https://rajpub.com/index.php/jam/issue/feed JOURNAL OF ADVANCES IN MATHEMATICS 2021-01-06T08:01:43+00:00 Editorial Office editor@rajpub.com Open Journal Systems https://rajpub.com/index.php/jam/article/view/8945 Golden Ratio 2020-12-30T04:06:07+00:00 Dr. Chetansing Rajput chetansingkrajput1129@gmail.com <p>This paper introduces the unique geometric features of 1:2: right triangle, which is observed to be the quintessential form of Golden Ratio (φ). The 1:2: triangle, with all its peculiar geometric attributes described herein, turns out to be the real ‘Golden Ratio Triangle’ in every sense of the term. This special right triangle also reveals the fundamental Pi:Phi (π:φ) correlation, in terms of precise geometric ratios, with an extreme level of precision. Further, this 1:2: triangle is found to have a classical geometric relationship with 3-4-5 Pythagorean triple. The perfect complementary relationship between1:2: <strong> </strong>triangle and 3-4-5 triangle not only unveils several new aspects of Golden Ratio, but it also imparts the most accurate π:φ correlation, which is firmly premised upon the classical geometric principles. Moreover, this paper introduces the concept of special right triangles; those provide the generalised geometric substantiation of all Metallic Means.</p> 2021-01-17T00:00:00+00:00 Copyright (c) 2021 Dr. Chetansing Rajput https://rajpub.com/index.php/jam/article/view/8912 On Pointwise Product Vector Measure Duality 2020-11-04T03:12:58+00:00 Levi Otanga Olwamba moduor@kabianga.ac.ke Maurice Oduor moduor@kabianga.ac.ke <p>This article is devoted to the study of pointwise product vector measure duality. The properties of Hilbert function space of integrable functions and pointwise sections of measurable sets are considered through the application of integral representation of product vector measures, inner product functions and products of measurable sets.</p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 Levi Otanga Olwamba, Maurice Oduor https://rajpub.com/index.php/jam/article/view/8927 For the Fourier transform of the convolution in and D' and Z' 2020-11-29T11:42:41+00:00 Vasko Rechkoski vaskorecko@yahoo.com Bedrije Bedzeti bedrije_a@hotmail.com Vesna Manova Erakovikj vesname@pmf.ukim.mk <p>In this paper, we give another proof of the known lemma considering the Fourier transform of the convolution of a distribution and a function. Also, we give its application in the mentioned spaces.</p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 Vasko Rechkoski, Bedrije Bedzeti, Vesna Manova Erakovikj