• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.51-62
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• 2021

Variational method has played an important role in solving problems of uniqueness and existence of the nonlinear works as well as analysis. It will also be extremely useful for researchers in all branches of natural sciences and engineers working with non-linear equations economy, optimization, game theory and medicine. Recently, the existence of infinitely many weak solutions for some non-local problems of Kirchhoff type with Dirichlet boundary condition are studied [14]. Here, a suitable method is presented to treat the elliptic partial derivative equations, especially (p(x), q(x))-Laplacian-like systems. This kind of equations are used in the study of fluid flow, diffusive transport akin to diffusion, rheology, probability, electrical networks, etc. Here, the existence of infinitely many weak solutions for some boundary value problems involving the (p(x), q(x))-Laplacian-like operators is proved. The method is based on variational methods and critical point theory.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1371-1385
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• 2022

For setting a general weight function on n dimensional complex space ℂⁿ, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.195-205
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• 2022

In this paper, we provide various characterizations for the composition operator on Lorentz spaces L(p, q), 1 < p ≤ ∞, 1 ≤ q ≤ ∞ to have finite ascent (descent) in terms of its inducing measurable transformation. At the end, in order to demonstrate our outcomes, some examples are given.

• Honam Mathematical Journal
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• v.16 no.1
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• pp.119-135
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• 1994

Let $Q_{n+p-1}(\alpha)$ denote the- dass of functions $$f(z)=z^{P}-\sum_{n=0}^\infty{a_{(p+k)}z^{p+k}$$ ($a_{p+k}{\geq}0$, $p{\in}N=\left{1,2,{\cdots}\right}$) which are analytic and p-valent in the unit disc $U=\left{z:{\mid}z:{\mid}<1\right}$ and satisfying $Re\left{\frac{D^{n+p-1}f(\approx))^{\prime}}{pz^{p-a}\right}>{\alpha},0{\leq}{\alpha}<1,n>-p,z{\in}U.$ In this paper we obtain sharp results concerning coefficient estimates, distortion theorem, closure theorems and radii of p-valent close-to- convexity, starlikeness and convexity for the class $Q_{n+p-1}$ ($\alpha$). We also obtain class preserving integral operators of the form $F(z)=\frac{c+p}{z^{c}}\int_{o}^{z}t^{c-1}f(t)dt.$ c>-p $F\left(z\right)=\frac{c+p}{z^{c}}\int_{0}^{z} t^{c-1}f\left(t \right)dt. \qquad c>-p$ for the class $Q_{n+p-1}$ ($\alpha$). Conversely when $F(z){\in}Q_{n+p-1}(\alpha)$, radius of p-valence of f(z) has been determined.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1111-1126
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• 2023

In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

• Clinical and Experimental Pediatrics
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• v.45 no.7
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• pp.917-922
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• 2002

An unbalanced translocation is frequently the result of inheritance of an unbalanced haploid set from a parent with a balanced translocation. Families in which one parent is a balanced translocation carrier fall into the following classes : Those in which none of the possible abnormal offsprings is viable; Those in which one type of offspring, usually the one with the smaller deletion, is born alive; Those in which two types of abnormal offspring are viable. We report a neonate whose karyotype was 46,XX,der(2)t(2;7)(q21;p21.2),der(20)t(2;20)(q21;p13). She was small for her gestational age and had multiple anomalies such as exophthalmos, corneal opacity, short neck, tongue tie, clinodactyly, atrial septal defect, patent ductus arteriosus and ventriculomegaly. Moreover, her mother's karyotype was 46,XX,der(2)t(2;7)(q21;p21.2),del(16)(q22.1),der(20)t(2;20)(q21;p13) but her father had normal karyotype. The same derivative chrosomes were found between mother and her infant, except for del(16)(q22.1) in her mother and these same unbalanced translocations in a two-generation family are extremely rare.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Korean Journal of Microbiology
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• v.40 no.2
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• pp.73-80
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• 2004

Coenzyme Q is a quinone derivative that acts as a lipid electron carrier in the respiratory chain located at mito-chondrial inner membrane in eucaryotes or plasma membrane in procaryotes and also functions as antioxidant. A putative Neurospora crassa coq-4 gene was cloned and functionally expressed in Saccharomyces cerevisiae coq4 mutant. Complemented S. cerevisaie mutant strain was able to produce coenzyme $Q_{6}$ and showed a normal growth rate. They also showed less sensitivities to polyunsaturated fatty acids such as linoleic acid or linolenic acid. The predicted sequence of N. crassa COQ4 is consisted of 347 amino acids with a molecular mass of 39.7 kDa and showed 35% identity and 52% similarity with that of S. cerevisiae.

• Journal of Life Science
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• v.13 no.6
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• pp.933-942
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• 2003

CoenzymeQ is a quinone derivative with a long isoprenoid side chain. It transports electrons in the respiratory chain located in the inner mitochondrial membrane of eukaryotes and the plasma membrane of prokaryotes. It also functions as an antioxidant. Saccharomyces cerevisine coq mutants, that are deficient coenzyme Q biosynthesis fail to aerobically grow. They are not able to grow on non-fermentable carbon sources, such as glycerol, either The putative $coq^{-7}$ gene involved in coenzyme Q biosynthesis of Neurospora crassa was cloned and used for complementation of S. cerevisiae coq7 mutant. The predicted amino acid sequence of N. crassa COQ7 showed about 58% homology with Coq7p of S. cerevisiae. The growth rate of S. cerevisiae $coq^7$ mutant transformed with the N. crassa $coq^{-7}$ gene was restored to the wild-type level. The complemented 5. cerevisiae strain was able to grow with glycerol as a sole carbon source and showed less sensitivities to linolenic acid, a polyunsaturated fatty acid.

• East Asian mathematical journal
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• v.24 no.4
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• pp.347-358
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• 2008

In this paper we investigate integral means inequalities for the integral operators $Q_{\lambda}^{\mu}$ and $P_{\lambda}^{\mu}$ applied to suitably normalized analytic functions. Further, we obtain some neighborhood and inclusion properties for a class of functions $G{\alpha}({\phi}, {\psi})$ (defined below). Several corollaries exhibiting the applications of the main results are considered in the concluding section.