Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation

Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter equation. Such solutions do not depend on a spectral parameter, and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter. Here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups $D_n$. These results may be used to determine constant solutions of the Yang--Baxter equation. We then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter equation with spectral parameter and give several examples, including a new 21-vertex model. We also describe this approach in terms of minimal-dimensional representations of the quantum doubles of the alternating group $A_4$ and the symmetric group $S_4$.Comment: 19 pages, no figures, changed introduction, added reference

Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry

The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model describes local interactions between non-Abelian anyons, with fusion rules given by the tensor product decompositions of the irreducible representations of D(D_3). The Bethe ansatz equations which characterise the exact solution are found through the use of functional relations satisfied by a set of mutually commuting transfer matrices.Comment: 19 page

Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure

Marketing Potential for Commercial Sorghum Malt in Northern Ghana

The study was conducted in four districts in the Northern and Volta regions of Ghana, to investigate the commercial potential of sorghum malt and the quality of sorghum and sorghum malt that small scale brewers prefer. The constraints these small scale maltsters and brewers encounter in their work were also investigated.  Purposeful sampling technique was employed to select the communities and snowball sampling was used to identify the brewers and maltsters in the communities. Two hundred and fifteen (215) respondents were interviewed in the four districts; three of the districts are located in the Northern Region and one district in the Volta Region of Ghana. The quality attributes of sorghum and sorghum malt preferred by the small scale breweries and maltsters include; good germination rate, presence of a characteristic flavor of malt, and that the malt should not look mouldy.  The sorghum grain should not contain foreign materials, whole/undamaged grain and that the grain should not look powdery. The quality factors of malt are very important as they determine the quality of the end product (pito) which is a determinant for good market. The common variety of sorghum used in the northern part of Volta region is the ‘Konkomba’ sorghum variety. While Naga red is most commonly used variety of sorghum in the Northern region followed by Chere and the mixture of Naga red and Chere. The constraints brewers and maltsters encountered in these areas include; shortage of sorghum, increase in sorghum price, malt losses due to bad weather during the raining season, poor market for pito during the raining season and lack of financial institutions to support them with funds. The commercial prospect for sorghum malt as revealed by the study indicates that 85% of the respondents were willing to purchase commercial sorghum malt. Key words: Sorghum varieties, Commercial sorghum malt, Marketing potentia

Programmable quantum gate arrays

We show how to construct quantum gate arrays that can be programmed to perform different unitary operations on a data register, depending on the input to some program register. It is shown that a universal quantum gate array - a gate array which can be programmed to perform any unitary operation - exists only if one allows the gate array to operate in a probabilistic fashion. The universal quantum gate array we construct requires an exponentially smaller number of gates than a classical universal gate array.Comment: 3 pages, REVTEX. Submitted to Phys. Rev. Let

Diversity Combiner in Adaptive Modulation over Fast and Frequency Selective Environment

Signal over fast and frequency selective channel suffers from Doppler and delay effects due to propagation mechanism such as reflection, refraction and diffraction resulting in poor quality reception. Maximal Ratio Combining (MRC) and Adaptive Modulation are some of the techniques previously used to address this problem, but each of these techniques suffers from signal fading and interference distortion as result of weak signal and delay spread respectively. Therefore, an Adaptive modulation technique which incorporates MRC is developed over fast and frequency selective Rayleigh fading channel. The system model in this study employed 10,000 bits randomly generated, gray encoded and modulated with M-ary Phase Shift Keying (M-PSK). The signals were filtered using square root raised cosine filter and then transmitted over fast and frequency selective Rayleigh fading channel. At the receiver, two paths at 100km/hr and 200km/hr were combined using MRC, the channel was estimated using Received Signal Strength Indicator (RSSI) to change the constellation size of the modulation in accordance with the severity of fading. The process was simulated using MATLAB software package. The performance of the proposed system was evaluated using Bit Error Rate (BER) at mobile speeds of 100km/hr and 200km/hr. At Signal to Noise Ratio (SNR) of 10dB, the BER values of 0.0003, 0.0013, 0.0686, and 0.3009 were obtained for conventional MRC with BPSK, QPSK, 8PSK, and 16PSK signaling scheme respectively as against 0.0011 for adaptive MPSK at a mobile speed of 100km/hr while at 200km/hr, the BER values of 0.0134, 0.0161, 0.1947, 0.4116 were obtained using MRC with BPSK, QPSK, 8PSK and 16PSK respectively as against 0.0134 for adaptive MPSK. In conclusion, adaptive modulation incorporating MRC gave the best result due to lower BER values obtained at all SNR considered. The effect of fast and frequency selective Rayleigh channel has been reduced at high speed. Keywords: Adaptive Modulation, Maximal Ratio Combining , M-PSK, Rayleigh Environment, Bit Error           Rate (BER), Signal to Noise Ratio (SNR)

Investigating the Convergence and Bit Error Rate of Adaptive Algorithms over Time Varying Rayleigh Fading Channel

The fastest growing segment of the communication industry is the mobile wireless communication system. However, the systems faced a lot of challenges such as delay in the propagation of signals due to time-varying channel and effect of high speed transmission over Rayleigh fading which result into Inter-Symbol Interference (ISI) distortion. Least Mean Square (LMS) and Normalized Least Mean Square (NLMS) have been previously used to adapt the system using the step size, and Eigen value. In this paper, the adaptive Algorithms over a time-varying channel were compared using convergence level, Bit Error Rate (BER), and Mean Square Error (MSE). The system model consists of bits to symbol converter, 16-QAM modulator and Raised Cosine transmit filter, all at the transmitter, time-varying Rayleigh fading with Additive White Gaussian Noise added, and at the receiver are Raised Cosine Receive filter, 16-QAM demodulator, then each of the Adaptive LMS and NLMS filters which received delay from the Random integer generator, and the integer/symbol to bit converter at the output. The system model was simulated using MATLAB/SIMULINK software package. The algorithms were evaluated using convergence MSE at SNR of 10, 20 and 30dB over different number of iterations to determine the convergence rate, constellation diagram and BER. The results obtained showed that the flat convergence level of LMS and NLMS at SNR of 10dB are obtained with 300 and 200 iterations respectively, while 200 and 150 iterations are obtained at SNR of 20 and at SNR 30, the convergence level are obtained at 150 and 100 iterations respectively. BER values of 0.1598 and 0.0858 are obtained for LMS and NLMS respectively. Therefore, LMS algorithm took more iterations than NLMS algorithm to achieve the same error, and also lower BER value of NLMS is also in agreement with the result. Keywords: Convergence, MSE, LMS algorithm, NLMS algorithm, Intersymbol interference (ISI)