• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.379-390
• /
• 2005

In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, an F-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of a saddle point are given.

• Kyungpook Mathematical Journal
• /
• v.13 no.2
• /
• pp.235-240
• /
• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• Journal of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.331-349
• /
• 2002

Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.

• Journal of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.177-190
• /
• 2015

Let X be a completely regular Hausdorff space, and E and F be Banach spaces. Let $C_{rc}(X,E)$ be the Banach space of all continuous functions $f:X{\rightarrow}E$ such that f(X) is a relatively compact set in E. We establish an integral representation theorem for bounded linear operators $T:C_{rc}(X,E){\rightarrow}F$. We characterize continuous operators from $C_{rc}(X,E)$, provided with the strict topologies ${\beta}_z(X,E)$ ($z={\sigma},{\tau}$) to F, in terms of their representing operator-valued measures.

• The Transactions of the Korea Information Processing Society
• /
• v.4 no.2
• /
• pp.606-615
• /
• 1997

This paper proposes an dffcient method for test pattern generation.Current test pattern genration systems generate a test vester for fault $F_{i+l}$ independently of the computation previously done for faults F1,F2...,Fi The proposed algorithm generates a test vector for fault $F_{i+l}$ by inheriting the test vector for fault Fi. A new test vector is grnerated from inherited values by gradually changing the inhderited values .The inherited values may partially activate a fauog and propagate the fault signal,Normally,this reduses the number of decision steps and backtracks in the second search.Experimental results for well-Known benchmark circuts show that the proposed algorithm is very efficient with small backtrack kimit;in combination eith other algorithms,it is very efficient for arbitrary backtrack limits.

• Journal of Korean Society of Forest Science
• /
• v.99 no.2
• /
• pp.186-196
• /
• 2010

Fertilization increases the crop productivity and produces high quality seedlings for plantation. We quantitatively measured both physical performances and nutrient responses of Fraxinus rhynchophylla, Fraxinus mandshurica, Pinus koraiensis, and Abies holophylla seedlings, which are commercially planted species in Korea, to nitrogen, phosphorus, and potassium fertilization. We analyzed the growth performances by using Dickson's quality index (QI) and the nutrient status by using vector diagnosis. Nitrogen or phosphorus treatment increased height and root collar diameter growth of F. rhynchophylla and F. mandshurica, however, did not increase those of P. koraiensis and A. holophylla. The order of QI was N > P > K > control for F. rhynchophylla, P ${\geq}$ N > Control ${\geq}$ P for F. mandshurica, P > Control ${\geq}$ K > N for P. koraiensis and A. holophylla. In F. rhynchophylla, fertilization diluted N concentration in tissues by 5-25% because growth responses were higher than fertilization uptake. P. koraiensis and A. holophylla showed N excess showing "toxic accumulation". F. rhynchophylla and F. mandshurica showed P deficiency with P fertilization, however, P. koraiensis and A. holophylla showed "luxury accumulation". Vector diagnosis indicated that more fertilization was applicable for F. rhynchophylla and F. mandshurica, and high fertilization rates were inefficient for P. koraiensis and A. holophylla. Both QI and vector diagnosis can be applied to verify seedling quality in the light of growth responses and nutrient status in fertilization trials.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.229-247
• /
• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• The Korean Journal of Applied Statistics
• /
• v.25 no.5
• /
• pp.829-835
• /
• 2012

When the input features are generated by factors in a classification problem, it is more meaningful to identify important factors, rather than individual features. The $F_{\infty}$-norm support vector machine(SVM) has been developed to perform automatic factor selection in classification. However, the $F_{\infty}$-norm SVM may suffer from estimation inefficiency and model selection inconsistency because it applies the same amount of shrinkage to each factor without assessing its relative importance. To overcome such a limitation, we propose the adaptive $F_{\infty}$-norm ($AF_{\infty}$-norm) SVM, which penalizes the empirical hinge loss by the sum of the adaptively weighted factor-wise $L_{\infty}$-norm penalty. The $AF_{\infty}$-norm SVM computes the weights by the 2-norm SVM estimator and can be formulated as a linear programming(LP) problem which is similar to the one of the $F_{\infty}$-norm SVM. The simulation studies show that the proposed $AF_{\infty}$-norm SVM improves upon the $F_{\infty}$-norm SVM in terms of classification accuracy and factor selection performance.

• Journal of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1059-1079
• /
• 2021

We show that given any chain transitive set of a C¹ generic diffeomorphism f, if a diffeomorphism f has the eventual shadowing property on the locally maximal chain transitive set, then it is hyperbolic. Moreover, given any chain transitive set of a C¹ generic vector field X, if a vector field X has the eventual shadowing property on the locally maximal chain transitive set, then the chain transitive set does not contain a singular point and it is hyperbolic. We apply our results to conservative systems (volume-preserving diffeomorphisms and divergence-free vector fields).

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.2
• /
• pp.251-259
• /
• 2015

Let $\mathbb{F}^d_q$ be a d-dimensional vector space over a finite field $\mathbb{F}^d_q$ with q elements. We endow the space $\mathbb{F}^d_q$ with a normalized counting measure dx. Let ${\sigma}$ be a normalized surface measure on an algebraic variety V contained in the space ($\mathbb{F}^d_q$, dx). We define the restricted averaging operator AV by $A_Vf(X)=f*{\sigma}(x)$ for $x{\in}V$, where $f:(\mathbb{F}^d_q,dx){\rightarrow}\mathbb{C}$: In this paper, we initially investigate $L^p{\rightarrow}L^r$ estimates of the restricted averaging operator AV. As a main result, we obtain the optimal results on this problem in the case when the varieties V are any nondegenerate algebraic curves in two dimensional vector spaces over finite fields. The Fourier restriction estimates for curves on $\mathbb{F}^2_q$ play a crucial role in proving our results.