Number Theoretic Model of Concurrent Access in Hypercube Interconnection Network

This paper proposes a mathematical logical model to use shared communication links in the hypercube interconnection network. To achieve our objective we have used the orthogonal property of binary coding used to label the processing nodes of the hypercube and applied binary coding based multiplexing technique and the XOR logic operation to separate the individual processing nodes data from the multiplexed signal. Keywords: Gray codes, Hypercube, 1’s complement logic, GIG codes, bipolar codes, orthogonal codes, Normalized inner product, Parallel computing System.

Optimization and Distance Function Proce-dures in Aberration Criteria of Efficient Frac-tional Factorial Design

An efficient orthogonal array was constructed with near balance and near the orthogonal property for the lowest common multiples of runs, using the balance coefficient criteria for determining near balance and J2 optimality criteria for orthogonal properties. The optimization and distance function forms of balance coefficient criteria were used for the classification of the designs. The Minimum Moment Aberration (MMA) and Minimum Aberration Projection (MAP) are compared using the optimization and distance function to determine the near balance criteria. The result indicated that, the MMA and MAP criteria was efficient using the optimization procedure of the balance coefficient.

A Prototype Orthogonal Vertical Beamforming for Indoor Wireless Communications

The concept of Orthogonal Vertical Beamforming (OVB) is proposed in this paper to eliminate interference when users remain at the same angle in the horizontal plane but are positioned at different distances. This orthogonal property helps systems avoid interference in the vertical direction of the mainbeam. A fully constructed prototype tested in a real indoor environment validates the proposed concept, revealing that the proposed OVB provides higher Signal Interference plus Noise Ratio (SINR) and Packet Error Rate (PER) in the vertical plane than conventional vertical beamforming and Orthogonal Beamforming.

The chaotic masking message model using orthogonal functions

The model for chaotic signal masking is proposed in the article. The digital signal in the bit representation is encoded using a family of orthogonal functions. Random white noise is superimposed on the resulting analog signal. The white noise amplitude is significantly greater than the amplitude of the signal. The functions orthogonal property is used to retrieve a useful signal. The advantage proposed this model is that it is not necessary to match the noise generators in the source and in the receiver of the message. The integration operation is required to retrieve the message. The using a simple rectangle scheme is discussed. The comparative computer experiment is based on two families of orthogonal functions: simple trigonometric functions and orthogonal Lagrange polynomials. It has been shown that using the trigonometric function family results in fewer errors when retrieving a message.

d-orthogonality of a generalization of both Laguerre and Hermite polynomials

In this work, we give a unification and generalization of Laguerre and Hermite polynomials for which the orthogonal property is replaced by d-orthogonality. We state some properties of these new polynomials.

Quantum codes from cyclic codes over the ring Fp[u]/〈u3 − u〉

In this paper, we study nonbinary quantum codes from cyclic codes over the ring [Formula: see text] for odd prime [Formula: see text]. We give the constructional properties of linear and cyclic codes over the ring [Formula: see text]. As an applications of these classes of codes, we obtain quantum codes over [Formula: see text] using self-orthogonal property. Moreover, we find some new nonbinary quantum codes with better parameters than the known quantum codes over [Formula: see text].

Reverberation Intensity Decaying in Range-Dependent Waveguide

In this paper, an analytic range-independent reverberation model based on the first-order perturbation theory is extended to range-dependent waveguide. This model considers the effect of bottom composite roughness: small-scale bottom rough surface provides dominating energy for reverberation, whereas large-scale roughness has the effect of forward and back propagation. For slowly varying bottom and short signal pulse, analytic small-scale roughness backscattering theory is adapted in range-dependent waveguides. A parabolic equation is used to calculate Green functions in range-dependent waveguides, and the orthogonal property of local normal modes is employed to estimate the modal spectrum of PE field. Synthetic tests demonstrate that the proposed reverberation model works well, and it can also predict the reverberation of range-independent waveguide as a special case.

Dynamic Characteristic Study of Riser with Complex Pre-stress Distribution

In this study, the dynamic characteristic problem of riser structure with complex pre-stress distribution is investigated. At first, the differential equation of the riser structure with complex pre-stress distribution is derived. The analytical expression of the free vibration of a riser structure with complex pre-stress distribution is discussed by using the orthogonal property of the trigonometric series. A top-tensioned riser (TTR) for example, the influences of the amplitude and direction of complex pre-stress on natural frequency and mode shape characteristics are compared. This study provides a new method for addressing the riser structure response problem with complex loading.

Oblique interaction between water waves and a partially submerged rectangular breakwater

A problem of oblique wave scattering by a rectangular breakwater floating in water of uneven depth is solved by applying matched eigenfunction expansion method. Three positions of breakwater are considered. The width and draft of breakwater are assumed to be finite, whereas its length is infinite. Breakwater is studied in the settings of without backwall and with a backwall. By using matching conditions at interface boundaries and making use of orthogonal property of eigenfunctions, the problem is converted to a system of algebraic equations. Breakwater’s position is proposed for which wave reflection, transmission, and force on wall are optimized. The breakwater with certain width and draft reflects more wave energy than the one with zero-draft. In the case of absence of wall, breakwater at lee side to the step induces least transmission of waves. In the case of presence of wall, suitable position of breakwater is suggested based on a range of wave frequency to mitigate force on wall. Optimum distances between wall and breakwater are found to attain less force on wall. Using Green’s identity, energy balance relation is derived to check accuracy in results. The findings are likely to be useful to assess the performance of a breakwater in different positions in water of uneven depth.