• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.905-915
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• 2000

In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method on the differential delay equation defined by $\omega(u)\;=\frac{1}{u}\;for\;1\lequ\leq2$ and $(u\omega(u))'\;=\omega(u-1)\;foru\geq2$, which was introduced by Buchstab. As Khajah et al.[1] applied the Recursive Tau Method on this problem, they had to apply that Method under the Mathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations. The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities of this Method to handle problems in different applications.

• East Asian mathematical journal
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• 제17권2호
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• pp.225-232
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• 2001

Let R be a prime ring with characteristic not two. U a (${\sigma},{\tau}$)-left Lie ideal of R and d : R$\rightarrow$R a non-zero derivation. The purpose of this paper is to invesitigate identities satisfied on prime rings. We prove the following results: (1) [d(R),a]=0$\Leftrightarrow$d([R,a])=0. (2) if $(R,a)_{{\sigma},{\tau}}$=0 then $a{\in}Z$. (3) if $(R,a)_{{\sigma},{\tau}}{\subset}C_{{\sigma},{\tau}}$ then $a{\in}Z$. (4) if $(U,a){\subset}Z$ then $a^2{\in}Z\;or\;{\sigma}(u)+{\tau}(u){\in}Z$, for all $u{\in}U$. (5) if $(U,R)_{{\sigma},{\tau}}{\subset}C_{{\sigma},{\tau}}$ then $U{\subset}Z$.

• 충청수학회지
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• 제26권1호
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• pp.53-69
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• 2013

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.471-477
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• 2007

In this paper we establish some recurrence relations satisfied by the quotient moments of the upper record values from the Weibull distribution. Suppose $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

• Bulletin of the Korean Chemical Society
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• 제22권11호
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• pp.1255-1260
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• 2001

The expansion of two different kinds of hydrodynamic size of polymethyl methacrylate (PMMA Mw: 1.56- 2.04 ${\times}$ 106 g/mol) has been measured by dynamic light scattering and viscometry above the Flory $\theta$ temperature of the variou s solvents such as n-butyl chloride, 3-heptanone, and 4-heptanone. The expansion of PMMA chains was analyzed in terms of universal temperature parameters and also compared with previous results of polystyrene (PS) system. First it was found that simple $\tau/{\tau}c$ parameter no longer had its universality for the expansion behavior of hydrodynamic size in the chemically different linear polymer chains. However after modifying ${\tau}/{\tau}c$ parameter into $(Mw/Ro2)3}2(\tau/\tauc)$, we observed a much better universality for both PMMA and PS systems. Here Mw, Ro, $\tau[=(T-{\theta}$)/${\theta}$]$, and ${\tau}c[=({\theta}-Tc)/Tc]$ are defined as the weight average molecular weight, the unperturbed end-to-end distance, the reduced temperature and the reduced critical temperature, respectively.

• 대한수학회지
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• 제44권6호
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• pp.1453-1467
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• 2007

By means of a Riccati transform some oscillation or nonoscillation criteria are established for nonlinear differential equations of second order $$(E_1)\;[p(t)|x#(t)|^{\alpha}sgn\;x#(t)]#+q(t)|x(\tau(t)|^{\alpha}sgn\;x(\tau(t))=0$$. $$(E_2),\;(E_3)\;and\;(E_4)\;where\;0<{\alpha}$$ and $${\tau}(t){\leq}t,\;{\tau}#(t)>0,\;{\tau}(t){\rightarrow}{\infty}\;as\;t{\rightarrow}{\infty}$$. In this paper we improve some previous results.

• 대한수학회보
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• 제41권2호
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• pp.387-391
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• 2004

Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.211-220
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• 2005

In this paper we obtain the transformations of the Ramanujan's tenth order mock theta functions under the modular group generators ${\tau}\;{\rightarrow}\;{\tau}\;+\;1\;and\;{\tau}\;{\rightarrow}\;-1/ {\tau}\;where\;q\;=\;e^{{\pi}it}$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제7권4호
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• pp.262-266
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• 2007

We characterize a fuzzy pairwise $\gamma$-irresolute continuous mapping on a fuzzy bitopological space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제7권3호
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• pp.188-192
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• 2007

We characterize a fuzzy pairwise ${\gamma}-irresolute$ continuous mapping on a fuzzy bitopological space.