We study dilations of cyclic polytopes with the vertices defined by a generator simplest cubic fields. In particular, for specific range values, we give precise number contained lattice points.

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of (C^ast)-dynamical systems with abelian groups on Hilbert (C^ast)-modules‎. ‎We show that if ((mathcal{A}‎, ‎G,alpha)) is a (C^ast)-dynamical system with (G) an abelian group‎, ‎then every completely positive definite covariant representation ((pi,varphi,E)) of ((mathcal{A}‎, ‎G,alpha)) on a Hilbert ...

Bronchial artery aneurysm (BAA) is a rare but potentially life-threatening clinical entity. Patients with multiple BAAs and multiple aneurysmal dilations are even rarer. In this case report, we will investigate a case of multiple BAAs and multiple aneurysmal dilations arising from 2 right bronchial artery branches presenting with hemoptysis. The patient was successfully treated with transcathet...

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ∈ L(R), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple constr...

BACKGROUND Urethral dilation has been recommended to treat voiding dysfunction that may occur after placement of tension-free vaginal tape (TVT) for the treatment of stress urinary incontinence. We report on a case of urethral erosion by the tape secondary to repetitive urethral dilations after surgery. CASE A urethral erosion by the tape was diagnosed by cystoscopy after three urethral dilat...

Abstract We consider the complex case of the S-inequality. It concerns the behaviour of Gaussian measures of dilations of convex and rotationally symmetric sets in Cn. We pose and discuss a conjecture that among all such sets measures of cylinders (i.e. the sets {z ∈ Cn | |z1| ≤ p}) decrease the fastest under dilations. Our main result in this paper is that this conjecture holds under the addit...