• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.825-831
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• 2021

The derivative of a polynomial p(z) of degree n, with respect to point α is defined by D_αp(z) = np(z) + (α - z)p'(z). Let p(z) be a polynomial having all its zeros in the unit disk |z| ≤ 1. The Sendov conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a zero of p'(z) within unit distance of each zero. In this paper, we obtain certain results concerning the location of the zeros of D_αp(z) with respect to a specific zero of p(z) and a stronger result than Sendov conjecture is obtained. Further, a result is obtained for zeros of higher derivatives of polynomials having multiple roots.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.975-1002
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• 2005

On the setting of the upper half-space H of the Eu­clidean n-space, we show the boundedness of weighted Bergman projection for 1 < p < $\infty$ and nonorthogonal projections for 1 $\leq$ p < $\infty$ . Using these results, we show that Bergman norm is equiva­ lent to the normal derivative norms on weighted harmonic Bergman spaces. Finally, we find the dual of b$\_{$^{1}$.

• Rapid Communication in Photoscience
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• v.2 no.2
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• pp.39-41
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• 2013

It is interesting to introduce viologen moiety into photoactive compounds such as porphyrin and anthracene in the study of supramolecular system such as pseudorotaxanes. For the construction of photoactive pseudorotaxane based on porphyrin-viologen-anthracene triad or its zinc derivative threaded with bis-p-phenylene-34-crown-10 macrocycle, porphyrin-viologen-anthracene triad 1 and its zinc derivative zinc porphyrin-viologen-anthracene triad 2 were prepared and their absorption and fluorescence spectral properties were measured.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.161-170
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• 1995

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$. A complete and simply connected complex space form is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$, according as c > 0, c = 0 or c < 0. Takagi [12] and Berndt [2] classified all homogeneous real hypersufaces of $P_nC$ and $H_nC$.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.243-249
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• 2003

We consider weighted Bergman spaces and radial derivatives on the spaces. We also prove that for each element f in B$\^$p, r/ there is a unique f in B$\^$p, r/ such that f is the radial derivative of f and for each f$\in$B$\^$r/(i), f is the radial derivative of some element of B$\^$r/(i) if and only if, lim f(tz)= 0 for all z$\in$H.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.127-142
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• 2018

In the present article, authors obtained certain fractional derivative and integral formulas involving incomplete ${\tau}$-hypergeometric function introduced by Parmar and Saxena [14]. Some interesting special cases and consequences of our main results are also considered.

• Archives of Pharmacal Research
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• v.16 no.2
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• pp.168-174
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• 1993

The michael adducts 2a, b were obtained from the reaction of the phenylacelyl derivative 1 with benzadehyde and p-anisaldehyde and p-anisaldehyde respectively. 2a and 2b were subjected to react with cyanoethanoic acid hydrazide, malononitrile, cyanothioacetamide, cyanoacetamide and 1, 1, 3-tricyano-2-amino propene to yield 4a-h and 5a, b respecitively. Hydrogen peroxide oxidation of 2a, b gave the aurone derivative 6a, b. The pyone derivatives 8a, b were obtained from 2a, b by addition of chioroacetyl chioride followed by dehydrochlorination.

• Journal of Microbiology and Biotechnology
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• v.16 no.1
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• pp.118-125
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• 2006

The region responsible for replication of the megaplasmid pAtC58 in the nopaline-type Agrobacterium tumefaciens strain C58 was determined. A derivative ofa Co1E1 vector, pBluscript SK-, incapable of autonomous replication in Agrobacterium spp, was cloned with a 7.6-kb Bg1II-HindIII fragment from a cosmid clone of pAtC58, which contains a region adjacent to the operon for the utilization of deoxyfructosyl glutamine (DFG). The resulting plasmid conferred resistance to carbenicillin on the A. tumefaciens strain UIA5 that is a plasmidfree derivative of C58. The plasmid was stably maintained in the strain even after consecutive cultures for generations. Analysis of nested deletions of the 7.6-kb fragment showed that a 4.3-kb BglII-XhoI region sufficiently confers replication of the derivative of the ColE1 vector on UIA5. The region comprises three ORFs, which have high homologies with repA, repB, and repC of plasm ids in virulent Agrobacterium spp. including pTiC58, pTiB6S3, pTi-SAKURA, and pRiA4b as well as those of symbiotic plasmids from Rhizobium spp. Phylogenie analysis showed that rep genes in pAtC58 are more closely related to those in pRiA4 than to pTi plasmids including pTiC58, suggesting that the two inborn plasmids, pTiC58 and pAtC58, harbored in C58 evolved from distinct origins.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.943-956
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• 2023

Let p(z) be a polynomial of degree n and for any complex number 𝛽, let D_𝛽p(z) = np(z) + (𝛽 - z)p'(z) denote the polar derivative of the polynomial with respect to 𝛽. In this paper, we consider the class of polynomial $$p(z)=(z-z_0)^s \left(a_0+\sum\limits_{{\nu}=0}^{n-s}a_{\nu}z^{\nu}\right)$$ of degree n having a zero of order s at z₀, |z₀| < 1 and the remaining n - s zeros are outside |z| < k, k ≥ 1 and establish upper bound estimates for the maximum of |D_𝛽p(z)| as well as |p(Rz) - p(rz)|, R ≥ r ≥ 1 on the unit disk.