Alkylation of ethyl bromomalonate by alkylcobaloximes

Allylcobaloximes react under very mild conditions with ethyl bromomalonate to yield allyl-substituted ethylmalonates in good yield. In the case of crotyl-, 3,3 dimethyl, allyl- and cinnamyl-cobaloximes, the substitution occurs with total rearrangement of the allyl groups. Similar rearrangements are observed during the reactions of propargyl- and allenylcobaloximes with BrCH(CO₂Et)₂ yielding allenyl- and propargyl-malonic esters respectively.     

Boundedness of the wavelet integral operator on weighted function spaces

The purpose of this paper is to study the boundedness of the wavelet integral operator on the Besov, BMO, and H ¹ spaces. Furthermore, for the basic wavelet with compact support, the boundedness of the wavelet transform on the weighted Besov spaces and on the weighted BMO spaces associated with a tempered weight function is also established.     

Cohen-Macaulay and Gorenstein property of Rees algebras of non-singular equimultiple prime ideals

We give criteria for the Cohen-Macaulay and Gorenstein property of Rees algebras of height 2 non-singular equimultiple prime ideals in terms of explicite representations of the associated graded rings. As consequences, we show that in general, the Cohen-Macaulay resp. Gorenstein property of such Rees algebras does not imply the Cohen-Macaulay resp. Gorenstein property of the base ring and that these properties depend upon the characteristic. Dedicated to the memrory of Professor Lê Van Thiêm Professor Lê Van Thiêm was the first directorof Hanoi Institute of Mathematics     

Hardy spaces of spaces of homogeneous type

Let be a space of homogeneous type, and be the generator of a semigroup with Gaussian kernel bounds on . We define the Hardy spaces of for a range of , by means of area integral function associated with the Poisson semigroup of , which is proved to coincide with the usual atomic Hardy spaces on spaces of homogeneous type.

     

On a class of graphs with prescribed mean curvature

We study a class of quasilinear elliptic equations on the unit ball of ℝ ⁿ in the divergence form ∑ _j=1 ⁿ D _j{G(|x|²,|Du|²)D _j u} =H(|x|) and get estimates on the boundary by using a modified barrier-function technique of Bernstein. We establish a maximum principle for the gradients of solutions and get a global gradient estimate. We prove that solutions with constant boundary condition must be radial. Finally, we apply these results to graphs {(x,u(x)):x∈H ⁿ } whereu:H ⁿ →ℝ is a smooth map of then-hyperbolic spaceH ⁿ =B(0,1) with the metric to get the existence of graphs with radial prescribed mean curvature.     

Structural and compositional heterogeneities in liquid aluminosilicate: insight from a grain structure model

Network structure as well as structural and compositional heterogeneities in aluminosilicate (Al₂O₃-2SiO₂) under compression is investigated by analysis and visualization of simulation data. Structural and compositional heterogeneities are clarified through analysis of topology structure and size distribution of TO _x -clusters (T = Si, Al; x = 3, 4, 5, 6) as well as OT _y -clusters (y = 2, 3, 4). The TO _x -cluster can be considered as TO _x -grains. It appears that the structure of aluminosilicate is the mixture of TO _x -grains with a different short-range order structure and this is the origin of structural heterogeneity. Regarding their composition, the OSi _y - and OAl _y -clusters can be considered as silica- and alumina-grains respectively, and the structure of aluminosilicate can thus be considered to be formed from silica- and alumina-grains. This results in compositional heterogeneity. Moreover, the degree of polymerization and polyamorphism as well as dynamic heterogeneity is also discussed in detail.     

Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.