The photophysical behaviour of a new pyrene derivative, 1-(4-N,N-dimethylaminophenylethynyl)pyrene (DMAPEPy), in various solvents has been studied. Due to the presence of an ethynyl link with a cylindrical pi cloud between the donor (N,N-dimethyl group) and the acceptor (pyrene), the molecule shows efficient intramolecular charge transfer, with a high extinction coefficient in all the solvents....

a polynomial   1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let   r be a prime k-algebra over a commutative ring   k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that   d is a nonzero derivation on r such that ...

In this article a review on the definition of the X- ray transform and some ofits applications in Nano crystallography is presented. We shall show that the X- raytransform is a special case of the Radon transform on homogeneous spaces when thetopological group E(n)- the Euclidean group - acts on ℝ2 transitively. First someproperties of the Radon transform are investigated then the relationship ...

Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights W = (w1, . . . , wn), W -homogeneous polynomials are polynomials which are homogeneous w.r.t the weighted degree degW (X α1 1 . . . X αn n ) = ∑ wiαi. Gröbner bases for weighted h...

Using the T -algebra machinery we show that the only strictly convex homogeneous cones in R with n ≥ 3 are the 2-cones, also known as Lorentz cones or second order cones. In particular, this shows that the p-cones are not homogeneous when p 6= 2, 1 < p <∞ and n ≥ 3, thus answering a problem proposed by Gowda and Trott.

Let Rn,d be the ring of invariants of d-tuples of n × n matrices under the simultaneous conjugation action of the general linear group. A minimal generating system and a homogeneous system of parameters of R3,3 are determined. Homogeneous systems of parameters of R3,2, R4,2 are also pointed out.

Let A = K[x1, . . . , xn] denote the polynomial ring in n variables over a field K with each deg xi = 1. Let I be a homogeneous ideal of A with I 6= A and HA/I the Hilbert function of the quotient algebra A/I. Given a numerical function H : N → N satisfying H = HA/I for some homogeneous ideal I of A, we write AH for the set of those integers 0 ≤ r ≤ n such that there exists a homogeneous ideal ...

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM [p] = α, then for some 1 ≤ n < ω the type p has n, but not n+ 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,א0)-homogeneous mod...

let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . in this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . as an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via the linear operator .