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• Author or Editor: J. Lee
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## Integral solutions in arithmetic progression for y2=x3+k

Periodica Mathematica Hungarica
Authors:
J. Lee
and
W. Vélez

## Abstract

Integral solutions toy 2=x 3+k, where either thex's or they's, or both, are in arithmetic progression are studied. When both thex's and they's are in arithmetic progression, then this situation is completely solved. One set of solutions where they's formed an arithmetic progression of length 4 had already been constructed. In this paper, we construct infinitely many sets of solutions where there are 4x's in arithmetic progression and we disprove Mohanty's Conjecture [8] by constructing infinitely many sets of solutions where there are 4, 5 and 6y's in arithmetic progression.

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## A construction of minimal asymptotic bases

Periodica Mathematica Hungarica
Author:
J. B. Lee

Jia and Nathanson [2] give a simple and explicit construction of minimal asymptotic bases of orderh for everyh=2. They constructed minimal asymptotic bases from partition of N by means of powers of 2. In this paper, we extend the results of that paper to asymptotic bases constructed from partitions of N by means ofg-adic representations forg=2. Corollary 3 shows that given partition N=W 0?W 1?...?W h-1 such that eachW i contains infinitely many pairs of consecutive integers we can construct a minimal asymptotic bases of orderh in infinitely many way.

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## Integrability of certain solutions of differential equations

Periodica Mathematica Hungarica
Author:
Sung J. Lee

Let L=Po(d/dt)n+P1(d/dt)n−1+...+Pn denote a formally self-adjoint differential expression on an open intervalI=(a, b) (−∞≦a<b≦∞). Here the Pk are complex valued with (n — k) continuous derivatives onI, and P0(t)≠ 0 onI. We discuss integrability of functions which are adjoint to certain fundamental solutions ofLy=λy, and a related consequence.

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## On nonnegatively curved 4-manifolds with discrete symmetry

Acta Mathematica Hungarica
Authors:
J. Kim
and
H. Lee

## Abstract

Let M be the closed, simply connected, 4-manifold with nonnegative sectional curvature, called a nonnegatively curved 4-manifold, with an effective and isometric Z m -action for a positive integer m ≧ 617. Assume that Z m acts trivially on the homology of M. The goal of this short paper is to prove that if the fixed point set of any nontrivial element of Z m has at most one two-dimensional component, then M is homeomorphic to S 4, # i l =1S 2 × S 2, l = 1, 2, or # j k = 1 ± CP 2, k = 1, 2, 3, 4, 5. The main strategy of this paper is to give an upper bound of the Euler characteristic χ(M) under the homological assumption of a Z m -action as above by using the Lefschetz fixed point formula.

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## On real hypersurfaces with η-parallel curvature tensor in complex space forms

Acta Mathematica Hungarica
Authors:
J. Lee
,
J. Pérez
, and
Y. Suh

## Abstract

The purpose of this paper is to give a complete classification of real hypersurfces M in complex space forms M n(c), c≠0 in terms of an η-parallel curvature tensor and a certain commutative condition defined on the distribution T 0={XT x M| Xξ} of M in M n(c).

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Scientometrics
Authors:
M. Lee
,
K. Om
, and
J. Koh

## Abstract

This article addresses the potential effectiveness of blind review in selecting and funding research proposals in a “scientifically small” country. By analyzing 474 responses of the blinded reviewers ever worked for Korea Science and Engineering Fund, it was found that blind review is fairly effective. About two thirds of the blinded reviewers were unable to recognize the applicants accurately. The applicant detection was affected by (1) physical age, (2) professional experience, and (3) geographical location of doctoral education of the applicant, (4) review experience, (5) rank of employing universities of the reviewers, and (6) similirity of research interest between an applicant and a reviewer. It was also found that blind review was more strongly advocated by those who had made a wrong guess or who had given up guessing. Implications of the findings and future research directions were discussed.

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## A Luecking type subspace, dualities and Toeplitz operators

Acta Mathematica Hungarica
Authors:
B. R. Choe
and
Y. J. Lee
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## Stability and convergence of modified Ishikawa iterative sequences with errors in Banach spaces

Acta Mathematica Hungarica
Authors:
S. S. Chang
,
W. H. J. Lee
, and
K. K. Tan

## Summary

Some stability and convergence theorems of the modified Ishikawa iterative sequences with errors for asymptotically nonexpansive mapping in the intermediate sense and asymptotically pseudo contractive and uniformly Lipschitzian mappings in Banach spaces are obtained.

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## Book reviews

Periodica Mathematica Hungarica
Authors:
L. Márki
,
A. Lee
,
R. Wiegandt
,
J. Bognár
,
Z. Magyar
, and
G. Stoyan
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## Book reviews

Periodica Mathematica Hungarica
Authors:
A. Lee
,
I. Bihari
,
M. Farkas
,
Gy. Terdik
,
R. Wiegandt
,
Z. Sebestyén
,
J. Lehel
, and
V. Totik
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