Universality of Coproducts in Categories of Lax Algebras

Categories of lax km1wu08161g3u66l/10485_2006_9019_Article_IEq1.gif" alt="$(T,V\,)$" align="middle" border="0">-algebras are shown to have pullback-stable coproducts if km1wu08161g3u66l/10485_2006_9019_Article_IEq2.gif" alt="$T$" align="middle" border="0"> preserves inverse images. The general result not only gives a common proof of this property in many topological categories but also shows that important topological categories, like the category of uniform spaces, are not presentable as a category of lax km1wu08161g3u66l/10485_2006_9019_Article_IEq3.gif" alt="$(T,V\,)$" align="middle" border="0">-algebras, with km1wu08161g3u66l/10485_2006_9019_Article_IEq4.gif" alt="$T$" align="middle" border="0"> preserving inverse images. Moreover, we show that any such category of km1wu08161g3u66l/10485_2006_9019_Article_IEq5.gif" alt="$(T,V\,)$" align="middle" border="0">-algebras has a concrete, coproduct preserving functor into the category of topological spaces.     

Synthesis of Spiro and Fused Five Membered <Emphasis Type="Italic">N</Emphasis>-Heterocycles from Alkylidenephosphoranes

Summary. km7f0berlwy/xxlarge8194.gif" alt="ensp" align="MIDDLE" BORDER="0">Triketoindan-2-oxime reacted readily with ethoxycarbonylmethylene triphenylphosphorane to give mainly the corresponding spiro-pyrrole (38%) along with the fused 1km7f0berlwy/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-hydroxydihydropyrrole (14%), whereas the spiro-dimer (29%) was obtained from the reaction of the oxime with methoxycarbonylmethylenetriphenyl phosphorane in addition to the corresponding 1km7f0berlwy/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-hydroxydihydropyrrole (31%). Conversely, Wittig products, mono-olefin (52%) and diolefin (<7%) along with the reduced substrate (10%), were observed when the oxime was treated with a cyano ylide. The reactions of the oxime with allyl- and vinyl phosphonium salts proceeded under phase-transfer catalysis to afford fused oxazole (46%) and spiro[2]oxazole (17%), while with the latter the fused 1km7f0berlwy/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-hydroxypyrrole (55%) was produced.Received February 26, 2003; accepted (revised) March 19, 2003 Published online August 28, 2003     

Optimality criteria and duality in multiple-objective optimization involving generalized invexity

A multiple-objective optimization problem involving generalized invex functions is considered. Kuhn-Tucker type necessary and sufficient conditions are obtained for a feasible point to be an efficient or properly efficient solution. Two dual programs are obtained. The results are given under weaker invexity assumptions.     

Synthesis of 2-O-ethyl analogues of 3′-azido- and 3′-fluoro-2′,3′-dideoxyuridines and evaluation of their biological activity against HIV

Summary 2-O-Ethyluracil and 2-O-ethylthymine were silylated with 1,1,1,3,3,3-hexamethyldisilazane and condensed in the presence ofTMS triflate with 2,3-dideoxy-3-fluoro-D-erythro-pentofuranoside, 3-azido-2,3-dideoxy-D-erythro-pentofuranoside, and 2,3-dideoxy-3-phthalimido-km75371m88/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-D-erythro-pentofuranose derivatives to give the corresponding 2-O-ethyl nucleosides. Deprotection with saturated methanolic ammonia afforded the 2km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">,3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dideoxy-3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-fluoro-2-O-ethyluridines, whereas 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-azido-2km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">,3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dideoxy-3-O-ethyluridine was obtained by deprotection with tetrabutylammonium fluoride in tetrahydrofuran. 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Amino-2km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">,3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dideoxy-3-O-ethyluridine could be obtained only by treatment of the corresponding 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-azido nucleoside with triphenylphosphine in pyridine. 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Deoxy-2-O-ethyl-3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-fluorothymidine (6b) showed moderate activity against HIV-1.

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Synthese von 2-O-Ethyl-Analogen von 3km75371m88/xhuge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Azido- und 3km75371m88/xhuge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Fluor-2km75371m88/xhuge8242.gif" alt="prime" align="BASELINE" BORDER="0">3km75371m88/xhuge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dideoxyuridinen und Bestimmung ihrer biologischen Aktivität gegenüber HIV

Zusammenfassung 2-O-Ethyluracil und 2-O-Ethylthymin wurden mit 1,1,1,3,3,3-Hexamethyldisilazan silyliert und in Gegenwart vonTMS-triflat mit 2,3-Dideoxy-3-fluoro-D-erythro-pentofuranosid, 3-Azido-2,3-dideoxy-D-erythro-pentofuranosid und 2,3-Dideoxy-3-phthalimido-km75371m88/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-D-erythro-pentofuranosederivaten zu den entsprechenden 2-O-Ethyl-Nucleosiden umgesetzt. Entfernung der Schutzgruppe mit gesättigter methanolischer Ammoniaklösung lieferte 2km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">,3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Dideoxy-3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-fluor-2-O-ethyluridin; 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Azido-2km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">,3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dideoxy-3-O-ethyl-uridin wurde durch Entschützung mit Tetrabutylammoniumfluorid in Tetrahydrofuran erhalten. 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Amino-2km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">,3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-dideoxy-3-O-ethyl-uridin konnte nur durch Behandeln des entsprechenden 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Azido-Nucleosids mit Triphenylphosphin in Pyridin hergestellt werden. 3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-Deoxy-2-O-ethyl-3km75371m88/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-fluor-thymidin (6b) zeigt geringe Aktivität gegenüber HIV-1.

     

Theory of weakly damped free-surface flows: A new formulation based on potential flow solutions

Several theories for weakly damped free-surface flows have been formulated. In this Letter we use the linear approximation to the Navier-Stokes equations to derive a new set of equations for potential flow which include dissipation due to viscosity. A viscous correction is added not only to the irrotational pressure (Bernoulli's equation), but also to the kinematic boundary condition. The nonlinear Schrödinger (NLS) equation that one can derive from the new set of equations to describe the modulations of weakly nonlinear, weakly damped deep-water gravity waves turns out to be the classical damped version of the NLS equation that has been used by many authors without rigorous justification.     

A note on the attainability of states by equalizing processes

In this paper, we consider km7/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">regions of attainabilitykm7/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> in certain state spaces as a function of the initial state under a well-defined and physically relevant class of processes. These processes are the continuous and km7/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">chaos-enhancingkm7/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> processes (in the sense of Ruch and Uhlmann). It turns out that these sets have complicated geometrical structures: They are polyhedra which are generally non-convex. The proof — a rather geometrical one — is given. A theorem of Hardy, Littlewood, and Polya and properties of bistochastic matrices are used crucially.     

Inequality of Petrović and Giaccardi for Convex Function of Higher Order

In this paper we use Lidstone polynomials to prove further generalization of Giaccardi generalization of the well-known Petrovikm400r38/xxlarge263.gif" alt="cacute" align="BASELINE" BORDER="0">km400r38/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0">s inequality.