We study in this paper a cutting-covering problem, defined by us in [2] and [3], the problem of covering a rectangular support with rectangular pieces cut from a roll. We first prove that the algorithm used in [2] and [3] for the rectangular cutting-covering problem without losses is not optimal. Starting from a decomposition of a natural number in sums of naturals we develop an algorithm for a...

In the paper we present the exact solutions of one-dimensional Non-linear Shrödinger Equation. The solutions correspond to the Bogoliubov excitations in Bose-gas with a local interaction. The obtained expression is used for evaluating the transmission coefficient of the excitations across a δ-functional potential barrier.

The lower frequency rQ 2-branch of the torsional split rotational spectrum of H OO H has been recorded for the first time near 1.05 THz with Doppler limited resolution employing a Backward Wave Oscillator as the radiation source. The position of the Q-branch lines can be predicted very closely from a set o f effective rotational constants derived individually for the two torsionally split level...

We address the question of exact controllability of the wave and Schrödinger equations perturbed by a singular inverse-square potential. Exact boundary controllability is proved in the range of subcritical coefficients of the singular potential and under suitable geometric conditions. The proof relies on the method of multipliers. The key point in the proof of the observability inequality is a ...

In a 4T pixel, the transfer gate (TG) “OFF” surface potential is one of the important parameters, which determines the pinned photodiode (PPD) full well capacity. The feed-forward effect measurement is a powerful tool to characterize the relationship of the PPD injection potential and the feed-forward electrons. In this paper, a parameter Vb is introduced to characterize the TG “OFF” surface po...

We characterize asymptotic collective behavior of rectangular random matrices, the sizes of which tend to infinity at different rates. It appears that one can compute the limits of all non commutative moments (thus all spectral properties) of the random matrices we consider because, when embedded in a space of larger square matrices, independent rectangular random matrices are asymptotically fr...

A plane graph is a planar graph with a fixed embedding in the plane. In a rectangular drawing of a plane graph, each vertex is drawn as a point, each edge is drawn as a horizontal or vertical line segment, and each face is drawn as a rectangle. A planar graph is said to have a rectangular drawing if at least one of its plane embeddings has a rectangular drawing. In this paper we give a linear-t...

This paper proposes two rectangular ring planar monopole antennas for wideband and ultra-wideband applications. Simple planar rectangular rings are used to design the planar antennas. These rectangular rings are designed in a way to achieve the wideband operations. The operating frequency band ranges from 1.85GHz to 4.95GHz and 3.12GHz to 14.15GHz. The gain varies from 1.83 dBi to 2.89 dBi for ...

The resonant modes of rectangular two-dimensional optical resonators were analyzed exactly. Based on the characteristics of the Bessel function, the resonant frequencies of the rectangular microcavities are expressed in a simple way. In addition, a simple rule to judge when the finite length of a rectangular resonator can be considered infinite is given in realistic applications. The solution t...

Rectangular arrays of Ni dots with small interdot separation have been fabricated in superconducting Nb films. The geometry of these rectangular arrays defines deep pinning potential channels. Two effects have been observed. ~i! When the vortices move perpendicular to the channels ~i.e., along the long side of the rectangular array! an enhancement of the background pinning is observed, as predi...