- P-ISSN1226-0657
- E-ISSN2287-6081
- KCI
4권 1호
초록
Abstract
We will construct the generalized law of cosines in a tetrahedron, in a natural way, which gives three dimensional Pythagoras' theorem and enables us to calculate the volume of an arbitrary tetrahedron.
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Abstract
Consider an <TEX>$r\;\times\;c$</TEX> contingency table under the full multinomial model in which each classification is ordered. The problem is to test the null hypothesis of independence. A number of tests have been proposed for this problem. In this article we show that all of these tests can be improved on in some sense for most cases. In fact the preceding tests sometimes are inadmissible in a strict sense. Furthermore, we show by example that in some cases improved tests can yield substantially improved power functions.
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In this paper, we characterize the existence of fixed points of a multivalued function by the existence of complete preorder on the given domain. Also we investigate relations between the completeness of a given order and the fixed point property of some multivalued functions.
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We consider the common and different results between the oscillation of galloping cable and the oscillation of suspension bridge cable through the long-term behavior. Numerical results are presented by using the second-order Runge-Kutta method under various initial conditions. There appeared to be nonlinear forms. Periodicity, symmetry, and longitudinality are differently appeared in two kinds of cables.
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Abstract
In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.
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Abstract
In this paper, we study the dynamics of a two-parameter unfolding system <TEX>$\chi$</TEX>' = y, y' = <TEX>$\beta$</TEX>y＋<TEX>$\alpha$</TEX>f(<TEX>$\chi\alpha\pm\chiy$</TEX>＋yg(<TEX>$\chi$</TEX>), where f(<TEX>$\chi$</TEX>,<TEX>$\alpha$</TEX>) is a second order polynomial in <TEX>$\chi$</TEX> and g(<TEX>$\chi$</TEX>) is strictly nonlinear in <TEX>$\chi$</TEX>. We show that the higher order term yg(<TEX>$\chi$</TEX>) in the system does not change qulitative structure of the Hopf bifurcations near the fixed points for small <TEX>$\alpha$</TEX> and <TEX>$\beta$</TEX> if the nontrivial fixed point approaches to the origin as <TEX>$\alpha$</TEX> approaches zero.
초록
Abstract
A new proof of the well-known identity involved in the Beta function B(p, q) is given by using the theory of hypergeometric series and a brief history of Gamma function is also provided. The method here is shown to be able to apply to evaluate some definite integrals.
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Abstract
In this work we will show that, in the sense of the Maximum overestimation factor, the absolute root bound functional derived from the new formula for the divided difference is better than the other known results in this area.
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Abstract
Some function of a complete finite measure space (for short, CFMS) into the duals and pre-duals of weakly compactly generated (for short, WCG) spaces are considered. We shall show that a universally weakly measurable function f of a CFMS into the dual of a WCG space has RS property and bounded weakly measurable functions of a CFMS into the pre-duals of WCG spaces are always Pettis integrable.
초록
Abstract
An atomic integral domain R is a half-factorial domain (HFD) if whenever <TEX>$\chi_1$</TEX>… <TEX>$\chi_{m}=y_1$</TEX>…<TEX>$y_n$</TEX> with each <TEX>$\chi_{i},y_j \in R$<TEX> irreducible, then m = n. In this paper, we show that if R[X] is an HFD, then <TEX>$Cl_{t}(R)$</TEX> <TEX>$\cong$</TEX> <TEX>$Cl_{t}$</TEX>(R[X]), and if <TEX>$G_1$</TEX> and <TEX>$G_2$</TEX> are torsion abelian groups, then there exists a Dedekind HFD R such that Cl(R) = <TEX>$G_1\bigoplus\; G_2$</TEX>.
초록
Abstract
The large deviations theorem of Cramer is extended to conditional probabilities in the following sense. Consider a random sample of pairs of random vectors and the sample means of each of the pairs. The probability that the first falls outside a certain convex set given that the second is fixed is shown to decrease with the sample size at an exponential rate which depends on the Kullback-Leibler distance between two distributions in an associated exponential familiy of distributions. Examples are given which include a method of computing the Bahadur exact slope for tests of certain composite hypotheses in exponential families.