• 대한수학회지
• /
• 제31권4호
• /
• pp.645-657
• /
• 1994

If S is a semiring of nonnegative reals, which linear operators T on the space of $m \times n$ matrices over S preserve the column rank of each matrix\ulcorner Evidently if P and Q are invertible matrices whose inverses have entries in S, then $T : X \longrightarrow PXQ$ is a column rank preserving, linear operator. Beasley and Song obtained some characterizations of column rank preserving linear operators on the space of $m \times n$ matrices over $Z_+$, the semiring of nonnegative integers in [1] and over the binary Boolean algebra in [7] and [8]. In [4], Beasley, Gregory and Pullman obtained characterizations of semiring rank-1 matrices and semiring rank preserving operators over certain semirings of the nonnegative reals. We considers over certain semirings of the nonnegative reals. We consider some results in [4] in view of a certain column rank instead of semiring rank.

• 대한수학회논문집
• /
• 제20권4호
• /
• pp.671-683
• /
• 2005

The set of all $m\;{\times}\;n$ matrices with entries in $\mathbb{Z}_+$ is de­noted by $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$. We say that a linear operator T on $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ is a (U, V)-operator if there exist invertible matrices $U\;{\in}\; \mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ and $V\;{\in}\;\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$ such that either T(X) = UXV for all X in $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$, or m = n and T(X) = $UX^{t}V$ for all X in $\mathbb{M}{m{\times}n}(\mathbb{Z}_+)$. In this paper we show that a linear operator T preserves the rank of matrices over the nonnegative integers if and only if T is a (U, V)­operator. We also obtain other characterizations of the linear operator that preserves rank of matrices over the nonnegative integers.

• 한국고분자학회:학술대회논문집
• /
• 한국고분자학회 2006년도 IUPAC International Symposium on Advanced Polymers for Emerging Technologies
• /
• pp.249-249
• /
• 2006

We have prepared an amphiphilic wedge-coil molecule consisting of a hydrophobic wedge-like segment and a hydrophilic poly(ethylene oxide) (PEO) segment. The wedge-coil block molecule self-assembles into cylindrical nanofibers in both polar as well as nonpolar solvents. Remarkably, the resulting nanofibers, as solvent polarity change from water to n-hexane, change from highly flexible coil-like to stiff rod-like characteristics. This dynamic switching in the stiffness of the nanofibers in response to solvent polarity is attributed to the structural inversion of cylindrical core from bulky dendritic segments with amorphous nature to crystallizable linear PEO segments.

• Kyungpook Mathematical Journal
• /
• 제49권1호
• /
• pp.167-181
• /
• 2009

Based on Ricatti equation $XA^{-1}X=B$ for two (positive invertible) operators A and B which has the geometric mean $A{\sharp}B$ as its solution, we consider a cubic equation $X(A{\sharp}B)^{-1}X(A{\sharp}B)^{-1}X=C$ for A, B and C. The solution X = $(A{\sharp}B){\sharp}_{\frac{1}{3}}C$ is a candidate of the geometric mean of the three operators. However, this solution is not invariant under permutation unlike the geometric mean of two operators. To supply the lack of the property, we adopt a limiting process due to Ando-Li-Mathias. We define reasonable geometric means of k operators for all integers $k{\geq}2$ by induction. For three positive operators, in particular, we define the weighted geometric mean as an extension of that of two operators.

• 전자공학회논문지B
• /
• 제29B권7호
• /
• pp.42-51
• /
• 1992

This paper suggests a measure constraint locus which is the loci of points satisfying the necessary constraint for optimality of a measure in the configuration space. The characterization of four measures for singularity avoidance is worked out by using the measure constraint locus. It gives a global look at the performance of an inverse kinematic algorithm whien each of measures in a kinematically redundant robot is used. The invertible workspace without singularities and the topological properties both on the configuration and operational spaces are analyzed. We discuss also some limitations, based on the topological arguments of measure constraint locus, of the inverse kinematic algorithms, and compare global properties of each of measure. Therfore, a new concept called measure constraint locus gives a methodology for obtaining a conservative joint trajectory without singularities for almost entire workspace.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1992년도 하계학술대회 논문집 A
• /
• pp.386-390
• /
• 1992

Algorithmic or kinematic singularities are inevitably a introduced if optimality criteria or augmented kinematic equations are used to resolve the redundancy of almost any manipulator with rotary joints. In this paper, a sufficient condition for a singularity-free optimal solution of the kinematic control of a redundant manipulator is derived and, specifically, algorithmic singularities are analyzed for optimality-based methods. A singularity-free space (SFS) to characterize the performance of a secondary task for a redundant manipulator using the sufficient condition for a redundant manipulator is defined. The SFS is a set of regions classified by the loci of configurations satisfying the inflection condition for manipulability measure in the Configuration space. Using SFS, the topological property of the Configuration space and the invertible workspace without singularities are analyzed.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2001년도 ICCAS
• /
• pp.33.1-33
• /
• 2001

We address a novel approach to identify a nonlinear dynamic system for Wiener models, which are composed of a linear dynamic system part followed by a nonlinear static part. The aim of system identification here is to provide the optimal mathematical model of both the linear dynamic and the nonlinear static parts in some appropriate sense. Assuming the nonlinear static part is invertible, we approximate the inverse function by a piecewise linear function. We estimate the piecewise linear inverse function by using the evolutionary computation approach such as genetic algorithm (GA) and evolution strategies (ES), while we estimate the linear dynamic system part by the least squares method. The results of numerical simulation studies indicate the usefulness of proposed approach to the Wiener model identification.

• 호남수학학술지
• /
• 제28권2호
• /
• pp.185-196
• /
• 2006

A scheme based on the cryptography for enforcing multilevel security in a system where hierarchy is represented by a partially ordered set was first introduced by Akl et al. But the key generation algorithm of Akl et al. is infeasible when there is a large number of users. In 1985, MacKinnon et al. proposed a paper containing a condition which prevents cooperative attacks and optimizes the assignment in order to overcome this shortage. In 2005, Kim et al. proposed key management systems for multilevel security using one-way hash function, RSA algorithm, Poset dimension and Clifford semigroup in the context of modern cryptography. In particular, the key management system using Clifford semigroup of imaginary quadratic non-maximal orders is based on the fact that the computation of a key ideal $K_0$ from an ideal $EK_0$ seems to be difficult unless E is equivalent to O. We, in this paper, show that computing preimages under the bonding homomorphism is not difficult, and that the multilevel cryptosystem based on the Clifford semigroup is insecure and improper to the key management system.

• Journal of applied mathematics & informatics
• /
• 제14권1_2호
• /
• pp.115-122
• /
• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.247-255
• /
• 2011

Invertible functions with a single cycle property have many cryptographic applications. The main context in which we study them in this paper is pseudo random generation and stream ciphers. In some cryptographic applications we need a generator which generates binary sequences of period long enough. A common way to increase the size of the state and extend the period of a generator is to run in parallel and combine the outputs of several generators with different period. In this paper we will characterize a secure quadratic polynomial on $\mathbb{Z}_{2^n}$, which generates a binary sequence of period long enough and without consecutive elements.