Search results for: prime spectrum of a ring

Authors: Elvira Kusniyanti, Hanni Garminia, Pudji Astuti

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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.

Keywords: dedekind domains, dedekind prime rings, dedekind modules, uniform modules

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Authors: Shai Sarussi

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The union of a nonempty chain of prime ideals in a noncommutative ring is not necessarily a prime ideal. 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.

Keywords: prime ideals, union-prime ideals, immediate neighbors, Kaplansky's conjecture

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Authors: Walaa Obaidallah Alqarafi, Wafaa Mohammed Fakieh, Alaa Abdallah Altassan

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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.

Keywords: prime graph, diameter, girth, polynomial ring, power series ring

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Authors: Nidal Ali

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Consider an algebraic number field K of degree n, A0 K is its ring of integers and a prime number p inert in K. Let F(u1, . . . , un, x) be the generic polynomial of integers of K. We will study in advance the stability of this polynomial and then, we will apply it in order to obtain all the monic irreducible polynomials in Fp[x] of degree d dividing n.

Keywords: generic polynomial, irreducibility, iteration, stability, inert prime, totally ramified

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Authors: Manoj Kumar Patel

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In this paper, we introduce and give various properties of weak* Rad-plus-supplemented and cofinitely weak* Rad-plus-supplemented modules over some special kinds of rings, in particular, artinian serial ring and semiperfect ring. Also prove that ring R is artinian serial if and only if every right and left R-module is weak* Rad-plus-supplemented. We provide the counter example which proves that weak* Rad-plus-supplemented module is the generalization of plus-supplemented and Rad-plus-supplemented modules. Furthermore, as an application of above finding results of this research article, our main focus is to characterized the semisimple ring, artinian principal ideal ring, semilocal ring, semiperfect ring, perfect ring, commutative noetherian ring and Dedekind domain in terms of weak* Rad-plus-supplemented module.

Keywords: cofinitely weak* Rad-plus-supplemented module , Dedekind domain, Rad-plus-supplemented module, semiperfect ring

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Authors: Inayatur Rehman

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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.

Keywords: soft sets, LA-rings, soft LA-rings, soft ideals, soft prime ideals, idealistic soft LA-rings, LA-ring homomorphism

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Authors: Rosy Joseph

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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.

Keywords: semirings, subdistributive ring of difference, subdistributive semiring, symmetric fuzzy numbers

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Authors: Shai Sarussi

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Suppose F is a field with valuation v and valuation domain Oᵥ, and R is an Oᵥ-algebra. It is known that there exists a filter quasi-valuation on R; the existence of a quasi-valuation yields several important connections between Oᵥ and R, in particular with respect to their prime spectra. In this paper, the notion of a module valuation is introduced. It is shown that any torsion-free module over Oᵥ has an induced module valuation. Moreover, several results connecting the filter quasi-valuation and module valuations are presented.

Keywords: valuations, quasi-valuations, prime spectrum, algebras over valuation domains

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Authors: Jerry Hu

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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.

Keywords: graph, independent set, G-wise relatively prime, probability

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Authors: Surinder Singh, Meenakshi

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In this paper MZI-FBG based optical add drop multiplexer is designed and its performance is analyzed in the ring network. In the ring network nodes are composed of optical add drop multiplexer, transmitter and receiver. OADM is used to add or drop any frequency at intermediate nodes without affecting other channels. In this paper the performance of the ring network is carried out by varying various kinds of fiber with or without amplifiers.

Keywords: OADM, ring network, MZI-FBG, transmitter

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Authors: Hua Jin, Il Kim

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The biocompatible tadpole-shaped polypeptides with one cyclic polypeptides ring and two alkyl chain tails were synthesized by N-heterocyclic carbine (NHC)-mediated ring-opening polymerization (ROP) of α-amino acid N-carboxyanhydrides (NCAs). First, the NHC precursor, denoted as [NHC(H)][HCO₃], with two alkyl chains at the nitrogen was prepared by a simple anion metathesis of imidazole(in)ium chlorides with KHCO₃. Then NHC releasing from the [NHC(H)][HCO₃] directly initiated the ROP of NCA to produce the cyclic polypeptides. Finally, the tadpole-shaped polypeptides with two regulable tails were obtained. The target polypeptides were characterized by nuclear magnetic resonance spectrum (1H NMR), Fourier transform infrared spectroscopy (FT-IR), gel permeation chromatography (GPC) and matrix-assisted laser desorption ionization-time of flight mass spectra (MALDI-TOF MS). This pioneering approach simplifies the synthesis procedures of tadpole-shaped polypeptides compared to other methods, which usually requires specific intramolecular ring-closure reaction.

Keywords: cyclic polypeptides, α-amino acid N-carboxyanhydrides, N-heterocyclic carbene, ring-opening polymerization, tadpole-shaped

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Authors: Masoud Karimi

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‎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.

Keywords: commutative ring‎, ‎girth‎, regular digraph‎, zero-divisor

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Authors: Shai Sarussi

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Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: integral domains, Alexandroff topology, prime spectrum of a ring, valuation domains

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Authors: Surjit Angra, Pooja Rani, Vinod Kumar

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In hydro power plant spiral casing and Stay ring is meant to guide the water flow to guide vane and runner. Spiral casing and Stay ring is subjected to static i.e. pressure load as well as fluctuating load acting on the structure due to water hammer effect in water conductor system. Finite element method has been used to calculate stresses on spiral casing and stay ring. These calculations were done for the maximum possible loading under operating condition "LC1 Quick Shut Down”. The design load is reached for the spiral casing and stay ring during the emergency closure of the guide apparatus "LC1 Quick Shut Down”. During this operation the forces from the head cover to the stay ring also reach their maximum.

Keywords: hydro-turbine, spiral casing, stay ring, structural analysis

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Authors: Jamal Laaouine, Mohammed Elhassani Charkani

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Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

Keywords: constacyclic code, repeated-root code, maximum distance separable, MDS codes, b-symbol distance, finite chain rings

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Authors: Abdelhakim Chillali, Abdelhamid Tadmori, Muhammed Ziane

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In this article we will study the elliptic curve defined over the ring An and we define the mathematical operations of ECC, which provides a high security and advantage for wireless applications compared to other asymmetric key cryptosystem.

Keywords: elliptic curves, finite ring, cryptography, study

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Authors: Yingxu Wang

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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.

Keywords: number theory, primes, twin-prime conjecture, dual primes (P x P), twin prime decomposition, formal proof, algorithm

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Authors: Jawad Abuhlail, Hamza Hroub

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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.

Keywords: lifting modules, second attached prime ideals, second representations, secondary representations, semisimple modules, second submodules

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Authors: Rafat M. Mohareb

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Several D-ring alkylated estrone analogues display exceptionally high affinity for estrogen receptors. In particular, compounds in which an E-ring is formed are known to be involved in the inhibition of steroidogenic enzymes. Such compounds also have an effect on steroid dehydrogenase activity and the ability to inhibit the detrimental action of the steroid sulfatase enzyme. Generally, E-ring extended steroids have been accessed by modification of the C17-ketone in the D-ring by either arylimine or oximino formation, addition of a carbon nucleophile or hydrazone formation. Other approaches have included ketone reduction, silyl enol ether formation or ring-closing metathesis (giving five- or six-membered E-rings). Chemical modification of the steroid D-ring provides a way to alter the functional groups, sizes and stereochemistry of the D-ring, and numerous structure-activity relationships have been established by such synthetic alterations. Steroids bearing heterocycles fused to the D-ring of the steroid nucleus have been of pharmaceutical interest. In the present paper, we report on the efficient synthesis of estrone possessing pyran, pyrimidine and thiazole ring systems. This study focused on the synthesis and biochemical evaluation of newly synthesized heterocyclic compounds which were then subjected through inhibitory evaluations towards human cancer and normal cell lines.

Keywords: estrone, heterocyclization, cytotoxicity, biomedicine

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Authors: Mehrnaz Mostafavi

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The current research aims to explore a method for creating nano-ring structures through chemical reduction. By employing a direct reduction process at a controlled, slow pace, and concurrently introducing specific reduction agents, the goal is to fabricate these unique nano-ring formations. The deliberate slow reduction of nanoparticles within this process helps prevent spatial hindrances caused by the reduction agents. The timing of the reduction of metal atoms, facilitated by these agents, emerges as a crucial factor influencing the creation of nano-ring structures. In investigation involves a chemical approach utilizing bovine serum albumin and human serum albumin as organic reducing agents to produce gold nano-rings. The controlled reduction of metal atoms at a slow pace and under specific pH conditions plays a pivotal role in the successful fabrication of these nanostructures. Optical spectroscopic analyses revealed distinctive plasmonic behavior in both visible and infrared spectra, owing to the collective movement of electrons along the inner and outer walls of the gold nano-rings. Importantly, these ring-shaped nanoparticles exhibit customizable plasmon resonances in the near-infrared spectrum, a characteristic absent in solid particles of similar sizes. This unique attribute makes the generated samples valuable for applications in Nanomedicine and Nanobiotechnology, leveraging the distinct optical properties of these nanostructures.

Keywords: nano-ring structure, nano-particles, reductant agents, plasmon resonace

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Authors: Isao Tomita

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Electrical conduction in a quasi-one-dimensional polycrystalline metallic ring with a long electron phase coherence length realized at low temperature is investigated. In this situation, the wave nature of electrons is important in the ring, where the electrical current I can be induced by a vector potential that arises from a static magnetic field applied perpendicularly to the ring’s area. It is shown that if the average grain size of the polycrystalline ring becomes large (or comparable to the Fermi wavelength), the electrical current I increases to ~I0, where I0 is a current in a disorder-free ring. The cause of this increasing effect is examined, and this takes place if the electron localization length in the polycrystalline potential increases with increasing grain size, which gives rise to coherent connection of tails of a localized electron wave function in the ring and thus provides highly coherent electrical conduction.

Keywords: electrical conduction, electron phase coherence, polycrystalline metal, magnetic field

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Authors: Anthony Overmars, Sitalakshmi Venkatraman

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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.

Keywords: Pythagorean triples, platonic triples, right angle triangles, co-prime numbers, cryptography

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Authors: D. H. Park, Y. H. Tak, H. H. Kwon, G. J. Kwon, H. G. Kim

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This study focused on developing forging technology of a large-diameter cam ring gear from the small bar. The analyses of temperature variation and deformation behavior of the material are important to obtain the optimal forging products. The hot compression test was carried out to know formability at high temperature. In order to define the optimum forging conditions including material temperature, strain and forging load, the finite element method was used to simulate the forging process of cam ring gear parts. Test results were in good agreement with the simulations. An existing cam ring gear is presented the chips generated by cutting the rod material and the durability issues, but this would be to develop a large-diameter cam ring gear forging parts for truck in order to solve the durability problem and the material waste.

Keywords: forging technology, cam ring, gear, truck, small bar

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Authors: Zainab Al-Maamari, Yassir Dinar

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The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

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Authors: Imam Muthohar, Budi Hartono, Sigit Priyanto, Hardiansyah Hardiansyah

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The eruption of Merapi Volcano in Yogyakarta, Indonesia in 2010 caused many casualties due to minimum preparedness in facing disaster. Increasing population capacity and evacuating to safe places become very important to minimize casualties. Regional government through the Regional Disaster Management Agency has divided disaster-prone areas into three parts, namely ring 1 at a distance of 10 km, ring 2 at a distance of 15 km and ring 3 at a distance of 20 km from the center of Mount Merapi. The success of the evacuation is fully supported by road network infrastructure as a way to rescue in an emergency. This research attempts to model evacuation process based on the rise of refugees in ring 1, expanded to ring 2 and finally expanded to ring 3. The model was developed using SATURN (Simulation and Assignment of Traffic to Urban Road Networks) program version 11.3. 12W, involving 140 centroid, 449 buffer nodes, and 851 links across Yogyakarta Special Region, which was aimed at making a preliminary identification of road networks considered vulnerable to disaster. An assumption made to identify vulnerability was the improvement of road network performance in the form of flow and travel times on the coverage of ring 1, ring 2, ring 3, Sleman outside the ring, Yogyakarta City, Bantul, Kulon Progo, and Gunung Kidul. The research results indicated that the performance increase in the road networks existing in the area of ring 2, ring 3, and Sleman outside the ring. The road network in ring 1 started to increase when the evacuation was expanded to ring 2 and ring 3. Meanwhile, the performance of road networks in Yogyakarta City, Bantul, Kulon Progo, and Gunung Kidul during the evacuation period simultaneously decreased in when the evacuation areas were expanded. The results of preliminary identification of the vulnerability have determined that the road networks existing in ring 1, ring 2, ring 3 and Sleman outside the ring were considered vulnerable to the evacuation of Mount Merapi eruption. Therefore, it is necessary to pay a great deal of attention in order to face the disasters that potentially occur at anytime.

Keywords: model, evacuation, SATURN, vulnerability

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Authors: Atef Ahmad Bleibel

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Most codes of practice, like ACI 318-14, require the use of strut-and-tie modeling to analyze and design reinforced concrete deep beams. Though, investigations that conducted on deep beams do not include ring deep beams of influential parameters. This work presents an analytical parametric study using strut-and-tie modeling stated by ACI 318-14 to predict load capacity of 20 reinforced concrete ring deep beam specimens with different parameters. The parameters that were under consideration in the current work are ring diameter (Dc), number of supports (NS), width of ring beam (bw), concrete compressive strength (f'c) and width of bearing plate (Bp). It is found that the load capacity decreases by about 14-36% when ring diameter increases by about 25-75%. It is also found that load capacity increases by about 62-189% when number of supports increases by about 33-100%, while the load capacity increases by about 25-75% when the beam ring width increases by about 25-75%. Finally, it is found that load capacity increases by about 24-76% when compressive strength increases by about 24-76%, while the load capacity increases by about 5-16% when Bp increases by about 25-75%.

Keywords: load parameters, reinforced concrete, ring deep beam, strut and tie

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Authors: Hashem Sazegar

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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.

Keywords: Bertrand-Chebyshev theorem, Landau’s problems, twin prime, Legendre’s conjecture, Oppermann’s conjecture

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Authors: Pongsawee Supanonth

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This research is the study of Spectrum Management and the increase in efficiency of Spectrum Utilization. It also proves that Cognitive Radio is a newer technology that will change the face of e-communications network today. This study used qualitative research methods by using in-depth interviews to collect data from a sample specific to those who work in Radio channel from 6 key informant and literature review from the related documents in online database. The result is the technique of Dynamic Spectrum Allocation that is the most suitable for Thailand. We conduct in-depth research for future purposes. Moreover, we can also develop a model that can be used in regulating and managing spectrum that is most suitable for Thailand. And also develop an important tool which can be of importance to allocation of spectrum as a natural resource appropriately. It will also guarantee quality and high benefit in a substantial way.

Keywords: cognitive radio, management of radio spectrum, spectrum management, spectrum scarcity

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Authors: Gurjit Kaur, Shashank Johri, Arpit Mehrotra

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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.

Keywords: CDMA, OCDMA, BER, OOC, PC, EPC, MPC, 2-D PC/PC, λc, λa

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Authors: Jeng-Shin Sheu, Qi-Xun Zheng

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This paper mainly discusses a method of separating speech when using a microphone array without knowing the number and direction of sound sources. In recent years, there have been many studies on the method of separating signals by using masking, but most of the separation methods must be operated under the condition of a known number of sound sources. Such methods cannot be used for real-time applications. In our method, this paper uses Circular-Integrated-Cross-Spectrum to estimate the statistical histogram distribution of the direction of arrival (DOA) to obtain the number of sound sources and sound in the mixed-signal Source direction. In calculating the relevant parameters of the ring integrated cross-spectrum, the phase (Phase of the Cross-Power Spectrum) and phase rotation factors (Phase Rotation Factors) calculated by the cross power spectrum of each microphone pair are used. In the part of separating speech, it uses the DOA weighting and shielding separation method to calculate the sound source direction (DOA) according to each T-F unit (time-frequency point). The weight corresponding to each T-F unit can be used to strengthen the intensity of each sound source from the T-F unit and reduce the influence of the remaining sound sources, thereby achieving voice separation.

Keywords: real-time, spectrum analysis, sound source localization, sound source separation

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