• Honam Mathematical Journal
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• v.45 no.1
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• pp.71-81
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• 2023

In this paper, we deal with some geometric properties including starlikeness and convexity of order 𝛽 of Ramanujan-type entire functions which are natural extensions of classical Ramanujan entire functions. In addition, we determine some conditions on the parameters such that the Ramanujan-type entire functions belong to the Hardy space and to the class of bounded analytic functions.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.47-56
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• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.

• Korean Journal of Biological Psychiatry
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• v.4 no.1
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• pp.36-42
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• 1997

Higher cognitive functions refer to the highest level of human intellectual functioning, including concept formation, reasoning, and executive functions. The executive functions can be conceptualized as having four components : volition, planning, purposive action, and effective performance. Because higher cognitive functions represent the most advanced stages of intellectual development, they are often highly susceptible to the effects of brain injuries and mental disorders. The ability to perform effectively within the environment is determined in large part by an individual's adequacy in performing such higher-order functions. Especially executive functions are necessary for appropriate, socially responsible, and effectively self-serving adult conduct. Threfore, an assessment of the psychiatric patient's performance in these areas will provide useful diagnostic information, as well as information concerning social and vocational prognosis.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1213-1235
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• 2016

We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from [12], where the meromorphic functions and the entire functions are of hyper order less than 1. An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.

• Journal of The Korean Association For Science Education
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• v.24 no.1
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• pp.171-182
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• 2004

The purpose of this study is to analyze lesson plans from third to sixth grades of science and to find out teaching strategies in respects of learning functions provided by preservice elementary teachers in education university. On the whole, to control students' learning process preservice teachers used more shared-regulation strategy than strong teacher-regulation one. Teaching activities for regulative learning function were most used in strategy of strong teacher-regulation, and in strategy of shared-regulation those for cognitive learning functions were most used. But teaching activities for affective learning functions were used a little considered in both teaching strategies. In introduction step of instruction, affective and regulative learning functions were more instructed by strong teacher-regulation strategy and cognitive learning functions were more instructed by shared-regulation strategy. The affective, cognitive, and regulative learning functions were largely planned by shared-regulation teaching strategy in development. The regulative learning functions were planned by strong teacher-regulation strategy than by shared-regulation strategy and affective learning functions were considered a little bit in consolidation. There was a tendency that strong teacherregulation strategy was increased in lessons for fifth and sixth grade.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.595-601
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• 2014

For analysis of the plates and membranes by numerical or analytical methods, the question of choice of the system of functions satisfying the different boundary conditions remains a major challenge to address. It is to this issue that is dedicated this work based on an approach of choice of combinations of trigonometric functions, which are shape functions of a bended beam with the boundary conditions corresponding to the plate support mode. To do this, the shape functions of beam vibrations for strength analysis of the rectangular plates by Kantorovich-Vlasov's method is considered. Using the properties of quasi-orthogonality of those functions allowed assessing to differential equation for every member of the series. Therefore it's proposed some new forms of integration of the beam functions, in order to simplify the problem.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.543-552
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• 2006

The purpose of the present paper is to introduce two novel subclasses $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$ and $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions with negative coefficients, involving Ruscheweyh derivative operator. The various results investigated in this paper include coefficient estimates, distortion inequalities, radii of close-to-convexity, starlikenes, and convexity for the functions belonging to the class $\mathcal{T}_{\mu}(n,{\lambda},{\alpha})$. These results are then appropriately applied to derive similar geometrical properties for the other class $\mathcal{H}_{\mu}(n,{\lambda},{\alpha};{\kappa})$ of analytic and univalent functions. Relevant connections of these results with those in several earlier investigations are briefly indicated.

• Journal of information and communication convergence engineering
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• v.2 no.3
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• pp.187-192
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• 2004

A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.3 s.258
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• pp.365-372
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• 2007

Revisited in this paper are Green's functions for unit concentrated forces in an infinite orthotropic Kirchhoff plate. Instead of obtaining Green's functions expressed in explicit forms in terms of Barnett-Lothe tensors and their associated tensors in cylindrical or dual coordinates systems, presented here are Green's functions expressed in two quasi-harmonic functions in a Cartesian coordinates system. These functions could be applied to thin plate problems regardless of whether the plate is homogeneous or inhomogeneous in the thickness direction. With a composite variable defined as $z=x_1+ipx_2$ which is adopted under the necessity of expressing the Green's functions in terms of two quasi-harmonic functions in a Cartesian coordinates system Stroh-like formalism for orthotropic Kirchhoffplates is evolved. Using some identities of logarithmic and arctangent functions given in this paper, the Green's functions are presented in terms of two quasi-harmonic functions. These forms of Green's functions are favorable to obtain the Newtonian potentials associated with defect problems. Thus, the defects in the orthotropic plate may be easily analyzed by way of the Green's function method.

• Journal of the Korean earth science society
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• v.35 no.5
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• pp.333-341
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• 2014

A new set of basis functions was constructed using the Rossby-Haurwitz waves, which are the eigenfunctions of nondivergent barotropic vorticity equations on the sphere. The basis functions were designed to be non-separable, that is, not factored into functions of either the longitude or the latitude. Due to this property, the nodal lines of the functions are aligned neither along with the meridian nor the parallel. The basis functions can be categorized into groups of which members have the same degree or the total wavenumber-like index on the sphere. The orthonormality of the basis functions were found to be close to the machine roundoffs, giving the error of $O(10^{-15})$ or $O(10^{-16})$ for double-precision computation (64 bit arithmetic). It was demonstrated through time-stepping procedure that the basis functions were also the eigenfunctions of the non-divergent barotropic vorticity equations. The projection of the basis functions was carried out onto the low-resolution geopotential field of Gaussian bell, and compared with the theory. The same projections were performed for the observed atmospheric-geopotential height field of 500 hPa surface to demonstrate decomposition into the fields that contain disturbance of certain range of horizontal scales. The usefulness of the new basis functions was thus addressed for application to the eigenmode analysis of the atmospheric motions on the global domain.