• 제목/요약/키워드: Coefficient of Determinant

검색결과 87건 처리시간 0.021초

Some Coefficient Inequalities Related to the Hankel Determinant for a Certain Class of Close-to-convex Functions

  • Sun, Yong;Wang, Zhi-Gang
    • Kyungpook Mathematical Journal
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    • 제59권3호
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    • pp.481-491
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    • 2019
  • In the present paper, we investigate the upper bounds on third order Hankel determinants for certain class of close-to-convex functions in the unit disk. Furthermore, we obtain estimates of the Zalcman coefficient functional for this class.

COEFFICIENT INEQUALITIES FOR A UNIFIED CLASS OF BOUNDED TURNING FUNCTIONS ASSOCIATED WITH COSINE HYPERBOLIC FUNCTION

  • Gagandeep Singh;Gurcharanjit Singh;Navyodh Singh;Navjeet singh
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제31권2호
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    • pp.201-216
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    • 2024
  • The aim of this paper is to study a new and unified class 𝓡αCosh of analytic functions associated with cosine hyperbolic function in the open unit disc E = {z ∈ ℂ : |z| < 1}. Some interesting properties of this class such as initial coefficient bounds, Fekete-Szegö inequality, second Hankel determinant, Zalcman inequality and third Hankel determinant have been established. Furthermore, these results have also been studied for two-fold and three-fold symmetric functions.

COEFFICIENT BOUNDS FOR INVERSE OF FUNCTIONS CONVEX IN ONE DIRECTION

  • Maharana, Sudhananda;Prajapat, Jugal Kishore;Bansal, Deepak
    • 호남수학학술지
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    • 제42권4호
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    • pp.781-794
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    • 2020
  • In this article, we investigate the upper bounds on the coefficients for inverse of functions belongs to certain classes of univalent functions and in particular for the functions convex in one direction. Bounds on the Fekete-Szegö functional and third order Hankel determinant for these classes have also investigated.

HANKEL DETERMINANT PROBLEMS FOR CERTAIN SUBCLASSES OF SAKAGUCHI TYPE FUNCTIONS DEFINED WITH SUBORDINATION

  • Singh, Gagandeep;Singh, Gurcharanjit
    • Korean Journal of Mathematics
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    • 제30권1호
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    • pp.81-90
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    • 2022
  • The present investigation is concerned with the estimation of initial coefficients, Fekete-Szegö inequality, second Hankel determinants, Zalcman functionals and third Hankel determinants for certain subclasses of Sakaguchi type functions defined with subordination in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results derived in this paper will pave the way for the further study in this direction.

Sharp Coefficient Bounds for the Quotient of Analytic Functions

  • Park, Ji Hyang;Kumar, Virendra;Cho, Nak Eun
    • Kyungpook Mathematical Journal
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    • 제58권2호
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    • pp.231-242
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    • 2018
  • We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

다중회귀모형에서 전진선택과 후진제거의 기하학적 표현 (Geometrical description based on forward selection & backward elimination methods for regression models)

  • 홍종선;김명진
    • Journal of the Korean Data and Information Science Society
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    • 제21권5호
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    • pp.901-908
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    • 2010
  • 다중회귀모형에서 변수선택법 중에서 전진선택과 후진제거의 과정을 기하학적으로 표현하는 그래픽적 방법을 제안한다. 반지름이 1인 반원의 제1사분면에는 전진선택 과정을, 제2사분면에는 후진제거 과정을 표현한다. 각 단계에서 회귀제곱합을 벡터로 표현하고, 추가제곱합 또는 부분결정계수를 벡터 사이의 각도로 나타내며 벡터의 끝을 연결할 때 통계적으로 유의하면 점선으로 표현하여 부분가설검정의 통계적 분석결과를 인지할 수 있도록 작성한다. 이 방법을 이용하면 전진선택과 후진제거 방법에 의한 최종모형을 비교 분석하고 전체적으로 모형의 적합도를 파악할 수 있다.

의복상품특성에 따른 소비자 위험지각 및 위험감소행동에 관한 연구 (Product Characteristics of Clothing and Risk Perception and Risk Reduction Behavior of Consumers.)

  • 김찬주
    • 복식
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    • 제25권
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    • pp.41-62
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    • 1995
  • This research was intended to investigate how risk perception and risk reduction behavior by consumers differ according to different product characteristics of clothing. The responses of 318 female college students living in Seoul and surrounding vicinities were collected and analyzed. Inner wear, blue-jean pants, coat were selected as representing each clothing product characteristics. Frequencies distribution, regression and correlation coefficient were utilized for statistical analysis. Results are as follows. 1. The type of perceived risk and risk reduction behavior differed according to product characteristics of clothing. Physical and performance risk were more highly perceived for the purchase of innerwear. However, for the purchase of jean pants and coat, socio-psycho-logical and economic risk were also perceived highly because the rate of fashion change, social symbolism, and coordination with other clothing items become more important characteristics. To reduce perceived risk, dependency on past purchase experiences and shop-ping were mostly preferred method regardless of product characteristics of clothing. 2. Risk type as determinant variables for predicting overall risk differed according to product characteristics of clothing. But fashionability and usefulness were common determinant risk variables, which identifies typical characteristics of clothing product.

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CERTAIN PROPERTIES OF THE CLASS OF UNIVALENT FUNCTIONS WITH REAL COEFFICIENTS

  • Milutin Obradovic;Nikola Tuneski
    • 대한수학회보
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    • 제60권5호
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    • pp.1253-1263
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    • 2023
  • Let 𝓤+ be the class of analytic functions f such that ${\frac{z}{f(z)}}$ has real and positive coefficients and f-1 be its inverse. In this paper we give sharp estimates of the initial coefficients and initial logarithmic coefficients for f, as well as, sharp estimates of the second and the third Hankel determinant for f and f-1. We also show that the Zalcman conjecture holds for functions f from 𝓤+.

A Unit Root Test for Multivariate Autoregressive Model with Multiple Unit Roots

  • Shin, Key-Il
    • Journal of the Korean Statistical Society
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    • 제26권3호
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    • pp.397-405
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    • 1997
  • Recently maximum likelihood estimators using unconditional likelihood function are used for testing unit roots. When one wants to use this method the determinant term of initial values in the multivariate unconditional likelihood function produces a complicated function of the elements in the coefficient matrix and variance matrix. In this paper an approximation of the determinant term is calculated and based on this aproximation an approximated unconditional likelihood function is calculated. The approximated unconditional maximum likelihood estimators can be used to test for unit roots. When multivariate process has one unit root the limiting distribution obtained by this method and the limiting distribution using exact unconditional likelihood function are the same.

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Effect of rotation on Stoneley waves in orthotropic magneto-thermoelastic media

  • Parveen, Lata;Himanshi, Himanshi
    • Wind and Structures
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    • 제35권6호
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    • pp.395-403
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    • 2022
  • The present research is concerned with the study of Stoneley wave propagation at the interface of two dissimilar homogeneous orthotropic magneto-thermoelastic solids with fractional order theory of type GN-III with three phase-lags and combined effect of hall current and rotation. With the help of appropriate boundary conditions the secular equations of Stoneley waves are obtained in the form of determinant. The characteristics of wave such as phase velocity, attenuation coefficient and specific loss are computed numerically. The effect of rotation on the Stoneley wave's phase velocity, attenuation coefficient, specific loss, displacement components, stress components and temperature change has been depicted graphically. Some particular cases are also derived in this problem.