Facile synthetic pathway to β-hydroxy-β-trifluoromethyl imines and their derivatives

Synthetic approach based on mediated addition of different trifluoromethylated building blocks to selected acyclic imines giving access to a variety of β-hydroxy-β-trifluoromethyl imines are elaborated. A reaction between fluorinated adducts and imines proceed easily giving the condensation products in good to excellent yields. β-Hydroxy-β-trifluoromethyl imines possessing trifluoromethyl group and exhibiting strong intramolecular hydrogen bonding are great precursors to different β-hydroxy-β-trifluoromethyl ketones and alcohols.     

Asymptotics of Christoffel functions on arcs and curves

For a system of smooth Jordan curves and arcs asymptotics for Christoffel functions is established. A separate new method is developed to handle the upper and lower estimates. In the course to the upper bound a theorem of Widom on the norm of Chebyshev polynomials is generalized.     

Jordan李超代数的一些性质

代数A称为不可分解的,如果A不能分解成理想的直和.证明了满足C(L_o)=C(L)={0}的Jordan李超代数L一些重要性质.     

HBa(D)空间的内插定理

研究了一类由H^p空间构成的Ba空间的内插性质，给出了H^Ba(D)空间的三个内插定理。     

Safety neighbournoods for the invariants of the matrix similarity

We give safety neighbourhoods for the necessary conditions in the change of the Jordan canonical form of a matrix under small perturbations. We also obtain the minimum distance from an n × n complex matrix which has less than k nonconstant invariant factors (2≤ k≤ n) to the set of matrices which have more or equal to k. When k= 2, we get in particular the distance from a nonderogatory matrix to the set of derogatory matrices.     

On functional identities in left ideals of prime rings

In the present paper we describe surjective Lie and Jordan maps onto left ideals of prime noncommutative rings. Further, we describe bijective linear maps of left ideals of centrally closed prime algebras preserving commutativity.     

Decidability for modules over a group ring - III

ABSTRACT

Representations of simple Jordan superalgebras of Hermitian 3?×?3 matrices over the exceptional simple alternative superalgebras B (1,2) and B (4,2) of characteristic 3 are studied. Every irreducible bimodule over these superalgebras up to isomorphism is either a regular bimodule or its opposite. As corollaries,some analogues of the Kronecker factorization theorem are proved for Jordan superalgebras that contain H₃(B (1,2)) and H₃(B(4,2)).     

Explicit Hilbert spaces for certain unipotent representations III

In this paper we construct a family of small unitary representations for real semisimple Lie groups associated with Jordan algebras. These representations are realized on L²-spaces of certain orbits in the Jordan algebra. The representations are spherical and one of our key results is a precise L²-estimate for the Fourier transform of the spherical vector. We also consider the tensor products of these representations and describe their decomposition.     

Minimality conditions on circularly ordered structures

We explore analogues of o‐minimality and weak o‐minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ?? there are differences. Our main result is a structure theory (with infinitely many doubly transitive examples related to Jordan permutation groups) for ?₀‐categorical weakly circularly minimal structures. There is a 5‐homogeneous (or ‘5‐indiscernible’) example which is not 6‐homogeneous, but any example which is k‐homogeneous for some k ≥ 6 is k‐homogeneous for all k. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)