On characterizations of spectra and tilings

In a recent paper, Lagarias, Reeds and Wang established a characterization of spectra and tilings that can be used to prove a conjecture of Jorgensen and Pedersen by Keller's criterion. Different techniques to prove these facts have also been developed by Kolountzakis, Iosevich and Pedersen. The primary aim of this paper is to present an elementary method of describing certain characterizations of spectra and tilings. To illustrate this method, we first give a simple proof of this characterization. We then use the method to derive some characteristic results connected with the dual Fuglede's spectral-set conjecture. The results here extend several known conclusions in a simple manner.     

On genetic algorithms for the packing of polygons

A genetic algorithm for placing polygons on a rectangular board is proposed. The algorithm is improved by combination with deterministic methods.     

SCF-MO study of the polyglycine II structure

Summary In order to get insight into the conditions that make polyglycine (PG)II a stable structure, the conformational features of three model molecules closely related to the PGII conformation were investigated. The model molecules selected were glycine dipeptide (AGN), glycine tripeptide (AGGN), and glycine tetrapeptide (AGGGN). Environmental effects were mimicked by means of formaldehyde molecules. The calculations were carried out at the SCF semiempirical level, using the AM1 method. The calculations show that of the three systems considered, only the AGGGN molecule presents a minimum energy conformation which corresponds to a PGII structure. The environmental conditions in which this conformation is found were also analyzed.     

Simplex pivots on the set packing polytope

This paper considers the set packing problem max{wx: Ax b, x 0 and integral}, whereA is anm × n 0–1 matrix,w is a 1 ×n weight vector of real numbers andb is anm × 1 vector of ones. In equality form, its linear programming relaxation is max{wx: (x, y) P(A)} whereP(A) = {(x, y):Ax +I _m y =b, x0,y0}. Letx ¹ be any feasible solution to the set packing problem that is not optimal and lety ¹ =b – Ax ¹; then (x ¹,y ¹) is an integral extreme point ofP(A). We show that there exists a sequence of simplex pivots from (x ¹,y ¹) to (x*,y*), wherex* is an optimal solution to the set packing problem andy* =b – Ax*, that satisfies the following properties. Each pivot column has positive reduced weight and each pivot element equals plus one. The number of pivots equals the number of components ofx* that are nonbasic in (x ¹,y ¹).This research was supported by NSF Grants ECS-8005360 and ECS-8307473 to Cornell University.     

Fractional Brownian motion and packing dimension

LetX(t) (tR ^N ) be a fractional Brownian motion of index inR ^d . For any compact setER ^N , we compute the packing dimension ofX(E).Partially supported by an NSF grant.     

Packing measure of the sample paths of fractional Brownian motion

Let be a fractional Brownian motion of index in If , then there exists a positive finite constant such that with probability 1,

where and - is the -packing measure of .

     

On the Performance of Video Resolution,Motion and Dynamism in Transmission Using Near-Capacity Transceiver for Wireless Communication

This article investigates the performance of various sophisticated channel coding and transmission schemes for achieving reliable transmission of a highly compressed video stream. Novel error protection schemes including Non-Convergent Coding (NCC) scheme, Non-Convergent Coding assisted with Differential Space Time Spreading (DSTS) and Sphere Packing (SP) modulation (NCDSTS-SP) scheme and Convergent Coding assisted with DSTS and SP modulation (CDSTS-SP) are analyzed using Bit Error Ratio (BER) and Peak Signal to Noise Ratio (PSNR) performance metrics. Furthermore, error reduction is achieved using sophisticated transceiver comprising SP modulation technique assisted by Differential Space Time Spreading. The performance of the iterative Soft Bit Source Decoding (SBSD) in combination with channel codes is analyzed using various error protection setups by allocating consistent overall bit-rate budget. Additionally, the iterative behavior of SBSD assisted RSC decoder is analyzed with the aid of Extrinsic Information Transfer (EXIT) Chart in order to analyze the achievable turbo cliff of the iterative decoding process. The subjective and objective video quality performance of the proposed error protection schemes is analyzed while employing H.264 advanced video coding and H.265 high efficient video coding standards, while utilizing diverse video sequences having different resolution, motion and dynamism. It was observed that in the presence of noisy channel the low resolution videos outperforms its high resolution counterparts. Furthermore, it was observed that the performance of video sequence with low motion contents and dynamism outperforms relative to video sequence with high motion contents and dynamism. More specifically, it is observed that while utilizing H.265 video coding standard, the Non-Convergent Coding assisted with DSTS and SP modulation scheme with enhanced transmission mechanism results in Eb/N0 gain of 20 dB with reference to the Non-Convergent Coding and transmission mechanism at the objective PSNR value of 42 dB. It is important to mention that both the schemes have employed identical code rate. Furthermore, the Convergent Coding assisted with DSTS and SP modulation mechanism achieved superior performance with reference to the equivalent rate Non-Convergent Coding assisted with DSTS and SP modulation counterpart mechanism, with a performance gain of 16 dB at the objective PSNR grade of 42 dB. Moreover, it is observed that the maximum achievable PSNR gain through H.265 video coding standard is 45 dB, with a PSNR gain of 3 dB with reference to the identical code rate H.264 coding scheme.     

The Packing Coefficient of Liquid 2-Phenylnaphthalene Molecules at 396 K

A method of measuring the angular intensity distribution of monochromatic MoK f radiation, u = 0.71069 Å scattered by a thin layer of liquid 2-phenylnaphthalene C 10 H 7 -C 6 H 5 is proposed and results of such an experiment are presented. Fourier analysis of this distribution by the procedure of Warren-Krutter-Morningstar yielded electron-density radial-distribution function (EDRDF). The curve of radiation intensity was analysed by the pair functions method. The determined mean, mutual distances between molecules of liquid studied are: [rbar] 1 = 5.30 Å, [rbar] 2 = 7.43 Å, [rbar] 3 = 12.35 Å. X-ray structural analysis was applied to determine the packing coefficient of 2-phenylnaphthalene molecules at 396 K. From the known volume of the first coordination sphere as well as the specific volume of the molecule V 0 and taking into regard the structural model of intermolecular interactions, the most probable value of the packing coefficient of the molecules was found to be [kbar] = 0.64. This value falls in the range of [kbar] values permissible for liquid phase. The results concern a wide class of molecular liquids, in particular polar compounds being naphthalene derivatives.