Ratio Mathematica
http://eiris.it/ojs/index.php/ratiomathematica
<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 mathematical and statistical models to social science, engineering, ecology, and economics;<br />-Decision making in conditions of uncertainty;<br />-Fuzzy logic;<br />-Probability;<br />-Algebraic hyperstructures;<br />-Discrete mathematics;<br />-New theories for dissemination and communication of mathematics;<br />-Epistemology of mathematics;<br />-Critique of the foundations of mathematics;<br />-Numbers theory;<br />-Foundations of the mathematics of uncertain.</p><p> </p><p><a href="/template_aggiornati_al_19-4-2019/RM-Tex.zip">Download template (Tex)</a></p><p><a href="/template_aggiornati_al_19-4-2019/RM-Word.zip">Download template (Word)</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>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> </p><p>## ISSN 2282-8214 ##</p><p>Publish or Perish 7.27.2949.7581 (basic 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: 2020-10-06 18:44:24 +0200<br />Cache date: 2020-10-06 18:45:30 +0200<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: 2020-10-06 18:45:30 +0200<br />Publication years: 1990-2020<br />Citation years: 30 (1990-2020)<br />Papers: 302<br />Citations: 824<br />Citations/year: 27.47 (acc1=32, acc2=18, acc5=1, acc10=0, acc20=0)<br />Citations/paper: 2.73<br />Authors/paper: 1.70/2.0/1 (mean/median/mode)<br />Age-weighted citation rate: 107.40 (sqrt=10.36), 76.57/author<br />Hirsch h-index: 15 (a=3.66, m=0.50, 337 cites=40.9% coverage)<br />Egghe g-index: 20 (g/h=1.33, 406 cites=49.3% coverage)<br />PoP hI,norm: 12<br />PoP hI,annual: 0.40</p><p> </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>Studies on A. Einstein , B. Podolsky and N. Rosen argument that ”quantum mechanics is not a complete theory,” I: Basic methods
http://eiris.it/ojs/index.php/ratiomathematica/article/view/516
<p>In 1935, A. Einstein expressed his view, jointly with B. Podolsky and N. Rosen, that ”quantum mechanics is not a complete theory” (EPR argument). Following decades of preparatory studies, R. M. Santilli published in 1998 a paper showing that the objections against the EPR argument are valid for point-like particles in vacuum (exterior dynamical systems), but the same objections are inapplicable (rather than being violated) for extended particles within hyperdense physical media (interior dynamical systems) because the latter systems appear to admit an identical classical counterpart when treated with the isotopic branch of hadronic mathematics and mechanics. In a more recent paper, Santilli has shown that quantum uncertainties of extended particles appear to progressively tend to zero when in the interior of hadrons, nuclei and stars, and appear to be identically null at the limit of gravitational collapse, essentially along the EPR argument. In this first paper, we review, upgrade and specialize the basic mathematical, physical and chemical methods for the study of the EPR argument. In two subsequent papers, we review the above results and provide specific illustrations and applications.</p>Ruggero Maria Santilli
Copyright (c) 2020 Ruggero Maria Santilli
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303852310.23755/rm.v38i0.516Studies on A. Einstein, B. Podolsky and N. Rosen argument that “quantum mechanics is not a complete theory,” II: Apparent confirmation of the EPR argument
http://eiris.it/ojs/index.php/ratiomathematica/article/view/517
<p>In1935, A.Einsteinexpressedhishistoricalview, jointly with B.Podolsky and N. Rosen, that quantum mechanics could be “completed” into a form recovering classical determinism at least under limit conditions (EPR argument). In the preceding Paper I, we have outlined the basic methods underlying the “completion” of quantum mechanics into hadronic mechanics for the representation of extended particles within physical media. In this Paper II, we study the isosymmetries for interior dynamical systems; we confirm the 1998 apparent proof that interior dynamical systems admit a classical counterpart; we confirm the 2019 apparent proof that Einstein’s determinism is progressively approached for extended particles in the interior of hadrons, nuclei and stars, while being fully achieved in the interior of gravitational collapse; and we show for the first time that the recovering of Einstein’s determinism in interior systems implies the removal of quantum mechanical divergencies. In the subsequent Paper III, we present a number of illustrative examples and novel applications in mathematics, physics and chemistry.</p>Ruggero Maria Santilli
Copyright (c) 2020 Ruggero Maria Santilli
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-30387113810.23755/rm.v38i0.517Studies on A. Einstein. B. Podolsky and N. Rosen argument that “quantum mechanics is not a complete theory,” III: Illustrative examples and applications
http://eiris.it/ojs/index.php/ratiomathematica/article/view/518
<p>In the preceding Papers I and II of this series, we have presented a review and upgrade of basic mathematical, physical and chemical methods, and provided a confirmation of the apparent proof of the EPR argument [1] that extended particles within physical media (interior dynamical problems) admit classical counterparts [9], while Einstein’s determinism appears to be progressively verified with the increase of the density of the medium [10]. In this third and final paper of the series, we shown that the EPT argument in general, and Einstein’s determinism in particular, appear to be progressively verified in the structure of mesons, baryon, nuclei, and molecular bonds while being fully verified at the limit of gravitational collapse. We additionally show, apparently for the first time, the validity of the EPR final statement to the effect that the wavefunction [of quantum mechanics] does not provide a complete description of the physical reality” since the covering isowavefunctions of hadronic mechanics provide an otherwise impossible representation of all characteristics of various physical and chemical interior systems existing in nature. </p><p> </p><p> </p>Ruggero Maria Santilli
Copyright (c) 2020 Ruggero Maria Santilli
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303813922210.23755/rm.v38i0.518Pairwise Paracompactness
http://eiris.it/ojs/index.php/ratiomathematica/article/view/495
The purpose of this paper is to introduce and study a new paracompactness in bitopological spaces using (<em>τ</em><em><sub>i</sub></em><em>, </em><em>τ</em><em><sub>j</sub></em>)-<em>g</em><sup>∗</sup><em>ωα</em>-closed sets. Further, the properties of (<em>τ</em><em><sub>i</sub></em><em>,</em><em> </em><em>τ</em><em><sub>j</sub></em>)-<em>g</em><sup>∗</sup><em>ωα</em>-closed sets, (<em>τ</em><em><sub>i</sub></em><em>,</em><em> </em><em>τ</em><em><sub>j</sub></em>)-<em>g</em><sup>∗</sup><em>ωα</em>- continuous functions and (<em>τ</em><em><sub>i</sub></em><em>, τ</em><em><sub>j</sub></em>)-<em>g</em><sup>∗</sup><em>ωα</em>-irresolute maps and (<em>τ</em><em><sub>i</sub></em><em>, </em><em>τ</em><em><sub>j</sub></em>)- <em>g</em><sup>∗</sup><em>ωα</em>-paracompact spaces are discussed in bitopological spaces.<p> </p>Pallavi S. MirajakarP.G. Patil
Copyright (c) 2020 Mirajakar and Patil
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303823323610.23755/rm.v38i0.495Some characterizations of fuzzy comultisets and quotient fuzzy multigroups
http://eiris.it/ojs/index.php/ratiomathematica/article/view/501
<p>The idea of fuzzy multisets has been applied to some group theoretic notions. Nonetheless, the notions of cosets and quotient groups have not been substantiated in fuzzy multigroup environment. The aim of this paper is to present the concepts of cosets and quotient groups in fuzzy multigroup context with some related results. To start with, the connection between fuzzy comultisets of fuzzy multigroups and the cosets of groups is established. Some characterizations of fuzzy comultisets are outlined with proofs. In addition, quotient fuzzy multigroup is proposed and some of its properties are explored. It is proven that a normal fuzzy multigroup of a fuzzy multigroup is commutative if and only if the quotient fuzzy multigroup is commutative. Finally, group theoretic isomorphism theorems are established in fuzzy multigroup setting.</p>Augustine Paul
Copyright (c) 2020 Augustine Paul
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303823725910.23755/rm.v38i0.501Geometrical foundations of the sampling design with fixed sample size
http://eiris.it/ojs/index.php/ratiomathematica/article/view/511
We study the sampling design with fixed sample size from a geometric point of view. The first-order and second-order inclusion probabilities are chosen by the statistician. They are subjective probabilities. It is possible to study them inside of linear spaces provided with a quadratic and linear metric. We define particular random quantities whose logically possible values are all logically possible samples of a given size. In particular, we define random quantities which are complementary to the Horvitz-Thompson estimator. We identify a quadratic and linear metric with regard to two univariate random quantities representing deviations. We use the α-criterion of concordance introduced by Gini in order to identify it. We innovatively apply to probability this statistical criterion.Pierpaolo Angelini
Copyright (c) 2020 Pierpaolo Angelini
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303826128510.23755/rm.v38i0.511Analytical and numerical solution of differential equations with generalized fuzzy derivative
http://eiris.it/ojs/index.php/ratiomathematica/article/view/519
<p>The aim of this work is to present a novel approach based on the fuzzy neural network for finding the numerical solution of the first order fuzzy differential equations under generalized H-derivation .The differentiability concept that used in this paper is the generalized differentiability since a first order fuzzy differential equation under this differentiability can have two solutions .The fuzzy trial solution of the fuzzy initial value problem is written as a sum of two parts. The first part satisfies the fuzzy condition, it contains no fuzzy adjustable parameters. The second part involves fuzzy feed-forward neural networks containing fuzzy adjustable parameters. This method, in comparison with existing numerical methods and the analytical solutions, shows that the use of fuzzy neural networks provides solutions with good generalization and high accuracy. </p>Basim Nasih Abood
Copyright (c) 2020 Basim Nasih Abood
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303828731110.23755/rm.v38i0.519Minimal Hv-Fields
http://eiris.it/ojs/index.php/ratiomathematica/article/view/522
<p>Hyperstructures have applications in mathematics and in other sciences, which range from biology, hadronic physics, leptons, linguistics, sociology, to mention but a few. For this, the largest class of the hyperstructures, the Hv-structures, is used. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quotients, the Hv-structures with the classical ones. Hv-numbers are elements of Hv-field, and they are used in representation theory. We focus on minimal Hv-fields.</p>Thomas Vougiouklis
Copyright (c) 2020 Thomas Vougiouklis
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303831332810.23755/rm.v38i0.522On the planarity of line Mycielskian graph of a graph
http://eiris.it/ojs/index.php/ratiomathematica/article/view/506
<p>The line Mycielskian graph of a graph <em>G</em>, denoted by <em>L<sub>μ</sub>(G)</em> is defined as the graph obtained from <em>L(G)</em> by adding q+1 new vertices <em>E' = e<sub>i</sub>' : 1 ≤ i ≤ q</em> and <em>e</em>, then for <em>1 ≤ i ≤ q</em> , joining <em>e<sub>i</sub>' </em>to the neighbours of <em>e<sub>i</sub> </em> and to <em>e</em>. The vertex <em>e</em> is called the root of <em>L<sub>μ</sub>(G). </em> This research paper deals with the characterization of planarity of line Mycielskian Graph <em>L<sub>μ</sub>(G)</em> of a graph. Further, we also obtain the characterization on outerplanar, maximal planar, maximal outerplanar, minimally nonouterplanar and 1-planar of <em>L<sub>μ</sub>(G).</em></p><p>Keywords : Planar graph, Outerplanar, Maximal planar, Maximal outerplanar, Minimally nonouterplanar and 1-planar.</p><p>2010 AMS subject classifications : 05C07, 05C10, 05C38, 05C60, 05C76.</p>Keerthi G. MirajkarAnuradha V Deshpande
Copyright (c) 2020 Keerthi G. Mirajkar, Anuradha V Deshpande
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303832933910.23755/rm.v38i0.506Approximation of functions by (C,2)(E,1) product summability method of Fourier series
http://eiris.it/ojs/index.php/ratiomathematica/article/view/504
<p>Various investigators such as Leindler [10], Chandra [1], Mishra et al. [7], Khan [11], Kushwaha [6] have determined the degree of approximation of 2 pai<em>-periodic </em>functions belonging to generalized Lipschitz class of functions through trigonometric Fourier approximation using different summability means. Recently H.K. Nigam [12] has determined that the Fourier series is summable under the summability means (C,2)(E,1) but he did not find the degree of approximation of function belonging to various classes. In this paper a theorem concerning the degree of approximation of function belonging to class by (C,2)(E,1) product summability method of Fourier series has been established which in turn generalizes the result of H. K. Nigam [12].</p>Jitendra Kumar Kushwaha
Copyright (c) 2020 Jitendra Kumar Kushwaha
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303834134810.23755/rm.v38i0.504Uniqueness of an entire function sharing fixed points with its derivatives
http://eiris.it/ojs/index.php/ratiomathematica/article/view/520
<p>The uniqueness problems of an entire functions that share a nonzero finite value have been studied and many results on this topic have been obtained. In this paper we prove a uniqueness theorem for an entire function, which share a linear polynomial, in particular fixed points, with its higher order derivatives.</p>MD Majibur RahamanImrul Kaish
Copyright (c) 2020 MD MAJIBUR RAHAMAN, IMRUL KAISH
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303834936510.23755/rm.v38i0.520On commutativity of prime and semiprime rings with generalized derivations
http://eiris.it/ojs/index.php/ratiomathematica/article/view/502
Let $R$ be a prime ring, extended centroid $C$ and $m, n, k \geq1$ are fixed integers. If $R$ admits a generalized derivation $F$ associated with a derivation $d$ such that $(F(x)\circ y)^{m}+(x\circ d(y))^{n}=0$ or $(F(x)\circ_{m} y)^{k} + x\circ_{n} d(y)$=0 for all $x, y \in I$, where $I$ is a nonzero ideal of $R$, then either $R$ is commutative or there exist $b\in U$, Utumi ring of quotient of $R$ such that $F(x)=bx$ for all $x \in R$. Moreover, we also examine the case $R$ is a semiprime ring.MD Hamidur Rahaman
Copyright (c) 2020 Md Hamidur Rahaman
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303836737510.23755/rm.v38i0.502A note on α−irresolute topological rings
http://eiris.it/ojs/index.php/ratiomathematica/article/view/523
<p>In [4], we introduced the notion of α−irresolute topological rings in Mathematics. This notion is independent of topological rings. In this note, we point out that under certain conditions an α−irresolute topological ring is topological ring and vice versa. We prove that the Minkowski sum A+B of an α−compact subset A ⊆ R and an α−closed subset B ⊆ R of an α−irresolute topological ring (R, =) is actually a closed subset of R. In the twilight of this note, we pose several questions which are worthy</p>Madhu Ram
Copyright (c) 2020 Madhu Ram
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303837738310.23755/rm.v38i0.523Supersolube subgroups
http://eiris.it/ojs/index.php/ratiomathematica/article/view/503
<p>A <a title="Subgroup" href="https://groupprops.subwiki.org/wiki/Subgroup">subgroup</a> H of a <a title="Group" href="https://groupprops.subwiki.org/wiki/Group">group</a> G is termed permutable (or quasi normal) in G if it satisfies the following equivalent conditions:</p><p>For any subgroup K of G, HK (the <a title="Product of subgroups" href="https://groupprops.subwiki.org/wiki/Product_of_subgroups">product of subgroups</a> H and K) is a group. For any subgroup K of G, HK= KH, i.e., H and K are <a title="Permuting subgroups" href="https://groupprops.subwiki.org/wiki/Permuting_subgroups">permuting subgroups</a>. For every g in G, H permutes with the cyclic subgroup generated by g. Also we say that G=AB is the mutually permutable product of the subgroups A and B if A permutes with every subgroup of B and B permutes with every subgroup of A. We say that the product is totally permutable if every subgroup of A permutes with every subgroup of B. In this paper we prove the following theorem.</p><p>Let G=AB be the mutually permutable product of the super soluble subgroups A and B. If CoreG(A∩B)=1, then G is super soluble.</p><p> </p>Behnam Razzagh
Copyright (c) 2020 Behnam Razzagh
http://creativecommons.org/licenses/by/4.0
2020-06-302020-06-303838539310.23755/rm.v38i0.503