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51.
Journal of Optimization Theory and Applications - In this paper, we study a general minimization vector problem which is expressed in terms of a perturbation mapping defined on a product of locally...  相似文献   
52.
For independent random variables X and Y, define % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaabofaruWrL9MCNLwyaGqbciaa-bcacqGHHjIUcaWFGaGaa8hw% aiaa-TcacaWFzbaaaa!4551!\[{\rm{S}} \equiv X + Y\]. When the conditional expectations % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGBbqefCuzVj3zPfgaiuGajaaqcaWFNbGccaGGOaGa% amiwaiaacMcacaGG8bGaam4uaiaac2facqGHHjIUcaWGHbGaaiikai% aadofacaGGPaaaaa!4BC4!\[E[g(X)|S] \equiv a(S)\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGBbGaamiAaiaacIcacaWGybGaaiykaiaacYhacaWG% tbGaaiyxaiabggMi6kaadkgacaGGOaGaam4uaiaacMcaaaa!4894!\[E[h(X)|S] \equiv b(S)\]are given, then under certain assumptions, the density function of X has the form of u(x)k()eax, where u(x) is uniquely determined by the functions a(·) and b(·).  相似文献   
53.
54.
Since Dantzig—Wolfe's pioneering contribution, the decomposition approach using a pricing mechanism has been developed for a wide class of mathematical programs. For convex programs a linear space of Lagrangean multipliers is enough to define price functions. For general mathematical programs the price functions could be defined by using a subclass of nondecreasing functions. However the space of nondecreasing functions is no longer finite dimensional. In this paper we consider a specific nonconvex optimization problem min {f(x):h j (x)g(x),j=1, ,m, xX}, wheref(·),h j (·) andg(·) are finite convex functions andX is a closed convex set. We generalize optimal price functions for this problem in such a way that the parameters of generalized price functions are defined in a finite dimensional space. Combining convex duality and a nonconvex duality we can develop a decomposition method to find a globally optimal solution.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.  相似文献   
55.
We study the following initial and boundary value problem: In section 1, with u0 in L2(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L2(0, T; H ∩ H2) ∩ L(0, T; H) if we assume u0 in H and f in C1(?,?). Numerical results are given for these two cases.  相似文献   
56.
57.
Exchangers with cyclic polyethers as anchor groups have a large range of applications such as separations of cations with a common anion, of anions with a common cation, and of neutral organic compounds, and the determination of water by elution chromatography. Some crown ether monomers, especially 4- and 4,4′-alkyl-substituted benzo-derivatives are suitable for extractions and their adducts with heteropoly acids are used as liquid ion-exchangers. The exchangers are also applied in thin-layer chromatography and thin-layer electrophoresis. Furthermore the exchangers are successfully used in preparative chemistry, e.g., in salt conversions in order to isolate salts which are difficult to prepare by other means, in isolation and purification of organic compounds, and for anion activation in organic reactions.  相似文献   
58.
Simple yet accurate expressions for the electrical double-layer interaction force and energy between the particles that hold for a wide range of surface potential is required in the modeling, simulation, and optimization of many processes employed in industry. In this paper, simple approximate expressions for the interaction are obtained based on the asymptotic results and the numerical solution to the Poisson-Boltzmann equation for identical parallel plates with constant surface potential up to 180/z(i) mV at 25 degrees C, and the Derjaguin approximation. Within the moderate surface potential range, the semianalytical expressions agree well with the exact numerical results and are convenient to use for the purpose of process modeling and simulation. Copyright 2000 Academic Press.  相似文献   
59.
The combination of Lewis and Bronsted acids catalyzed the addition of beta-ketoesters to cyclic diene. Lactonization occurs in situ to afford fused bicyclic lactones directly. The catalysis provides an expedient route to bicylic lactones via a zip-process.  相似文献   
60.
The syntheses, structures, and N2 adsorption properties of six new supramolecular metallacycles are reported. Flexible ditopic linkers, 1-4, with systematically varied lengths and conformational degrees of freedom were synthesized utilizing ester linkages. They were used in combination with (dppp)M(OTf)2, where M = Pt(II) and Pd(II), and cis-(Me3P)2Pt(OTf)2 to form flexible supramolecular metallacycles 5-10 in 88-98% isolated yields. Their structures were characterized via multinuclear NMR and X-ray crystallography. The metallacycles stack to form porous structures in the crystalline state. The pore dimensions depend on both the phosphorus ligands attached to the metals and the flexible linkers. Adsorption studies on the porous materials show that 5a, 6, 8, and 9 held 11.7, 16.5, 5.7, and 6.8 cm3/g STP of N2 at 77 K, respectively. A guest-exchange study with nitromethane and toluene reveals that the nanopore in 5 is flexible, a property which was transferred from the linker to the supramolecular structure in the solid state.  相似文献   
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