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31.
F. G. Tricomi (1923- ), S. Gellerstedt (1935- ), F. I . Frankl (1945- ), A. V. Bitsadze and M. A. Lavrentiev (1950- ), M. H. Protter (1953- ) and most of the recent workers in the field of mixed type boundary value problems have considered only one parabolic line of degeneracy. The problem with more than one parabolic line of degeneracy becomes more complicated. The above researchers and many others have restricted their attention to the Chaplygin equation:K(y)·uxx+uyy =f(x,y) and not considered the "generalized Chaplygin equation:"Lu=K(y)·uxx+uyy+r(x,y)·u=f(x,y) because of the difficulties that arise when r1=non-trivial(≠0). Also it is unusual for anyone to study such problems in a doubly connected region. In this paper 1 consider a case of this type with two parabolic lines of degeneracy, r2=non-trivial(≠0).in a doubly connected region, and such that boundary conditions are prescribed only on the-exterior boundary" of the mixed domain, and 1 obtain umqueness results for quasnegutar solutions of the characteristic and non-characteristic Problem by applying the b,c energy integral method in the mixed domain.  相似文献   
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Optimization Letters - By reviewing the Logarithmic–quadratic proximal (LQP) method, in this paper we suggest and analyze a new LQP alternating direction scheme for the separable constrained...  相似文献   
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Copper(ii), nickel(ii) and zinc(ii) complexes of the peptides Ac-HVVH-NH(2) and Ac-HAAHVVH-NH(2) have been studied by potentiometric, UV-vis, CD, EPR and NMR spectroscopic measurements. Both tetra and heptapeptides can form relatively stable macrochelates with copper(ii), nickel(ii) and zinc(ii) ions, in which the ligands are coordinated via the side-chain imidazole functions. Formation of the macrochelates slightly suppresses, but cannot prevent the copper(ii) and nickel(ii) ion promoted deprotonation and coordination of the amide functionalities. The overall stoichiometry of the major species is [MH(-3)L](-) with a 4N (= N(-),N(-),N(-),N(im)) coordination mode. In the case of Ac-HAAHVVH-NH(2), coordination isomers of this species can exist with a preference for copper(ii) or nickel(ii) binding at the internal histidyl residue. In the copper(ii)-Ac-HAAHVVH-NH(2) system, the presence of the two anchoring sites results in the formation of dinuclear complexes. The existence of these species requires the involvement of amide functions in metal binding. Both equilibrium and spectroscopic data support the fact that the copper(ii) ions of the dinuclear species are independent from each other providing a good chance for the formation of various mixed metal complexes. It was found that zinc(ii) is not able to significantly alter the copper(ii) binding of the heptapeptide, but it can occupy the uncoordinated histidyl sites. The formation of the copper(ii)-nickel(ii) mixed species was obtained in alkaline solutions and CD spectra suggest the statistical distribution of the two metal ions among the histidyl residues. The binding of HAAHVVH to palladium(ii) is exclusive below pH 8 and the mixed metal species of palladium(ii) and copper(ii) ions are formed only in slightly basic solutions.  相似文献   
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Chromatin proteins are believed to represent reactive sites for metal ion binding. We have synthesized the 31 amino acid peptide Ac-NSFVNDIFERIAGEASRLAHYNKRSTITSRE-NH2, corresponding to the 63-93 fragment of the histone H2B and studied its interaction with Cu(II) and Ni(II). Potentiometric and spectroscopic studies (UV-vis, CD, NMR and EPR) showed that histidine 21 acts as an anchoring binding site for the metal ion. Complexation of the studied peptide with Cu(II) starts at pH 4 with the formation of the monodentate species CuH2L. At physiological pH values, the 3N complex (N(Im), 2N(-)), CuL is favoured while at basic pH values the 4N (N(Im), 3N(-)) coordination mode is preferred. Ni(II) forms several complexes with the peptide starting from the distorted octahedral NiH2L at about neutral pH, to a square planar complex where the peptide is bound through a (N(Im), 3N(-)) mode in an equatorial plane at basic pH values. These results could be important in revealing more information about the mechanism of metal induced toxicity and carcinogenesis.  相似文献   
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The development of efficient sensors for the determination of the water content in organic solvents is highly desirable for a number of chemical industries. Presented herein is a Mg2+ metal–organic framework (MOF), which exhibits the remarkable capability to rapidly detect traces of water (0.05–5 % v/v) in various organic solvents through an unusual turn‐on luminescence sensing mechanism. The extraordinary sensitivity and fast response of this MOF for water, and its reusability make it one of the most powerful water sensors known.  相似文献   
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As an especially unique target for chemical synthesis, diazonamide A has the potential to be constructed through a plethora of synthetic routes, each attended by different challenges and opportunities for discovery. In this article, we detail our second total synthesis of diazonamide A through a sequence entirely distinct from that employed in our first campaign, one whose success required the development of several special strategies and tactics. We also disclose our complete studies regarding the chemical biology of diazonamide A and its structural congeners, and more fully delineate the scope of our protocol for Robinson-Gabriel cyclodehydration using pyridine-buffered POCl(3).  相似文献   
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In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982-2005 we established the Hyers-Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002-2005 the authors of this paper investigated the Hyers-Ulam stability of additive and quadratic mappings on restricted domains. In this paper we improve our bounds and thus our results obtained, in 2003 for Jensen type mappings and establish new theorems about the Ulam stability of additive mappings of the second form on restricted domains. Besides we introduce alternative Jensen type functional equations and investigate pertinent stability results for these alternative equations. Finally, we apply our recent research results to the asymptotic behavior of functional equations of these alternative types. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology.  相似文献   
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