http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
김성훈 서울대학교 교육연구소 2010 Asia Pacific Education Review Vol.11 No.2
The primary purpose of this study is to investigate the mathematical characteristics of the test reliability coefficient rho(XX)' as a function of item response theory (IRT) parameters and present the lower and upper bounds of the coefficient. Another purpose is to examine relative performances of the IRT reliability statistics and two classical test theory (CTT) reliability statistics (Cronbach's alpha and Feldt-Gilmer congeneric coefficients) under various testing conditions that result from manipulating large-scale real data. For the first purpose, two alternative ways of exactly quantifying rho(XX)' are compared in terms of computational efficiency and statistical usefulness. In addition, the lower and upper bounds for rho(XX)' are presented in line with the assumptions of essential tau-equivalence and congeneric similarity, respectively. Empirical studies conducted for the second purpose showed across all testing conditions that (1) the IRT reliability coefficient was higher than the CTT reliability statistics; (2) the IRT reliability coefficient was closer to the Feldt-Gilmer coefficient than to the Cronbach's alpha coefficient; and (3) the alpha coefficient was close to the lower bound of IRT reliability. Some advantages of the IRT approach to estimating test-score reliability over the CTT approaches are discussed in the end.
Sharp Coefficient Bounds for the Quotient of Analytic Functions
Park, Ji Hyang,Kumar, Virendra,Cho, Nak Eun Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.2
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.
Some Bounds for Zeros of a Polynomial with Restricted coefficients
Mahnaz Shafi Chishti,Vipin Kumar Tyagi,Mohammad Ibrahim Mir 한국수학교육학회 2024 純粹 및 應用數學 Vol.31 No.1
For a Polynomial P(z)= SMALLSUM _{j=0}^{n} `a _{j} z ^{j} with a_j ≥ a_j−1, a_0 > 0 (j = 1, 2, ..., n), a classical result of Enestrom-Kakeya says that all the zeros of P(z) lie in |z| ≤ 1. This result was generalized by A. Joyal et al. [3] where they relaxed the non-negative condition on the coefficents. This result was further generalized by Dewan and Bidkham [9] by relaxing the monotonicity of the coefficients. In this paper, we use some techniques to obtain some more generalizations of the results [3], [8], [9].
Om Ahuja,Nisha Bohra,Asena Cetinkaya,Sushil Kumar 경북대학교 자연과학대학 수학과 2021 Kyungpook mathematical journal Vol.61 No.1
In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szeg¨o inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.
Coefficient bounds for bi-univalent analytic functions associated with Hohlov operator
TRAILOKYA PANIGRAHI,G. Murugusundaramoorthy 장전수학회 2013 Proceedings of the Jangjeon mathematical society Vol.16 No.1
In the present paper, the authors introduce and investigate two newsubclasses of the function class ∑ of bi-univalent analytic functions in the openunit disk Δ associated with Hohlov operator. The bounds on the coefficients|a2|, |a3| and |a4| for the functions in these new subclasses of ∑ are obtained. Relevant connection of the results presented here with those obtained in earlierwork are also pointed out.
COEFFICIENT ESTIMATES FOR A NEW GENERAL SUBCLASS OF ANALYTIC BI-UNIVALENT FUNCTIONS
Bulut, Serap The Kangwon-Kyungki Mathematical Society 2021 한국수학논문집 Vol.29 No.3
In a very recent paper, Yousef et al. [Anal. Math. Phys. 11: 58 (2021)] introduced two new subclasses of analytic and bi-univalent functions and obtained the estimates on the first two Taylor-Maclaurin coefficients |a<sub>2</sub>| and |a<sub>3</sub>| for functions belonging to these classes. In this study, we introduce a general subclass 𝔅<sup>h,p</sup><sub>Σ</sub>(λ, μ, 𝛿) of analytic and bi-univalent functions in the unit disk 𝕌, and investigate the coefficient bounds for functions belonging to this general function class. Our results improve the results of the above mentioned paper of Yousef et al.
Coefficient Bounds for Bi-spirallike Analytic Functions
Soren, Madan Mohan,Mishra, Akshaya Kumar Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.4
In the present paper, we introduce and investigate two new subclasses, namely; the class of strongly ${\alpha}$-bi-spirallike functions of order ${\beta}$ and ${\alpha}$-bi-spirallike functions of order ${\rho}$, of the function class ${\Sigma};$ of normalized analytic and bi-univalent functions in the open unit disk $$U=\{z:z{\in}C\;and\;{\mid}z{\mid}<1\}$$. We find estimates on the coefficients ${\mid}a_2{\mid}$, ${\mid}a_3{\mid}$ and ${\mid}a_4{\mid}$ for functions in these two subclasses.
COEFFICIENT BOUNDS FOR CERTAIN SUBCLASSES OF COMPLEX ORDER TYPE β
Anessa Oshah,MASLINA DARUS 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.4
In the present work, we aim at determine the coefficient bounds for certain subclasses of convex functions of complex order, which are introduced here by means of a family of nonhomogeneous Cauchy-Euler differential equations.
Coefficient bounds for certain subclasses of meromorphic and bi-univalent functions
Trailokya Panigrahi 대한수학회 2013 대한수학회보 Vol.50 No.5
In the present investigation, the author introduces two interesting subclasses of normalized meromorphic univalent functions w = f(z) defined on ˜ := {z 2 C : 1 < |z| < 1} whose inverse f−1(w) is also univalent meromorphic in ˜. Estimates for the initial coefficients are obtained for the functions in these new subclasses.
Coefficient bounds for $p$-valently close-to-convex functions associated with vertical strip domain
Serap Bulut 강원경기수학회 2021 한국수학논문집 Vol.29 No.2
By considering a certain univalent function that maps the unit disk $\mathbb{U}$ onto a strip domain, we introduce new subclasses of analytic and $p$-valent functions and determine the coefficient bounds for functions belonging to these new classes. Relevant connections of some of the results obtained with those in earlier works are also provided.