báo cáo hóa học:" Research Article Global Estimates for Singular Integrals of the Composition of the Maximal Operator and the Green’s Operator" doc

... CorporationJournal of Inequalities and ApplicationsVolume 2010, Article ID 723234, 12 pagesdoi:10.1155/2010/723234 Research Article Global Estimates for Singular Integrals of the Composition of the Maximal Operator ... inequalities for these composite operators with singular factors. In paper 11, they keep working on the same topic and derive global estimates for the singular integrals of these composite operatorsin ... domains. The purpose of this paper is to estimate the Poincar´e type inequalities for the composition of the maximal operator and the Green’s operator over the δ-John domain.2. Deﬁnitions and LemmasWe...

Báo cáo hóa học: "Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear" docx

... α31α32 0, then 1.1 reduces to the system 1.4 of Part I.Recently, the work in 18–20 studied the existence, uniform boundedness, and uniform convergence of global solutions for the Lotka-Volterra ... Moreover, global asymptoticstability of the positive equilibrium point for 1.1 is proved by an important lemma of 21. The proof is complete and complement the uniform convergence theorem in18–20.2. ... in the case that the space dimension n  1. In this paper, weconsider mainly the existence and uniform boundedness of global solutions for the model1.1 with nonlinear density restriction and...

Báo cáo hóa học: " Research Article WKB Estimates for 2 × 2 Linear Dynamic Systems on Time Scales" potx

... show that it istrue for the discrete scale only for the appropriate choice of graininess depending on a parameterε. The proof is based on the truncation of WKB s eries and WKB estimates. Copyright ... 1.41then all conditions of Theorem 1.2 are satisﬁed see proof of Example 1.5 in the next section for any real numbers b, a/ 0, and estimate 1.18 with m  1istrue.Note that for continuous ... Oτ−4.2.42So if μ  ε, then 1.26 and all other conditions of Theorem 1.2 are satisﬁed, and 1.18 is truewith m  1.Acknowledgment The author wants to thank Professor Ondrej Dosly for his comments...

Báo cáo hóa học: "Research Article A Method for Visualizing Independent Spatio-Temporal Patterns of Brain Activity" potx

... corresponding to the extremeeigenvalues of the transformed covariance matrices have maximal variance for one class and minimal variance for the other class. First, for the two classes (1 and 2), the class-labeled ... study of these brain potentials, it isimportant to characterize both the spatial and temporal mor-phologies of the responses for a better understanding of both the physiology and function of the ... study of these brain potentials, it is important to characterize both the spatial and temporal morphologies of the responses for a better understanding of both the physiology and function of the brain....

Báo cáo hóa học: " Research Article Global Existence, Uniqueness, and Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation" ppt

... ends the proof of Theorem 2.4.Acknowledgments The authors express their sincere gratitude to the anonymous referees for a number of valuable comments and suggestions. The work was supported by the ...  t−p/p−2.4.15This is 2.9 and we complete the proof of Theorem 2.3.Journal of Inequalities and Applications 15 The applications of Lemma 4.1 and 4.19 yields thatutt22∇ut22utα1α1≤ ... Lp and W1,p0 for LpΩ and W1,p0Ω and relevant normsby ·p and ·1,p, respectively. In general, ·Xdenotes the norm of Banach space X.Wealso denote by ·, · and ·, · the...

Báo cáo hóa học: " Research Article Global Asymptotic Stability of Solutions to Nonlinear Marine Riser Equation" ppt

... 1.2where EI is the flexural rigidity of the riser, Neffis the “effective tension”, a is the coefficient of the Coriolis force, b is the coefficient of the nonlinear drag force, and m is the mass linedensity. ... terms see, e.g. 3, 4,where theorems on asymptotic stability of the zero solution and estimates of the zero solution and the estimates of the rate of decay of solutions to second order wave ... zero when t →∞. Moreover the polynomial decay rate for solutions is established.There are many articles devoted to the investigation of the asymptotic behavior of solutions of nonlinear wave equations...

báo cáo hóa học:" Research Article Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities" pot

... Σνkdenote the closure of set of those solutions of 1.1,1.2 which belong to Φνk. The main results of this paper are the following.Theorem 1.5. Let (A1)–(A4) hold.a If f∞ 0, then there ... studied; see 1–5 and the references therein. However, relatively little is known about the global structure of solutions in the case that f0 ∞, and few global results were found in the available ... best of our knowledge, there is no paperto discuss the global structure of nodal solutions of 1.1, 1.2 with f0 ∞.In this paper, we obtain a complete description of the global structure of...

báo cáo hóa học:" Research Article Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation" ppt

... ∞utt  0 and limt → ∞∇utp 0. The proof of Theorem 2.8 is thus ﬁnished.4 Journal of Inequalities and ApplicationsLemma 2.5. Assume that the hypotheses in Theorem 2.4 hold, thenr − ... studied. The existence of global solutions for this problem is proved by constructing a stable set in W1,p0Ω and show the asymptotic behavior of the global solutions through the use of an important ... r>pand k1,k2 ,and are some positive constants.Because the p-Laplace operator Δpis nonlinear operator, the reasoning of proof and computation is greatly diﬀerent from the Laplace operator...

báo cáo hóa học:" Research Article Some Estimates of Integrals with a Composition Operator" potx

... 0.HerexBis the center of the ball B.We omit the proof since it is the same as the proof of Theorem 3.2.8 Journal of Inequalities and ApplicationsProof. First, by using the H¨older inequality and ... apply the composition of the three operators under the consideration to certain harmonic forms and toobtain some estimates for certain integrals which are useful in studying the properties of the solutions ... some estimates of integrals with a composition operator, namely, composition of homotopy, diﬀerential, and Green’s operators T ◦ d ◦ G, with the Lipschitz and BMO norms. Wealso have estimates of...

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

... converges to the equilibrium.Proof of Theorem 1.4. The four parts of the proof are as follows.a fx, y is increasing in both x and y on m∗,M∗2. By Lemma 5.2 the hypotheses of Theorem ... completes the proof of Theorem 1.4. Since Theorem 1.4 is just a version of Theorem 1.2obtained by an aﬃne change of coordinates, we have also proved Theorem 1.2 as well.6. Proof of Theorem 1.5 The ... x and increasing in y ,and d fx, y is increasing in x and decreasing in y.We present several lemmas before completing the proof of Theorem 1.4.By considering the restriction of the map T of...

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