The separation theorem

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  • Recently, odd-even high-order harmonic generation (HHG) emitted from asymmetric molecules has paid much attention since its application in extracting molecular structures and probing molecular dynamics. In which, the ratio of the even and odd harmonics in HHG spectra is an important quantity characterized the molecular asymmetry. This even-to-odd ratio has been explained by the gerade and ungerade components of the temporal transition dipole. Though, the separating procedure of the temporal transition dipole has not been published in the previous study.

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  • In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green’s functions are investigated and existence results for positive solutions of the nonlinear boundary value problem are established. Upper and lower bounds for these positive solutions also are given.

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  • The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite.

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  • The induction hypotheses Application to endoscopic and stable expansions Cancellation of p-adic singularities Separation by infinitesimal character Elimination of restrictions on f Local trace formulas Local Theorem 1 Weak approximation Global Theorems 1 and 2 10. Concluding remarks Introduction This paper is the last of three articles designed to stabilize the trace formula. Our goal is to stabilize the global trace formula for a general connected group, subject to a condition on the fundamental lemma that has been established in some special cases.

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  • In a world of geo-political, social and economic uncertainty, strategic financial management is in a process of change, which requires a reassessment of the fundamental assumptions that cut across the traditional boundaries of the subject. Read on and you will not only appreciate the major components of contemporary finance but also find the subject much more accessible for future reference.

    pdf109p sn_buon 29-11-2012 64 11   Download

  • The design theorem of traditional zoom lens uses mechanical motion to precisely adjust the separations between individual or groups of lenses; therefore, it is more complicated and requires multiple optical elements. Conventionally, the types of zoom lens can be divided into optical zoom and digital zoom.

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  • Mục tiêu của đề tài là trình bày các định lý tách tập lồi. Các định lý này có nhiều ứng dụng trong quy hoạch toán học. ABSTRACT The aim of this topic is to introduce separation theorem of convex sets. This theorem has many applications in mathematical programming. 1. Mở đầu. Khái niệm tập lồi trong không gian vectơ là sự khái quát khái niệm hình lồi trong hình học sơ cấp. Nó giữ vai trò quan trọng trong nhiều vấn đề giải tích hàm. Đặc biệt, lý thuyết các hàm và tập lồi ( gọi là giải tích lồi)...

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  • Chapter 19 EXAMPLES AND ADDENDA The separate sections of this chapter are not related to one another except in so far as they illustrate or extend the results of Chapter 18 . © 1 . The central limit theorem for homogeneous Markov chains Consider a homogeneous Markov chain with a finite number of states (labelled 1, 2, . . ., k) and transition matrix P = (p i ;) (see, for instance, Chapter III of [47] ) . If Xn is the state of the system at time n, we have the sequence of random variables X1 , X2 , . . ., Xn...

    pdf25p dalatngaymua 30-09-2010 98 8   Download



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