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). This periodical has a long tradition, indeed its first issue was published in 1990. It aims to publish original research articles in the fields of Mathematics and Statistics. However, contributions with applications of Mathematics and Statistics to Social Science, Business Administration, Engineering, Programming, Economics, Management, Fuzzy Logic, and Probability, are welcome. Only English-language publications are accepted. </p><p>The main topics of interest for Ratio Mathematica are:</p><p><strong>Foundations of Mathematics:</strong> Epistemology of Mathematics, Critique of the Foundations of Mathematics, Elementary Mathematics from a higher point of view, Elementary Theory of Numbers, Foundations of Mathematics of Uncertain; Criticism of the Foundations of Computer Science.</p><p><strong>Applications of Mathematics:</strong> Applications to Engineering and Economics, Applications for Management and Business Administration, Decision making in conditions of uncertainty, Theory of Games, Fuzzy Logic and Applications, Probability, Statistics and Applications.</p><p><strong>New theories and applications:</strong> Algebraic hyperstructures and Applications, Discrete Mathematics and Applications, Fuzzy structures.</p><p><strong>New theories and practices for dissemination and communication of mathematics:</strong> Communication of History and Fundations, Communication of Discrete Mathematics, Communication of Probability and Statistics, Communication with Media.</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="https://zbmath.org/journals/?s=0&q=ratio+mathematica">zbMATH</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><strong>Publish or Perish Statistics </strong></p><p>## "Ratio Mathematica" ##</p><p>Publish or Perish 6.21.6145.6594</p><p>### Search terms ###</p><p>Publication/Journal: "Ratio Mathematica"<br />Years: all</p><p><br />### Data retrieval ###</p><p>Data source: Google Scholar<br />Query date: dom 28 gen 2018 07:52:36<br />Cache date: gio 25 gen 2018 08:03:23<br />Query result: [0] Operazione completata.</p><p><br />### Metrics ###</p><p>Publication years: 1990-2017<br />Citation years: 28 (1990-2018)<br />Papers: 276<br />Citations: 544<br />Citations/year: 19.43<br />Citations/paper: 1.97<br />Citations/author: 369.58<br />Papers/author: 192.00<br />Authors/paper: 1.73/2.0/1 (mean/median/mode)<br />Age-weighed citation rate: 61.33 (sqrt=7.83), 38.97/author<br />Hirsch h-index: 11 (a=4.50, m=0.39, 215 cites=39.5% coverage)<br />Egghe g-index: 16 (g/h=1.45, 266 cites=48.9% coverage)<br />PoP hI,norm: 9<br />PoP hI,annual: 0.32</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>Sums of Generalized Harmonic Series with Periodically Repeated Numerators (a,b) and (a,a,b,b)
http://eiris.it/ojs/index.php/ratiomathematica/article/view/405
<p>This paper deals with certain generalization of the alternating harmonic series - the generalized convergent harmonic series with periodically repeated numerators (a,b) and (a,a,b,b). Firstly, we find out the value of the numerators b of the first series, for which the series converges, and determine the formula for the sum s(a) of this series. Then we determine the value of the numerators b of the second series, for which this series converges, and derive the formula for the sum s(a,a) of this second series. Finally, we verify these analytically obtained results and compute the sums of these series by using the computer algebra system Maple 16 and its basic programming language.</p>Radovan Potucek
Copyright (c) 2018 Radovan Potucek
http://creativecommons.org/licenses/by/4.0
2018-07-072018-07-073451410.23755/rm.v34i0.405On Rough Sets and Hyperlattices
http://eiris.it/ojs/index.php/ratiomathematica/article/view/350
<p>In this paper, we introduce the concepts of upper and lower rough hyper fuzzy ideals (filters) in a hyperlattice and their basic properties are discussed. Let $\theta$ be a hyper congruence relation on $L$. We show that if $\mu$ is a fuzzy subset of $L$, then $\overline{\theta}(<\mu>)=\overline{\theta}(<\overline{\theta}(\mu)>)$ and $\overline{\theta}(\mu^*) =\overline{\theta}((\overline{\theta}(\mu))^*)$, where $<\mu>$ is the least hyper fuzzy ideal of $L$ containing $\mu$ and $$\mu^*(x) = sup\{\alpha \in [0, 1]: x \in I( \mu_{\alpha} )\}$$ for all $x \in L$. Next, we prove that if $\mu $ is a hyper fuzzy ideal of $L$, then $\mu$ is an upper rough fuzzy ideal. Also, if $\theta$ is a $\wedge-$complete on $L$ and $\mu $ is a hyper fuzzy prime ideal of $L$ such that $\overline{\theta}(\mu)$ is a proper fuzzy subset of $L$, then $\mu$ is an upper rough fuzzy prime ideal. Furthermore, let $\theta$ be a $\vee$-complete congruence relation on $L$. If $\mu $ is a hyper fuzzy ideal, then $\mu$ is a lower rough fuzzy ideal and if $\mu $ is a hyper fuzzy prime ideal such that $\underline{\theta}(\mu)$ is a proper fuzzy subset of $L$, then $\mu$ is a lower rough fuzzy prime ideal.</p>Ali Akbar EstajiFereshteh Bayati
Copyright (c) 2018 Ali Akbar Estaji, Fereshteh Bayati
http://creativecommons.org/licenses/by/4.0
2018-07-072018-07-0734153310.23755/rm.v34i0.350On a Geometric Representation of Probability Laws and of a Coherent Prevision-Function According to Subjectivistic Conception of Probability
http://eiris.it/ojs/index.php/ratiomathematica/article/view/401
<p>We distinguish the two extreme aspects of the logic of certainty by identifying their corresponding structures into a linear space. We extend probability laws P formally admissible in terms of coherence to random quantities. We give a geometric representation of these laws P and of a coherent prevision function P which we previously defined in an original way. We are the first in the world to do this kind of work: it is the foundation of our next and extensive study concerning the formulation of a geometric, wellorganized and original theory of random quantities.</p>Pierpaolo AngeliniAngela De Sanctis
Copyright (c) 2018 Pierpaolo Angelini, angela de sanctis
http://creativecommons.org/licenses/by/4.0
2018-07-072018-07-0734354710.23755/rm.v34i0.401A New Provably Secure Cryptosystem Using Dedekind Domain Direct Product Approach
http://eiris.it/ojs/index.php/ratiomathematica/article/view/404
<p>We would like to prevent, detect, and protect communication and information systems' attacks, which include unauthorized reading of a message of file and traffic analysis or active attacks, such as modification of messages or files, and denial of service by providing cryptographic techniques. If we prove that an encryption algorithm is based on mathematical NP-hard problems, we can prove its security. In this paper, we present a new NTRU-Like public-key cryptosystem with security provably based on the worst-case hardness of the approximate lattice problems (NP-hard problems) in some structured lattices (ideal lattices) in order to attain the applicable objectives of preserving the confidentiality of communication and information system resources (includes hardware, software, firmware, information/data, and telecommunications). Our proposed scheme is an improvement of ETRU cryptosystem. ETRU is an NTRU-Like public-key cryptosystem based on the Eisenstein integers Z [f_3 ] where f_3 is a primitive cube root of unity. ETRU has heuristic security and it has no proof of security. We show that our cryptosystem has security stronger than that of ETRU, over cartesian product of dedekind domains and extended cyclotomic polynomials. We prove the security of our main algorithm from the R-SIS and R-LWE problems as NP-hard problems.</p>Amir Hassani Karbasi
Copyright (c) 2018 Amir Hassani Karbasi
http://creativecommons.org/licenses/by/4.0
2018-07-072018-07-0734496510.23755/rm.v34i0.404Algebraic Spaces and Set Decompositions
http://eiris.it/ojs/index.php/ratiomathematica/article/view/415
<p>The contribution is growing up from certain parts of scientiﬁc work by professor Boruvka in several ways. Main focus is on the decomposition theory, especially algebraized decompositions of groups. Professor Boruvka in his excellent and well-known book [3] has developed the decomposition (partition) theory, where the fundamental role belongs to so called generating decompositions. Furthermore, the contribution is also devoted to hypergroups, to algebraic spaces called also quasi-automata or automata without outputs. There is attempt to develop more fresh view point on this topic.</p>Jan ChvalinaBedřich Smetana
Copyright (c) 2018 Bedřich Smetana, Jan Chvalina
http://creativecommons.org/licenses/by/4.0
2018-07-072018-07-0734677610.23755/rm.v34i0.415Notes on the Solutions of the First Order Quasilinear Differential Equations
http://eiris.it/ojs/index.php/ratiomathematica/article/view/414
<p>The system of the quasilinear differential first order equations with the antisymetric matrix and the same element f (t,x(t)) on the main diagonal have the property that r'(t) = f (t,x(t))r(t), where r(t) ≥ 0 is the po- lar function of the system. In special cases, when values f (t,x(t)) and g (t,x(t)) are only dependent on r^2 (t), t ∈ Jo we can find the general solution of the system (1) explicitly.</p>Alena VagaskáDusan Mamrilla
Copyright (c) 2018 Alena Vagaská, Dusan Mamrilla
http://creativecommons.org/licenses/by/4.0
2018-07-072018-07-0734778310.23755/rm.v34i0.414Some Kinds of Homomorphisms on Hypervector Spaces
http://eiris.it/ojs/index.php/ratiomathematica/article/view/416
<p>In this paper, we introduce the concepts of homomorphism of type 1, 2 and 3 and good homomorphism. Then we investigate some properties of them.</p>Elham ZangiabadiZohreh Nazari
Copyright (c) 2018 Elham Zangiabadi, Zohreh Nazari
http://creativecommons.org/licenses/by/4.0
2018-07-072018-07-0734859310.23755/rm.v34i0.416