Ratio Mathematica
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<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. Only English-language publications are accepted.</p><p>The main topics of interest for Ratio Mathematica are:</p><p>-Advances in theoretical mathematics and statistics;<br />-Applications of mathematics and statistics to social science, engineering, ecology, and economics;<br />-Decision-making in conditions of uncertainty;<br />-Fuzzy logic;<br />-Probability theory;<br />-New theories for dissemination and communication of mathematics and statistics.</p><p> </p><p><a href="https://www.dropbox.com/s/kekzw8mwpx9eqdl/Template%20Ratio%20Mathematica.zip?dl=0">DOWNLOAD THE JOURNAL'S TEMPLATE</a></p><p> </p><p><a href="/ojs/index.php/ratiomathematica/author/submit/1">Submit your original paper online</a> (If you do not have access credentials, please contact fabmatu@gmail.com to ask for user and password)</p><p> </p><p><strong>Indexing</strong>: Ratio Mathematica is abstracted and indexed in: </p><p><a title="DOAJ" href="https://doaj.org/toc/2282-8214?source=%7B%22query%22%3A%7B%22filtered%22%3A%7B%22filter%22%3A%7B%22bool%22%3A%7B%22must%22%3A%5B%7B%22term%22%3A%7B%22index.issn.exact%22%3A%222282-8214%22%7D%7D%2C%7B%22term%22%3A%7B%22_type%22%3A%22article%22%7D%7D%5D%7D%7D%2C%22query%22%3A%7B%22match_all%22%3A%7B%7D%7D%7D%7D%2C%22sort%22%3A%5B%7B%22bibjson.year.exact%22%3A%7B%22order%22%3A%22desc%22%7D%7D%2C%7B%22bibjson.month.exact%22%3A%7B%22order%22%3A%22desc%22%7D%7D%5D%2C%22from%22%3A0%2C%22size%22%3A100%7D" target="_blank">DOAJ</a></p><p><a href="http://index.pkp.sfu.ca/index.php/browse/index/1071?sortOrderId=6">PKP (Public Knowledge Project)</a></p><p><a href="https://www.worldcat.org/">OCLC WorldCat</a></p><p><a href="https://scholar.google.it/scholar?hl=it&q=+Ratio+Mathematica&btnG=&lr=">Google Scholar</a></p><p><a href="http://agriculture.academickeys.com/jour_main.php">AcademicKeys</a></p><p><a href="http://journalseek.net/cgi-bin/journalseek/journalsearch.cgi?field=issn&query=1592-7415">Genamics</a></p><p><a href="http://www.journaltocs.ac.uk/index.php?action=search&subAction=hits&journalID=37603&userQueryID=8709&high=1&ps=30&page=1&items=0&journal_filter=&journalby=">JournalTOCs</a></p><p><a href="http://acnp.unibo.it/cgi-ser/start/it/cnr/df-p.tcl?catno=2401374&libr=&person=false&B=2&proposto=NO&year_poss_from=&year_poss_to=">ANCP</a></p><p><a href="http://www.sbn.it/opacsbn/opac/iccu/free.jsp">OPAC SBN</a></p><p><a href="http://www.proquest.com/">PROQUEST</a></p><p><a href="https://bib-pubdb1.desy.de/record/411706">PUBDB</a></p><p><a href="http://rzblx1.uni-regensburg.de/ezeit/searchres.phtml?jq_type1=ZD&jq_term1=2642712-6">ELECTRONIC MAGAZINE LIBRARY</a></p><p>The printed copies of the journal are stored at the <strong>National Library of Florence</strong> and <strong>Provincial Library of Pescara, Italy</strong>.</p><p> </p><p>## ISSN 2282-8214 ##</p><p>Publish or Perish 7.28.3033.7654 (extended report)<br />Windows (x64) edition, running on Windows 10.0.19041 (x64)</p><p>### Search terms ###</p><p>ISSN: 2282-8214<br />Years: all</p><p><br />### Data retrieval ###</p><p>Data source: Google Scholar<br />Search date: 2021-01-16 11:36:51 +0100<br />Cache date: 2021-01-16 11:37:59 +0100<br />Search result: [0] No error</p><p>Important: This data source provides only abbreviated data. 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: 2021-01-16 11:37:59 +0100<br />Publication years: 1990-2020<br />Citation years: 31 (1990-2021)<br />Papers: 317<br />Citations: 842<br />Citations/year: 27.16 (acc1=30, acc2=15, acc5=0, acc10=0, acc20=0)<br />Citations/paper: 2.66<br />Authors/paper: 1.71/2.0/1 (mean/median/mode)<br />Age-weighted citation rate: 91.53 (sqrt=9.57), 63.95/author<br />Hirsch h-index: 15 (a=3.74, m=0.48, 340 cites=40.4% coverage)<br />Egghe g-index: 20 (g/h=1.33, 410 cites=48.7% coverage)<br />PoP hI,norm: 12<br />PoP hI,annual: 0.39</p>APAVen-USRatio Mathematica1592-7415<p>This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:</p><ul><li>Free access for all users worldwide</li><li>Increased visibility and readership</li><li>Rapid publication</li><li>No spatial constraints</li><li>Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)</li></ul><h2>Copyright and Licensing Terms</h2><p>Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. <br />For further information visit: <a href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</a>. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards:</p><p><img id="__wp-temp-img-id" title="" src="http://www.eiris.it/ratio_numeri/ratio_accessori/cc.png" alt="Creative Commonce Licence" width="88" height="31" /></p>A simple goodness-of-fit test for continuous conditional distributions
http://eiris.it/ojs/index.php/ratiomathematica/article/view/524
<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>Peter J. VeazieZhiqiu Ye
Copyright (c) 2020 Peter J. Veazie, Zhiqiu Ye
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2020-12-302020-12-303973210.23755/rm.v39i0.524Modelling the shape of sunspot cycle using a modified Maxwell-Boltzmann probability distribution function
http://eiris.it/ojs/index.php/ratiomathematica/article/view/532
<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>Amaranathan SabarinathGirija Puthumana BeenaAjimandiram Krishnankuttynair Anilkumar
Copyright (c) 2020 Beena et al.
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2020-12-302020-12-3039335410.23755/rm.v39i0.532New structure of norms on R^n and their relations with the curvature of the plane curves
http://eiris.it/ojs/index.php/ratiomathematica/article/view/552
<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>Amir VeisiAli Delbaznasab
Copyright (c) 2020 Amir Veisi, Ali Delbaznasab
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2020-12-302020-12-3039556710.23755/rm.v39i0.552Parameter estimation of p-dimensional Rayleigh distribution under weighted loss function
http://eiris.it/ojs/index.php/ratiomathematica/article/view/561
In 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.Arun Kumar RaoHimanshu Pandey
Copyright (c) 2020 Rao and Pandey
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2020-12-302020-12-3039697710.23755/rm.v39i0.561On some computational and applications of finite fields
http://eiris.it/ojs/index.php/ratiomathematica/article/view/521
<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>Jean Pierre Muhirwa
Copyright (c) 2020 Muhirwa Jean Pierre
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2020-12-302020-12-30397911010.23755/rm.v39i0.521Teaching as a decision-making model: strategies in mathematics from a practical requirement
http://eiris.it/ojs/index.php/ratiomathematica/article/view/559
<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>Viviana VentreEva Ferrara DenticeRoberta Martino
Copyright (c) 2020 Viviana Ventre, Eva Ferrara Dentice, Roberta Martino
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2020-12-302020-12-303911113610.23755/rm.v39i0.559On homomorphisms from Cn to Cm
http://eiris.it/ojs/index.php/ratiomathematica/article/view/562
<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>Sivadasan VinodGopinadhan Sathikumari Biju
Copyright (c) 2020 S Vinod, GS Biju
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2020-12-302020-12-303913714510.23755/rm.v39i0.562Frattini submultigroups of multigroups
http://eiris.it/ojs/index.php/ratiomathematica/article/view/534
<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>Joseph Achile OtuweMusa Adeku Ibrahim
Copyright (c) 2020 J.A. Otuwe, M.A. Ibrahim
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2020-12-302020-12-303914716310.23755/rm.v39i0.534KCD indices and coindices of graphs
http://eiris.it/ojs/index.php/ratiomathematica/article/view/550
<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>Keerthi G. MirajkarAkshata Morajkar
Copyright (c) 2020 Keerthi G. Mirajkar, Akshata Morajkar
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2020-12-302020-12-303916518610.23755/rm.v39i0.550CAS wavelet approximation of functions of Holder class and solutions of Fredholm integral equation
http://eiris.it/ojs/index.php/ratiomathematica/article/view/549
<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>Shyam LalSatish Kumar
Copyright (c) 2020 Shyam Lal, Satish Kumar
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2020-12-302020-12-303918721210.23755/rm.v39i0.549Uniqueness of an entire function sharing a polynomial with its linear differential polynomial
http://eiris.it/ojs/index.php/ratiomathematica/article/view/554
In 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.Imrul KaishNasir Uddin Gazi
Copyright (c) 2020 Imrul Kaish, Nasir Uddin Gazi
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2020-12-302020-12-303921322810.23755/rm.v39i0.554On homomorphism of fuzzy multigroups
http://eiris.it/ojs/index.php/ratiomathematica/article/view/553
<p>In this paper, the homomorphism of fuzzy multigroups is briefly delineated following [2] and their corresponding isomorphism theorems are considered.</p>Johnson Aderemi AwololaM.A. Ibrahim
Copyright (c) 2020 Johnson Aderemi Awolola
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2020-12-302020-12-303922923610.23755/rm.v39i0.553On a class of sets between a-open sets and gδ-open sets
http://eiris.it/ojs/index.php/ratiomathematica/article/view/535
<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>Jagadeesh B. Toranagatti
Copyright (c) 2020 Jagadeesh B. Toranagatti
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2020-12-302020-12-303923725210.23755/rm.v39i0.535Determine the value d(M(G)) for non-abelian p-groups of order q = pnk of Nilpotency c
http://eiris.it/ojs/index.php/ratiomathematica/article/view/560
<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>Behnam Razzaghmaneshi
Copyright (c) 2020 Behnam Razzaghmaneshi
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2020-12-302020-12-303925325910.23755/rm.v39i0.560Thermodynamic behavior of the polytropic gas in cosmology
http://eiris.it/ojs/index.php/ratiomathematica/article/view/564
<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>Prasanta DasKangujam Priyokumar Singh
Copyright (c) 2020 Prasanta Das, Kangujam Priyokumar Singh
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2020-12-302020-12-303926126810.23755/rm.v39i0.564