• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.285-294
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• 2016

We define new inductive mean constructed by a mean on a complete metric space, and see its convergence when the intrinsic mean is given. We also give many examples of inductive matrix means and claim that the limit of inductive mean constructed by the intrinsic mean is not the Karcher mean, in general.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.163-174
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• 1991

This is a continuation of the author's previous work [17]. In this paper, we consider mainly variational inequalities for single-valued functions. We first obtain a generalization of the variational type inequality of Juberg and Karamardian [10] and apply it to obtain strengthened versions of the Hartman-Stampacchia inequality and the Brouwer fixed point theorem. Next, we obtain fairly general versions of Browder's variational inequality [5] and its subsequent generalizations due to Brezis et al [4], Takahashk [23], Shih and Tan [19], Simons [20], and others. Finally, in this paper, we obtain a variational inequality for non-real locally convex t.v.s. which generalizes a result of Shih and Tan [19].

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.361-373
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• 1995

Three remarks are offered, pertaining to classes of estimators Pitman-dominating a given estimator. The first remark concerns incorporating general loss in the construction of such classes. The second remark concerns Pitman domination comparisons amongst the members of such classes. The third remark concerns construction of such a class in the location-scale case.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.347-353
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• 2011

In [1], Maffei proved a certain relationship between quiver varieties of type A and the geometry of partial flag varieties over the nilpotent cone. This relation was conjectured by Naka-jima, and Nakajima proved his conjecture for a simple case. In the Maffei's proof, the key step was a reduction of the general case of the conjecture to the simple case treated by Nakajima through a certain isomorphism. In this paper, we study properties of this isomorphism.

• East Asian mathematical journal
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• v.18 no.1
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• pp.1-13
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• 2002

Some Miller-Mocanu type arguments are used here in order to establish a general starlikeness condition involving the familiar Ruscheweyh derivative. Relevant connections with the various known starlikeness conditions are also indicated. This paper concludes with several remarks and observations in regard especially to the nonsharpness of the main starlike condition presented here.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.433-443
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• 2005

In 1994, Lim-Xu asked whether the Maluta's constant D(X) < 1 implies the fixed point property for asymptotically nonexpansive mappings and gave a partial solution for this question under an additional assumption for T, i.e., weakly asymptotic regularity of T. In this paper, we shall prove that the result due to Lim-Xu is also satisfied for more general non-Lipschitzian mappings in reflexive Banach spaces with weak uniform normal structure. Some applications of this result are also added.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.55-60
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• 1984

In [2], D. Downing and W.A. Kirk obtained a number of fixed point theorems for set-valued maps in matric and Banach spaces. The authors considered maps which are more general than the contractions with nonempty and closed mapping values, and obtain results for maps satisfying certain "inwardness" conditions. A key aspect of their approach is the application of a general fixed point theorem due to Caristi [1]. On the other hand, in [6], the present author obtained a number of equivalent formulations of the well-known result of I. Ekeland [3, 4] on the variational principle for approximate solutions of minimization problems. Some of such formulations include sharpened forms of the Caristi theorem. In this paper, using one of such formulations, we show that Theorems 1-3 and Corollaries 1-5 of [2] are substantially improved by giving geometric estimations of fixed points.ed points.

• Wind and Structures
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• v.10 no.2
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• pp.177-208
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• 2007

Few mathematical methods attracted theoretical and applied researches, both in the scientific and humanist fields, as the Proper Orthogonal Decomposition (POD) made throughout the last century. However, most of these fields often developed POD in autonomous ways and with different names, discovering more and more times what other scholars already knew in different sectors. This situation originated a broad band of methods and applications, whose collation requires working out a comprehensive viewpoint on the representation problem for random quantities. Based on these premises, this paper provides and discusses the theoretical foundations of POD in a homogeneous framework, emphasising the link between its general position and formulation and its prevalent use in wind engineering. Referring to this framework, some applications recently developed at the University of Genoa are shown and revised. General remarks and some prospects are finally drawn.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.991-1001
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• 2015

In this work we obtain conditions for nonspecial line bundles on general ${\kappa}$-gonal curves failing to be normally generated. Let L be a nonspecial very ample line bundle on a general ${\kappa}$-gonal curve X with ${\kappa}{\geq}4$ and $deg\mathcal{L}{\geq}{\frac{3}{2}}g+{\frac{g-2}{{\kappa}}}+1$. If L fails to be normally generated, then L is isomorphic to $\mathcal{K}_X-(ng^1_{\kappa}+B)+R$ for some $n{\geq}1$, B and R satisfying (1) $h^0(R)=h^0(B)=1$, (2) $n+3{\leq}degR{\leq}2n+2$, (3) $deg(R{\cap}F){\leq}1$ for any $F{\in}g^1_k $. Its converse also holds under some additional restrictions. As a corollary, a very ample line bundle $\mathcal{L}{\simeq}\mathcal{K}_X-g^0_d+{\xi}^0_e$ is normally generated if $g^0_d{\in}X^{(d)}$ and ${\xi}^0_e{\in}X^{(e)}$ satisfy $d{\leq}{\frac{g}{2}}-{\frac{g-2}{\kappa}}-3$, supp$(g^0_d{\cap}{\xi}^0_e)={\phi}$ and deg$(g^0_d{\cap}F){\leq}{\kappa}-2$ for any $F{\in}g^1_k$.

• Korean Journal of Logic
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• v.15 no.1
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• pp.155-190
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• 2012

As far as Hilbert's Program is concerned, there seems to be important differences in the development of Wittgenstein's thoughts. Wittgenstein's main claims on this theme in his middle period writings, such as Wittgenstein and the Vienna Circle, Philosophical Remarks and Philosophical Grammar seem to be different from the later writings such as Wittgenstein's Lectures on the Foundations of Mathematics (Cambridge 1939) and Remarks on the Foundations of Mathematics. To show that differences, I will first briefly survey Hilbert's program and his philosophy of mathematics, that is to say, formalism. Next, I will illuminate in what respects Wittgenstein was influenced by and criticized Hilbert's formalism. Surprisingly enough, Wittgenstein claims in his middle period that there is neither metamathematics nor proof of consistency. But later, he withdraws his such radical claims. Furthermore, we cannot find out any evidences, I think, that he maintained his formerly claims. I will illuminate why Wittgenstein does not raise such claims any more.