http://eiris.it/ojs/index.php/ratiomathematica/issue/feedRatio Mathematica2020-12-31T14:16:23+01:00Fabrizio Maturofabrizio.maturo@unicampania.itOpen Journal Systems<p><strong>RATIO MATHEMATICA - JOURNAL OF MATHEMATICS, STATISTICS, AND APPLICATIONS</strong></p><p>Ratio Mathematica is an International, double peer-reviewed, open access journal, published every six months (June-December). Ratio Mathematica publishes original research articles on theoretical Mathematics and Statistics. However, contributions with applications to Social Science, Engineering, and Economics are welcome. 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Any ellipses (... marks) shown in this report originate with the data source; they are NOT caused by subsequent processing in Publish or Perish.</p><p><br />Metrics</p><p>Reference date: 2021-02-01 09:18:25 +0100<br />Publication years: 1990-2020<br />Citation years: 31 (1990-2021)<br />Papers: 317<br />Citations: 855<br />Citations/year: 27.58 (acc1=31, acc2=16, acc5=0, acc10=0, acc20=0)<br />Citations/paper: 2.70<br />Authors/paper: 1.71/2.0/1 (mean/median/mode)<br />Age-weighted citation rate: 94.70 (sqrt=9.73), 66.19/author<br />Hirsch h-index: 15 (a=3.80, m=0.48, 346 cites=40.5% coverage)<br />Egghe g-index: 20 (g/h=1.33, 418 cites=48.9% coverage)<br />PoP hI,norm: 12<br />PoP hI,annual: 0.39<br />Fassin hA-index: 3</p>http://eiris.it/ojs/index.php/ratiomathematica/article/view/524A simple goodness-of-fit test for continuous conditional distributions2020-12-30T15:55:57+01:00Peter J. Veaziepeter_veazie@urmc.rochester.eduZhiqiu YeZhiqiu_Ye@URMC.Rochester.edu<p>This paper presents a pragmatic specification test for conditional continuous distributions with uncensored data. We employ Monte Carlo (MC) experiments and the 2011 Medical Expenditure Panel Survey data to examine coverage and power to discern deviations from correct model specification in distribution and parameterization. We carry out MC experiments using 2000 runs for sample sizes 500 and 1000. The experiments show that the test has accurate coverage under correct specification, and that the test can discern deviations from correct specification in both the distributional family and parameterization. The power increases as sample size increases. The empirical example shows the test’s ability to identify specific distributions from other candidates using real cost data. Although the test can be used as a goodness-of-fit test for marginal distributions, it is particularly useful as an easy-to-use test for conditional continuous distributions, even those with one observation per pattern of explanatory variables.</p>2020-12-30T10:32:13+01:00Copyright (c) 2020 Peter J. Veazie, Zhiqiu Yehttp://eiris.it/ojs/index.php/ratiomathematica/article/view/532Modelling the shape of sunspot cycle using a modified Maxwell-Boltzmann probability distribution function2020-12-30T15:57:04+01:00Amaranathan Sabarinatha_sabarinath@yahoo.co.inGirija Puthumana Beenabeenamabhi@gmail.comAjimandiram Krishnankuttynair Anilkumarak_anilkumar@isro.gov.in<p><strong>Abstract</strong></p><p>The 11 year sunspot number cycle has been a fascinating phenomenon for many scientists in the last three centuries. Various mathematical functions have been used for modelling the 11 year sunspot number cycles. In this paper, we present a new model, which is derived from the well known Maxwell-Boltzmann probability distribution function. A modification has been carried out by introducing a new parameter, called <em>area</em> parameter to model sunspot number cycle using Maxwell-Boltzmann probability distribution function. This parameter removes the normality condition possessed by probability density function, and fits an arbitrary sunspot cycle of any magnitude. The new model has been fitted in the actual monthly averaged sunspot cycles and it is found that, the Hathaway-Wilson-Reichmann measure, goodness of fit is high. The estimated parameters of the sunspot number cycles 1 to 24 has been presented in this paper. A Monte Carlo based simple random search is used for nonlinear parameter estimation. Prediction has been carried out for the next sunspot number cycles 25 through a model by averaging of recent cycle’s model parameters. This prediction can be used for simulating a more realistic sunspot cycle profile. Through extensive Monte Carlo simulations, large number of sunspot cycle profile could be generated and these can be used in the orbital dynamics studies. <strong></strong></p>2020-12-30T10:32:13+01:00Copyright (c) 2020 Beena et al.http://eiris.it/ojs/index.php/ratiomathematica/article/view/552New structure of norms on R^n and their relations with the curvature of the plane curves2020-12-30T15:54:58+01:00Amir Veisiveisi75@gmail.comAli Delbaznasabdelbaznasab@gmail.com<p>Let $f_1, f_2, \ldots, f_n$ be fixed nonzero real-valued functions on $\mathbb{R}$, the real numbers. Let $\varphi_n(X_n)= \big(x_1^2f_1^2+x_2^2f_2^2+ \ldots + x_n^2f_n^2 \big)^{\frac{1}{2}}$, where $X_n=(x_1, x_2, \ldots, x_n) \in \mathbb{R}^n$. We show that $\varphi_n$ has properties similar to a norm on the normed linear space. Although $\varphi_n$ is not a norm on $\mathbb{R}^n$ in general, it induces a norm on $\mathbb{R}^n$. For the nonzero function $F : \mathbb{R}^2 \to \mathbb{R}$, a curvature formula for the implicit curve $G(x, y)=F^2(x, y)=0$ at any regular point is given. A similar result is presented when $F$ is a nonzero function from $\mathbb{R}^3$ to $\mathbb{R}$. In continued, we concentrate on $F(x, y)=\int_a^b \varphi_2(x, y)dt$. It is shown that the curvature of $F(x, y)=c$ when $c>0$ is a positive multiple of $c^2$. Particularly, we observe that $F(x, y)=\int_0^{\frac{\pi}{2}} \sqrt{x^2 \cos^2 t + y^2 \sin^2 t} dt$ is an elliptic integral of the second kind.</p>2020-12-30T10:32:14+01:00Copyright (c) 2020 Amir Veisi, Ali Delbaznasabhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/561Parameter estimation of p-dimensional Rayleigh distribution under weighted loss function2020-12-30T15:57:42+01:00Arun Kumar Raoarunrao1972@gmail.comHimanshu Pandeyhimanshu_pandey62@yahoo.comIn this paper, p-dimensional Rayleigh distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of p-dimensional Rayleigh distribution by using quasi and inverted gamma priors. The Bayes estimators of the scale parameter have been obtained under squared error and weighted loss functions.2020-12-30T10:32:14+01:00Copyright (c) 2020 Rao and Pandeyhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/521On some computational and applications of finite fields2020-12-30T15:58:05+01:00Jean Pierre Muhirwamuhijeapi@gmail.com<p>Finite field is a wide topic in mathematics. Consequently, none can talk about the whole contents of finite fields. That is why this research focuses on small content of finite fields such as polynomials computational, ring of integers modulo p where p is prime or a power of prime. Most of the times, books which talk about finite fields are rarely to be found, therefore one can know how arithmetic computational on small finite fields works and be able to extend to the higher order. This means how integer and polynomial arithmetic operations are done for Z p such as addition, subtraction, division and multiplication in Z p followed by reduction of p (modulo p). Since addition is the same as subtraction and division is treated as the inverse of the multiplication, thus in this paper, only addition and multiplication arithmetic operations are applied for the considered small finite fields (Z 2 − Z 17 ). With polynomials, one can learn from this paper how arithmetic computational through polynomials over finite fields are performed since these polynomials have coefficients drawn from finite fields. The paper includes also construction of polynomials over finite fields as an extension of finite fields with polynomials. This lead to arithmetic computational tables for the finite fields F q [x]/f(x), where f(x) is irreducible over F q . From the past decades, many researchers complained about the applications of some topics in pure mathematics and therefore the finite fields play more important role in coding theory, which involves error-coding detection and error-correction as well as cyclic codes. As a result, this research paper shows these applications among others.</p>2020-12-30T10:32:14+01:00Copyright (c) 2020 Muhirwa Jean Pierrehttp://eiris.it/ojs/index.php/ratiomathematica/article/view/559Teaching as a decision-making model: strategies in mathematics from a practical requirement2020-12-30T15:51:54+01:00Viviana Ventreviviana.ventre@unicampania.itEva Ferrara Denticeeva.ferraradentice@unicampania.itRoberta Martinorobertamartino54@gmail.com<p>The need in the current social context to adopt teaching methods that can stimulate students and lead them towards autonomy, awareness and independence in studying could conflict with the needs of students with specific learning disorders, especially in higher education, where <em>self-learning and self-orientation</em> are required. In this sense, the choice of effective teaching strategies becomes a decision-making problem and must therefore be addressed as such. This article discusses some mathematical models for choosing effective methods in mathematics education for students with specific learning disorders. It moves from the case study of a student with specific <em>reading and writing disorders enrolled in the mathematical analysis course 1 of the degree course in architecture and describes the personalized teaching strategy created for him.</em></p>2020-12-30T10:32:14+01:00Copyright (c) 2020 Viviana Ventre, Eva Ferrara Dentice, Roberta Martinohttp://eiris.it/ojs/index.php/ratiomathematica/article/view/562On homomorphisms from Cn to Cm2020-12-30T15:58:25+01:00Sivadasan Vinodwenod76@gmail.comGopinadhan Sathikumari Bijugsbiju@cet.ac.in<p>In this paper, using elementary algebra and analysis, we characterize and compute all continuous homomorphism from Cn to Cm. Also we prove that the cardinality of the set of all non-continous group homomorphism from Cn to Cm is at least the cardinality of the continuum.</p>2020-12-30T10:32:14+01:00Copyright (c) 2020 S Vinod, GS Bijuhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/534Frattini submultigroups of multigroups2020-12-30T15:52:16+01:00Joseph Achile Otuwetalk2josephotuwe2016@gmail.comMusa Adeku Ibrahimtalk2josephotuwe2016@gmail.com<p>In this paper, we introduce and study maximal submultigroups and present some of its algebraic properties. Frattini submultigroups as an extension of Frattini subgroups is considered. A few submultigroups results on the new concepts in connection to normal, characteristic, commutator, abelian and center of a multigroup are established and the ideas of generating sets, fully and non-fully Frattini multigroups are presented with some significant results.</p>2020-12-30T10:32:14+01:00Copyright (c) 2020 J.A. Otuwe, M.A. Ibrahimhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/550KCD indices and coindices of graphs2020-12-30T15:52:29+01:00Keerthi G. Mirajkarkeerthi.mirajkar@gmail.comAkshata Morajkarakmorajkar@gmail.com<p>The relationship between vertices of a graph is always an interesting fact, but the relations of vertices and edges also seeks attention. Motivation of the relationship between vertices and edges of a graph has helped to arise with a set of new degree based topological indices and coindices named KCD indices and coindices. These indices and coindices are elaborated by establishing a set of properties. More fascinating results of some graph operations using KCD indices are developed in this article.</p>2020-12-30T10:32:14+01:00Copyright (c) 2020 Keerthi G. Mirajkar, Akshata Morajkarhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/549CAS wavelet approximation of functions of Holder class and solutions of Fredholm integral equation2020-12-31T14:16:23+01:00Shyam Lalshyam_lal@rediffmail.comSatish Kumarsatishkumar3102@gmail.com<p>In this paper, cosine and sine wavelet is considered. Two new CAS wavelet estimators E(1) 2k;2M+1(f) and E(2) 2k;2M+1(f) for the approximation of a function f whose first derivative f' and second derivative f '' belong to Hölder's class Hα [0; 1) of order 0 <α≤1, have been obtained. These estimators are sharper and best in wavelet analysis.Using CAS wavelet a computational method has been developed to solve Fredholm integral equation of second kind. In this process, Fredholm integral equations are reduced into a system of linear equations. Approximation of function by CAS wavelet method is applied in obtaining the solution of Fredholm integral equation of second kind. CAS wavelet coefficient matrices are prepared using the properties of CAS wavelets.Two examples are illustrated to show the validity and efficiency of the technique discussed in this paper.</p>2020-12-30T10:32:14+01:00Copyright (c) 2020 Shyam Lal, Satish Kumarhttp://eiris.it/ojs/index.php/ratiomathematica/article/view/554Uniqueness of an entire function sharing a polynomial with its linear differential polynomial2020-12-30T15:52:57+01:00Imrul Kaishimrulksh3@gmail.comNasir Uddin Gazinsrgazi@gmail.comIn this paper we consider an entire function when it shares a polynomial with its linear differential polynomial. Our result is an improvement of a result of P. Li.2020-12-30T10:32:15+01:00Copyright (c) 2020 Imrul Kaish, Nasir Uddin Gazihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/553On homomorphism of fuzzy multigroups2020-12-30T15:53:09+01:00Johnson Aderemi Awololaremsonjay@yahoo.comM.A. Ibrahimbrahim@abu.edu.ng<p>In this paper, the homomorphism of fuzzy multigroups is briefly delineated following [2] and their corresponding isomorphism theorems are considered.</p>2020-12-30T10:32:15+01:00Copyright (c) 2020 Johnson Aderemi Awololahttp://eiris.it/ojs/index.php/ratiomathematica/article/view/535On a class of sets between a-open sets and gδ-open sets2020-12-30T15:53:22+01:00Jagadeesh B. Toranagattijagadeeshbt2000@gmail.com<p>In this paper, a new class of sets called Da-open sets are introduced and investigated with the help of gδ-open and δ-closed sets. Relationships between this new class and other related classes of sets are established and as an application Da-continuous functions have been dened to study its properties in terms of Da-open sets.Finally, some properties of Da-closed graph and (D.a)-closed graphs are investigated.</p>2020-12-30T10:32:15+01:00Copyright (c) 2020 Jagadeesh B. Toranagattihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/560Determine the value d(M(G)) for non-abelian p-groups of order q = pnk of Nilpotency c2020-12-30T15:53:34+01:00Behnam RazzaghmaneshiB_razzagh@yahoo.com<p>In this paper we prove that if <em>n</em>, <em>k </em>and <em>t </em>be positive integer numbers such that <em>t </em>< <em>k </em>< <em>n </em>and <em>G </em>is a non abelian <em>p</em>-group of order <em>p</em><em>nk </em>with derived subgroup of order <em>p</em><em>kt </em>and nilpotency class c, then the minimal number of generators of <em>G </em>is at most <em>p</em>1 2 ((<em>nt</em>+<em>kt</em>−2)(2<em>c</em>−1)(<em>nt</em>−<em>kt</em>−1)+<em>n</em>. In particular, |<em>M</em>(<em>G</em>)| _ <em>p</em>1 2 (<em>n</em>(<em>k</em>+1)−2)(<em>n</em>(<em>k</em>−1)−1)+<em>n</em>, and the equality holds in this last bound if and only if <em>n </em>= 1 and <em>G </em>= <em>H </em>×<em>Z</em>, where <em>H </em>is extra special <em>p</em>-group of order <em>p</em>3<em>n </em>and exponent <em>p</em>, and <em>Z </em>is an elementary abelian <em>p</em>-group.</p>2020-12-30T10:32:15+01:00Copyright (c) 2020 Behnam Razzaghmaneshihttp://eiris.it/ojs/index.php/ratiomathematica/article/view/564Thermodynamic behavior of the polytropic gas in cosmology2020-12-30T16:00:02+01:00Prasanta Dasprasantadasp4@gmail.comKangujam Priyokumar Singhpkangujam18@gmail.com<p>In this paper, we investigate on the thermodynamic behavior of Polytropic gas as a candidate for dark energy by considering the relation P=KP^(1+1/n), where and are the Polytropic constant and Polytropic index respectively. Furthermore, indicates the pressure and is the energy density of the ﬂuid such that where and represent the internal energy and volume, respectively. At first, we find an exact expression for the energy density of the Polytropic gas using thermodynamics and later on, discuss different physical parameters. Finally our study shows that the Polytropic gas may be used to describe the expansion history of the universe from the dust dominated era to the current accelerated era and it is thermodynamically stable.</p>2020-12-30T10:32:15+01:00Copyright (c) 2020 Prasanta Das, Kangujam Priyokumar Singh