cfd for simulation of acid mine drainage generation and subsequent pollutants transportation through groundwater flow systems and rivers
computational fluid dynamics, second edition
Ngày tải lên :
01/04/2014, 10:45
... University of Alabama in Huntsville It is considered adequate for four semester courses with three credit hours each: CFD I (Chapters through and through 11), CFD II (Chapters through and 12 through ... 16), CFD III (Chapters 17 through 20), and CFD IV (Chapters 21 through 27) In this way, the elementary topics for both FDM and FEM can be covered in CFD I with advanced materials for both FDM and ... EDITION the counterparts for FEM are covered in Chapters through 11 Incompressible and compressible flows are treated in Chapters and for FDM and in Chapters 12 through 14 for FEM, respectively FVM...
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Báo cáo toán học: " Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments" pptx
Ngày tải lên :
20/06/2014, 20:20
... −4t and for a.a t ∈ I0 we have f (t, α(−t)) = − = α (t), f (t, β(−t)) = − < β (t) Hence α and β are lower and upper solutions for problem (12) by virtue of Remark Finally, for a.a t ∈ I0 and ... continuity of f , there exists y3 ≤ y1 such that f (y3 ) = λ and f (y) ≥ λ for all y ∈ [y3 , y1 ], (21) and this choice of y3 also provides that f (y3 ) ≤ f (y) for all y ≥ y3 , (22) and, by virtue of ... k(t) for all t ∈ I− and β (t) = m ≥ max y≤maxI β(t) f (y) for all t ∈ I0 (25) So we deduce from (24) and (25) that α and β are lower and upper solutions for problem (13) Rub´n Figueroa∗ and...
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báo cáo hóa học:" Research Article Nonoscillation of First-Order Dynamic Equations with Several Delays" pdf
Ngày tải lên :
21/06/2014, 11:20
... The graph of 30 iterates for the solutions of 4.11 and 4.13 illustrates the result of Theorem 4.5, √ here y t > x t for all t ∈ 3, ∞ √N Corollary 4.8 Let x be a solution of 3.1 , and Y ·, s ... N, x0 , ϕ and αi for all i ∈ 1, n for all i ∈ 1, n N N ϕt for t ∈ t−1 , t0 T , are the same as in 2.1 and Bi , g ∈ Crd t0 , ∞ T , R Theorem 4.5 Suppose that Ai ≥ Bi for all i ∈ 1, n N and g ≥ ... 2t3 √ for t ∈ √ x t ≡ for t ∈ 1, √ N 3, ∞ √ N 4.11 , where x Δ x t √ t3 − x t √ t3 − t for t ∈ √ 4.12 N and yΔ t y t3 t3 − t3 for t ∈ √ y t ≡ for t ∈ 1, √ 3, ∞ √ N , 4.13 √ N Denoting by x and...
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STABILITY OF PERIODIC SOLUTIONS OF FIRST-ORDER DIFFERENCE EQUATIONS LYING BETWEEN LOWER AND UPPER pptx
Ngày tải lên :
23/06/2014, 00:20
... see [1, 2], that the existence of α and β, a pair of lower and upper solutions of problem (PN ), such that α ≤ β in JN , does not imply the existence of a solution of this problem Alberto Cabada ... conclude that there exist ψ and φ the minimum and the maximum of the aforementioned set and, clearly, they match up the minimal and the maximal solutions, respectively, in [α,β] of problem (PN ) Stability ... it is clear that, for D large enough, αD and βD , defined for every n ∈ JN as αD (n) = n − D and βD (n) = −n + D, is a pair of lower and upper solutions that are no solutions of problem (PN ) (with...
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báo cáo hóa học: " Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type" doc
Ngày tải lên :
21/06/2014, 02:20
... existence theorems for PVPs (1.1), (1.3) and a couple of examples to illustrate how our newly developed results work In Sect we focus on the existence of solutions for (1.2) and also an example ... function r(t) = -||x(t) ||2, t Î [0, 1], where x(t) is a solution of (3.6), for the rest part of the proof we proceed as in the proof of Theorem 3.1 Corollary 3.2 Let f be a scalar-valued function ... equations of mixed type in the form of (1.2) The results presented in the following three statements are similar to Theorem 2.1, Theorem 2.2 and Corollary 2.2, respectively So we omit all the proofs...
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báo cáo hóa học:" Periodic boundary value problems for nonlinear first-order impulsive dynamic equations on time scales" pot
Ngày tải lên :
21/06/2014, 17:20
... fixed point theorem for operators on cone, in this article, some results of one and two positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic ... (0, T )T , < t1 < · · · < tm < T, and for each k = 1, 2, , m, x(t+ ) = limh→0+ x(tk + h) and x(t− ) = limh→0− x(tk + h) represent the right and left limits of k k x(t) at t = tk We always ... similar to the proof of (3.4), we have 12 Φu = τ u, u ∈ K ∩ ∂Ω7 , τ ≥ (3.16) By Theorem 1.1, we conclude that Φ has two fixed points u∗∗ ∈ K ∩ (Ω6 \Ω7 ) and u∗∗∗ ∈ K ∩ (Ω7 \Ω5 ), and u∗∗ and u∗∗∗ are...
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Báo cáo hóa học: " Research Article First-Order Singular and Discontinuous Differential Equations" docx
Ngày tải lên :
21/06/2014, 20:20
... ε, t0 L , and since ε ∈ 0, L was fixed arbitrarily, the proof of Step is complete Conclusion The construction of y∞ and Step imply that y∞ ≥ x∗ and the definition of x∗ and Step yn on In and then ... 2/3 n for all t, x between the graphs of α and β and r ≤ x ≤ 1/r Therefore Theorem 5.4 implies the existence of a weak solution of 7.7 between α and β Moreover, since f is positive between α and ... Lower and Upper Solutions Another modification of the concepts of lower and upper solutions concerns the possibility of allowing jumps in their graphs Since the task of finding a pair of lower and...
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Báo cáo hoa học: " Research Article Multiple Positive Solutions for Nonlinear First-Order Impulsive Dynamic Equations on Time Scales with Parameter" ppt
Ngày tải lên :
21/06/2014, 20:20
... tk h and x t− limh → 0− x tk h represent the right and k 1, 2, , m, x tk k left limits of x t at t tk The theory of impulsive differential equations is emerging as an important area of investigation, ... Preliminaries Throughout the rest of this paper, we always assume that the points of impulse tk are rightdense for each k 1, 2, , m We define PC {x ∈ 0, σ T x tk T −→ R : xk ∈ C Jk , R , k and x t− ... and discrete calculus,” Results in Mathematics, vol 18, no 1-2, pp 18–56, 1990 V Lakshmikantham, S Sivasundaram, and B Kaymakcalan, Dynamic Systems on Measure Chains, vol 370 of Mathematics and...
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Báo cáo hóa học: " Research Article Maximum Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations" potx
Ngày tải lên :
22/06/2014, 03:20
... function of 2.1 We use also formula 1.12 connecting C t, s and the Cauchy function C0 t, s of 1.10 Note that C0 t, s is a solution of 2.6 as a function of the first argument t for every fixed s and ... fulfilled for every s ∈ 0, ∞ Then C t, s > 0, ∂/∂t C0 t, s ≥ and (∂/∂t C t, s ≥ for ≤ s ≤ t < ∞ Proof According to Lemma 2.11, we have C0 t, s > for ≤ s ≤ t < ∞ The positivity of the → L∞ and formula ... the inequalityf t ≥ Sf t for t ∈ 0, ∞ , positivity of S and nonnegativity of ∂/∂t C0 t, s for ≤ s ≤ t < ∞ imply the inequalities x t ≥ 0, x t ≥ for t ∈ 0, ∞ The proofs of Theorems 3.1–3.6 follows...
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Báo cáo hóa học: " Research Article Iterated Oscillation Criteria for Delay Dynamic Equations of First Order" pdf
Ngày tải lên :
22/06/2014, 11:20
... < and Γn ξn > for all n ∈ N Therefore, there exists ζn ∈ τ ξn , ξn T such that Γn ζn ≤ and Γn σ ζn ≥ for all n ∈ N Clearly, {ζn }n∈N ⊂ t1 , ∞ T is a nondecreasing divergent sequence Then, for ... proof is done Theorem 2.6 Assume that there exists n0 ∈ N such that 2.26 and 2.11 hold Then, every solution of 1.9 is oscillatory on t0 , ∞ T Proof The proof follows from Lemmas 2.1, 2.2, and ... conditions for oscillation of delay differential equations,” Journal of Mathematical Analysis and Applications, vol 219, no 1, pp 165–178, 1998 J Shen and X Tang, “New oscillation criteria for linear...
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Báo cáo hóa học: "OSCILLATION CRITERIA FOR FIRST-ORDER FORCED NONLINEAR DIFFERENCE EQUATIONS" ppt
Ngày tải lên :
22/06/2014, 22:20
... essentially new and of high degree of generality Also, for related results in oscillation of forced differential equations, we refer to our earlier paper [2] Oscillation criteria for (1.1) In order ... (4.27) and also for forced neutral second-order nonlinear difference equations of the form Δ2 x(n) − c(n)x[n − τ] + q1 (n)xμ [n − τ + 1] = q2 (n)xλ [n − τ + 1] + e(n) (4.28) The formulations of these ... H(n + 1,n) > 0, m > n ≥ 0, and for k = n = m − 1, are fulfilled Oscillation of (1.3) We will combine some of our results in Sections and to obtain oscillation criteria for (1.3) Theorem 4.1 Let...
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FIRST- AND SECOND-ORDER DYNAMIC EQUATIONS WITH IMPULSE F. M. ATICI AND D. C. BILES Received 3 pdf
Ngày tải lên :
23/06/2014, 00:20
... concept of lower and upper solutions of problem (3.1)–(3.5) as follows F M Atici and D C Biles 127 Definition 3.1 The functions α and β are, respectively, a lower and an upper solution of problem ... shows that Gun → G uniformly on compact subsets of J2 Hence, by Subclaims and 4, Schauder’s fixed point theorem applies to G, finishing the proof of Claim 2.4 Claims 2.3 and 2.4 yield the desired ... satisfied and α, β are lower and upper solutions of (2.1)–(2.3) with α(t) ≤ β(t) for all t ∈ J Then, there exists a solution u to (2.1)– (2.3) such that u ∈ [α,β] F M Atici and D C Biles 123 Proof...
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Đề tài " Sharp local wellposedness results for the nonlinear wave equation " pot
Ngày tải lên :
15/03/2014, 09:20
... HART F SMITH AND DANIEL TATARU Proof of Proposition 8.2 For the purpose of this proof we consider the case ω = (0, 0, , 1), and dispense with the indices ω and r Then xω = xn , and xω = x ... in turn ε2 For the proof of Propositions 5.1 and 5.2 it suffices to consider the case where θ = (0, , 0, 1) and r = We fix this choice, and suppress θ and r in our notation Instead of (xθ , xθ ... u) ∂j u = Q(t, x, u; du) , for a different Q of the same form, and by combining terms we may assume that g0j = for j = This means that the coefficients of the Lorentzian form · , · g are given by...
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Đề tài " Propagation of singularities for the wave equation on manifolds with corners " ppt
Ngày tải lên :
15/03/2014, 09:20
... ∅ and WFb (B) ⊂ K, and it lies in a bounded subset of Ψ−∞ (X) for B ∈ B Thus, BEu H (X) ≤ C1 u H (X) by Lemma 3.2 On b the other hand, BG ∈ Ψ0 (X) and indeed in a bounded subset of Ψ0 (X) for ... neighborhood of q0 in Σ contains a set of the form (5.1) Proof of Lemma 5.1 We now show that if π −1 (O) is open, then ˆ so is O That is, we need to show for any set O with π −1 (O) open, and ˆ for any ... well and, again, q lies on the right-hand side Therefore the left-hand side is indeed a subset of the right-hand side To see the converse direction, i.e that the right-hand side is a subset of...
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Báo cáo khoa học: "EXPRESSING DISJUNCTIVE AND NEGATIVE FEATURE CONSTRAINTS CLASSICAL FIRST-ORDER LOGIC" pdf
Ngày tải lên :
24/03/2014, 02:20
... unification of el and e7 is the intersection of the principal filters generated by (1) and (2), it is also the set of satisfying models for the conjunction of (1') and (2') with the formula Xl ... generator of the satisfying principal filter of the conjunction of such constraints is the unification of the generators of the satisfying principal filters of each of the conjuncts Thus the set of ... setvalues (A1) For all Constants c and attributes a, a(c) = 3- (A2) For all distinct pairs of constants Cl, c2, Cl ~ c2 (A3) For all attributes a, a(3-) = ± (A4) For all constants c, c ~ ± (A5) For all...
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a hierarchical classification of first-order
Ngày tải lên :
28/04/2014, 10:06
... point of view of finite word instead of infinite word reading automata, as for instance in [6,10,11,12,13,14,15] Unfortunately, as opposed to the case of infinite words, the classification theory of ... The obtained hierarchical classification of neural networks consists of a decidable pre-well ordering of width and height ω ω , and a decidability procedure of this hierarchy is provided Notably, ... spiking configurations of both the activation and input cells of N at time t are respectively called the state of N at time t and the input submitted to N at time t An input stream of N is then defined...
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Solutions to the Acoustic Wave Acoustic Wave Equation
Ngày tải lên :
28/04/2014, 14:16
... wavelength Spherical Wave Green’s function, asymptotic Green’s function Energy of an Acoustic Wave du Work Performed: dy dz F=Pdzdy dx dW = (Pdzdy)du = PdV W = (Pdzdy)du = PdV Hooke’s Law dP ... Ae = Ae i(k x + k z - (2) wt) x z i(k r - wt) k = (k , k z ) x (2) = |k|(sin , cos ) k Equation of a line: k r = cnst k is Perpendicular to Wavefront z r k k = |r||k| cos(O) = constant Any pt ... z - (2) wt) x z i(k r - wt) k = (k , k z ) x x= sinO z (2) = |k|(sin , cos ) k z= cosO Equation of a line: k r = cnst = 2pi/|k| Time (s) Apparent Velocity dx/dt=apparent V x = x dz/dt=apparent...
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Báo cáo sinh học: " Periodic solutions for a class of higher order difference equations" potx
Ngày tải lên :
18/06/2014, 22:20
... solutions for a class of higher-order difference equations Huantao Zhu1 and Weibing Wang∗2 Hunan College of Information, Changsha, Hunan 410200, P.R China Department of Mathematics, Hunan University of ... Z → Z and τ (n + ω) = τ (n), ω, m, k ∈ N, and obtained existence theorem for single and multiple positive periodic solutions of (1.3) Our aim of this article is to study the existence of periodic ... i=1 Clearly, the fixed point of Tp in X is a periodic solution of (1.1) Proof of Theorem 1.1 Let p = r and Ω = {x ∈ X : m ≤ x(n) ≤ M for n ∈ Z}, then Ω is a closed and convex set If r = 1, then...
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