Search results for: cyclic semigroup

Authors: Zsolt Lipcsey, Sampson Marshal Imeh

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We investigate a certain characterisation for rank of a semigroup by Howie and Ribeiro (1999), to ascertain the relevance of the concept of independence. There are cases where the concept of independence fails to be useful for this purpose. One would expect the basic element to be the maximal independent subset of a given semigroup. However, we construct examples for semigroups where finite basis exist and the basis is larger than the number of independent elements.

Keywords: generating sets, independent set, rank, cyclic semigroup, basis, commutative

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Authors: Chanon Promsakon, Sayan Panma

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Let S be a finite semigroup, A a subset of S and f an endomorphism on S. The endo-Cayley digraph of a semigroup S corresponding to a connecting set A and an endomorphism f, denoted by endo − Cayf (S, A) is a digraph whose vertex set is S and a vertex u is adjacent to a vertex v if and only if v = f(u)a for some a ∈ A. A digraph D is called undirected if any edge uv in D, there exists an edge vu in D. We consider the undirectedness of an endo-Cayley of a cyclic group of order prime, Zp. In this work, we investigate conditions for connecting sets and endomorphisms to make endo-Cayley digraphs of cyclic groups of order primes be undirected. Moreover, we give some conditions for an undirected endo-Cayley of cycle group of any order.

Keywords: endo-Cayley graph, undirected digraphs, cyclic groups, endomorphism

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Authors: Chollawat Pookpienlert, Jintana Sanwong

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An element a of a semigroup S is called left (right) regular if there exists x in S such that a=xa² (a=a²x) and said to be intra-regular if there exist u,v in such that a=ua²v. Let T(X) be the semigroup of all full transformations on a set X under the composition of maps. For a fixed nonempty subset Y of X, let Fix(X,Y)={α ™ T(X) : yα=y for all y ™ Y}, where yα is the image of y under α. Then Fix(X,Y) is a semigroup of full transformations on X which fix all elements in Y. Here, we characterize left regular, right regular and intra-regular elements of Fix(X,Y) which characterizations are shown as follows: For α ™ Fix(X,Y), (i) α is left regular if and only if Xα\Y = Xα²\Y, (ii) α is right regular if and only if πα = πα², (iii) α is intra-regular if and only if | Xα\Y | = | Xα²\Y | such that Xα = {xα : x ™ X} and πα = {xα⁻¹ : x ™ Xα} in which xα⁻¹ = {a ™ X : aα=x}. Moreover, those regularities are equivalent if Xα\Y is a finite set. In addition, we count the number of those elements of Fix(X,Y) when X is a finite set. Finally, we determine the maximal congruence ρ on Fix(X,Y) when X is finite and Y is a nonempty proper subset of X. If we let | X \Y | = n, then we obtain that ρ = (Fixn x Fixn) ∪ (H ε x H ε) where Fixn = {α ™ Fix(X,Y) : | Xα\Y | < n} and H ε is the group of units of Fix(X,Y). Furthermore, we show that the maximal congruence is unique.

Keywords: intra-regular, left regular, maximal congruence, right regular, transformation semigroup

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Authors: Nuttawoot Nupo, Sayan Panma

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A semigroup S is said to be a left (right) zero semigroup if S satisfies the equation xy=x (xy=y) for all x,y in S. In addition, the semigroup S is called a left (right) group if S is isomorphic to the direct product of a group and a left (right) zero semigroup. The Cayley digraph Cay(S,A) of a semigroup S with a connection set A is defined to be a digraph with the vertex set S and the arc set E(Cay(S,A))={(x,xa) | x∈S, a∈A} where A is any subset of S. All sets in this research are assumed to be finite. Let D be a digraph together with a vertex set V and an arc set E. Let u and v be two different vertices in V and I a nonempty subset of V. The vertices u and v are said to be independent if (u,v)∉E and (v,u)∉E. The set I is called an independent set of D if any two different vertices in I are independent. The independence number of D is the maximum cardinality of an independent set of D. Moreover, the vertices u and v are said to be path independent if there is no dipath from u to v and there is no dipath from v to u. The set I is called a path independent set of D if any two different vertices in I are path independent. The path independence number of D is the maximum cardinality of a path independent set of D. In this research, we describe a lower bound and an upper bound of the independence number of Cayley digraphs of left groups and right groups. Some examples corresponding to those bounds are illustrated here. Furthermore, the exact value of the path independence number of Cayley digraphs of left groups and right groups are also presented.

Keywords: Cayley digraphs, independence number, left groups, path independence number, right groups

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Authors: Poonam Yadav, Dong Bok Lee

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Isothermal oxidation at 800°C for 50h and Cyclic oxidation at 600°C and 800°C for 40h of Pure Ti and Ti64 were performed in a muffle furnace. In Cyclic oxidation, massive scale spallation occurred, and the oxide scale cracks and peels off were observed at high temperature, it represents oxide scale that formed during cyclic oxidation was spalled out owing to stresses due to thermal shock generated during repetitive oxidation and subsequent cooling. The thickness of scale is larger in cyclic oxidation than the isothermal case. This is due to inward diffusion of oxygen through oxide scales and/or pores and cracks in cyclic oxidation.

Keywords: cyclic, diffusion, isothermal, cyclic

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Authors: Jing Li, Xiuli Li

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This paper studies a special class of linear codes, called skew cyclic codes, over the ring R= F_q+uF_q+…+u^k-1F_q, where q is a prime power. A Gray map ɸ from R to F_q and a Gray map ɸ' from Rⁿ to Fⁿ_q are defined, as well as an automorphism Θ over R. It is proved that the images of skew cyclic codes over R under map ɸ' and Θ are cyclic codes over F_q, and they still keep the dual relation.

Keywords: skew cyclic code, gray map, automorphism, cyclic code

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Authors: Xuezhang Hou

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A control problem of a flexible Lamina formulated by partial differential equations with viscoelastic boundary conditions is studied in this paper. The problem is written in standard form of linear infinite dimensional system in an appropriate energy Hilbert space. The semigroup approach of linear operators is adopted in investigating wellposedness of the closed loop system. A variable structural control for the system is proposed, and meanwhile an equivalent control method is applied to the thin plate system. A significant result on control theory that the thin plate can be approximated by ideal sliding mode in any accuracy in terms of semigroup approach is obtained.

Keywords: partial differential equations, flexible lamina, variable structural control, semigroup of linear operators

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Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Eusebio Jr. Lina, Ederlina Nocon

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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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Authors: Leonid Borisov, Yuri Orlov

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We obtain explicit formulas of finitely multiple approximations of the equilibrium density matrix for the case of the harmonic oscillator using Chernoff's theorem and the notion of semigroup which is Chernoff equivalent to average semigroup. Also we found explicit formulas for the corresponding approximate Wigner functions and average values of the observable. We consider a superposition of τ -quantizations representing a wide class of linear quantizations. We show that the convergence of the approximations of the average values of the observable is not uniform with respect to the Gibbs parameter. This does not allow to represent approximate expression as the sum of the exact limits and small deviations evenly throughout the temperature range with a given order of approximation.

Keywords: Chernoff theorem, Feynman formulas, finitely multiple approximation, harmonic oscillator, Wigner function

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Authors: Deepshikha Verma, V. N. Rajasekharan Pillai

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The present study reports the synthesis of cyclic PNC-28 peptides with solid-phase peptide synthesis method. In the first step, we synthesize the linear PNC-28 Peptide and in the second step, we cyclize (N-to-C or head-to-tail cyclization) the linear PNC-28 peptide. The molecular formula of cyclic PNC-28 peptide is C64H88N12O16 and its m/z mass is ≈1233.64. Elemental analysis of cyclic PNC-28 is C, 59.99; H, 6.92; N, 13.12; O, 19.98. The characterization of LC-MS, CD, FT-IR, and 1HNMR has been done to confirm the successful synthesis and cyclization of linear PNC-28 peptides.

Keywords: CD, FTIR, 1HNMR, cyclic peptide

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Authors: L. Pavithra, R. Sharmila, Shivani Sridhar

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Columns severe structural damage needs proportioning a significant portion of earthquake energy can be dissipated yielding in the beams. Presence of axial load along with cyclic loading has a significant influence on column. The objective of this paper is to present the analytical results of columns subjected to biaxial cyclic loading.

Keywords: RC column, Seismic behaviour, cyclic behaviour, biaxial testing, ductile behaviour

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Authors: S. A. Naeini, Z. Eftekhari

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Liquefaction phenomenon in sand is nowadays a classical soil mechanics subject. Using a cyclic triaxial test apparatus, we use non-woven geotextile reinforcement to improve the liquefaction resistance of sand. The layer configurations used are zero, one, two and three horizontal reinforcing layers in a triaxial test sample. The influences of the number of geotextile layers, and cyclic stress ratio (CSR) were studied and described. The results illustrated that the geotextile inclusion increases liquefaction resistance.

Keywords: liquefaction resistance, geotextile, sand, cyclic triaxial test, cyclic stress ratio

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: Yanisa Chaiya, Jintana Sanwong

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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.

Keywords: Green’s relations, ideals, linear transformation semi-groups, principle ideals

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Authors: E. E. S. Uy, T. Noda, K. Nakai, J. R. Dungca

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Cyclic threshold shear strain is the cyclic shear strain amplitude that serves as the indicator of the development of pore water pressure. The parameter can be obtained by performing either cyclic triaxial test, shaking table test, cyclic simple shear or resonant column. In a cyclic triaxial test, other researchers install measuring devices in close proximity of the soil to measure the parameter. In this study, an attempt was made to estimate the cyclic threshold shear strain parameter using full-field measurement technique. The technique uses a camera to monitor and measure the movement of the soil. For this study, the technique was incorporated in a strain-controlled consolidated undrained cyclic triaxial test. Calibration of the camera was first performed to ensure that the camera can properly measure the deformation under cyclic loading. Its capacity to measure deformation was also investigated using a cylindrical rubber dummy. Two-dimensional image processing was implemented. Lucas and Kanade optical flow algorithm was applied to track the movement of the soil particles. Results from the full-field measurement technique were compared with the results from the linear variable displacement transducer. A range of values was determined from the estimation. This was due to the nonhomogeneous deformation of the soil observed during the cyclic loading. The minimum values were in the order of 10-2% in some areas of the specimen.

Keywords: cyclic loading, cyclic threshold shear strain, full-field measurement, optical flow

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Ahmed Hosny Abdel-Rahman, Mohamed Abdel-Moneim

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Reinforced earth structures are generally subjected to cyclic loading generated from earthquakes. This paper presents a summary of the results and analyses of a testing program carried out in a large-scale multi-function geosynthetic testing apparatus that accommodates soil samples up to 1.0 m3. This apparatus performs different shear and pullout tests under both static and cyclic loading. The testing program was carried out to investigate the controlling factors affecting soil/geogrid interaction under cyclic loading. The extensibility of the geogrids, the applied normal stresses, the characteristics of the cyclic loading (frequency, and amplitude), and initial static load within the geogrid sheet were considered in the testing program. Based on the findings of the testing program, the effect of these parameters on the pullout resistance of geogrids, as well as the displacement mobility under cyclic loading were evaluated. Conclusions and recommendations for the design of reinforced earth walls under cyclic loading are presented.

Keywords: geogrid, soil, interface, cyclic loading, pullout, large scale testing

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Authors: Ying Yi Wu

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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.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Khyati Sharma, A. Satyanarayana Reddy

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The topic of how many subgroups exist within a certain finite group naturally arises in the study of finite groups. Over the years, different researchers have investigated this issue from a variety of angles. The significant contributions of the key mathematicians over the time have been summarized in this article. To this end, we classify finite groups into three categories viz. (a) Groups for which the number of subgroups is less than |G|, (b) equals to |G|, and finally, (c) greater than |G|. Because every element of a finite group generates a cyclic subgroup, counting cyclic subgroups is the most important task in this endeavor. A brief survey on the number of cyclic subgroups of finite groups is also conducted by us. Furthermore, we also covered certain arithmetic relations between the order of a finite group |G| and the number of its distinct cyclic subgroups |C(G)|. In order to provide pertinent context and possibly reveal new novel areas of potential research within the field of research on finite groups, we finally pose and solicit a few open questions.

Keywords: abstract algebra, cyclic subgroup, finite group, subgroup

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Authors: Rashid S. Mohammad, Shicheng Zhang, Sun Lu, Syed Jamal-Ud-Din, Xinzhe Zhao

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A compositional reservoir simulation model (CMG-GEM) was used for cyclic CO₂ injection process in unconventional tight reservoir. Cyclic CO₂ injection is an enhanced oil recovery process consisting of injection, shut-in, and production. The study of cyclic CO₂ injection and hydrocarbon recovery in ultra-low permeability reservoirs is mainly a function of rock, fluid, and operational parameters. CMG-GEM was used to study several design parameters of cyclic CO₂ injection process to distinguish the parameters with maximum effect on the oil recovery and to comprehend the behavior of cyclic CO₂ injection in tight reservoir. On the other hand, permeability reduction induced by asphaltene precipitation is one of the major issues in the oil industry due to its plugging onto the porous media which reduces the oil productivity. In addition to asphaltene deposition, solubility of CO₂ in the aquifer is one of the safest and permanent trapping techniques when considering CO₂ storage mechanisms in geological formations. However, the effects of the above uncertain parameters on the process of CO₂ enhanced oil recovery have not been understood systematically. Hence, it is absolutely necessary to study the most significant parameters which dominate the process. The main objective of this study is to improve techniques for designing cyclic CO₂ injection process while considering the effects of asphaltene deposition and solubility of CO₂ in the brine in order to prevent asphaltene precipitation, minimize CO₂ emission, optimize cyclic CO₂ injection, and maximize oil production.

Keywords: tight reservoirs, cyclic O₂ injection, asphaltene, solubility, reservoir simulation

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Authors: Z. Adnan, M. M. Habib

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The laboratory tests for measuring the effects of small strain to the shear strength and maximum stiffness development of post-cyclic degradation of hemic peat are reviewed in this paper. A series of laboratory testing has been conducted to fulfil the objective of this research to study the post-cyclic behaviour of peat soil and focuses on the small strain characteristics. For this purpose, a number of strain-controlled static, cyclic and post-cyclic triaxial tests were carried out in undrained condition on hemic peat soil. The shear strength and maximum stiffness of hemic peat are evaluated immediately after post-cyclic monotonic testing. There are two soil samples taken from West Johor and East Malaysia peat soil. Based on these laboratories and field testing data, it was found that the shear strength and maximum stiffness of peat soil decreased in post-cyclic monotonic loading than its initial shear strength and stiffness. In particular, degradation in shear strength and stiffness is more sensitive for peat soil due to fragile and uniform fibre structures. Shear strength of peat soil, τ_max = 12.53 kPa (Beaufort peat, BFpt) and 36.61 kPa (Parit Nipah peat, PNpt) decreased than its initial 58.46 kPa and 91.67 kPa. The maximum stiffness, G_max = 0.23 and 0.25 decreased markedly with post-cyclic, G_max = 0.04 and 0.09. Simple correlations between the G_max and the τ_max effects due to small strain, ε = 0.1, the G_max values for post-cyclic are relatively low compared to its initial G_max. As a consequence, the reported values and patterns of both the West Johor and East Malaysia peat soil are generally the same.

Keywords: post-cyclic, strain, maximum stiffness, shear strength

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Authors: Raquib Ahsan, Md. Mahir Asif, Md. Zahidul Alam

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A huge portion of old masonry buildings in Bangladesh are vulnerable to earthquake. In most of the cases these buildings contain unreinforced masonry wall which are most likely to be subjected to earthquake damages. Due to deterioration of mortar joint and aging, shear resistance of these unreinforced masonry walls dwindle. So, retrofitting of these old buildings has become an important issue. Among many researched and experimented techniques, ferrocement retrofitting can be a low cost technique in context of the economic condition of Bangladesh. This study aims at investigating the behavior of ferrocement retrofitted unconfined URM walls under different types of cyclic loading. Four 725 mm × 725 mm masonry wall units were prepared with bricks jointed by stretcher bond with 12.5 mm mortar between two adjacent layers of bricks. To compare the effectiveness of ferrocement retrofitting a particular type wire mesh was used in this experiment which is 20 gauge woven wire mesh with 12.5 mm × 12.5 mm square opening. After retrofitting with ferrocement these wall units were tested by applying cyclic deformation along the diagonals of the specimens. Then a comparative study was performed between the retrofitted specimens and control specimens for both partially reversed cyclic load condition and cyclic compression load condition. The experiment results show that ultimate load carrying capacities of ferrocement retrofitted specimens are 35% and 27% greater than the control specimen under partially reversed cyclic loading and cyclic compression respectively. And before failure the deformations of ferrocement retrofitted specimens are 43% and 33% greater than the control specimen under reversed cyclic loading and cyclic compression respectively. Therefore, the test results show that the ultimate load carrying capacity and ductility of ferrocement retrofitted specimens have improved.

Keywords: cyclic compression, cyclic loading, ferrocement, masonry wall, partially reversed cyclic load, retrofitting

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Authors: A. Baqqal, O. Abduhamid, H. Abdul-Hameed, T. Messager, G. Ayoub

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In this contribution, the effect of crystal content on the cyclic response of semi-crystalline polyethylene is studied over a large strain range. Experimental observations on a high-density polyethylene with 72% crystal content and an ultralow density polyethylene with 15% crystal content are reported. The cyclic stretching does appear a thermoplastic-like response for high crystallinity and an elastomeric-like response for low crystallinity, both characterized by a stress-softening, a hysteresis and a residual strain, whose amount depends on the crystallinity and the applied strain. Based on the experimental observations, a unified viscoelastic-viscoplastic constitutive model capturing the polyethylene cyclic response features is proposed. A two-phase representation of the polyethylene microstructure allows taking into consideration the effective contribution of the crystalline and amorphous phases to the intermolecular resistance to deformation which is coupled, to capture the strain hardening, to a resistance to molecular orientation. The polyethylene cyclic response features are captured by introducing evolution laws for the model parameters affected by the microstructure alteration due to the cyclic stretching.

Keywords: cyclic loading unloading, polyethylene, semi-crystalline polymer, viscoelastic-viscoplastic constitutive model

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Authors: Jaegu Choi, Jae-Mean Koo, Chang-Sung Seok, Byungwoo Moon

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Since massive earthquakes in the world have been reported recently, the safety of nuclear power plants for seismic loading has become a significant issue. Seismic loading is the reverse cyclic loading, consisting of repeated tensile and compression by longitudinal and transverse wave. Up to this time, the study on characteristics of fracture toughness under reverse cyclic loading has been unsatisfactory. Therefore, it is necessary to obtain the fracture toughness under reverse cyclic load for the integrity estimation of nuclear power plants under seismic load. Fracture resistance (J-R) curves, which are used for determination of fracture toughness or integrity estimation in terms of elastic-plastic fracture mechanics, can be derived by the fracture resistance test using single specimen technique. The objective of this paper is to study the effects of reverse cyclic loading on a fracture resistance curve of ESG specimen, having a similar stress gradient compared to the crack surface of the real pipe. For this, we carried out the fracture toughness test under the reverse cyclic loading, while changing incremental plastic displacement. Test results showed that the J-R curves were decreased with a decrease of the incremental plastic displacement.

Keywords: reverse cyclic loading, j-r curve, ESG specimen, incremental plastic displacement

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Authors: Ankit Shai

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CRC or Cyclic Redundancy Check is one of the most common, and one of the most powerful error-detecting codes implemented on modern computers. Most of the modern communication protocols use some error detection algorithms in digital networks and storage devices to detect accidental changes to raw data between transmission and reception. Cyclic Redundancy Check, or CRC, is the most popular one among these error detection codes. CRC properties are defined by the generator polynomial length and coefficients. The aim of this project is to implement an efficient FPGA based CRC-8 that accepts a 32 bit input, taking into consideration optimal chip area and high performance, using VHDL. The proposed architecture is implemented on Xilinx ISE Simulator. It is designed while keeping in mind the hardware design, complexity and cost factor.

Keywords: cyclic redundancy checker, CRC-8, 32-bit input, FPGA, VHDL, ModelSim, Xilinx

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Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

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In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: elasto-plasticity, uncertainty, soils, fokker-planck equation, fourier spectral method, finite difference method

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Authors: Poonam Yadav, Dong Bok Lee

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In this study, the Ti-6Al-4V alloy was isothermally and cyclically oxidized at 800oC for 40 hours in air, and its oxidation behavior was characterized in terms of its oxidation rate, scaling rate, and scale spallation tendency. The isothermal oxidation tests indicated that Ti-6Al-4V oxidized fast and almost linearly, forming thick oxide scales. However, the scales that formed during isothermal oxidation were adherent. The cyclic oxidation tests indicated that the scales that formed on Ti-6Al-4V were highly susceptible to spallation owing to the large growth stress arisen and the thermal stress imposed during thermal cyclings. The formed scales frequently delaminated into several pieces owing to the excessive stress aroused by the repetitive thermal shock. Particularly, excessive oxidation and heavy spallation occurred at the edge of Ti-6Al-4V during cyclic oxidation.

Keywords: cyclic, isothermal, oxidation, spallation

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Authors: Isa Ahmadi, Ramin Khamedi

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In this paper, the elasto-plastic and cyclic torsion of a shaft is studied using a finite element method. The Prager kinematic hardening theory of plasticity with the Ramberg and Osgood stress-strain equation is used to evaluate the cyclic loading behavior of the shaft under the torsional loading. The material of shaft is assumed to follow the non-linear strain hardening property based on the Prager model. The finite element method with C1 continuity is developed and used for solution of the governing equations of the problem. The successive substitution iterative method is used to calculate the distribution of stresses and plastic strains in the shaft due to cyclic loads. The shear stress, effective stress, residual stress and elastic and plastic shear strain distribution are presented in the numerical results.

Keywords: cyclic loading, finite element analysis, Prager kinematic hardening model, torsion of shaft

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