• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.345-351
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• 2011

Taylor's formula is a powerful tool in analysis. In this study, we assume that an operator is m-times Fr$\acute{e}$chet-differentiable and satisfies a Lipschitz condition. We then obtain some Taylor formulas using only the Lipschitz constants. Applications are also provided.

• The Pure and Applied Mathematics
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• v.21 no.3
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• pp.207-218
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• 2014

The principal object of this paper is to study a class of matrix polynomials associated with Humbert polynomials. These polynomials generalize the well known class of Gegenbauer, Legendre, Pincherl, Horadam, Horadam-Pethe and Kinney polynomials. We shall give some basic relations involving the Humbert matrix polynomials and then take up several generating functions, hypergeometric representations and expansions in series of matrix polynomials.

• Journal of Information Display
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• v.4 no.1
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• pp.9-13
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• 2003

An overview of author activity in the area diffractive LCDs are given. The formation of colour spectrum DL CDs is made by switchable phase diffraction gratings created in a LC layer due to using of comb-like electrodes. The offered DLCDs functionate without polarizes, have high contrast and spectral of pure colours, broad viewing ngles. The existing production equipment can be adapted to manufacturing of DLCD without considerable alterations.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.1-15
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• 2005

We study continuous fields and K-groups of crossed products of C＊-algebras. It is shown under a reasonable assumption that there exist continuous fields of C＊ -algebras between crossed products of C＊ -algebras by amenable locally compact groups and tensor products of C＊ -algebras with their group C＊ -algebras, and their K-groups are the same under the additional assumptions.

• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.103-118
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• 2003

We estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group $C^{*}-algebras$ of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.307-319
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• 2010

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.103-110
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• 2008

In this paper, we obtain the general solution and the stability of the cubic functional equation f(2x + y, 2z + w) + f(2x - y, 2z - w) = 2f(x + y, z + w) + 2f(x - y, z - w) + 12f(x, z). The cubic form $f(x,\;y)\;=\;ax^3\;+\;bx^2y\;+\;cxy^2\;+\;dy^3$ is a solution of the above functional equation.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.111-120
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• 2008

A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.53-71
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• 2018

In this paper, we provide two different descriptions for a relative derived category with respect to a subcategory ${\mathcal{X}}$ of an abelian category ${\mathcal{A}}$. First, we construct an exact model structure on certain exact category which has as its homotopy category the relative derived category of ${\mathcal{A}}$. We also show that a relative derived category is equivalent to homotopy category of certain complexes. Moreover, we investigate the existence of certain recollements in such categories.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1501-1509
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• 2020

We discuss the decomposition of degree two basic cohomology for codimension four taut Riemannian foliation according to the holonomy invariant transversal almost complex structure J, and show that J is C^∞ pure and full. In addition, we obtain an estimate of the dimension of basic J-anti-invariant subgroup. These are the foliated version for the corresponding results of T. Draghici et al. [3].