Let A be a Z-graded associative algebra and let ρ be an irreducible N-graded representation of A on W with finite-dimensional homogeneous subspaces. Then it is proved that ρ(Ã) = glJ (W ), where à is the completion of A with respect to a certain topology and glJ (W ) is the subalgebra of EndW , generated by homogeneous endomorphisms. It is also proved that an N-graded vector space W with finite...

1 m⇥ 1 vectors of ones a Speed of sound A m⇥ 1 vector of homogeneous tangent solution weights B m⇥ 1 vector with projection of tangent onto homogeneous tangent solutions CD Drag coe cient CL Lift coe cient D Drag D Design variable of interest f , F Objective functions or instantaneous contribution to objective functions G Objective function sensitivities g n⇥ 1 linearization of instantaneous co...

 ‎In this article‎, ‎we first‎ ‎show that non-Noetherian Artinian uniserial modules over‎ ‎commutative rings‎, ‎duo rings‎, ‎finite $R$-algebras and right‎ ‎Noetherian rings are $1$-atomic exactly like $Bbb Z_{p^{infty}}$‎. ‎Consequently‎, ‎we show that if $R$ is a right duo (or‎, ‎a right‎ ‎Noetherian) ring‎, ‎then the Noetherian dimension of an Artinian‎ ‎module with homogeneous uniserial dim...

A tournament Tis called homogeneous just in case every isomorphism of subtournaments of smaller cardinality can be lifted to an automorphism of T. It is shown that there are precisely three homogeneous tournaments of power N(). Some analogous results for 2-tournaments are obtained. In this paper we characterize countable tournaments which are homogeneous in the sense of Fraissé [1]. As far as w...

background: the heterogeneous composition of the human body presents numerous tissue types and cavities with widely differing radiologic properties. the aim of the present work was to develop a low cost homogeneous and heterogeneous phantom and the absorbed dose were measured by ionization chamber for different radiotherapy treatment techniques and compared with treatment planning system absorb...

We extend Picard's theorem on the existence of elliptic solutions of the second kind of linear homogeneous n th-order scalar ordinary diierential equations with coeecients being elliptic functions (associated with a common period lattice) to linear homogeneous rst-order n n systems. In particular, the qualitative structure of the general solution in terms of elliptic and exponential functions, ...

We classify the tube domains in C 4 with affinely homogeneous base whose boundary contains a non-degenerate affinely homogeneous hypersurface. It follows that these domains are holo-morphically homogeneous and amongst them there are four new examples of unbounded homogeneous domains (that do not have bounded realisations). These domains lie to either side of a pair of Levi-indefinite hypersurfa...

We prove that cubic homogeneous bent functions f : V2n → GF(2) exist for all n ≥ 3 except for n = 4.

It is proved that a compact Kähler manifold whose Ricci tensor has two distinct constant non-negative eigenvalues is locally the product of two Kähler–Einstein manifolds. A stronger result is established for the case of Kähler surfaces. Without the compactness assumption, irreducible Kähler manifolds with Ricci tensor having two distinct constant eigenvalues are shown to exist in various situat...

Hydrogenolysis is an important synthetic method in organic chemistry, and has been widely applied in industrial processes, natural product synthesis, and the removal of waste materials. In practice, most hydrogenolysis reactions have been used for the synthesis of racemic or achiral compounds. Very few studies on asymmetric homogeneous hydrogenolysis have been reported. The first example, repor...