Complex networks constructed from irrational number sequences

In this paper, we construct (d, r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r = 0,1,...,d-1), and the undirected edges indicate the adjacency between two consecutive groups. (3, r) and (4, r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.

on a class of pseudorandom sequences from elliptic curves over finite fields

Following the idea of Xing et al., we investigate a general method for constructing families of pseudorandom sequences with low correlation and large linear complexity from elliptic curves over finite fields in this correspondence. With the help of the tool of exponential sums on elliptic curves, we study their periods, linear complexities, linear complexity profiles, distributions of r-patterns, periodic correlation, partial period distributions, and aperiodic correlation in detail. The results show that they have nice randomness.

incomplete exponential sums over galois rings with applications to some binary sequences derived from z(2l)

IEEE Computer Society

Investigation of Interfacial Tensions for Carbon Dioxide Aqueous Solutions by Perturbed-Chain Statistical Associating Fluid Theory Combined with Density-Gradient Theory

The perturbed-chain statistical associating fluid theory and density-gradient theory are used to construct an equation of state (EOS) applicable for the phase behaviors of carbon dioxide aqueous solutions. With the molecular parameters and influence parameters respectively regressed from bulk properties and surface tensions of pure fluids as input, both the bulk and interfacial properties of carbon dioxide aqueous solutions are satisfactorily correlated by adjusting the binary interaction parameter (k(ij)). Our results show that the constructed EOS is able to describe the interfacial properties of carbon dioxide aqueous solutions in a wide temperature range, and illustrate the influences of temperature, pressure, and densities in each phase on the interfacial properties.

Continuous-flow polymerase chain reaction microfluidics by using spiral capillary channel embedded on copper

This paper presents a novel method for performing polymerase chain reaction (PCR) amplification by using spiral channel fabricated on copper where a transparent polytetrafluoroethylene ( PTFE) capillary tube was embedded. The channel with 25 PCR cycles was gradually developed in a spiral manner from inner to outer. The durations of PCR mixture at the denaturation, annealing and extension zones were gradually lengthened at a given flow rate, which may benefit continuous-flow PCR amplification as the synthesis ability of the Taq polymerase enzyme usually weakens with PCR time. Successful continuous-flow amplification of DNA fragments has been demonstrated. The PCR products of 249, 500 and 982 bp fragments could be obviously observed when the flow rates of PCR mixture were 7.5, 7.5 and 3.0 mm s(-1), respectively, and the required amplification times were about 25, 25, and 62 min, respectively. Besides, the successful segmented-flow PCR of three samples ( 249, 500 and 982 bp) has also been reported, which demonstrates the present continuous-flow PCR microfluidics can be developed for high-throughput genetic analysis.

Magnetic frustration induced quantum phase transitions in the S=1/2 vertically asymmetric diamond chain

This work was supported by the National Basic Research Program of China (973 Program) grant No. G2009CB929300 and the National Natural Science Foundation of China under Grant Nos. 60521001 and 60776061.

Nonlinear elastic waves in a monatomic chain with nonlinear interaction

Nonlinear wave equation for a one-dimensional anharmonic crystal lattice in terms of its microscopic parameters is obtained by means of a continuum approximation. Using a small time scale transformation, the nonlinear wave equation is reduced to a combined KdV equation and its single soliton solution yields the supersonic kink form of nonlinear elastic waves for the system.