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Vol.7 No.1
Abstract
An extension of <TEX>$H\"{o}lder's$</TEX> inequality whose discrete form is described as follows is given. Let <TEX>$\nu$</TEX> be a positive measure on a space Y, <TEX>$\nu(Y)\;\neq\;0$</TEX>, and let <TEX>$f_{j}$</TEX>(j = 1,2,...,n) be positive ν-integrable functions on Y. If <TEX>${\alpha}_j$</TEX> > 0(j = 1,2,...,n) and <TEX>${\beta}_j$</TEX>(j = 1,2,...,k < n) are related to be (equation omitted) then (equation omitted).
Abstract
Let M be an n-dimensional CR submanifold CR dimension n - l of a complex projective space M. We characterize M of <TEX>$\bar{M}$</TEX> in terms of an estimations of the length of the derivative of Ricci tensor of the length of Ricci tensor.
Abstract
The purpose of the paper is to show that in the Fraenkel-Mostowski topos, the category of the Boolean algebras has enough injectives.
Abstract
The quadratic fields generated by <TEX>$x^2$</TEX>=ax+1(<TEX>$\alpha\geq$</TEX>1) are studied. The regulators are relatively small and are known at one. The class numbers are relatively large and easy to compute. We shall find all the values of p, where p=<TEX>$\alpha^2$</TEX>+4 is a prime in <TEX>$\mathbb{Z}$</TEX>, such that <TEX>$\mathbb{Q}(\sprt{p})$</TEX> has class numbers 1, 3 and 5.
Abstract
We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.
Abstract
Johnson and Skoug [Pacific J. Math. 83(1979), 157-176] introduced the concept of scale-invariant measurability in Wiener space. And the applied their results in the theory of the Feynman integral. A converse measurability theorem for Wiener space due to the <TEX>$K{\ddot{o}}ehler$</TEX> and Yeh-Wiener space due to Skoug[Proc. Amer. Math. Soc 57(1976), 304-310] is one of the key concept to their discussion. In this paper, we will extend the results on converse measurability in Wiener space which Chang and Ryu[Proc. Amer. Math, Soc. 104(1998), 835-839] obtained to abstract Wiener space.
Abstract
We will characterize isomorphisms from the adjoint of a certain tridiag-onal algebra <TEX>$AlgL_{2n}$</TEX> onto <TEX>$AlgL_{2n}$</TEX>. In this paper the following are proved: A map <TEX>$\Phi{\;}:{\;}(AlgL_{2n})^{*}{\;}{\longrightarrow}{\;}AlgL_{2n}$</TEX> is an isomorphism if and only if there exists an operator S in <TEX>$AlgL_{2n}$</TEX> with all diagonal entries are 1 and an invertible backward diagonal operator B such that <TEX>${\Phi}(A){\;}={\;}SBAB^{-1}S^{-1}$</TEX>.
Abstract
Let(<TEX>$X^{\ast},\tau^{\ast}$</TEX>) be the space with one point Lindeloffication topology of space (X,<TEX>$\tau$</TEX>). This paper offers the definition of the space with one point Lin-deloffication topology of a topological space and proves that the retraction regu-lar closed function f: <TEX>$K^{\ast}(X^{\ast}$</TEX>) defined f(<TEX>$A^{\ast})=A^{\ast}$</TEX> if p <TEX>$\in A^{\ast}$</TEX> or (<TEX>$f(A^{\ast})=A^{\ast}-{p}$</TEX> if <TEX>$p \in A^{\ast}$</TEX> is a homomorphism. There are two examples in this paper to show that the retraction regular closed function f is neither a surjection nor an injection.