... is the vapor pressure of contaminant, Mw is the molecular weight of contaminant, R is the Ideal Gas Constant, and T is the absolute temperature In the case of absence of any liquid phase ofthe ... in the x, y, and z directions and ρ is the density of water (ML–3) The three terms in the left-hand side ofthe above general equation represent the net advective flow across the element; the ... construct the potential lines for the flow of a pond receiving recharge with water exiting the upstream boundary ofthe pond Use the following values: uniform velocity ofthe aquifer, U = 1, radius of...
... đầu hay mm Tần suất AV block thấp Huang and Wood, 2nd ed Catheter ablation of cardiac arrhythmias.2011 “Catheter ablation of AVNRT is the most scaring ablation procedure” Mark E Josephson, MD ... đốt bên ∆ Koch Bên trần xoang vành Thực hành chuẩn Theo dõi dẫn truyền ngược nhịp nối Ngưng đốt có block dẫn truyền ngược 1:1 Thực hành chuẩn Theo dõi nhịp nối nhanh Ngưng đốt nhịp nối
... with each other under the control ofthe Board of Directors Being aware ofthe important role of THQV in the whole system of Techcombank, managers and staff at THQV continually try their best ... expanded the scope and form of lending to customers The orientation ofthe branch: expanding, strengthening and improving the operational efficiency ofthe office agency To attract more customers, the ... not carry out the contract, the collateral is under the decision ofthe bank 2.3 The history emergence of consumer loans The crisis in the banking system started in the 1970s, when the brokers...
... flow in the second aquifer in Kumamoto city is roughly indicated by the arrows in Fig The main water flow is from the western foot of Mt Aso to Ariake Sea through the middle-southern part ofthe ... point of no 19 located near Group area Other two sampling points are located at right in the middle ofthe city where the impermeable bed is lacking and also are nearby the alluvial area On the other ... reductive atmosphere in the subsurface environment of Group and Group areas From these results, the following hypothesis was proposed: the groundwater in the first aquifer of this area is contaminated...
... unacceptable risks The risk assessment process focuses on the question of whether there is an unacceptable risk, which will depend on the circumstances ofthe site and the context ofthe decision The selection ... development ofthe conceptual model (in particular the results of site investigation); the selection of criteria and assumptions; the evaluation ofthe potential risks; and the basis for the decision ... manner Users of these Model Procedures should ensure that they are fully aware ofthe requirements ofthe CDM Regulations and implement them accordingly Decisions At the end of this stage the implementation...
... especially in the growing and constantly changing society Therefore, the use of marketing tools to uncover the needs of individual customers can be seen that the initial success ofthe bank, then banks ... needs of its customers, create the specific image ofthe products and services to stimulate customers’ demand This is also the basis for customer to distinguish the banks from the others Then the ... 1 1.1 Rationale ofthe research 1 1.2 .The objectives ofthe study 2 1.5 Methodology ofthe study 2 1.6 Scope ofthe study ...
... fixed point theorem 1 Introduction and main results Let R denote the set ofthe real numbers, Z the integers and N the positive integers In this article, we investigate the existence of periodic ... 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 g(u) ... and approved the final manuscript 11 Acknowledgments The authors would like to thank the referee for the comments which help to improve the article The study was supported by the NNSF of China (10871063)...
... domain and p = 2, the results of Theorems 1.1, 1.2 are improvements ofthe main results of [18] Remark 1.5 As Ω is a bounded smooth domain and p ≠ 2, μ = 0, then the results of Theorems 1.1, 1.2 ... μand w
... decay ofthe solutions energy, depending on the decay rate ofthe relaxation functions g(s) and h(s) For the problem (1.1) in ℝn, we mention the work of Kafini and Messaoudi [10] Motivated by the ... state the local existence and the uniqueness ofthe solution of problem (1.1), whose proof can be found in Han and Wang [19] (Theorem 2.1) with slight modification, so we will omit its proof In the ... the situation where the internal dissipation acts on a part of Ω and the viscoelastic dissipation acts on the other part They established both exponential and polynomial decay results under the...
... In the proof of Theorem 1.1, the condition that F2 n, x ≥ for n, x ∈ J × R, |x| ≤ in F1 , is only used in thethe proofs of assumption ii of Lemma 2.1 Therefore, we only proves assumption ii of ... satisfy the (PS)-condition If I is bounded from below, then c infE I is a critical value of I Proofs of Theorems Proof of Theorem 1.1 In our case, it is clear that I 0 We show that I satisfies the ... that I u ≥ α, that is, assumption ii of Lemma 2.1 holds The proof of Theorem 1.2 is completed 14 Advances in Difference Equations Proof of Theorem 1.4 In view of Lemma 2.4, I ∈ C1 E, R We first...
... Now, we begin the proof of Theorem 1.1 By Theorem 3.4, we obtain that Eλa,b has a positive solution uλ in H0 Ω Proof of Theorem 1.2 In this section, we will establish the existence ofthe second ... Proof The proof is immediate from 2.6 and 2.7 Moreover, we have the following result Lemma 2.4 If λ ∈ 0, Λ0 , then M0 Ω λa,b ∅ where Λ0 is the same as in 1.1 Proof Suppose the contrary Then there ... give some propertiesof Nehari manifold In Sections and 4, we complete proofs of Theorems 1.1 and 1.2 Nehari Manifold In this section, we will give some propertiesof Nehari manifold As the energy...
... Problems h t ≡ 0, Korman investigated the uniqueness of positive solutions ofthe problem 1.1 by techniques of bifurcation theory However, the existence of sign-changing solution for this problem ... called the quasiderivatives of y t To apply Elias’s theory, we have to prove that 1.4 can be rewritten to the form of 1.6 , that is, the linear operator Mu L u : u 1.8 has a factorization ofthe ... u This completes the proof ofthe theorem u emt cos mt u m 2.18 is equivalent to 2.8 Theorem 2.5 Let (H1) hold and h satisfy (H2) Then i Equation 1.4 has an infinite number of positive eigenvalues...
... Hence by the assumption ofthe theorem we have that P is a contraction mapping then in view ofthe Banach fixed point theorem, P has a unique fixed point which is corresponding to the solution of Equation ... u∗ , in [γ, λ]S Proof We shall prove the existence ofthe maximal solution since the existence ofthe minimal solution follows from the dual arguments Firstly we consider the mapping Φȷ : [γ, ... follows : ∫t (P u)(t) := ϕ(θ) + (t − τ )α−1 F (τ, u, v)dτ Γ(α) (7) Then by the assumption ofthe theorem and thepropertiesofthe fractional calculus we obtain that ∫t (t − τ )α−1 |F (τ, u, v)|dτ...
... [12, Theorem 3.1]) In [50], Fan extended the Brezis– Nirenberg type theorem to the case ofthe p(x)-Kirchhoff [50, Theorem 1.1] The Theorem 1.1 of [50] concerns with the Dirichlet problems, but the ... increasing, we have vε ≥ uλ1 , that is, uλ2 − ε ≥ uλ1 on Ω The proof of Theorem 1.1 is complete Let us now turn to the proof of Theorem 1.2 Proof of Theorem 1.2 Let (1.4)–(1.8) hold Let λ > λ∗ Take λ1 ... we need the global regularity results for the weak solution of Pλ Ap- plying Theorems 4.1 and 4.4 of [44] and Theorem 1.3 of [37], we can easily get the following f results involving ofthe regularity...
... comments, which improved the quality of this paper The work was supported by the NSF of China, the NSF of Jiangxi Province of China 2008GQS0057 , the Youth Foundation of Jiangxi Provincial Education ... |ε t − e t |dt < 2.1 Then 1.1 has a unique T -periodic solution Proof Existence For the proof of existence, we use Lemma 1.1 First, let us consider the homotopic equation of 1.1 : ϕ x t λf x t ... ϕp s , Liu 7, Theorem proved that 1.1 has a unique T -periodic solution ϕp s , Theorem 2.1 under the assumptions A1 and A2 Thus, even for the case of ϕ s is a generalization of 7, Theorem In...
... z ≥ 0, then then unique solution u ofthe problem 2.5 satisfies u t ≥ γ u , 2.7 t∈ η,1 where γ min{αη, α − η / − αη , η} We need the following propertiesofthe Green’s function Hn in the sequel ... solution of 1.3 , we mean a vector x, y ∈ C 0, ∩ C2 0, × C 0, ∩ C2 0, such that x, y satisfies 1.3 and x > 0, y > on 0, The proofs of our main result Theorem 1.1 is based on the Guo’s fixed-point theorem ... problem ofthe second kind for the SturmLiouville operator,” Differential Equations, vol 23, no 8, pp 979–987, 1987 A V Bitsadze, “On the theory of nonlocal boundary value problems,” Soviet Mathematics—Doklady,...
... conditions of Theorem 3.4 In addition, the conditions of Theorem 3.4 are also easy to check Acknowledgments This work is sponsored by the National Natural Science Foundation of China 10671012 and the ... be the number if it exists with the property that given ε > there is a neighborhood U of t with y ρ t −y s − y∇ t ρ t − s
... 2.10 then we have the following theorem Theorem 2.9 Adding condition 2.10 to the hypotheses of Theorem 2.8 one obtains uniqueness ofthe fixed point of f In our considerations, we will work in the ... completes the proof Remark 3.5 gives us the following theorem which is a better result than that 6, Theorem 3.3 because the solution of our problem 1.1 is positive in 0, and strictly increasing Theorem ... Krasnoselskii’s fixed point theorem and nonlinear alternative of Leray-Schauder type in a cone and assuming certain hypotheses on the function f In the uniqueness ofthe solution is not treated...
... they apply the mountain pass theorem to get the nontrivial solutions ofthethe system In 30 , the author obtains the existence and multiplicity of solutions for the following problem: − div ... 3.26 1,q x Since the restriction operator is continuous, then un , υn u, υ in W0 Br × W Br Because ofthe compactness of Fr , the first expression on the right-hand side ofthe equation tends ... existence of solutions ofthe system; these results correspond to the sublinear and superlinear cases for p 2, respectively Inspired by the above-mentioned papers, we concern the existence of nontrivial...