Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 579

Search results for: polynomial ring

579 From Convexity in Graphs to Polynomial Rings

Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.


This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

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578 Generic Polynomial of Integers and Applications

Authors: Nidal Ali


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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577 Chebyshev Polynomials Relad with Fibonacci and Lucas Polynomials

Authors: Vandana N. Purav


Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials.


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576 Transformations between Bivariate Polynomial Bases

Authors: Dimitris Varsamis, Nicholas Karampetakis


It is well known that any interpolating polynomial P(x,y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis etc. The aim of this paper is twofold: a) to present transformations between the coordinates of the polynomial P(x,y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: bivariate interpolation polynomial, polynomial basis, transformations, interpolating polynomial

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575 Introduction to Paired Domination Polynomial of a Graph

Authors: Puttaswamy, Anwar Alwardi, Nayaka S. R.


One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs.

Keywords: domination polynomial, paired dominating set, paired domination number, paired domination polynomial

Procedia PDF Downloads 150
574 On the Zeros of the Degree Polynomial of a Graph

Authors: S. R. Nayaka, Putta Swamy


Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained.

Keywords: degree polynomial, regular graph, minimum and maximum degree, graph operations

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573 Rings Characterized by Classes of Rad-plus-Supplemented Modules

Authors: Manoj Kumar Patel


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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572 A Characterization of Skew Cyclic Code with Complementary Dual

Authors: Eusebio Jr. Lina, Ederlina Nocon


Cyclic codes are a fundamental subclass of linear codes that enjoy a very interesting algebraic structure. The class of skew cyclic codes (or θ-cyclic codes) is a generalization of the notion of cyclic codes. This a very large class of linear codes which can be used to systematically search for codes with good properties. A linear code with complementary dual (LCD code) is a linear code C satisfying C ∩ C^⊥ = {0}. This subclass of linear codes provides an optimum linear coding solution for a two-user binary adder channel and plays an important role in countermeasures to passive and active side-channel analyses on embedded cryptosystems. This paper aims to identify LCD codes from the class of skew cyclic codes. Let F_q be a finite field of order q, and θ be an automorphism of F_q. Some conditions for a skew cyclic code to be LCD were given. To this end, the properties of a noncommutative skew polynomial ring F_q[x, θ] of automorphism type were revisited, and the algebraic structure of skew cyclic code using its skew polynomial representation was examined. Using the result that skew cyclic codes are left ideals of the ring F_q[x, θ]/〈x^n-1〉, a characterization of a skew cyclic LCD code of length n was derived. A necessary condition for a skew cyclic code to be LCD was also given.

Keywords: LCD cyclic codes, skew cyclic LCD codes, skew cyclic complementary dual codes, theta-cyclic codes with complementary duals

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571 The K-Distance Neighborhood Polynomial of a Graph

Authors: Soner Nandappa D., Ahmed Mohammed Naji


In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.

Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials

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570 Simulation Analysis of Optical Add Drop Multiplexer in a Ring Network

Authors: Surinder Singh, Meenakshi


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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569 On the Girth of the Regular Digraph of Ideals of a ‎Commutative ‎Ring

Authors: Masoud Karimi


‎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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568 On Modules over Dedekind Prime Rings

Authors: Elvira Kusniyanti, Hanni Garminia, Pudji Astuti


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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567 Structural Analysis of Hydro-Turbine Spiral Casing and Stay Ring Using Ansys

Authors: Surjit Angra, Pooja Rani, Vinod Kumar


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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566 Improved of Elliptic Curves Cryptography over a Ring

Authors: Abdelhakim Chillali, Abdelhamid Tadmori, Muhammed Ziane


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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565 Hosoya Polynomials of Zero-Divisor Graphs

Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim


The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: Hosoya polynomial, wiener index, Hyper-Wiener index, zero-divisor graphs

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564 Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm

Authors: Suparman


Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

Keywords: piecewise regression, bayesian, reversible jump MCMC, segmentation

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563 Heterocyclic Ring Extension of Estrone: Synthesis and Cytotoxicity of Fused Pyrin, Pyrimidine and Thiazole Derivatives

Authors: Rafat M. Mohareb


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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562 Highly Conductive Polycrystalline Metallic Ring in a Magnetic Field

Authors: Isao Tomita


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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561 Development of Forging Technology of Cam Ring Gear for Truck Using Small Bar

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


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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560 Analysis of Road Network Vulnerability Due to Merapi Volcano Eruption

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


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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559 Parameters Affecting Load Capacity of Reinforced Concrete Ring Deep Beams

Authors: Atef Ahmad Bleibel


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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558 Modeling and Simulation of a CMOS-Based Analog Function Generator

Authors: Madina Hamiane


Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

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557 Material Detection by Phase Shift Cavity Ring-Down Spectroscopy

Authors: Rana Muhammad Armaghan Ayaz, Yigit Uysallı, Nima Bavili, Berna Morova, Alper Kiraz


Traditional optical methods for example resonance wavelength shift and cavity ring-down spectroscopy used for material detection and sensing have disadvantages, for example, less resistance to laser noise, temperature fluctuations and extraction of the required information can be a difficult task like ring downtime in case of cavity ring-down spectroscopy. Phase shift cavity ring down spectroscopy is not only easy to use but is also capable of overcoming the said problems. This technique compares the phase difference between the signal coming out of the cavity with the reference signal. Detection of any material is made by the phase difference between them. By using this technique, air, water, and isopropyl alcohol can be recognized easily. This Methodology has far-reaching applications and can be used in air pollution detection, human breath analysis and many more.

Keywords: materials, noise, phase shift, resonance wavelength, sensitivity, time domain approach

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556 A Polyimide Based Split-Ring Neural Interface Electrode for Neural Signal Recording

Authors: Ning Xue, Srinivas Merugu, Ignacio Delgado Martinez, Tao Sun, John Tsang, Shih-Cheng Yen


We have developed a polyimide based neural interface electrode to record nerve signals from the sciatic nerve of a rat. The neural interface electrode has a split-ring shape, with four protruding gold electrodes for recording, and two reference gold electrodes around the split-ring. The split-ring electrode can be opened up to encircle the sciatic nerve. The four electrodes can be bent to sit on top of the nerve and hold the device in position, while the split-ring frame remains flat. In comparison, while traditional cuff electrodes can only fit certain sizes of the nerve, the developed device can fit a variety of rat sciatic nerve dimensions from 0.6 mm to 1.0 mm, and adapt to the chronic changes in the nerve as the electrode tips are bendable. The electrochemical impedance spectroscopy measurement was conducted. The gold electrode impedance is on the order of 10 kΩ, showing excellent charge injection capacity to record neural signals.

Keywords: impedance, neural interface, split-ring electrode, neural signal recording

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555 Stabilization Control of the Nonlinear AIDS Model Based on the Theory of Polynomial Fuzzy Control Systems

Authors: Shahrokh Barati


In this paper, we introduced AIDS disease at first, then proposed dynamic model illustrate its progress, after expression of a short history of nonlinear modeling by polynomial phasing systems, we considered the stability conditions of the systems, which contained a huge amount of researches in order to modeling and control of AIDS in dynamic nonlinear form, in this approach using a frame work of control any polynomial phasing modeling system which have been generalized by part of phasing model of T-S, in order to control the system in better way, the stability conditions were achieved based on polynomial functions, then we focused to design the appropriate controller, firstly we considered the equilibrium points of system and their conditions and in order to examine changes in the parameters, we presented polynomial phase model that was the generalized approach rather than previous Takagi Sugeno models, then with using case we evaluated the equations in both open loop and close loop and with helping the controlling feedback, the close loop equations of system were calculated, to simulate nonlinear model of AIDS disease, we used polynomial phasing controller output that was capable to make the parameters of a nonlinear system to follow a sustainable reference model properly.

Keywords: polynomial fuzzy, AIDS, nonlinear AIDS model, fuzzy control systems

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554 Upsetting of Tri-Metallic St-Cu-Al and St-Cu60Zn-Al Cylindrical Billets

Authors: Isik Cetintav, Cenk Misirli, Yilmaz Can


This work investigates upsetting of the tri-metallic cylindrical billets both experimentally and analytically with a reduction ratio 30%. Steel, brass, and copper are used for the outer and outmost rings and aluminum for the inner core. Two different models have been designed to show material flow and the cavity took place over the two interfaces during forming after this reduction ratio. Each model has an outmost ring material as steel. Model 1 has an outer ring between the outmost ring and the solid core material as copper and Model 2 has a material as brass. Solid core is aluminum for each model. Billets were upset in press machine by using parallel flat dies. Upsetting load was recorded and compared for models and single billets. To extend the tests and compare with experimental procedure to a wider range of inner core and outer ring geometries, finite element model was performed. ABAQUS software was used for the simulations. The aim is to show how contact between outmost ring, outer ring and the inner core are carried on throughout the upsetting process. Results have shown that, with changing in height, between outmost ring, outer ring and inner core, the Model 1 and Model 2 had very good interaction, and the contact surfaces of models had various interface behaviour. It is also observed that tri-metallic materials have lower weight but better mechanical properties than single materials. This can give an idea for using and producing these new materials for different purposes.

Keywords: tri-metallic, upsetting, copper, brass, steel, aluminum

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553 On CR-Structure and F-Structure Satisfying Polynomial Equation

Authors: Manisha Kankarej


The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, integrability condition, Nijenhuis tensor

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552 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation

Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha


In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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551 Assessment of Residual Stress on HDPE Pipe Wall Thickness

Authors: D. Sersab, M. Aberkane


Residual stresses, in high-density polyethylene (HDPE) pipes, result from a nonhomogeneous cooling rate that occurs between the inner and outer surfaces during the extrusion process in manufacture. Most known methods of measurements to determine the magnitude and profile of the residual stresses in the pipe wall thickness are layer removal and ring slitting method. The combined layer removal and ring slitting methods described in this paper involves measurement of the circumferential residual stresses with minimal local disturbance. The existing methods used for pipe geometry (ring slitting method) gives a single residual stress value at the bore. The layer removal method which is used more in flat plate specimen is implemented with ring slitting method. The method permits stress measurements to be made directly at different depth in the pipe wall and a well-defined residual stress profile was consequently obtained.

Keywords: residual stress, layer removal, ring splitting, HDPE, wall thickness

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550 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra

Authors: Zuhier Altawallbeh


In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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