Character expansion developed in real space renormalization group (RSRG) approach is applied to U(1) lattice gauge theory with θ-term in 2 dimensions. Topological charge distribution P (Q) is shown to be of Gaussian form at any β(inverse coupling constant). The partition function Z(θ) at large volume is shown to be given by the elliptic theta function. It provides the information of the zeros of partition function as an analytic function of ζ = e iθ (θ = theta parameter). These partition function zeros lead to the phase transition at θ = π. Analytical results will be compared with the MC simulation results. In MC simulation, we adopt (i)"set method" and (ii)"trial function method".

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The study aimed to determine the effect of reactive agility with the FITLIGHT training system on the speed of the visual reaction time and dribbling skill of basketball players. Participants were divided into an experimental group (n = 10; age, 14.80 ± 0.79 years; height, 163.80 ± 3.46 cm; weight, 55.90 ± 0.99 kg; training, 4.50 ± 0.53 years) and a control group (n = 10; age, 14.60 ± 0.70 years; height, 163.30 ± 3.47 cm; weight, 56.10 ± 0.74 kg; training, 4.30 ± 0.48 years). Reactive agility was assessed through a modified t-test, visual reaction time was assessed using the Li Lafayette instrument Visual Reaction Time Apparatus 63014 response panel, and dribbling skills were assessed through dribbling testing. The results showed improved agility through the modified agility t-test (11%; p = 0.001), an increased speed of visual reaction time for both the right and left hands (23–31%), and improved dribbling skills (19%; p = 0.001) for the experimental group using the FITLIGHT reactive agility software. The results also showed increased skills of the experimental group when compared to the control group. Differences in variability emerged between 6 and 14.1% in favor of the experimental group. Therefore, the researchers recommended that attention should be paid to activating the role of the FITLIGHT reactive agility training to improve and develop the physical, visual, and skill capabilities of basketball players. The researchers propose that FITLIGHT can be effectively used in the basketball training process.

The two dimensional CP' model with a B term is simulated. We compute the topological charge distribution P(Q) by employing the "set method" and "trial function method", which are effective in calculations for a very wide range of Q and large volume. The distribution P(Q) exhibits Gaussian behavior in the small /3 (inverse coupling constant) region and deviates from this in the large (3 region. The free energy and its moment are calculated as a function of B. For small /3, the partition function is given by the elliptic theta function, and the distribution of its zeroes on the complex B plane leads to a first order phase transition at B = TC. In the large (3 region, on the other hand, this first order phase transition disappears, but definite conclusion concerning the transition is not reached due to large errors. § 1. Introduction 175The two dimensional cpN-I model is a suitable laboratory to study dynamics of QCD. Topology is expected to play an important role in the non-perturbative nature of the dynamics of such theories. Numerical studies of the topological aspects of the cpN-l model have made much progress.l)-3 ) However, a full understanding of the dynamics of the model requires study of an additional contribution of the imaginary part of the action, i.e., the 8 term. The degeneracy of the different topological sectors is resolved into a unique vacuum labeled by the parameter 8. As shown by certain analytic studies, various models with the 8 term, in general, exhibit a rich phase structure. 4 H) It is then worthwhile to study effects of the e term on the cpN-I model. 8 > From a realistic point of view also, it is significant to clarify the matter of strong CP violation in QCD.Introduction of the 8 term precludes ordinary simulations because of the complex Boltzmann factor. An idea to circumvent this problem is to introduce the constrained updating of the fields, in which the topological charge, being a functional of the dynamical fields, is constrained to take a given value Q. Thus the phase factor eieQ is factored out so that the partition function is given by the summation of the probability distribution P( Q) weighted by e; 8 Q over all possible values of the topological charge Q. This algorithm was adopted in simulating the two dimensional U(l) gauge model. 4 > So far, topological aspects of the CP' model have been studied considerably, both theoretically and numerically. Most works, however, are limited to theories without the 8 term. This is one of our motives for studying the effects of the 8 term on the model by means of Monte Carlo simulations. We present here the results for P( Q) and the free energy F( 8) and its moments as a function of 0 by surveying a compara-

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Theoretical and experimental studies on the effect of the volute design parameters on the centrifugal compressor range of stable operation and pressure rise coefficient were investigated. In the theoretical study, the effect of the symmetric and tangent volute area ratios (AR) on the diffuser pressure recovery factor and flow stability was investigated. In the experimental study, different configurations of a symmetrical and tangent (overhung) volutes with different ARs from 0.4 to 0.8 were investigated. Comparisons between the two different types of volute design parameters on compressor stable flow range and pressure rise coefficient were made. Effect of the gab between the diffuser vanes and the volute casing on the compressor stability was investigated. This gap was changed from 0 to 0.4 of the impeller exit width in five tests. The pressure fluctuation leading to stall was observed at the vaneless region. Stall and surge were detected by analysing both the fluctuations of pressure signals and the power spectrum density. The effect of different volute configurations and clearance on stall initiation, and hence compressor stable operation, were discussed. The theoretical results show that the increase in the symmetric volute exit radius increases the pressure recovery factor in the diffuser. Experimental data show that the increase in the AR of symmetric and tangent volutes increases the compressor range of stable operation as well as pressure rise coefficient.

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