Search results for: semiring

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semiring</title> <meta name="description" content="Search results for: semiring"> <meta name="keywords" content="semiring"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" 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id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="semiring"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 3</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: semiring</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3</span> Semirings of Graphs: An Approach Towards the Algebra of Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gete%20Umbrey">Gete Umbrey</a>, <a href="https://publications.waset.org/abstracts/search?q=Saifur%20Rahman"> Saifur Rahman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graphs are found to be most capable in computing, and its abstract structures have been applied in some specific computations and algorithms like in phase encoding controller, processor microcontroller, and synthesis of a CMOS switching network, etc. Being motivated by these works, we develop an independent approach to study semiring structures and various properties by defining the binary operations which in fact, seems analogous to an existing definition in some sense but with a different approach. This work emphasizes specifically on the construction of semigroup and semiring structures on the set of undirected graphs, and their properties are investigated therein. It is expected that the investigation done here may have some interesting applications in theoretical computer science, networking and decision making, and also on joining of two network systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graphs" title="graphs">graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=join%20and%20union%20of%20graphs" title=" join and union of graphs"> join and union of graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=semiring" title=" semiring"> semiring</a>, <a href="https://publications.waset.org/abstracts/search?q=weighted%20graphs" title=" weighted graphs"> weighted graphs</a> </p> <a href="https://publications.waset.org/abstracts/103053/semirings-of-graphs-an-approach-towards-the-algebra-of-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/103053.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">148</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2</span> A Study on Ideals and Prime Ideals of Sub-Distributive Semirings and Its Applications to Symmetric Fuzzy Numbers </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rosy%20Joseph">Rosy Joseph</a> </p> <p class="card-text"><strong>Abstract:</strong></p> From an algebraic point of view, Semirings provide the most natural generalization of group theory and ring theory. In the absence of additive inverse in a semiring, one had to impose a weaker condition on the semiring, i.e., the additive cancellative law to study interesting structural properties. In many practical situations, fuzzy numbers are used to model imprecise observations derived from uncertain measurements or linguistic assessments. In this connection, a special class of fuzzy numbers whose shape is symmetric with respect to a vertical line called the symmetric fuzzy numbers i.e., for α ∈ (0, 1] the α − cuts will have a constant mid-point and the upper end of the interval will be a non-increasing function of α, the lower end will be the image of this function, is suitable. Based on this description, arithmetic operations and a ranking technique to order the symmetric fuzzy numbers were dealt with in detail. Wherein it was observed that the structure of the class of symmetric fuzzy numbers forms a commutative semigroup with cancellative property. Also, it forms a multiplicative monoid satisfying sub-distributive property.In this paper, we introduce the algebraic structure, sub-distributive semiring and discuss its various properties viz., ideals and prime ideals of sub-distributive semiring, sub-distributive ring of difference etc. in detail. Symmetric fuzzy numbers are visualized as an illustration. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=semirings" title="semirings">semirings</a>, <a href="https://publications.waset.org/abstracts/search?q=subdistributive%20ring%20of%20difference" title=" subdistributive ring of difference"> subdistributive ring of difference</a>, <a href="https://publications.waset.org/abstracts/search?q=subdistributive%20semiring" title=" subdistributive semiring"> subdistributive semiring</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetric%20fuzzy%20numbers" title=" symmetric fuzzy numbers"> symmetric fuzzy numbers</a> </p> <a href="https://publications.waset.org/abstracts/84413/a-study-on-ideals-and-prime-ideals-of-sub-distributive-semirings-and-its-applications-to-symmetric-fuzzy-numbers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/84413.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">212</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1</span> Symmetry Properties of Linear Algebraic Systems with Non-Canonical Scalar Multiplication</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Krish%20Jhurani">Krish Jhurani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenspaces" title="eigenspaces">eigenspaces</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvectors" title=" eigenvectors"> eigenvectors</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20subspaces" title=" invariant subspaces"> invariant subspaces</a>, <a href="https://publications.waset.org/abstracts/search?q=near-rings" title=" near-rings"> near-rings</a>, <a href="https://publications.waset.org/abstracts/search?q=non-canonical%20scalar%20multiplication" title=" non-canonical scalar multiplication"> non-canonical scalar multiplication</a>, <a href="https://publications.waset.org/abstracts/search?q=semirings" title=" semirings"> semirings</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetry%20properties" title=" symmetry properties"> symmetry properties</a> </p> <a href="https://publications.waset.org/abstracts/167875/symmetry-properties-of-linear-algebraic-systems-with-non-canonical-scalar-multiplication" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167875.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">123</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a 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Search results for: semiring