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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus…
Hemant Kumar Pathak
The purpose of this note is to point out several obscure places in the results of Ahmed and Zeyada [J. Math. Anal. Appl. 274 (2002) 458-465]. In order to rectify and improve the results of Ahmed and Zeyada, we introduce the concepts of locally quasi-nonexpans…
Weiwei Xiao, Weijun Luan
n this paper, the relative widths of some sets in are studied. Relative widths is the further development of Kolmogorov widths and it is a new problem in approximation theory which aroused some mathematics workers great interest recently. We present some basi…
Moawia Alghalith
We present a methodology that allows endogenous derivation of the moments of the probability distributions. In doing so, we, present an alternative objective function and alternative concept of risk aversion. In addition, we show that the risk measure depends…
Gulshan Singh, W. M. Shah, Yash Paul
If is a polynomial of degree , having all its zeros in |z|≤K, K≥1 , then it was proved by Aziz and Rather [2] that for every real or complex number with |a| ≥K, . In this paper, we sharpen above result for the polynomials p(z) of degree n＞3
Amara Chandoul
Let D≠1 be a positive non-square integer and k≥2 be any fixed integer. Extending the work of A. Tek-can, here we obtain some formulas for the integer solutions of the Pell equation X<sup>2</sup> - Dy<sup>2</sup> = ± k<sup>2</sup> .
Junliang Wu, Pingping Zhang
In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar m…
Huashui Zhan
Let be a simply connected complete Riemannian manifold with dimension n≥3 . Suppose that the sectional curvature satisfies , where p is distance function from a base point of M, a, b are constants and . Then there exist harmonic functions on M .
Moawia Alghalith
In contrast to the Euler method and the subsequent methods, we provide solutions to nonlinear ordinary differential equations. Consequently, our method does not require convergence. We apply our method to a second-order nonlinear ordinary differential equatio…
Pinheiro Marcia
In this short, but fundamental, note, we start progressing towards a mathematically sound definition of the real functional classes 2sK
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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
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