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1.
Xanthates were easily prepared by adsorption of alcohol on KF-Al2O3 followed by treatment of carbon disulfide and iodomethane at room temperature. Pyrolysis of benzyl xanthate affords to a complex mixture of products. A radical process was proposed to explain the nature of products obtained. 相似文献
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Solvent-Free Condensation of Methyl Pyridinium and Quinolinium Salts with Aldehydes Catalyzed by DBU
Methylpyridinium and methylquinolinium salts were condensed under solvent-free conditions with aromatic aldehydes in the presence of 1,8-diazabicyclo[5.4.]undec-7-ene (DBU) as catalyst, by grinding at room temperature. The products are dyes or useful intermediates. The DBU can be easily recycled and reused. 相似文献
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Messaoud Boulbrachene 《Mathematical Methods in the Applied Sciences》2019,42(16):5305-5316
In this paper, we extend the approach developed by the author for the standard finite element method in the L∞‐norm of the noncoercive variational inequalities (VI) (Numer Funct Anal Optim.2015;36:1107‐1121.) to impulse control quasi‐variational inequality (QVI). We derive the optimal error estimate, combining the so‐called Bensoussan‐Lions Algorithm and the concept of subsolutions for VIs. 相似文献
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Messaoud Bounkhel 《Set-Valued and Variational Analysis》2014,22(1):221-245
In a general Hausdorff topological vector space E, we associate to a given nonempty closed set S???E and a bounded closed set Ω???E, the minimal time function T S,Ω defined by $T_{S,\Omega}(x):= \inf \{ t> 0: S\cap (x+t\Omega)\not = \emptyset\}$ . The study of this function has been the subject of various recent works (see Bounkhel (2012, submitted, 2013, accepted); Colombo and Wolenski (J Global Optim 28:269–282, 2004, J Convex Anal 11:335–361, 2004); He and Ng (J Math Anal Appl 321:896–910, 2006); Jiang and He (J Math Anal Appl 358:410–418, 2009); Mordukhovich and Nam (J Global Optim 46(4):615–633, 2010) and the references therein). The main objective of this work is in this vein. We characterize, for a given Ω, the class of all closed sets S in E for which T S,Ω is directionally Lipschitz in the sense of Rockafellar (Proc Lond Math Soc 39:331–355, 1979). Those sets S are called Ω-epi-Lipschitz. This class of sets covers three important classes of sets: epi-Lipschitz sets introduced in Rockafellar (Proc Lond Math Soc 39:331–355, 1979), compactly epi-Lipschitz sets introduced in Borwein and Strojwas (Part I: Theory, Canad J Math No. 2:431–452, 1986), and K-directional Lipschitz sets introduced recently in Correa et al. (SIAM J Optim 20(4):1766–1785, 2010). Various characterizations of this class have been established. In particular, we characterize the Ω-epi-Lipschitz sets by the nonemptiness of a new tangent cone, called Ω-hypertangent cone. As for epi-Lipschitz sets in Rockafellar (Canad J Math 39:257–280, 1980) we characterize the new class of Ω-epi-Lipschitz sets with the help of other cones. The spacial case of closed convex sets is also studied. Our main results extend various existing results proved in Borwein et al. (J Convex Anal 7:375–393, 2000), Correa et al. (SIAM J Optim 20(4):1766–1785, 2010) from Banach spaces and normed spaces to Hausdorff topological vector spaces. 相似文献
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We prove several existence theorems for second order differential inclusions of the form , when K and F are set-valued mappings taking nonconvex and convex values, respectively, in a Hilbert space H. To cite this article: M. Bounkhel, D. Laouir-Azzam, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
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Jean-Philippe Chancelier Marouen Messaoud Agnès Sulem 《Mathematical Methods of Operations Research》2007,65(2):239-259
The aim of this paper is to solve the fixed point problems:
where
is a finite set, L is contractive and B is a nonexpansive operator and
where
and
are general control sets, the operators L
w
are contractive and operators B
z
are nonexpansive. For these two problems, we give conditions which imply existence and uniqueness of a solution and provide
a policy iteration algorithm which converges to the solution. The proofs are slightly different for the two problems since
the set of controls is finite for (1) while it is not necessary the case for problem (2). Equation (2) typically arises in
numerical analysis of quasi variational inequalities and variational inequalities associated to impulse or singular stochastic
control. 相似文献
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In this Note, we prove a theorem on the extension of a negative (or positive) plurisubharmonic current T (i.e. such that ) with condition on the slices with respect to some coordinates. This theorem generalizes a result proved by El Mir–Ben Messaoud relative to d-closed positive currents with a condition on slices. The method consists first of proving a Chern–Levine–Nirenberg inequality for a positive (or negative) psh current, which is a generalization of results obtained by Bedford–Taylor, Demailly and Sibony for d-closed positive currents. Also we prove an Oka type inequality for positive psh currents, thereby generalizing former results by Ben Messaoud–El Mir concerning positive currents with a negative . To cite this article: M. Toujani, H. Ben Messaoud, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献