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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…
Prosper Kouadio Kimou, François Emmanuel Tanoé, Kouassi Vincent Kouakou
In this paper we prove in a new way, the well known result, that Fermat’s equation<i> </i><i>a</i><sup>4</sup> + <i>b</i><sup>4</sup> = <i>c</i><sup>4</sup>, is not solvable in <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mi>!…
Léopold Dèkpassi Keuméan, François Emmanuel Tanoé
Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow> <mrow><mo>(</mo> <mrow> <mi>a</mi><mn>,</mn><mi>b</mi><mn>,</mn><mi>c</mi></m…
Nicholas Simon Gonchar
To implement the previously formulated principles of sustainable economic development, all solutions of the linear system of equations and inequalities, which are satisfied by the vector of real consumption, are completely described. It is established that th…
John Richard Wisdom
Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before <i>ζ</i> (such that <img src="https://html.scirp.org/…
Meiyin Wang, Wanzhou Ye
The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the op…
Lyndon O. Barton
This paper presents an alternate graphical procedure ( Method 2 ), to that presented in earlier publications entitled, “ A Procedure for Trisecting an Acute Angle ” and “ A Key to Solving the Angle Trisection Problem ” . The procedure, when applied to the 30…
Kiyoyuki Tchizawa, Shuya Kanagawa
When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce paramet…
Murphy E. Egwe, Samuel S. Sangodele
Let <i>G</i> be a locally compact Lie group and <img src="https://html.scirp.org//file/5302366-rId13.svg?20240402112528" /> its Lie algebra. We consider a fuzzy analogue of <i>G,</i> denoted by <img src="https://html.scirp.org//file/5302366-rId15.svg?20240402…
Nicholas O. Okeke, Murphy E. Egwe
Given a compact and regular Hausdorff measure space ( X , μ ), with μ a Radon measure, it is known that the generalised space M ( X ) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L ∞ ( X , μ ) on X . We c…
Panchanan Pramanik, Susmita Pramanik, Sabyasachi Sen
The Fermat–Pramanik series are like below: . The mathematical principle has been established by factorization principle. The Fermat-Pramanik tree can be grown. It produces branched Fermat-Pramanik series using same principle making Fermat-Pramanik chain. Bran…
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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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