• East Asian mathematical journal
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• v.31 no.1
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• pp.103-107
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• 2015

We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.

• Structural Engineering and Mechanics
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• v.28 no.4
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• pp.373-386
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• 2008

In this study stochastic analysis of non-linear dynamical systems under ${\alpha}$-stable, multiplicative white noise has been conducted. The analysis has dealt with a special class of ${\alpha}$-stable stochastic processes namely sub-Gaussian white noises. In this setting the governing equation either of the probability density function or of the characteristic function of the dynamical response may be obtained considering the dynamical system forced by a Gaussian white noise with an uncertain factor with ${\alpha}/2$- stable distribution. This consideration yields the probability density function or the characteristic function of the response by means of a simple integral involving the probability density function of the system under Gaussian white noise and the probability density function of the ${\alpha}/2$-stable random parameter. Some numerical applications have been reported assessing the reliability of the proposed formulation. Moreover a proper way to perform digital simulation of the sub-Gaussian ${\alpha}$-stable random process preventing dynamical systems from numerical overflows has been reported and discussed in detail.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.359-375
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• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.557-569
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• 2010

Suppose that n is a positive integer. For any real number $\alpha$($\beta$ resp.) with $\alpha$ < 1 ($\beta$ > 1 resp.), let $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with f(0) = f'(0) = $\cdots$ = $f^{(n-1)}(0)$ = $f^{(n)}(0)-1\;=\;0$, Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) > $\alpha$ (Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) < $\beta$ resp.) in $\mathbb{D}$, and for any ${\lambda}\;{\in}\;\bar{\mathbb{D}}$, let $K^{(n)}({\alpha},\;{\lambda})$ $K^{(n)}({\beta},\;{\lambda})$ resp.) denote a subclass of $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) whose elements satisfy some condition about derivatives. For any fixed $z_0\;{\in}\;\mathbb{D}$, we shall determine the two regions of variability $V^{(n)}(z_0,\;{\alpha})$, ($V^{(n)}(z_0,\;{\beta})$ resp.) and $V^{(n)}(z_0,\;{\alpha},\;{\lambda})$ ($V^{(n)}(z_0,\;{\beta},\;{\lambda})$ resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy $f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\alpha})$ ($f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\beta})$ resp.) when f ranges over the classes $K^{(n)}(\alpha)$ ($K^{(n)(\beta)$ resp.) and $K^{(n)}({\alpha},\;{\lambda})$ ($K^{(n)}({\beta},\;{\lambda})$ resp.), respectively.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.55-60
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• 1997

A continuum structure function(CSF) is a non-decreasing mapping from the unit hypercube to the unit interval. The reliability importance of component $i$ in a CSF at system level ${\alpha}$, $R_i({\alpha})$) say, is zero if and only if component $i$ is almost irrelevant to the system at level ${\alpha}$. A condition to check whether a component is almost irrelevant to the system is presented. It is shown that $R^{(m)}_i({\alpha}){\rightarrow}R_i({\alpha})$ uniformly as $m{\rightarrow}{\infty}$ where each $R^{(m)}_i({\alpha})$ is readily calculated.

• Journal of the Korean Society of Physical Medicine
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• v.4 no.3
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• pp.201-207
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• 2009

Purpose：The purpose of this study was to investigate the effect of $\alpha$-wave music and art appreciation on hand function in stroke with hemiplegia. Methods：A total of 32 stroke with hemiplegia participated in this study experimental group(16 subjects) received $\alpha$-wave music and art appreciation with general neurologic therapy. Control group(16 subjects) received general neurologic therapy. All subjects were assessed for hand function(manual dexterity, power grip, pinch grip, two point discrimination(parm, finger), tactile sense(parm, finger) using a purdue pegboard, dynamometer, pinch gauge, two-point anethesiometer and semmes-weinstein monofilament wire. The data were analyzed using paired and independent t-test. Results：The results were as follows : 1. In the experimental group, manual dexterity were significantly increased between pre and post intervention(p<.05). 2. In the experimental group, tactile sesne in finger were sifnificantly increased between pre and post intervention(p<.05). Conclusion：The results of this study shows that $\alpha$-wave music and art appreciation affect the hand function of hemiplegic side with regard to manual dexterity and tactile sense.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.229-241
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• 1997

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

• The Journal of Korean Physical Therapy
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• v.20 no.1
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• pp.75-79
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• 2008

Purpose: The purpose of this study was to investigate the effect of $\alpha$-wave music and art appreciation on hand function. Methods: A total of 22 university students participated in this study (10 males and 12 females). Twelve subjects received $\alpha$-wave music and art appreciation. The other subjects received neither. All subjects were assessed for hand function (manual dexterity, power grip, pinch, lateral pinch, tactile sense) using a Purdue pegboard, dynamometer, pinch gauge, and Semmes-Weinstein monofilament wire. The data were analyzed using paired and independent t-tests. Results: The results were as follows: 1. In the experimental group, manual dexterity and tactile sense were significantly increased between pre- and post-intervention (p<0.05). Within the control group, manual dexterity and power grip were significantly increased between pre- and post-test (p<0.05). 2. With regard to dexterity and tactile sense, the experimental group experienced a significant post-intervention increase compared to the control group (p<0.05). There was no significant difference in power grip, pinch, or lateral pinch changes between the two groups (p>0.05). Conclusion: The results of this study show that $\alpha$-wave music and art appreciation affect hand function with regard to manual dexterity and tactile sense.

• The Korean Journal of Pharmacology
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• v.12 no.2 s.20
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• pp.43-49
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• 1976

The facts that $PGE_2$ produced diuresis in the rabbit when given into a lateral ventricle of the brain and that $PGF_{2{\alpha}}$ is abundantly found in the brain prompted us to investigate the effects of $PGF_{2{\alpha}}$ introduced directly into the ventricle on the renal function. $PGF_{2{\alpha}}$ given intraventriculary in doses of $10{\mu}g\;and\;100{\mu}g$ elicited prompt diuresis, 10-fold increase of sodium excretion and two-fold increment of potassium excretion. Free water reabsorption also increased along with the increased osmolar clearance. Neither renal plasma flow nor glomerular filtration rate did change significantly. This, along with the fact that the percentage of reabsorbed sodium filtered decreased from 99.5 to 93.9, indicates the tubular site of the diuretic and natriuretic action. Atropine pretreatment did not influence the renal effects of intraventricular $PGF_{2{\alpha}}$. Intravenously administered $PGF_{2{\alpha}}$ in doses of 30 to $100{\mu}g$ did not produce any significant change in renal function. Intraventricular $PGF_{2{\alpha}}$ had no effect on the systemic blood pressure, whereas intravenous administration brought about a transient hypotension. These observations suggest that $PGF_{2{\alpha}}$ induces diuresis and natriuresis via central mechanism, that the site of the action resides in renal tubules, and that the reabsorption of sodium is inhibited in the proximal tubule, possibly through mediation of certain humoral agent. Overall, it is suggested that $PGF_{2{\alpha}}$ might play a roll in regulating renal function through the center.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.