Journal of Progressive Research in Mathematics Journal of Progressive Research in Mathematics Scitech Research Organisation en-US Journal of Progressive Research in Mathematics 2395-0218 Certain Subclasses Of Harmonic Starlike Functions Associated With q-Analouge Of Ruscheweyh Operator <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> S. R. Swamy PK Mamatha ##submission.copyrightStatement## 2020-08-20 2020-08-20 16 4 3109 3121 A Geometric Construction of Multiwavelet Sets of L^2(R) and H^2(R) <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> Shiva Mittal ##submission.copyrightStatement## 2020-08-20 2020-08-20 16 4 3122 3132 Fuzzy Parameterized Complex Multi-Fuzzy Soft Expert Set in Prediction of Coronary Artery Disease <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> Imad Al-Zuhairi Yousef Al-Qudah Wathek Chammam Mohammed Khalaf Ahmed El moasry Hamza Qaqazeh Mohammed Almousa ##submission.copyrightStatement## 2020-09-04 2020-09-04 16 4 3133 3157 Properties On A New Comprehensive Family Of Holomorphic Functions Associated With Ruscheweyh Derivative and Generalized Multiplier Transformations <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> S. R. Swamy Maslina Darus Y Sailaja ##submission.copyrightStatement## 2020-09-08 2020-09-08 16 4 3158 3166 A note on almost Trans-1-Golden submersions <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> T. Tshikuna-Matamba ##submission.copyrightStatement## 2020-09-21 2020-09-21 16 4 3167 3176 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] <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> Ikorong Annouk Paul Archambault ##submission.copyrightStatement## 2020-09-22 2020-09-22 16 4 3177 3181