• 대한수학회보
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• 제24권1호
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• pp.13-17
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• 1987

Let S denote the class of nivalent functions normalized so that f(0)=f'(0)-1=0 in vertical bar z vertical bar <1. Let $S_{\alpha}$$^{*}$, -.pi./2<.alpha.<.pi./2, denote the subclass of S that satisfies Re $e^{i{\alpha}}$zf'(z)/f(z).geq.0 in vertical bar z vertical bar <1; then f is called .alpha.-spiral-like and the case .alpha.=0 is the class of normalized starlike functions [6, pp.52]. Let T denote the class of functions f normalized as above and satisfying Im z[Im f(z)]..geq.0 in vertical bar z vertical bar <1; then f is called typically real and T contains those functions of S whose coefficients are real [6, pp.55]. Also, in view of [6, pp.231], let B(.lambda.) be the class of function normalized as above and map vertical bar z vertical bar <1 onto the complement of an arc with radial angle .lambda.(0<.lambda.<.pi./2). The radial angle is meant to be the angle between the tangent and radial vectors to the arc. This note includes a sharp version for Corollary 1 of [2] when f.mem. $S_{\alpha}$$^{*}$ as well as a logarithmic coefficient estimate.nt estimate.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.717-723
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• 2021

The purpose of the present paper is to give sufficient conditions for normalized Dini function which is the special combination of the generalized Bessel function of first kind to be in the classes k-starlike functions and k-uniformly convex functions.

• 호남수학학술지
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• 제41권1호
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• pp.101-116
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• 2019

In this paper our aim is to establish some geometric properties (like starlikeness, convexity and close-to-convexity) for the generalized and normalized Dini functions. In order to prove our main results, we use some inequalities for ratio of these functions in normalized form and classical result of Fejer.

• 대한수학회논문집
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• 제33권2호
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• pp.535-547
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• 2018

In the present investigation our main aim is to give lower bounds for the ratio of some normalized q-Bessel functions and their sequences of partial sums. Especially, we consider Jackson's second and third q-Bessel functions and we apply one normalization for each of them.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.243-258
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• 2023

A normalized analytic function f defined on the unit disk 𝔻 is starlike of reciprocal order α, 0 ≤ α < 1, if Re(f(z)/(zf'(z))) > α for all z ∈ 𝔻. Such functions are starlike and therefore univalent in 𝔻. Using the well-known Miller-Mocanu differential subordination theory, sufficient conditions involving differential inclusions are obtained for a normalized analytic function to be starlike of reciprocal order α. Furthermore, a few conditions are derived for a function f to belong to a subclass of reciprocal starlike functions, satisfying |f(z)/(zf'(z)) - 1| < 1 - α.

• Bulletin of the Korean Chemical Society
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• 제6권5호
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• pp.264-266
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• 1985

Orthogonalized Slater-type orbitals and Ortho-normalized Slater-type orbitals were derived from the conventional Slater-type orbitals (STO's) by use of the continuous orthonormalizing which is expanded from the Schmidt's orthogonalizing procedure. These orbitals have the merits which STO's have not, such as; they are ortho-normalized each other and have the same numbers of the radial nodes that the real hydrogenlike wave functions do, so that they must be a good basis functions of LCAO MO procedures, i.e., the best approximate representation of SCF method.

• 대한수학회보
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• 제33권4호
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• pp.497-501
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• 1996

Let B denote the unit ball in $C^n(n \geq 1)$, and $\upsilon$ the 2n-dimensional Lebesgue measure on B normalized so that $\upsilon(B) = 1$, while $\sigma$ is the normalized surface measure on the boundary S of B.

• 대한수학회지
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• 제53권5호
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• Genomics & Informatics
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• 제18권4호
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• pp.41.1-41.8
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• 2020

We provide an algorithm for the construction and analysis of autocorrelation (information) functions of gene nucleotide sequences. As a measure of correlation between discrete random variables, we use normalized mutual information. The information functions are indicative of the degree of structuredness of gene sequences. We construct the information functions for selected gene sequences. We find a significant difference between information functions of genes of different types. We hypothesize that the features of information functions of gene nucleotide sequences are related to phenotypes of these genes.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.371-385
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• 2017

Jain and Saraswat (2012) introduced new generalized f-information divergence measure, by which we obtained many well known and new information divergences. In this work, we introduce new information inequalities in absolute form on this new generalized divergence by considering convex normalized functions. Further, we apply these inequalities for getting new relations among well known divergences, together with numerical verification. Application to the Mutual information is also presented. Asymptotic approximation in terms of Chi- square divergence is done as well.