in advanced gas cooled reactors

... Method 14.3 Finite Point Method (FPM) 14.4 Example Problems 14.4.1 Sharp Fin Induced Shock Wave Boundary Layer Interactions 14.4.2 Asymmetric Double Fin Induced Shock Wave Boundary Layer Interaction ... Finite Element Analysis in Fluid Dynamics, McGraw-Hill ——— [1999] Transitions and interactions of inviscid/viscous, compressible/incompressible and laminar/turbulent flows Int J Num Methods in ... unstructured grids are treated in Chapter 19 Various computing techniques, including domain decomposition, multigrid methods, and parallel processing, are given in Chapter 20 Applications of numerical...

Ngày tải lên: 01/04/2014, 10:45

... solutions obtained both in Propositions and satisfy a slightly stronger condition than the one required in Definition Competing interests The authors declare that they have no competing interests ... Hartung et al [8] and references therein As main improvements in this article with regard to previous works in the literature we can cite the following: (1) The deviating argument τ depends at each ... completely continuous operator from C(I) into itself (one has to take Remark into account) Therefore, Schauder’s Theorem ensures that T has a nonempty and compact set of fixed points in C(I), which...

Ngày tải lên: 20/06/2014, 20:20

... n ∈ N, t0 ∈ T is the initial point, x0 ∈ R is the initial value, ϕ ∈ Crd t−1 , t0 T , R is the initial function such that ϕ has a finite left-sided limit at the initial point provided that it ... ∈ Crd t1 , ∞ T , R0 Advances in Difference Equations 13 and −Λ ∈ R t1 , ∞ T , R imply that e−Λ t, s is nondecreasing in s, hence e −Λ 1/e−Λ t, s is nonincreasing in s see 4, Theorem 2.36 Without ... t1 , ∞ T , R imply that e−Λ t, s is nondecreasing in s, hence e −Λ 1/e−Λ t, s is nonincreasing in s see 4, Theorem 2.36 From 4.15 and Advances in Difference Equations 17 Lemma 2.6, for all t...

Ngày tải lên: 21/06/2014, 11:20

... initial N problem (Pξ ), kn ∈ N, in ∈ IN , and n = kn N + in N Proof Let uξ and v be the unique solutions of (Pξ ) and (Pξ ), respectively By definition, uξ = v in JN Since f is N-periodic in ... following properties hold (1) {αm }m∈N is a strictly increasing sequence which converges uniformly in JN to ψ, the minimal solution in [α,β] of problem (PN ) (2) {βm }m∈N is a strictly decreasing ... following problem ∆u(n) = − arctan u(n) − in , n ∈ [kN,kN + N − 1], k ∈ N, (4.1) where for every k ∈ N, in ∈ IN is given as n = kN + in Obviously f (n,x) = − arctan(x − in ) is a continuous...

Ngày tải lên: 23/06/2014, 00:20

... Taking into account that min{20x2 + 10x4 − 10|x|3 − e(|x| + |x|2 + |x|3 )} ≥ −0.15, x∈R It is clearly that for Xing and Fu Advances in Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 ... obtain some new results Xing and Fu Advances in Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 Page 10 of 17 Theorem 2.5 Let g and m be as in ... China (10971139), Shanghai municipal education commission(No 10YZ72)and Shanghai municipal education commission(No 09YZ149) Competing interests The authors declare that they have no competing interests,...

Ngày tải lên: 21/06/2014, 02:20

... Classification: 39A10; 34B15 1 Introduction Let T be a time scale, i.e., T is a nonempty closed subset of R Let 0, T be points in T, an interval (0, T )T denoting time scales interval, that is, (0, T ... problem (in the one-dimension case) studied by [39] In the remainder of this section, we state the following fixed point theorem [37] Theorem 1.1 Let X be a Banach space and K ⊂ X be a cone in X Assume ... easy to obtain following result: Lemma 2.4 Φ maps K into K Main results For convenience, we denote f = lim+ sup max f (t, u) , u f ∞ = lim sup max f0 = lim+ inf f (t, u) , u f∞ = lim inf u→0 u→0...

Ngày tải lên: 21/06/2014, 17:20

... vinf t inf u t : u upper solution of 1.1 , u ≤ g a.e , t ∈ I 2.15 ∗ Theorem in implies that also vinf is the least Carath´ odory solution of 1.1 , thus u∗ e inf ∗ ∗ vinf ≤ U on I Hence uinf uinf ... concerns the possibility of allowing jumps in their graphs Since the task of finding a pair of lower and upper solutions is by no means easy in general, and bearing in mind that constant lower and ... actually asserts that u∗ , as defined in 2.8 , is the least inf uinf , as defined in 2.2 Carath´ odory solution, but it is easy to prove that in that case u∗ e inf Indeed, let U be an arbitrary upper...

Ngày tải lên: 21/06/2014, 20:20

... points, a, b ⊂ T, p is regressive and right-dense continuous, f : T × R → R is given function, Ik ∈ C R, R The paper 21 obtained the existence of one solution to problem 1.2 by using the nonlinear ... T, 1.4 Advances in Difference Equations By using the fixed point index, some existence, multiplicity and nonexistence criteria of positive solutions to the problem 1.4 were obtained for suitable ... least three fixed points x1 , x2 , x3 in K c satisfying x1 < d, a < α x2 , x3 > d with α x3 < a 1.6 Preliminaries Throughout the rest of this paper, we always assume that the points of impulse tk...

Ngày tải lên: 21/06/2014, 20:20

... ordinary and partial differential equations Although in many cases, speaking about maximum principles, authors mean quite different definitions of maximum principles such as e.g., corresponding inequalities, ... the operators in the spaces of discontinuous functions, for example, in the spaces of summable or essentially bounded functions Operator 1.5 , which is a linear combination of the internal superposition ... Journal of Inequalities and Applications 19 Repeating the argumentation used in the proof of Lemma 2.13, we obtain that this sequence of nondecreasing functions xm converges to the nondecreasing solution...

Ngày tải lên: 22/06/2014, 03:20

... lim inf on both sides of 2.22 , we get lim inf yx t ≥ lim inf zn0 t αn0 t t→∞ t→∞ ≥ lim inf zn0 t lim inf αn0 t t→∞ 2.17 2.23 t→∞ lim inf yx t lim inf αn0 t , t→∞ t→∞ which implies that lim inft ... obtain the main results of 7, by letting n0 in Theorem 2.6 In this case, we have β1 t ≡ for all t ∈ t0 , ∞ T Note that 2.1 and 2.26 , respectively, reduce tos lim inf α1 t > 1, t → ∞ which indicates ... 1.3 has been given in 6, Corollary , which coincides in the discrete case with our main result as lim inf pn t > t→∞ nτ τ τ , 1.7 where pn is defined by a similar recursion in , as ⎧ ⎪1, ⎪ ⎨ pn...

Ngày tải lên: 22/06/2014, 11:20

... Lemma 2.1(ii) in (2.8) to obtain m−1 H(m,n)e(n) − (1 − μ) μμ/(1−μ) × P μ/(1−μ) (m,n) H(m,n)q1 (n) H(m,k) n=k 1/(1−μ) ≤ −x(k) (2.10) Taking limsup as m → ∞ in the above inequality, we obtain a contradiction ... apply Lemma 2.1(ii) in (2.20) to obtain ∞ > x(n + 1) ≥ e(n) − (1 − μ)μμ/(1−μ) − p(n) μ/(1−μ) 1/(1−μ) q1 (n), n ≥ k (2.22) Taking limsup as n → ∞ in the above inequality, we obtain a contradiction ... Theorem 2.2, we obtain (2.8) Now m−1 H(m,n)e(n) H(m,k) n=k (2.13) m−1 ≥ −x(k) + h(m,n)x(n + 1) − H(m,n)b(n)xμ (n + 1) H(m,k) n=k Proceeding as in the proof of Theorem 2.2, taking liminf of both sides...

Ngày tải lên: 22/06/2014, 22:20

... × R → R is continuous (L) L1 ∈ C(R4 , R) is nondecreasing in the second variable, nonincreasing in the fourth Moreover, L2 : R2 → R is a continuous function and it is nonincreasing with respect ... discontinuities in the solution As mentioned in [17] and other works in the reference list, applications involving impulse effects can be found in biology, medicine, physics, economics, pharmacokinetics, ... its first variable (I) I is continuous and strictly increasing with respect to the first variable and nonincreasing in the second variable We consider the following modified truncated problem: y...

Ngày tải lên: 23/06/2014, 00:20

... wave equation was independently obtained in Bahouri-Chemin [3] and Tataru [28]; both show well-posedness for the nonlinear problem with s > n+1 + The key step in the proof in [28] shows that ... uniformly continuous dependence on the initial data This in general is not expected to hold for nonlinear hyperbolic equations Indeed, even a small perturbation of the solution suffices in order to ... result, it also follows that certain Strichartz estimates hold for the corresponding linear equation (1.3) Interpolation of (1.4) with (1.5), combined with Sobolev embedding estimates, yields Dx ρ v...

Ngày tải lên: 15/03/2014, 09:20

... Mazzeo for his continuing interest in this project and for his patience when I tried to explain him the main ideas in the early days of this project, and Victor Ivri˘ for his interest in, and his support ... commutator estimates, in particular the construction of the commutants, are very similar to those arising in the proof of the propagation of singularities in N -body scattering in previous works ... the local coordinate charts map into [0, ∞)k × Rn−k rather than into Rn Here k varies with the coordinate chart We write ∂ X for the set of points p ∈ X such that in any local coordinates φ = (φ1...

Ngày tải lên: 15/03/2014, 09:20

Ngày tải lên: 17/03/2014, 14:44

... identical elements distinct f r o m the d e n o t a t i o n of_L Even t h o u g h there are infinitely m a n y instances of the s c h e m a in (A5) (since there are infinitely m a n y terms) ... of feature structure constraints must be extended Kasper and Rounds [11] provide a formal framework for investigating such constraints by reviving a distinction originally made (as far as I am ... different interpretations of feature structure constraints have been investigated, such as the classical and intuitionistic interpretations of negation in feature structure constraints [14],...

Ngày tải lên: 24/03/2014, 02:20

... cos O Vz = z ; ρ k k=|k|(sin O, cos O) z κ x = V = x sin O x Summary k=|k|(sin O, cos O) = p w w Slowness Vector Motivation: Spatial aliasing X< x Geophone sampling interval p ... T = T sinO Time (s) Examples: dx/dt = v/sinO v/sinO=v x= z = O=90 Time (s) Examples: dx/dt = v/sinO x z = = O=0 = 0.0 Time (s) 0.45 0.0 X (ft) 250 Outline Plane Wave: Dispersion relationship, ... , 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 V z = z z T x T = T sinO Time (s)...

Ngày tải lên: 28/04/2014, 14:16

... i=1 Hence, Tr (Ω) ⊆ Ω Since X is finite-dimensional and g(u), f (n, u) are continuous in u, one easily show that Tr is completely continuous in Ω Therefore, Tr has a fixed point x ∈ Ω by Lemma 3.2, ... denote the set of the real numbers, Z the integers and N the positive integers In this article, we investigate the existence of periodic solutions of the following high-order functional difference equation ... difference equations (1.1) using the well-known Schauder’s fixed point theorem Our results extend the known results in the literature The main results of this article are following sufficient conditions...

Ngày tải lên: 18/06/2014, 22:20