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An ideal is called union-prime if it is a union of a nonempty chain of prime ideals but is not a prime. In this paper, some relations between chains of prime ideals and the induced chains of union-prime ideals are shown; in particular, the cardinality of such chains and the cardinality of the sets of cuts of such chains are discussed. For a ring R and a nonempty full chain of prime ideals C of R, several characterizations for the property of immediate neighbors in C are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=prime%20ideals" title="prime ideals">prime ideals</a>, <a href="https://publications.waset.org/abstracts/search?q=union-prime%20ideals" title=" union-prime ideals"> union-prime ideals</a>, <a href="https://publications.waset.org/abstracts/search?q=immediate%20neighbors" title=" immediate neighbors"> immediate neighbors</a>, <a href="https://publications.waset.org/abstracts/search?q=Kaplansky%27s%20conjecture" title=" Kaplansky's conjecture"> Kaplansky's conjecture</a> </p> <a href="https://publications.waset.org/abstracts/131024/union-primes-and-immediate-neighbors" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/131024.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">138</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">1469</span> Application of Soft Sets to Non-Associative Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Inayatur%20Rehman">Inayatur Rehman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Molodtstove developed the theory of soft sets which can be seen as an effective tool to deal with uncertainties. Since the introduction of this concept, the application of soft sets has been restricted to associative algebraic structures (groups, semi groups, associative rings, semi-rings etc.). Acceptably, though the study of soft sets, where the base set of parameters is a commutative structure, has attracted the attention of many researchers for more than one decade. But on the other hand there are many sets which are naturally endowed by two compatible binary operations forming a non-associative ring and we may dig out examples which investigate a non-associative structure in the context of soft sets. Thus it seems natural to apply the concept of soft sets to non-commutative and non-associative structures. In present paper, we make a new approach to apply Molodtsoves notion of soft sets to LA-ring (a class of non-associative ring). We extend the study of soft commutative rings from theoretical aspect. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=soft%20sets" title="soft sets">soft sets</a>, <a href="https://publications.waset.org/abstracts/search?q=LA-rings" title=" LA-rings"> LA-rings</a>, <a href="https://publications.waset.org/abstracts/search?q=soft%20LA-rings" title=" soft LA-rings"> soft LA-rings</a>, <a href="https://publications.waset.org/abstracts/search?q=soft%20ideals" title=" soft ideals"> soft ideals</a>, <a href="https://publications.waset.org/abstracts/search?q=soft%20prime%20ideals" title=" soft prime ideals"> soft prime ideals</a>, <a href="https://publications.waset.org/abstracts/search?q=idealistic%0D%0Asoft%20LA-rings" title=" idealistic soft LA-rings"> idealistic soft LA-rings</a>, <a href="https://publications.waset.org/abstracts/search?q=LA-ring%20homomorphism" title=" LA-ring homomorphism "> LA-ring homomorphism </a> </p> <a href="https://publications.waset.org/abstracts/33475/application-of-soft-sets-to-non-associative-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33475.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">469</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">1468</span> Zero Divisor Graph of a Poset with Respect to Primal Ideals</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hossein%20Pourali">Hossein Pourali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we extend the concepts of primal and weakly primal ideals for posets. Further, the diameter of the zero divisor graph of a poset with respect to a non-primal ideal is determined. The relation between primary and primal ideals in posets is also studied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Eassociated%20prime%20ideal" title="‎associated prime ideal">‎associated prime ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8E%E2%80%8Eideal" title=" ‎‎ideal"> ‎‎ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8E%E2%80%8Eprimary%20ideal" title=" ‎‎primary ideal"> ‎‎primary ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=primal%20ideal%E2%80%8E" title=" primal ideal‎"> primal ideal‎</a>, <a href="https://publications.waset.org/abstracts/search?q=prime%E2%80%8E%20%E2%80%8Eideal" title=" prime‎ ‎ideal"> prime‎ ‎ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=semiprime%20ideal" title=" semiprime ideal"> semiprime ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Eweakly%20primal%20ideal" title=" ‎weakly primal ideal"> ‎weakly primal ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=zero%20divisors%20graph" title=" zero divisors graph"> zero divisors graph</a> </p> <a href="https://publications.waset.org/abstracts/67163/zero-divisor-graph-of-a-poset-with-respect-to-primal-ideals" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67163.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">261</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">1467</span> Second Representation of Modules over Commutative Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jawad%20Abuhlail">Jawad Abuhlail</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamza%20Hroub"> Hamza Hroub</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let R be a commutative ring. Representation theory studies the representation of R-modules as (possibly finite) sums of special types of R-submodules. Here we are interested in a class of R-modules between the class of semisimple R-modules and the class of R-modules that can be written as (possibly finite) sums of secondary R-submodules (we know that every simple R-submodule is secondary). We investigate R-modules which can be written as (possibly finite) sums of second R-submodules (we call those modules second representable). Moreover, we investigate the class of (main) second attached prime ideals related to a module with such representation. We provide sufficient conditions for an R-module M to get a (minimal) second representation. We also found the collection of second attached prime ideals for some types of second representable R-modules, in particular within the class of injective R-modules. As we know that every simple R-submodule is second and every second R-submodule is secondary, we can see the importance of the second representable R-module. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lifting%20modules" title="lifting modules">lifting modules</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20attached%20prime%20ideals" title=" second attached prime ideals"> second attached prime ideals</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20representations" title=" second representations"> second representations</a>, <a href="https://publications.waset.org/abstracts/search?q=secondary%20representations" title=" secondary representations"> secondary representations</a>, <a href="https://publications.waset.org/abstracts/search?q=semisimple%20modules" title=" semisimple modules"> semisimple modules</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20submodules" title=" second submodules"> second submodules</a> </p> <a href="https://publications.waset.org/abstracts/99517/second-representation-of-modules-over-commutative-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99517.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">203</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">1466</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">218</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">1465</span> Derivation of BCK\BCI-Algebras</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tumadhir%20Fahim%20M%20Alsulami">Tumadhir Fahim M Alsulami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The concept of this paper builds on connecting between two important notions, fuzzy ideals of BCK-algebras and derivation of BCI-algebras. The result we got is a new concept called derivation fuzzy ideals of BCI-algebras. Followed by various results and important theorems on different types of ideals. In chapter 1: We presented the basic and fundamental concepts of BCK\ BCI- algebras as follows: BCK/BCI-algebras, BCK sub-algebras, bounded BCK-algebras, positive implicative BCK-algebras, commutative BCK-algebras, implicative BCK- algebras. Moreover, we discussed ideals of BCK-algebras, positive implicative ideals, implicative ideals and commutative ideals. In the last section of chapter 1 we proposed the notion of derivation of BCI-algebras, regular derivation of BCI-algebras and basic definitions and properties. In chapter 2: It includes 3 sections as follows: Section 1 contains elementary concepts of fuzzy sets and fuzzy set operations. Section 2 shows O. G. Xi idea, where he applies fuzzy sets concept to BCK-algebras and we studied fuzzy sub-algebras as well. Section 3 contains fuzzy ideals of BCK-algebras basic definitions, closed fuzzy ideals, fuzzy commutative ideals, fuzzy positive implicative ideals, fuzzy implicative ideals, fuzzy H-ideals and fuzzy p-ideals. Moreover, we investigated their concepts in diverse theorems and propositions. In chapter 3: The main concept of our thesis on derivation fuzzy ideals of BCI- algebras is introduced. Chapter 3 splits into 4 sections. We start with General definitions and important theorems on derivation fuzzy ideal theory in section 1. Section 2 and 3 contain derivations fuzzy p-ideals and derivations fuzzy H-ideals of BCI- algebras, several important theorems and propositions were introduced. The last section studied derivations fuzzy implicative ideals of BCI-algebras and it includes new theorems and results. Furthermore, we presented a new theorem that associate derivations fuzzy implicative ideals, derivations fuzzy positive implicative ideals and derivations fuzzy commutative ideals. These concepts and the new results were obtained and introduced in chapter 3 were submitted in two separated articles and accepted for publication. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=BCK" title="BCK">BCK</a>, <a href="https://publications.waset.org/abstracts/search?q=BCI" title=" BCI"> BCI</a>, <a href="https://publications.waset.org/abstracts/search?q=algebras" title=" algebras"> algebras</a>, <a href="https://publications.waset.org/abstracts/search?q=derivation" title=" derivation"> derivation</a> </p> <a href="https://publications.waset.org/abstracts/148017/derivation-of-bckbci-algebras" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/148017.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">131</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">1464</span> Some Properties in Jordan Ideal on 3-Prime Near-Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdelkarim%20Boua">Abdelkarim Boua</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelhakim%20Chillali"> Abdelhakim Chillali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study of non-associative structures in algebraic structures has become a separate entity; for, in the case of groups, their corresponding non-associative structure i.e. loops is dealt with separately. Similarly there is vast amount of research on the nonassociative structures of semigroups i.e. groupoids and that of rings i.e. nonassociative rings. However it is unfortunate that we do not have a parallel notions or study of non-associative near-rings. In this work we shall attempt to generalize a few known results and study the commutativity of Jordan ideal in 3-prime near-rings satisfying certain identities involving the Jordan ideal. We study the derivations satisfying certain differential identities on Jordan ideals of 3-prime near-rings. Moreover, we provide examples to show that hypothesis of our results are necessary. We give some new results and examples concerning the existence of Jordan ideal and derivations in near-rings. These near-rings can be used to build a new codes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=3-prime%20near-rings" title="3-prime near-rings">3-prime near-rings</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=Jordan%20ideal" title=" Jordan ideal"> Jordan ideal</a>, <a href="https://publications.waset.org/abstracts/search?q=derivations" title=" derivations"> derivations</a> </p> <a href="https://publications.waset.org/abstracts/52456/some-properties-in-jordan-ideal-on-3-prime-near-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52456.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">314</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">1463</span> On the Girth of the Regular Digraph of Ideals of a ‎Commutative ‎Ring</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Masoud%20Karimi">Masoud Karimi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> ‎Let R be a commutative ring‎. ‎The regular digraph of ideals of R, which is denoted by‎ Γ(R)‎, ‎is a digraph whose vertex-set is the set of all ‎non-‎trivial ideals of R and‎, ‎for every‎ two distinct vertices I and J‎, ‎there is an arc from I to J‎, ‎whenever I contains‎ a non-zero-divisor on J. In this article, ‎we ‎show ‎that an indecomposable ‎Noetherian ring ‎‎‎R ‎is ‎Artinian ‎local ‎if ‎and ‎only ‎if Z(I)=Z(R) ‎for ‎every ‎non-nilpotent ‎ideal ‎‎‎I‎. ‎Then ‎we ‎conclude ‎that ‎‎the ‎girth ‎of‎ Γ(R)‎ ‎is ‎not ‎equal ‎to ‎four. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=commutative%20ring%E2%80%8E" title="commutative ring‎">commutative ring‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Egirth%E2%80%8E" title=" ‎girth‎"> ‎girth‎</a>, <a href="https://publications.waset.org/abstracts/search?q=regular%20digraph%E2%80%8E" title=" regular digraph‎"> regular digraph‎</a>, <a href="https://publications.waset.org/abstracts/search?q=zero-divisor" title=" zero-divisor"> zero-divisor</a> </p> <a href="https://publications.waset.org/abstracts/14244/on-the-girth-of-the-regular-digraph-of-ideals-of-a-commutative-ring" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14244.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">288</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">1462</span> Semigroups of Linear Transformations with Fixed Subspaces: Green’s Relations and Ideals</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yanisa%20Chaiya">Yanisa Chaiya</a>, <a href="https://publications.waset.org/abstracts/search?q=Jintana%20Sanwong"> Jintana Sanwong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let V be a vector space over a field and W a subspace of V. Let Fix(V,W) denote the set of all linear transformations on V with fix all elements in W. In this paper, we show that Fix(V,W) is a semigroup under the composition of maps and describe Green’s relations on this semigroup in terms of images, kernels and the dimensions of subspaces of the quotient space V/W where V/W = {v+W : v is an element in V} with v+W = {v+w : w is an element in W}. Let dim(U) denote the dimension of a vector space U and Vα = {vα : v is an element in V} where vα is an image of v under a linear transformation α. For any cardinal number a let a'= min{b : b > a}. We also show that the ideals of Fix(V,W) are precisely the sets. Fix(r) ={α ∊ Fix(V,W) : dim(Vα/W) < r} where 1 ≤ r ≤ a' and a = dim(V/W). Moreover, we prove that if V is a finite-dimensional vector space, then every ideal of Fix(V,W) is principle. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Green%E2%80%99s%20relations" title="Green’s relations">Green’s relations</a>, <a href="https://publications.waset.org/abstracts/search?q=ideals" title=" ideals"> ideals</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20transformation%20semi-groups" title=" linear transformation semi-groups"> linear transformation semi-groups</a>, <a href="https://publications.waset.org/abstracts/search?q=principle%20ideals" title=" principle ideals"> principle ideals</a> </p> <a href="https://publications.waset.org/abstracts/59302/semigroups-of-linear-transformations-with-fixed-subspaces-greens-relations-and-ideals" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59302.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">295</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">1461</span> Pairwise Relative Primality of Integers and Independent Sets of Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jerry%20Hu">Jerry Hu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let G = (V, E) with V = {1, 2, ..., k} be a graph, the k positive integers a₁, a₂, ..., ak are G-wise relatively prime if (aᵢ, aⱼ ) = 1 for {i, j} ∈ E. We use an inductive approach to give an asymptotic formula for the number of k-tuples of integers that are G-wise relatively prime. An exact formula is obtained for the probability that k positive integers are G-wise relatively prime. As a corollary, we also provide an exact formula for the probability that k positive integers have exactly r relatively prime pairs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph" title="graph">graph</a>, <a href="https://publications.waset.org/abstracts/search?q=independent%20set" title=" independent set"> independent set</a>, <a href="https://publications.waset.org/abstracts/search?q=G-wise%20relatively%20prime" title=" G-wise relatively prime"> G-wise relatively prime</a>, <a href="https://publications.waset.org/abstracts/search?q=probability" title=" probability"> probability</a> </p> <a href="https://publications.waset.org/abstracts/162507/pairwise-relative-primality-of-integers-and-independent-sets-of-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/162507.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">100</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">1460</span> The Various Forms of a Soft Set and Its Extension in Medical Diagnosis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Biplab%20Singha">Biplab Singha</a>, <a href="https://publications.waset.org/abstracts/search?q=Mausumi%20Sen"> Mausumi Sen</a>, <a href="https://publications.waset.org/abstracts/search?q=Nidul%20Sinha"> Nidul Sinha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to deal with the impreciseness and uncertainty of a system, D. Molodtsov has introduced the concept of ‘Soft Set’ in the year 1999. Since then, a number of related definitions have been conceptualized. This paper includes a study on various forms of Soft Sets with examples. The paper contains the concepts of domain and co-domain of a soft set, conversion to one-one and onto function, matrix representation of a soft set and its relation with one-one function, upper and lower triangular matrix, transpose and Kernel of a soft set. This paper also gives the idea of the extension of soft sets in medical diagnosis. Here, two soft sets related to disease and symptoms are considered and using AND operation and OR operation, diagnosis of the disease is calculated through appropriate examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=kernel%20of%20a%20soft%20set" title="kernel of a soft set">kernel of a soft set</a>, <a href="https://publications.waset.org/abstracts/search?q=soft%20set" title=" soft set"> soft set</a>, <a href="https://publications.waset.org/abstracts/search?q=transpose%20of%20a%20soft%20set" title=" transpose of a soft set"> transpose of a soft set</a>, <a href="https://publications.waset.org/abstracts/search?q=upper%20and%20lower%20triangular%20matrix%20of%20a%20soft%20set" title=" upper and lower triangular matrix of a soft set"> upper and lower triangular matrix of a soft set</a> </p> <a href="https://publications.waset.org/abstracts/59585/the-various-forms-of-a-soft-set-and-its-extension-in-medical-diagnosis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59585.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">349</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">1459</span> A Discovery of the Dual Sequential Pattern of Prime Numbers in P x P: Applications in a Formal Proof of the Twin-Prime Conjecture</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yingxu%20Wang">Yingxu Wang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work presents basic research on the recursive structures and dual sequential patterns of primes for the formal proof of the Twin-Prime Conjecture (TPC). A rigorous methodology of Twin-Prime Decomposition (TPD) is developed in MATLAB to inductively verify potential twins in the dual sequences of primes. The key finding of this basic study confirms that the dual sequences of twin primes are not only symmetric but also infinitive in the unique base 6 cycle, except a limited subset of potential pairs is eliminated by the lack of dual primality. Both theory and experiments have formally proven that the infinity of twin primes stated in TPC holds in the P x P space. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=number%20theory" title="number theory">number theory</a>, <a href="https://publications.waset.org/abstracts/search?q=primes" title=" primes"> primes</a>, <a href="https://publications.waset.org/abstracts/search?q=twin-prime%20conjecture" title=" twin-prime conjecture"> twin-prime conjecture</a>, <a href="https://publications.waset.org/abstracts/search?q=dual%20primes%20%28P%20x%20P%29" title=" dual primes (P x P)"> dual primes (P x P)</a>, <a href="https://publications.waset.org/abstracts/search?q=twin%20prime%20decomposition" title=" twin prime decomposition"> twin prime decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=formal%20proof" title=" formal proof"> formal proof</a>, <a href="https://publications.waset.org/abstracts/search?q=algorithm" title=" algorithm"> algorithm</a> </p> <a href="https://publications.waset.org/abstracts/182326/a-discovery-of-the-dual-sequential-pattern-of-prime-numbers-in-p-x-p-applications-in-a-formal-proof-of-the-twin-prime-conjecture" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182326.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">73</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">1458</span> On Modules over Dedekind Prime Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elvira%20Kusniyanti">Elvira Kusniyanti</a>, <a href="https://publications.waset.org/abstracts/search?q=Hanni%20Garminia"> Hanni Garminia</a>, <a href="https://publications.waset.org/abstracts/search?q=Pudji%20Astuti"> Pudji Astuti</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research studies an interconnection between finitely generated uniform modules and Dedekind prime rings. The characterization of modules over Dedekind prime rings that will be investigated is an adoption of Noetherian and hereditary concept. Dedekind prime rings are Noetherian and hereditary rings. This property of Dedekind prime rings is a background of the idea of adopting arises. In Noetherian area, it was known that a ring R is Noetherian ring if and only if every finitely generated R-module is a Noetherian module. Similar to that result, a characterization of the hereditary ring is related to its projective modules. That is, a ring R is hereditary ring if and only if every projective R-module is a hereditary module. Due to the above two results, we suppose that characterization of a Dedekind prime ring can be analyzed from finitely generated modules over it. We propose a conjecture: a ring R is a Dedekind prime ring if and only if every finitely generated uniform R-module is a Dedekind module. In this article, we will generalize a concept of the Dedekind module for non-commutative ring case and present a part of the above conjecture. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dedekind%20domains" title="dedekind domains">dedekind domains</a>, <a href="https://publications.waset.org/abstracts/search?q=dedekind%20prime%20rings" title=" dedekind prime rings"> dedekind prime rings</a>, <a href="https://publications.waset.org/abstracts/search?q=dedekind%20modules" title=" dedekind modules"> dedekind modules</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20modules" title=" uniform modules"> uniform modules</a> </p> <a href="https://publications.waset.org/abstracts/32475/on-modules-over-dedekind-prime-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32475.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">446</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">1457</span> Pythagorean-Platonic Lattice Method for Finding all Co-Prime Right Angle Triangles</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anthony%20Overmars">Anthony Overmars</a>, <a href="https://publications.waset.org/abstracts/search?q=Sitalakshmi%20Venkatraman"> Sitalakshmi Venkatraman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between these two ancient disparaging theorists. This work has wide applications in information security where cryptography involves improved ways of finding tuples of prime numbers for secure communication systems. In particular, this paper has direct impact in enhancing the encryption and decryption algorithms in cryptography. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pythagorean%20triples" title="Pythagorean triples">Pythagorean triples</a>, <a href="https://publications.waset.org/abstracts/search?q=platonic%20triples" title=" platonic triples"> platonic triples</a>, <a href="https://publications.waset.org/abstracts/search?q=right%20angle%20triangles" title=" right angle triangles"> right angle triangles</a>, <a href="https://publications.waset.org/abstracts/search?q=co-prime%20numbers" title=" co-prime numbers"> co-prime numbers</a>, <a href="https://publications.waset.org/abstracts/search?q=cryptography" title=" cryptography"> cryptography</a> </p> <a href="https://publications.waset.org/abstracts/80590/pythagorean-platonic-lattice-method-for-finding-all-co-prime-right-angle-triangles" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80590.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">249</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">1456</span> Intuitionistic Fuzzy L-Ideals and Intuitionistic Fuzzy L-Filters in L -Group</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Poonam%20Kumar%20Sharma">Poonam Kumar Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we study the concept of an intuitionistic fuzzy l-ideal and an intuitionistic fuzzy l-filter of an ordered group. We provide several characterizations for an intuitionistic fuzzy l-ideal and an intuitionistic fuzzy l-filter from different perspectives. We observe that for any intuitionistic fuzzy convex sub l-group, we can find an intuitionistic fuzzy l-ideal and an intuitionistic fuzzy l-filter containing it. Lastly, the intersection of some intuitionistic fuzzy l-ideals and an intuitionistic fuzzy l-filters containing it can be used to express any intuitionistic fuzzy convex sub l-group. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=intuitionistic%20L-fuzzy%20sub%20l-group" title="intuitionistic L-fuzzy sub l-group">intuitionistic L-fuzzy sub l-group</a>, <a href="https://publications.waset.org/abstracts/search?q=Intuitionistic%20L-fuzzy%20convex%20sub%20l-group" title=" Intuitionistic L-fuzzy convex sub l-group"> Intuitionistic L-fuzzy convex sub l-group</a>, <a href="https://publications.waset.org/abstracts/search?q=Intuitionistic%20L-fuzzy%20l-ideals" title=" Intuitionistic L-fuzzy l-ideals"> Intuitionistic L-fuzzy l-ideals</a>, <a href="https://publications.waset.org/abstracts/search?q=Intuitionistic%20L-fuzzy%20l-filters" title=" Intuitionistic L-fuzzy l-filters"> Intuitionistic L-fuzzy l-filters</a> </p> <a href="https://publications.waset.org/abstracts/196120/intuitionistic-fuzzy-l-ideals-and-intuitionistic-fuzzy-l-filters-in-l-group" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/196120.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">17</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">1455</span> Soft Power: Concept and Role in Country Policy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Talip%20Turkmen">Talip Turkmen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> From the moment the first beats, the first step into the world mankind finds him in a struggle to survive. Most important case to win this fight is power. Power is one of the most common concepts which we encounter in our life. Mainly power is ability to reach desired results on someone else or ability to penetrate into the behavior of others. Throughout history merging technology and changing political trade-offs caused the change of concept of power. Receiving a state of multipolar new world order in the 21st century and increasing impacts of media have narrowed the limits of military power. With increasing globalization and peaceful diplomacy this gap, left by military power, has filled by soft power which has ability to persuade and attract. As concepts of power soft power also has not compromised yet. For that reason it is important to specify, sources of soft power, soft power strategies and limits of soft power. The purpose of this study was to analyze concept of soft power and importance of soft power in foreign relations. This project focuses on power, hard power and soft power relations, sources of soft power and strategies to gain soft power. Datas in this project was acquired from other studies on soft power and foreign relations. This paper was prepared in terms of concept and research techniques. As a result of data gained in this study the one of important topics in international relations is balance between soft power. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=soft%20power" title="soft power">soft power</a>, <a href="https://publications.waset.org/abstracts/search?q=foreign%20policy" title=" foreign policy"> foreign policy</a>, <a href="https://publications.waset.org/abstracts/search?q=national%20power" title=" national power"> national power</a>, <a href="https://publications.waset.org/abstracts/search?q=hard%20power" title=" hard power"> hard power</a> </p> <a href="https://publications.waset.org/abstracts/33910/soft-power-concept-and-role-in-country-policy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33910.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">466</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">1454</span> Functionalized Ultra-Soft Rubber for Soft Robotics Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shib%20Shankar%20Banerjeea">Shib Shankar Banerjeea</a>, <a href="https://publications.waset.org/abstracts/search?q=Andreas%20Ferya"> Andreas Ferya</a>, <a href="https://publications.waset.org/abstracts/search?q=Gert%20Heinricha"> Gert Heinricha</a>, <a href="https://publications.waset.org/abstracts/search?q=Amit%20Das"> Amit Das</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recently, the growing need for the development of soft robots consisting of highly deformable and compliance materials emerge from the serious limitations of conventional service robots. However, one of the main challenges of soft robotics is to develop such compliance materials, which facilitates the design of soft robotic structures and, simultaneously, controls the soft-body systems, like soft artificial muscles. Generally, silicone or acrylic-based elastomer composites are used for soft robotics. However, mechanical performance and long-term reliabilities of the functional parts (sensors, actuators, main body) of the robot made from these composite materials are inferior. This work will present the development and characterization of robust super-soft programmable elastomeric materials from crosslinked natural rubber that can serve as touch and strain sensors for soft robotic arms with very high elastic properties and strain, while the modulus is altered in the kilopascal range. Our results suggest that such soft natural programmable elastomers can be promising materials and can replace conventional silicone-based elastomer for soft robotics applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=elastomers" title="elastomers">elastomers</a>, <a href="https://publications.waset.org/abstracts/search?q=soft%20materials" title=" soft materials"> soft materials</a>, <a href="https://publications.waset.org/abstracts/search?q=natural%20rubber" title=" natural rubber"> natural rubber</a>, <a href="https://publications.waset.org/abstracts/search?q=sensors" title=" sensors"> sensors</a> </p> <a href="https://publications.waset.org/abstracts/120552/functionalized-ultra-soft-rubber-for-soft-robotics-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/120552.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">160</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">1453</span> A Proof for Goldbach's Conjecture</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hashem%20Sazegar">Hashem Sazegar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In 1937, Vinograd of Russian Mathematician proved that each odd large number can be shown by three primes. In 1973, Chen Jingrun proved that each odd number can be shown by one prime plus a number that has maximum two primes. In this article, we state one proof for Goldbach’conjecture. Introduction: Bertrand’s postulate state for every positive integer n, there is always at least one prime p, such that n < p < 2n. This was first proved by Chebyshev in 1850, which is why postulate is also called the Bertrand-Chebyshev theorem. Legendre’s conjecture states that there is a prime between n2 and (n+1)2 for every positive integer n, which is one of the four Landau’s problems. The rest of these four basic problems are; (i) Twin prime conjecture: There are infinitely many primes p such that p+2 is a prime. (ii) Goldbach’s conjecture: Every even integer n > 2 can be written asthe sum of two primes. (iii) Are there infinitely many primes p such that p−1 is a perfect square? Problems (i), (ii), and (iii) are open till date. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bertrand-Chebyshev%20theorem" title="Bertrand-Chebyshev theorem">Bertrand-Chebyshev theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=Landau%E2%80%99s%20problems" title=" Landau’s problems"> Landau’s problems</a>, <a href="https://publications.waset.org/abstracts/search?q=twin%20prime" title=" twin prime"> twin prime</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%E2%80%99s%20conjecture" title=" Legendre’s conjecture"> Legendre’s conjecture</a>, <a href="https://publications.waset.org/abstracts/search?q=Oppermann%E2%80%99s%20conjecture" title=" Oppermann’s conjecture"> Oppermann’s conjecture</a> </p> <a href="https://publications.waset.org/abstracts/30678/a-proof-for-goldbachs-conjecture" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30678.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">406</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">1452</span> Performance Analysis and Comparison of Various 1-D and 2-D Prime Codes for OCDMA Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gurjit%20Kaur">Gurjit Kaur</a>, <a href="https://publications.waset.org/abstracts/search?q=Shashank%20Johri"> Shashank Johri</a>, <a href="https://publications.waset.org/abstracts/search?q=Arpit%20Mehrotra"> Arpit Mehrotra</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we have analyzed and compared the performance of various coding schemes. The basic ID prime sequence codes are unique in only dimension i.e. time slots whereas 2D coding techniques are not unique by their time slots but with their wavelengths also. In this research we have evaluated and compared the performance of 1D and 2D coding techniques constructed using prime sequence coding pattern for OCDMA system on a single platform. Results shows that 1D Extended Prime Code (EPC) can support more number of active users compared to other codes but at the expense of larger code length which further increases the complexity of the code. Modified Prime Code (MPC) supports lesser number of active users at λc=2 but it has a lesser code length as compared to 1D prime code. Analysis shows that 2D prime code supports lesser number of active users than 1D codes but they are having large code family and are the most secure codes compared to other codes. The performance of all these codes is analyzed on basis of number of active users supported at a Bit Error Rate (BER) of 10-9. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CDMA" title="CDMA">CDMA</a>, <a href="https://publications.waset.org/abstracts/search?q=OCDMA" title=" OCDMA"> OCDMA</a>, <a href="https://publications.waset.org/abstracts/search?q=BER" title=" BER"> BER</a>, <a href="https://publications.waset.org/abstracts/search?q=OOC" title=" OOC"> OOC</a>, <a href="https://publications.waset.org/abstracts/search?q=PC" title=" PC"> PC</a>, <a href="https://publications.waset.org/abstracts/search?q=EPC" title=" EPC"> EPC</a>, <a href="https://publications.waset.org/abstracts/search?q=MPC" title=" MPC"> MPC</a>, <a href="https://publications.waset.org/abstracts/search?q=2-D%20PC%2FPC" title=" 2-D PC/PC"> 2-D PC/PC</a>, <a href="https://publications.waset.org/abstracts/search?q=%CE%BBc" title=" λc"> λc</a>, <a href="https://publications.waset.org/abstracts/search?q=%CE%BBa" title=" λa"> λa</a> </p> <a href="https://publications.waset.org/abstracts/35194/performance-analysis-and-comparison-of-various-1-d-and-2-d-prime-codes-for-ocdma-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35194.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">515</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">1451</span> Associations Between Positive Body Image, Physical Activity and Dietary Habits in Young Adults</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Samrah%20Saeed">Samrah Saeed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Introduction: This study considers a measure of positive body image and the associations between body appreciation, beauty ideals internalization, dietary habits, and physical activity in young adults. Positive body image is assessed by Body Appreciation Scale 2. It is used to assess a person's acceptance of the body, the degree of positivity, and respect for the body.Regular physical activity and healthy eating arebasically important for the body, and they play an important role in creating a positive image of the body. Objectives: To identify the associations between body appreciation and beauty ideals internalization. To compare body appreciation and body ideals internalization among students of different physical activity. To explore the associations between dietary habits (unhealthy, healthy), body appreciation and body ideals internalization. Research methods and organization: Study participants were young adult students, aged 18-35, both male and female.The research questionnaire consisted of four areas: body appreciation, beauty ideals internalization, dietary habits, and physical activity.The questionnaire was created in Google Forms online survey platform.The questionnaire was filled out anonymously Result and Discussion: Physical dissatisfaction, diet, eating disorders and exercise disorders are found in young adults all over the world.Thorough nutrition helps people understand who they are by reassuring them that they are okay without judging or accepting themselves. Social media can positively influence body image in many ways.A healthy body image is important because it affect self-esteem, self-acceptance, and your attitude towards food and exercise. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pysical%20activity" title="pysical activity">pysical activity</a>, <a href="https://publications.waset.org/abstracts/search?q=dietary%20habits" title="dietary habits">dietary habits</a>, <a href="https://publications.waset.org/abstracts/search?q=body%20image" title="body image">body image</a>, <a href="https://publications.waset.org/abstracts/search?q=beauty%20ideals%20internalization" title="beauty ideals internalization">beauty ideals internalization</a>, <a href="https://publications.waset.org/abstracts/search?q=body%20appreciation" title="body appreciation">body appreciation</a> </p> <a href="https://publications.waset.org/abstracts/148433/associations-between-positive-body-image-physical-activity-and-dietary-habits-in-young-adults" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/148433.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">106</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">1450</span> Prime Graphs of Polynomials and Power Series Over Non-Commutative Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Walaa%20Obaidallah%20Alqarafi">Walaa Obaidallah Alqarafi</a>, <a href="https://publications.waset.org/abstracts/search?q=Wafaa%20Mohammed%20Fakieh"> Wafaa Mohammed Fakieh</a>, <a href="https://publications.waset.org/abstracts/search?q=Alaa%20Abdallah%20Altassan"> Alaa Abdallah Altassan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Algebraic graph theory is defined as a bridge between algebraic structures and graphs. It has several uses in many fields, including chemistry, physics, and computer science. The prime graph is a type of graph associated with a ring R, where the vertex set is the whole ring R, and two vertices x and y are adjacent if either xRy=0 or yRx=0. However, the investigation of the prime graph over rings remains relatively limited. The behavior of this graph in extended rings, like R[x] and R[[x]], where R is a non-commutative ring, deserves more attention because of the wider applicability in algebra and other mathematical fields. To study the prime graphs over polynomials and power series rings, we used a combination of ring-theoretic and graph-theoretic techniques. This paper focuses on two invariants: the diameter and the girth of these graphs. Furthermore, the work discusses how the graph structures change when passing from R to R[x] and R[[x]]. In our study, we found that the set of strong zero-divisors of ring R represents the set of vertices in prime graphs. Based on this discovery, we redefined the vertices of prime graphs using the definition of strong zero divisors. Additionally, our results show that although the prime graphs of R[x] and R[[x]] are comparable to the graph of R, they have different combinatorial characteristics since these extensions contain new strong zero-divisors. In particular, we find conditions in which the diameter and girth of the graphs, as they expand from R to R[x] and R[[x]], do not change or do change. In conclusion, this study shows how extending a non-commutative ring R to R[x] and R[[x]] affects the structure of their prime graphs, particularly in terms of diameter and girth. These findings enhance the understanding of the relationship between ring extensions and graph properties. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=prime%20graph" title="prime graph">prime graph</a>, <a href="https://publications.waset.org/abstracts/search?q=diameter" title=" diameter"> diameter</a>, <a href="https://publications.waset.org/abstracts/search?q=girth" title=" girth"> girth</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20ring" title=" polynomial ring"> polynomial ring</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20series%20ring" title=" power series ring"> power series ring</a> </p> <a href="https://publications.waset.org/abstracts/192430/prime-graphs-of-polynomials-and-power-series-over-non-commutative-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192430.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">31</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">1449</span> Soft Power in International Politics: Defense and Continued Relevance</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shivani%20Yadav">Shivani Yadav</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper will first elaborate on the concept of soft power as formulated by Joseph Nye, who argues that soft power is as important as hard power in international politics as it replaces coercion with non-coercive forms of co-optation and attraction. The central tenet of the paper is to extrapolate the continued relevance of soft power in international relations in the 21st century. It is argued that the relevance of soft power, in concurrence with hard power, is on the rise in the international system. This is found to be emanating out of two factors. First, the state-centric practice of international relations has expanded to allow other actors to participate in policymaking. This has led to the resources for power generation to become varied, largely move away from the control of governments, and to produce both hard and soft power attributes. Second, as the currency of coercive power seems to be devaluing in global politics, the role of intangible factors like soft power is getting more important in policymaking. The paper will then go on to elaborate on the critiques of the formulation of soft power from various perspectives, as well as the defenses to these critiques presented by soft power proponents. The paper will reflect on the continued relevance of soft power in international politics by giving the example of India, and how soft power has continued to serve its policy objectives over the years. It is observed that even as India is recognized as a rising superpower today, yet it has made a continuous effort in cultivating its soft power resources, which have proven to be its assets in furthering its foreign policy interests. In conclusion, the paper makes the point that soft power, in conjunction with hard power, will shape international politics in the coming times. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=foreign%20policy" title="foreign policy">foreign policy</a>, <a href="https://publications.waset.org/abstracts/search?q=India%E2%80%99s%20soft%20power" title=" India’s soft power"> India’s soft power</a>, <a href="https://publications.waset.org/abstracts/search?q=international%20politics" title=" international politics"> international politics</a>, <a href="https://publications.waset.org/abstracts/search?q=smart%20power" title=" smart power"> smart power</a>, <a href="https://publications.waset.org/abstracts/search?q=soft%20power" title=" soft power"> soft power</a> </p> <a href="https://publications.waset.org/abstracts/126997/soft-power-in-international-politics-defense-and-continued-relevance" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/126997.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">269</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">1448</span> Preliminary Geophysical Assessment of Soil Contaminants around Wacot Rice Factory Argungu, North-Western Nigeria</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20I.%20Augie">A. I. Augie</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Alhassan"> Y. Alhassan</a>, <a href="https://publications.waset.org/abstracts/search?q=U.%20Z.%20Magawata"> U. Z. Magawata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Geophysical investigation was carried out at wacot rice factory Argungu north-western Nigeria, using the 2D electrical resistivity method. The area falls between latitude 12˚44′23ʺN to 12˚44′50ʺN and longitude 4032′18′′E to 4032′39′′E covering a total area of about 1.85 km. Two profiles were carried out with Wenner configuration using resistivity meter (Ohmega). The data obtained from the study area were modeled using RES2DIVN software which gave an automatic interpretation of the apparent resistivity data. The inverse resistivity models of the profiles show the high resistivity values ranging from 208 Ωm to 651 Ωm. These high resistivity values in the overburden were due to dryness and compactness of the strata that lead to consolidation, which is an indication that the area is free from leachate contaminations. However, from the inverse model, there are regions of low resistivity values (1 Ωm to 18 Ωm), these zones were observed and identified as clayey and the most contaminated zones. The regions of low resistivity thereby indicated the leachate plume or the highly leachate concentrated zones due to similar resistivity values in both clayey and leachate. The regions of leachate are mainly from the factory into the surrounding area and its groundwater. The maximum leachate infiltration was found at depths 1 m to 15.9 m (P1) and 6 m to 15.9 m (P2) vertically, as well as distance along the profiles from 67 m to 75 m (P1), 155 m to 180 m (P1), and 115 m to 192 m (P2) laterally. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=contaminant" title="contaminant">contaminant</a>, <a href="https://publications.waset.org/abstracts/search?q=leachate" title=" leachate"> leachate</a>, <a href="https://publications.waset.org/abstracts/search?q=soil" title=" soil"> soil</a>, <a href="https://publications.waset.org/abstracts/search?q=groundwater" title=" groundwater"> groundwater</a>, <a href="https://publications.waset.org/abstracts/search?q=electrical" title=" electrical"> electrical</a>, <a href="https://publications.waset.org/abstracts/search?q=resistivity" title=" resistivity"> resistivity</a> </p> <a href="https://publications.waset.org/abstracts/114399/preliminary-geophysical-assessment-of-soil-contaminants-around-wacot-rice-factory-argungu-north-western-nigeria" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/114399.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">168</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">1447</span> Recruitment Model (FSRM) for Faculty Selection Based on Fuzzy Soft</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20S.%20Thakur">G. S. Thakur</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a Fuzzy Soft Recruitment Model (FSRM) for faculty selection of MHRD technical institutions. The selection criteria are based on 4-tier flexible structure in the institutions. The Advisory Committee on Faculty Recruitment (ACoFAR) suggested nine criteria for faculty in the proposed FSRM. The model Fuzzy Soft is proposed with consultation of ACoFAR based on selection criteria. The Fuzzy Soft distance similarity measures are applied for finding best faculty from the applicant pool. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20soft%20set" title="fuzzy soft set">fuzzy soft set</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20sets" title=" fuzzy sets"> fuzzy sets</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20soft%20distance" title=" fuzzy soft distance"> fuzzy soft distance</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20soft%20similarity%20measures" title=" fuzzy soft similarity measures"> fuzzy soft similarity measures</a>, <a href="https://publications.waset.org/abstracts/search?q=ACoFAR" title=" ACoFAR"> ACoFAR</a> </p> <a href="https://publications.waset.org/abstracts/12838/recruitment-model-fsrm-for-faculty-selection-based-on-fuzzy-soft" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12838.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">355</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">1446</span> Variation in the Morphology of Soft Palate</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hema%20Lattupalli">Hema Lattupalli </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Introduction: The palate forms a partition between the oral cavity and nasal cavity. The palate is made up of two parts hard palate and soft palate. The Hard palate forms the anterior part of the palate, the soft palate forms a movable muscular fold covered by mucous membrane that is suspended from the posterior border of a hard palate. Aim and Objectives: Soft palate morphological variations have a great paucity in the literature. It’s also believed that the soft palate has no such important anatomical variations. There is a variable presentation of the soft palate morphology in the lateral cephalograms. The aim of this study is to identify the velar morphology. Materials and Methods: 100 normal subjects between the age group of 20 – 35 were taken for the study. Method: Lateral Cephalogram (radiologic study). Results: Different shapes of the soft palate were observed in the lateral cephalograms. The morphology of soft palate was classified into six types 1.Leaf like (50 cases) most common type, 2.Straight line (20 cases), 3.S shaped (4 cases) very rare, 4.Butt like (10 cases), 5. Rat tail (6 cases), 6. Hook shaped (10 cases). Conclusion: This classification helps us to understand the better diversity of the velar morphology in mid-sagittal plane. These findings help us to understand the etiology of OSAS. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=soft%20palate" title="soft palate">soft palate</a>, <a href="https://publications.waset.org/abstracts/search?q=cephalometric%20radiographs" title=" cephalometric radiographs"> cephalometric radiographs</a>, <a href="https://publications.waset.org/abstracts/search?q=morphology" title=" morphology"> morphology</a>, <a href="https://publications.waset.org/abstracts/search?q=cleft%20palate" title=" cleft palate"> cleft palate</a>, <a href="https://publications.waset.org/abstracts/search?q=obstructive%20sleep%20apnoea%20syndrome" title=" obstructive sleep apnoea syndrome"> obstructive sleep apnoea syndrome</a> </p> <a href="https://publications.waset.org/abstracts/40979/variation-in-the-morphology-of-soft-palate" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40979.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">369</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">1445</span> On the Cyclic Property of Groups of Prime Order</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ying%20Yi%20Wu">Ying Yi Wu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=group%20theory" title="group theory">group theory</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20groups" title=" finite groups"> finite groups</a>, <a href="https://publications.waset.org/abstracts/search?q=cyclic%20groups" title=" cyclic groups"> cyclic groups</a>, <a href="https://publications.waset.org/abstracts/search?q=prime%20order" title=" prime order"> prime order</a>, <a href="https://publications.waset.org/abstracts/search?q=classification." title=" classification."> classification.</a> </p> <a href="https://publications.waset.org/abstracts/163778/on-the-cyclic-property-of-groups-of-prime-order" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163778.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">94</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">1444</span> Occurrence of High Nocturnal Surface Ozone at a Tropical Urban Area</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Dey">S. Dey</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20Sibanda"> P. Sibanda</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Gupta"> S. Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Chakraborty"> A. Chakraborty</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The occurrence of high nocturnal surface ozone over a tropical urban area (23̊ 32′16.99″ N and 87̊ 17′ 38.95″ E) is analyzed in this paper. Five incidences of nocturnal ozone maxima are recorded during the observational span of two years (June, 2013 to May, 2015). The maximum and minimum values of the surface ozone during these five occasions are 337.630 μg/m<sup>3</sup> and 13.034 μg/m<sup>3</sup> respectively. HYSPLIT backward trajectory analyses and wind rose diagrams support the horizontal transport of ozone from distant polluted places. Planetary boundary layer characteristics, concentration of precursor (NO<sub>2</sub>) and meteorology are found to play important role in the horizontal and vertical transport of surface ozone during nighttime. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nocturnal%20ozone" title="nocturnal ozone">nocturnal ozone</a>, <a href="https://publications.waset.org/abstracts/search?q=planetary%20boundary%20layer" title=" planetary boundary layer"> planetary boundary layer</a>, <a href="https://publications.waset.org/abstracts/search?q=horizontal%20transport" title=" horizontal transport"> horizontal transport</a>, <a href="https://publications.waset.org/abstracts/search?q=meteorology" title=" meteorology"> meteorology</a>, <a href="https://publications.waset.org/abstracts/search?q=urban%20area" title=" urban area"> urban area</a> </p> <a href="https://publications.waset.org/abstracts/53051/occurrence-of-high-nocturnal-surface-ozone-at-a-tropical-urban-area" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/53051.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">294</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">1443</span> Improvement of Bearing Capacity of Soft Clay Using Geo-Cells</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Siddhartha%20Paul">Siddhartha Paul</a>, <a href="https://publications.waset.org/abstracts/search?q=Aman%20Harlalka"> Aman Harlalka</a>, <a href="https://publications.waset.org/abstracts/search?q=Ashim%20K.%20Dey"> Ashim K. Dey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Soft clayey soil possesses poor bearing capacity and high compressibility because of which foundations cannot be directly placed over soft clay. Normally pile foundations are constructed to carry the load through the soft soil up to the hard stratum below. Pile construction is costly and time consuming. In order to increase the properties of soft clay, many ground improvement techniques like stone column, preloading with and without sand drains/band drains, etc. are in vogue. Time is a constraint for successful application of these improvement techniques. Another way to improve the bearing capacity of soft clay and to reduce the settlement possibility is to apply geocells below the foundation. The geocells impart rigidity to the foundation soil, reduce the net load intensity on soil and thus reduce the compressibility. A well designed geocell reinforced soil may replace the pile foundation. The present paper deals with the applicability of geocells on improvement of the bearing capacity. It is observed that a properly designed geocell may increase the bearing capacity of soft clay up to two and a half times. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bearing%20capacity" title="bearing capacity">bearing capacity</a>, <a href="https://publications.waset.org/abstracts/search?q=geo-cell" title=" geo-cell"> geo-cell</a>, <a href="https://publications.waset.org/abstracts/search?q=ground%20improvement" title=" ground improvement"> ground improvement</a>, <a href="https://publications.waset.org/abstracts/search?q=soft%20clay" title=" soft clay"> soft clay</a> </p> <a href="https://publications.waset.org/abstracts/51250/improvement-of-bearing-capacity-of-soft-clay-using-geo-cells" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51250.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">327</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">1442</span> Integral Domains and Alexandroff Topology</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shai%20Sarussi">Shai Sarussi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let S be an integral domain which is not a field, let F be its field of fractions, and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R ∩ F = S and F R = A. A topological space whose set of open sets is closed under arbitrary intersections is called an Alexandroff space. Inspired by the well-known Zariski-Riemann space and the Zariski topology on the set of prime ideals of a commutative ring, we define a topology on the set of all S-nice subalgebras of A. Consequently, we get an interplay between Algebra and topology, that gives us a better understanding of the S-nice subalgebras of A. It is shown that every irreducible subset of S-nice subalgebras of A has a supremum; and a characterization of the irreducible components is given, in terms of maximal S-nice subalgebras of A. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexandroff%20topology" title="Alexandroff topology">Alexandroff topology</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20domains" title=" integral domains"> integral domains</a>, <a href="https://publications.waset.org/abstracts/search?q=Zariski-Riemann%20space" title=" Zariski-Riemann space"> Zariski-Riemann space</a>, <a href="https://publications.waset.org/abstracts/search?q=S-nice%20subalgebras" title=" S-nice subalgebras"> S-nice subalgebras</a> </p> <a href="https://publications.waset.org/abstracts/154343/integral-domains-and-alexandroff-topology" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/154343.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">113</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">1441</span> Performance Evaluation of One and Two Dimensional Prime Codes for Optical Code Division Multiple Access Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gurjit%20Kaur">Gurjit Kaur</a>, <a href="https://publications.waset.org/abstracts/search?q=Neena%20Gupta"> Neena Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have analyzed and compared the performance of various coding schemes. The basic ID prime sequence codes are unique in only dimension, i.e. time slots, whereas 2D coding techniques are not unique by their time slots but with their wavelengths also. In this research, we have evaluated and compared the performance of 1D and 2D coding techniques constructed using prime sequence coding pattern for Optical Code Division Multiple Access (OCDMA) system on a single platform. Analysis shows that 2D prime code supports lesser number of active users than 1D codes, but they are having large code family and are the most secure codes compared to other codes. The performance of all these codes is analyzed on basis of number of active users supported at a Bit Error Rate (BER) of 10-9. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=CDMA" title="CDMA">CDMA</a>, <a href="https://publications.waset.org/abstracts/search?q=OCDMA" title=" OCDMA"> OCDMA</a>, <a href="https://publications.waset.org/abstracts/search?q=BER" title=" BER"> BER</a>, <a href="https://publications.waset.org/abstracts/search?q=OOC" title=" OOC"> OOC</a>, <a href="https://publications.waset.org/abstracts/search?q=PC" title=" PC"> PC</a>, <a href="https://publications.waset.org/abstracts/search?q=EPC" title=" EPC"> EPC</a>, <a href="https://publications.waset.org/abstracts/search?q=MPC" title=" MPC"> MPC</a>, <a href="https://publications.waset.org/abstracts/search?q=2-D%20PC%2FPC" title=" 2-D PC/PC"> 2-D PC/PC</a>, <a href="https://publications.waset.org/abstracts/search?q=%CE%BBc" title=" λc"> λc</a>, <a href="https://publications.waset.org/abstracts/search?q=%CE%BBa" title=" λa"> λa</a> </p> <a href="https://publications.waset.org/abstracts/45035/performance-evaluation-of-one-and-two-dimensional-prime-codes-for-optical-code-division-multiple-access-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45035.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">339</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=soft%20prime%20ideals&page=2">2</a></li> <li class="page-item"><a class="page-link" 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