Embedding of dendriform algebras into Rota-Baxter algebras

Following a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (in press), DOI: 10.1093/imrn/rnr266] we define what is a dendriform dior trialgebra corresponding to an arbitrary variety Var of binary algebras (associative, commutative, Poisson, etc.). We call such algebras di- or tri-Var-dendriform algebras, respectively. We prove in general that the operad governing the variety of di- or tri-Var-dendriform algebras is Koszul dual to the operad governing di- or trialgebras corresponding to Var^!. We also prove that every di-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of weight zero in the variety Var, and every tri-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of nonzero weight in Var.     

On the nonstationary motion of a viscous incompressible liquid over a rotating ball

We consider the free boundary problem for the Navier–Stokes equations governing a nonstationary motion of a layer of a viscous incompressible liquid that covers the surface of a rigid ball rotating around a fixed axis with constant angular velocity ω. The liquid is subject to the gravitation force generated by the mass of the ball. The self-gravitation forces between the liquid particles and capillary forces on the free surface are not taken into account. We consider the problem of stability of the regime of the rigid rotation of the liquid with the same angular velocity and prove that it is stable if |ω| is less than a certain constant. Bibliography: 10 titles. Translated from Problems in Mathematical Analysis 39 February, 2009, pp. 91–145.     

Mass transfer effects in preparative chromatography of eremomycin on polymeric sorbents

This work is devoted to the study of the regularities of the sorption of the new antibacterial antibiotic eremomycin on carboxylic sorbents. The main sorption kinetic equilibrium and dynamic parameters for realization of one-act preparative chromatographic process were determined and the difference between gel-like and structurally segregated carboxylic cation exchangers was analyzed. The optimal conditions for sorption and complete desorption of eremomycin were found.     

An estimate for the solutions of stokes equations in exterior domains

A boundary value problem for the Stokes equations is examined in an exterior domain ⁿ with a uniform Dirichlet condition on the boundary and a homogeneous condition at infinity. It is shown that estimating the norm L _p() of the second derivatives of the velocity vector field by the same norm of the exterior forces vector field is correct for p < n/2, but not for p n/2. This estimate is valid also for p n/2 if the boundary conditions are modified at infinity. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akademii Nauk SSSR, Vol. 180, pp. 105–120, 1990.     

Cyclic and acyclic sulfonimides in reactions with Rh(II)-ketocarbenoids: a new access to chemoselective O-functionalization of the imidic carbonyl groups

Catalytic decomposition of diazoacetylacetone, diazoacetoacetic, diazomalonic, and diazoacetic esters using dirhodium tetraacetate in the presence of isothiazol-3(2H)-one 1,1-dioxides and a number of N-(arenesulfonyl)carboxamides in solutions of methylene chloride or dichloroethane gives rise to O-alkylation of the imidic carbonyl groups by Rh(II)-carbenoids and the formation of O-alkylimidates as the final products. The reaction proceeds with high chemoselectivity via carbonyl ylides and offers a powerful method for the synthesis in good yields of the imidates with polyfunctional O-alkyl groups. On the basis of X-ray analysis and 1H- and 13C-NMR studies it was shown that the resulting acyclic O-alkylimidates have the E-configuration in the solid state and in solution. Unlike acyclic analogues, the cyclic carbonyl ylide derived from substituted diazosaccharin by intramolecular cyclization of the appropriate diketocarbenoid is capable of reacting with DMAD in a 1,3-cycloaddition process.     

An estimate of the solutions of a stationary problem for the Navier-Stokes equations

It is shown that the solutions of a nonlinear stationary problem for the Navier-Stokes equations in a bounded domain Ω ? ?³ with boundary conditions $\vec \upsilon \left| {_{\partial \Omega } } \right. = \vec a(x)$ satisfy the inequality $\left. {_{x \in \Omega }^{\sup } } \right|\left. {\vec v(x)} \right| \leqslant c\left( {\left. {_{x \in \partial \Omega }^{\sup } } \right|\left. {\vec a(x)} \right|} \right)$ for arbitrary Reynolds numbers. Bibliography: 9 titles.     

Restricted Set Addition in Groups I: The Classical Setting

The existing results are surveyed and several new results areproved for the cardinality of the restricted doubling 2^A ={a' + a':a',a' A,a' a'}, where A G is a subset of theset of elements of an (additively written) group G. In particular,known estimates for G = Z and G = Z/pZ are improved and a first-of-a-kindgeneral estimate valid for arbitrary G is given.     

Sum-free sets in abelian groups

We show that there is an absolute constant δ>0 such that the number of sum-free subsets of any finite abelian groupG is