in this paper, we study b-focal curves of biharmonic b -general helices according to bishop frame in the heisenberg group heis   finally, we characterize the b-focal curves of biharmonic b- general helices in terms of bishop frame in the heisenberg group heis

We adopt the notion of combability of groups defined in [Ghys2]. An example is given of a combable group which is not residually finite. Two of the eight 3-dimensional geometries, e Sl2(R) and H ×R, are quasiisometric. Three dimensional geometries are classified up to quasiisometry. Seifert fibred manifolds over hyperbolic orbifolds have bicombable fundamental groups. Every combable group satis...

Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme for exactly reconstructing it from its discrete samples. We analyze the relationship between concentration (or compactness) in the temporal/spectral domains of the (i) continuous-time and (ii) discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which presc...

A natural generalization of the Heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long range order in the ground state of several 1D systems with continuous group symmetries. In this letter we use it to rule out the occurrence ...

In this paper, we establish a general weighted Hardy type inequality for the $ p- $Laplace operator with Robin boundary condition. We provide various concrete examples to illustrate our results different weights. Furthermore, present some Heisenberg-Pauli-Weyl inequalities terms on balls centred at origin radius R in \mathbb{R} ^n $.

We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did not seem to be feasible. As a consequence of our bilinear inequality one proves dimension-free boundedness for the Riesz-Hermite transforms on L with linear growth in terms of p. A feature of the proof...

In this work, by combining Carlson-type and Nash-type inequalities for the Weinstein transform $\mathscr{F}_W$ on $\mathbb{K}=\mathbb{R}^{d-1}\times[0,\infty)$, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also local-type $\mathscr{F}_W$, deduce a Heisenberg-Pauli-Weyl-type inequality transform.

We first present a generalization of the Robertson-Heisenberg uncertainty principle. This applies to mixed states and contains covariance term. For faithful states, we characterize when inequality is an equality. next principle version for real-valued observables. Sharp versions conjugates observables are considered. The theory illustrated with examples dichotomic close discussion coarse graini...

We formulate uncertainty relations for arbitrary N observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev....