Some remarks on a representation of a group, II

On Some Characterization of Generalized Representation Wave-Packet Frames Based on Some Dilation Group

In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...

Some Remarks on Elementary Divisor Rings II

Some Remarks on Newton’s Algorithm - Ii

We consider Newton’s algorithm as well as a variant, the Gauss– Newton algorithm, to solve a system of nonlinear equations F (x) = 0, where x ∈ R , F : R → R. We use a line search method to ensure global convergence. The exact form of our algorithm depends on the rank of the Jacobian J(x) of F . Computational results on some standard test problems are presented, which show that the algorithm ma...

some remarks on regular subgroups of the affine group

‎let $v$ be a vector space over a field $f$ of characteristic $pgeq 0$ and let‎ ‎$t$ be a regular subgroup of the affine group $agl(v)$‎. ‎in the finite dimensional case we show that‎, ‎if $t$ is abelian or $p>0$‎, ‎then $t$ is unipotent‎. ‎for $t$ abelian‎, ‎pushing forward some ideas used in [a‎. ‎caranti‎, ‎f‎. ‎dalla volta and m‎. ‎sala‎, ‎abelian regular subgroups of the affine group and r...

SOME REMARKS ON a($(m))

It was conjectured in 1964 by A. Makowski & A. Schinzel [4] that, for every natural number vim). i • >-n " 2 " They remarked also that even the weaker result (i) i n f ^ W) > 0 (2) n is still unproved. Carl Pomerance [5] gave a proof of (2). Also S. W. Graham et al. [2] stated in the abstract, their result, .5 7 6 < l i m j r f « < U m s u p ^ i)) < 1, where P m is the product of the first m pr...