Journal of Progressive Research in Mathematics 2020-09-22T16:27:50+00:00 Managing Editor Open Journal Systems Journal of Progressive Research in Mathematics Certain Subclasses Of Harmonic Starlike Functions Associated With q-Analouge Of Ruscheweyh Operator 2020-09-05T17:48:38+00:00 S. R. Swamy PK Mamatha <p>In this work, we introduce and study a subclass of harmonic uniformly <em>β</em> - starlike functions defined by <em>q</em>-analogue of Ruscheweyh derivative operator. Coefficient bounds, extreme points, distortion bounds, convolution conditions and convex combination are determined for functions in this class. Also, properties of the class preserving under. The generalized Bernardi-Libera –Livingston integral operator and the <em>q</em>-Jackson integral operator are discussed. Furthermore, many of our results are either extensions or new approaches to those corresponding to previously known results.</p> 2020-08-20T04:35:02+00:00 ##submission.copyrightStatement## A Geometric Construction of Multiwavelet Sets of L^2(R) and H^2(R) 2020-09-04T06:58:02+00:00 Shiva Mittal <p>In the present article we construct symmetric multiwavelet sets of finite order in L^2(R) and multiwavelet sets in H^2(R) by considering the geometric construction determining wavelet sets provided by N. Arcozzi, B. Behera and S. Madan for large classes of minimally supported frequency wavelets of L^2(R) and H^2(R).</p> 2020-08-20T00:00:00+00:00 ##submission.copyrightStatement## Fuzzy Parameterized Complex Multi-Fuzzy Soft Expert Set in Prediction of Coronary Artery Disease 2020-09-04T11:37:23+00:00 Imad Al-Zuhairi Yousef Al-Qudah Wathek Chammam Mohammed Khalaf Ahmed El moasry Hamza Qaqazeh Mohammed Almousa <p>In this work, state the risk and treatment of coronary artery disease our aim. The weighted fuzzy parameterized complex multi-fuzzy soft expert set plays the main roads to arrive a maple treatment. We take a reality values of the a asymptotes systolic blood pressure, lowdensity lipoprotein cholesterol, maximum heart rate, blood sugar, old peak and age of nine patients and transform by FORTRAN program to weighted fuzzy parameterized complex multifuzzy soft expert set. By Kong algorithm state the positive and negative decision, from these decisions state the degree of risk and treatments. Our decision helps the hospital doctor to state the treatments drug therapy or intervention.</p> 2020-09-04T11:37:22+00:00 ##submission.copyrightStatement## Properties On A New Comprehensive Family Of Holomorphic Functions Associated With Ruscheweyh Derivative and Generalized Multiplier Transformations 2020-09-08T08:15:45+00:00 S. R. Swamy Maslina Darus Y Sailaja <p>In the present paper, a new comprehensive family of holomorphic functions, which includes various new subfamilies of holomorphic functions as well as some very well-known ones, is introduced. Sharp results concerning coefficient inequalities and distortion bounds of functions belonging to these families are determined. Furthermore, functions with negative coefficients belonging to these families are also investigated.</p> 2020-09-08T08:12:51+00:00 ##submission.copyrightStatement## A note on almost Trans-1-Golden submersions 2020-09-21T03:15:11+00:00 T. Tshikuna-Matamba <p>In this Note, two types of submersions whose total space is an almost trans-1-Golden manifold are studied. The study focuses on the transference of structures from the total space to the base one and the the geometry of the fibers.</p> 2020-09-21T03:15:11+00:00 ##submission.copyrightStatement## An Original note on Fermat numbers, on numbers of the form Wn and on numbers of the form 10k + 8 + Fn [ where Wn ∈ {22 + Fn, 2 n + Fn}, n is an integer ≥ 0, Fn is a Fermat number and k is an integer ≥ 0] 2020-09-22T16:27:50+00:00 Ikorong Annouk Paul Archambault <p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">A Fermat number is a number of the form Fn = 2^2^ n+ 1, where n is an integer ≥ 0. A Fermat composite (see [1] or [2] or [4] ) is a non prime Fermat number. Fermat composites and Fermat primes are characterized via divisibility in [4] and [5] (A Fermat prime (see [1] or [2] or [4] ) is a prime Fermat number). It is known (see [4]) that for every j ∈ {0, 1, 2, 3, 4}, Fj is a Fermat prime and it is also known (see [2] or [3]) that F5 and F6 are Fermat composites. In this paper, we show [via elementary arithmetic congruences] the following result (T.). For every integer n ≥ 2, Fn − 1 ≡ 1 mod[j] (where j ∈ {3, 5}). Result (T) immediately implies that for every fixed integer k ≥ 0, there exists at most two primes of the form 10k + 8 + Fn [in particular , for every fixed integer k ≥ 0, the numbers of the form 10k + 8 + Fn (where n is an integer ≥ 2) are all composites]. Result (T.) also implies that there are infinitely many composite numbers of the form 2n + Fn and there exists no prime number of form 22+Fn. Result (T.) coupled with a special case of a Theorem of Dirichlet help us to explain why it is natural to conjecture that there are infinitely many Fermat primes.</p> 2020-09-22T16:27:50+00:00 ##submission.copyrightStatement##