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It is proved that the fundamental group of the space of harmonic polynomials of degree n(n ≥ 2), with the same Gaussian curvature is not trivial. Furthermore, we give an example of topologically noneq...
A Note on the Central Limit Theorem for the Eigenvalue Counting Function of Wigner and Covariance matrices
Central Limit Theorem the Eigenvalue Counting Function
2010/11/23
This note presents some central limit theorems for the eigenvalue counting function of Wigner matrices in the form of suitable translations of results by Gustavsson and O'Rourke on the limiting behavi...
A note on q-Bernstein polynomials
q-Bernstein polynomials q-Euler numbers q-Stirling numbers
2010/11/26
Recently, Simsek-Acikgoz([17]) and Kim-Jang-Yi([9]) have studied the q-extension of Bernstein polynomials. In this paper we propose the q-extension of Bern-stein polynomials of degree n, which are dif...
A Note on Some New Refinements of Jensen's Inequality for Convex Functions
Convex function Jensen's inequality Refinements of Jensen's inequality
2010/1/25
In this note, we obtain two new refinements of Jensen's inequality for convex functions.
A Note on Quasiconvexity and Rank-one Convexity for 2$\times$2 Matrices
Quasiconvexity 2$\times$2 Matrices Rank-one Convexity
2009/1/22
We report on an attempt to find a counterexample to the statement that rank-one convexity does not imply quasiconvexity in the case of 2$\times$2 matrices. The failure of such attempt is a consequence...
A Note on the Closedness of the Convex Hull and Its Applications
Convex Hull Applications spannability
2009/1/22
This paper answers the following question motivated by the problem of spannability of functions. When is the convex hull of an unbounded (closed) set closed? We provide necessary and sufficient condit...
We use a parabolic region to prove certain inequalities for uniformly p-valent functions in the open unit disk D.
NOTE ON THE DIOPHANTINE EQUATION
2007/12/13
<正> Dr.Erd(?)s conjectured that the Diophantine equation(1)x~x y~y=z~zhas no integer solution, if,x>1,y>1.z>1.In the present note,Ⅰshall prove that his conjecture is correct ouly (?)(x,y)=1 and(1)has ...