtesy of the Gas Processors Suppliers Association equations of state and pvt analysis 10 ... densities Source: GPSA Engineering Data Book, 10th ed Tulsa, OK: Gas Processors Suppliers Association, 1987 Courtesy of the Gas Processors Suppliers Association 15 equations of state and pvt analysis ... composition z As the Convergence pressures for binary systems Source: GPSA Engineering Data Book, 10th ed Tulsa, OK: Gas Processors Suppliers Association, 1987 Courtesy of the Gas Processors Suppliers...
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sustainable infrastructure the guide to green engineering and design - s. bry sarte
... brings all these resource systems together and shows how to integrate them into sustainable project designs Because both design processes and solutions are scale specific, designers must consider ... performance-based systems such as SmartCode and the benchmarks established by the American Society of Landscape Architects’ (ASLA) Sustainable Sites Initiative, or education-based systems such as the ... architects, designers, community members, and artists The book is divided into three sections Part I: The Process and Systems of Sustainable Design introduces the integrative design process that is essential...
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báo cáo hóa học:" Research Article Green’s Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions ˇ Svetlana Roman and Arturas Stikonas ¯" pptx
... are stated Chung and Yau 13 study discrete Green s functions and their relationship with discrete Laplace equations They discuss several methods for deriving Green s functions Liu et al 14 give ... problems, conditions for positiveness of Green s functions, and solutions with various BCs, for example, NBCs The structure of the paper is as follows In Section 2, we review the properties of ... determinants and linear functionals We construct a special basis of the solutions in Section and introduce some functions that are independent of this basis The expression of the solution to the second-order...
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báo cáo hóa học:" Research Article Global Estimates for Singular Integrals of the Composition of the Maximal Operator and the Green’s Operator" doc
... NY, USA, 1983 S Ding, “Norm estimates for the maximal operator and Green s operator,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol 16, supplement S1 , pp 72–78, 2009 A Banaszuk and ... u are Ls -integrable 0-form s Differential forms, the Green s operator, and maximal operators are widely used not only in analysis and partial differential equations, but also in physics; see 2–4, ... write ,l s, Ω 1.7 uI dxJ , {1, 2, , n} − I, and d : D Ω, ∧l −1 I −1 u is given by d 1.6 Ω |u |s dx 1 /s 1.9 The differential forms can be used to describe various systems of PDEs and to express different...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
... rest of this section for 1.15 Advances in Difference Equations 21 Standing Assumption (SA) Assume p / q and that there exist m∗ , M∗ with L ≤ m∗ < M∗ ≤ U such that for 1.15 and its associated function ... when such solutions exist This matter has been treated in 12 This work is organized as follows The main results are stated in Section Results from literature which are used here are given in Section ... 2 Advances in Difference Equations whose dynamics differ significantly from other equations in this class There are a total of 42 cases that arise from 1.1 in the manner just discussed, under...
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Báo cáo hóa học: "TERMINAL VALUE PROBLEM FOR SINGULAR ORDINARY DIFFERENTIAL EQUATIONS: THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS OF GROUND STATES" pdf
... (3.119) This means that there exists a singular point P ∈ E0 of the map ∗ , that is, there is a solution ρ = ρ(r) ∈ ᐄ(P) which remains left asymptotic in Ω and so it satisfies the left asymptotic ... the segment E, “moves” in a natural way (initially, when ρ(r) < 0) toward the positive pρ -semiaxis and then (when ρ(r) ≥ 0) toward the positive ρ-semiaxis (see Figures 2.1–2.4) As a result, assuming ... equation and explained the physical significance of its solutions In a recent paper [4], Bonheure et al obtained some A P Palamides and T G Yannopoulos results on existence and multiplicity of the singular...
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PERIODIC SOLUTIONS OF NONLINEAR SECOND-ORDER DIFFERENCE EQUATIONS ´ JESUS RODRIGUEZ AND DEBRA LYNN pdf
... cos(Nθ)cos(θ) − sin(Nθ)sin(θ) − cos(θ) = cos(Nθ) − sin(Nθ) sin(θ) cos(Nθ) − + sin(Nθ)cos(θ) − sin(Nθ) cos(θ) cos(Nθ) − − sin(Nθ)cos(θ) = cos(Nθ)sin(θ) cos(Nθ) − − sin(θ) cos(Nθ) − + cos(Nθ) − sin(Nθ)cos(θ) ... cos(Nθ) − sin(Nθ)cos(θ) (A.6) + sin2 (Nθ)sin(θ) = cos(Nθ) − + sin2 (Nθ) sin(θ) = − 2cos(Nθ) + cos2 (Nθ) + sin2 (Nθ) sin(θ) = − cos(Nθ) sin(θ) = − cos(Nθ) 4c − b2 = (iii) In this case, we suppose ... G Kelley and A C Peterson, Difference Equations, Academic Press, Massachusetts, 1991 D G Luenberger, Introduction to Dynamic Systems Theory, Models, and Applications, John Wiley & Sons, New York,...
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BEHAVIOR OF THE POSITIVE SOLUTIONS OF FUZZY MAX-DIFFERENCE EQUATIONS G. STEFANIDOU AND G. pptx
... D Benest and C Froeschl´ (eds.), Analysis and Modelling of Discrete Dynamical Systems, Ade vances in Discrete Mathematics and Applications, vol 1, Gordon and Breach Science Publishers, Amsterdam, ... (2.4) G Stefanidou and G Papaschinopoulos 155 We say that xn is a positive solution of (1.1) (resp., (1.2)) if xn is a sequence of positive fuzzy numbers which satisfies (1.1) (resp., (1.2)) We say ... ), n = 1,2, , a ∈ (0,1] satisfies system (3.7) (i) Firstly, suppose that (5.14) is satisfied We define the set E ⊂ (0,1] as follows: for any a ∈ E there exists an ma ∈ {1,2} such that A1,l,a ≤ uma...
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attrators for parametric delay differential equations without uniqueness and their upper semicontinuous behavious
... different state spaces The structure of the paper is as follows In Section we study the existence and estimates of solutions for a general class of parameterized delay differential equations A multi-valued ... achieves this goal, and moreover, it ensures the existence of new attractors and establishes their relation with the ones obtained in the previous section Theorem 12 Assume that Hypothesis holds Then, ... The usual notation for a delay function will be a subscript: xt (s) = x(t + s) where it has sense Hypothesis Let Λ ⊂ R be a closed interval, and suppose that positive numbers < T∗ < T ∗ , and functions...
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