STATISTICAL PROPERTIES OF PSEUDORANDOM SEQUENCES

Random numbers (in one sense or another) have applications in computer simulation, Monte Carlo integration, cryptography, randomized computation, radar ranging, and other areas. It is impractical to generate random numbers in real life, instead sequences of numbers (or of bits) that appear to be ``random yet repeatable are used in real life applications. These sequences are called pseudorandom sequences. To determine the suitability of pseudorandom sequences for applications, we need to study their properties, in particular, their statistical properties. The simplest property is the minimal period of the sequence. That is, the shortest number of steps until the sequence repeats. One important type of pseudorandom sequences is the sequences generated by feedback with carry shift registers (FCSRs). In this dissertation, we study statistical properties of N-ary FCSR sequences with odd prime connection integer q and least period (q-1)/2. These are called half-ℓ-sequences. More precisely, our work includes: The number of occurrences of one symbol within one period of a half-ℓ-sequence; The number of pairs of symbols with a fixed distance between them within one period of a half-ℓ-sequence; The number of triples of consecutive symbols within one period of a half-ℓ-sequence. In particular we give a bound on the number of occurrences of one symbol within one period of a binary half-ℓ-sequence and also the autocorrelation value in binary case. The results show that the distributions of half-ℓ-sequences are fairly flat. However, these sequences in the binary case also have some undesirable features as high autocorrelation values. We give bounds on the number of occurrences of two symbols with a fixed distance between them in an ℓ-sequence, whose period reaches the maximum and obtain conditions on the connection integer that guarantee the distribution is highly uniform. In another study of a cryptographically important statistical property, we study a generalization of correlation immunity (CI). CI is a measure of resistance to Siegenthaler\u27s divide and conquer attack on nonlinear combiners. In this dissertation, we present results on correlation immune functions with regard to the q-transform, a generalization of the Walsh-Hadamard transform, to measure the proximity of two functions. We give two definitions of q-correlation immune functions and the relationship between them. Certain properties and constructions for q-correlation immune functions are discussed. We examine the connection between correlation immune functions and q-correlation immune functions

Research on the Relationship Among Dual Open Innovation, Social Ties and New Product Market Performance

With the increasing competition in the market and the reduction of product lifecycle, “open innovation” has become the dominant approach for increasing a company’s new product market performance. Social ties are the important external social capital of enterprises, which play key roles for enterprises maintaining advantages in the fierce competition environment. Under dual open innovation model, enterprises’ network mainly involves business ties, government ties and university ties. Based on social capital theory, this article discusses the mediating mechanism of university ties, government ties, business ties in the process of dual open innovation influence new product market performance. We initially selected a random sample of 400 firms from 18 cities in East and Mid-China from a registration list of the local industrial and commercial bureau. In total, we had 270 valid questionnaires. Results show that both inbound and outbound open innovation openness have positive effect on business ties, government ties and university ties. Business ties and university ties have significant positive effect on new product market performance. Through the test of mediating effect, we found that the influence of inbound open innovation openness on new product market performance need to be played through business ties and university ties, the influence of outbound open innovation openness on new product market performance need to be played through business ties. Keywords: open innovation; business ties; government ties; university ties; new product market performanc

Mode Interferences of VLF Waves in the Presence of an Anisotropic Terrestrial Waveguide

It is known that the very low frequency (VLF) signals propagating at long distances over a terrestrial waveguide will experience a diurnal interference across the sunrise and sunset transitions. Early studies indicated that cascaded terrestrial waveguides can be applied to investigate the cycle-clip behaviors of amplitude and phase for VLF waves, with an abrupt effective height change by 20 km to represent the night and day transitions. Based on the knowledge, this chapter starts with some basic concepts on VLF wave propagation in the presence of an anisotropic terrestrial waveguide. Then, by performing the method of field matching at the discontinuous junctions, the coefficients of transmitted and scattered vectors are resulted from two derived matrix equations. Finally, the synthetic fields are calculated to simulate the VLF waves, which are subjected to an oblique geomagnetic field during long-distance propagation. The purpose of the present chapter is to illustrate the disturbing nature during sunrise and sunset for the VLF waves with periodic variations in amplitudes interfered by multimodes over long propagation paths

Restarted Hessenberg method for solving shifted nonsymmetric linear systems

It is known that the restarted full orthogonalization method (FOM) outperforms the restarted generalized minimum residual (GMRES) method in several circumstances for solving shifted linear systems when the shifts are handled simultaneously. Many variants of them have been proposed to enhance their performance. We show that another restarted method, the restarted Hessenberg method [M. Heyouni, M\'ethode de Hessenberg G\'en\'eralis\'ee et Applications, Ph.D. Thesis, Universit\'e des Sciences et Technologies de Lille, France, 1996] based on Hessenberg procedure, can effectively be employed, which can provide accelerating convergence rate with respect to the number of restarts. Theoretical analysis shows that the new residual of shifted restarted Hessenberg method is still collinear with each other. In these cases where the proposed algorithm needs less enough CPU time elapsed to converge than the earlier established restarted shifted FOM, weighted restarted shifted FOM, and some other popular shifted iterative solvers based on the short-term vector recurrence, as shown via extensive numerical experiments involving the recent popular applications of handling the time fractional differential equations.Comment: 19 pages, 7 tables. Some corrections for updating the reference

Theory of electric-field-induced metal-insulator transition in doped manganites

The insulator to metal transition (IMT) induced by the application of an electric field in doped manganites is investigated theoretically. Starting from the double-exchange mechanism with the long-range Coulomb interaction included, we find that the electric field may suppress the charge ordering and drive the system from the antiferromagnetic and charge-ordered state with an energy gap at the Fermi level to the ferromagnetic and gapless state, resulting in the IMT. A numerical simulation is performed for manganite films with intrinsic inhomogeneities, and an important impact of the inhomogeneities on this electric-field-induced transition is obtained. Our results can naturally account for the recently observed electric-filed-induced IMT phenomenon in manganites.published_or_final_versio