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Let R be a commutative ring with unity and R+, U(R), and Z*(R) be the additive group, the set of unit elements, and the set of all nonzero zero-divisors of R, respectively. We denote by ℂAY(R) and GR, the Cayley graph Cay(R+, Z*(R)) and the unitary Cayley graph Cay(R+, U(R)), respectively. For an Artinian ring R, Akhtar et al. (2009) studied GR. In this article, we study ℂAY(R) and determine the clique number, chromatic number, edge chromatic number, domination number, and the girth of ℂAY(R). We also characterize all rings R whose ℂAY(R) is planar. Moreover, we determine all finite rings R whose ℂAY(R) is strongly regular. We prove that ℂAY(R) is strongly regular if and only if it is edge... 

When a transparent plane-parallel plate is illuminated at a boundary region by a parallel monochromatic beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. The intensity of the diffraction fringes varies periodically with changes in the optical path difference of the light passing through the plate edge. The optical path difference depends on the incident angle of the light, the refractive index of the plate and surrounding medium, and the wavelength of the light. Plotting the intensity of the diffraction fringes versus optical path difference provides a general phase shift method for phase... 

Let R be a commutative ring with unity and R+ and Z*(R) be the additive group and the set of all nonzero zero-divisors of R, respectively. We denote by ℂ𝔸𝕐(R) the Cayley graph Cay(R+, Z*(R)). In this article, we study ℂ𝔸𝕐(R). Among other results, it is shown that for every zero-dimensional nonlocal ring R, ℂ𝔸𝕐(R) is a connected graph of diameter 2. Moreover, for a finite ring R, we obtain the vertex connectivity and the edge connectivity of ℂ𝔸𝕐(R). As a result, ℂ𝔸𝕐(R) gives an algebraic construction for vertex transitive graphs of maximum connectivity. In addition, we characterize all zero-dimensional semilocal... 

It is well known that all starlike trees, i.e. trees with exactly one vertex of degree at least three, are determined by their Laplacian spectrum. A double starlike tree is a tree with exactly two vertices of degree at least three. In 2009, the following question was posed: Are all the double starlike trees determined by their Laplacian spectra? In this direction, it was proved that one special double starlike tree Hn(p,p) is determined by its Laplacian spectrum, where Hn(p,q) is a tree obtained by joining p pendant vertices to an end vertex of a path of order and then joining pendant vertices to another end of the path. Also, the banana tree Bn,k is a tree obtained by joining a vertex to... 

Let G be a simple graph of order n. We mean by dominating set, a set S C V(G) such that every vertex of G is either in S or adjacent to a vertex in S. The domination polynomial of G is the polynomial Σni=1 (G,i)xi where d((g,i) is the number of dominating sets of G of size i. Two graphs G and H are said to be V-equivalent, written G H, if D((G, x) = D(H, x). The D-equivalence class of G is [G] = { H H G }. Recently, the determination of D-equivalence class of a given graph, has been of interest. In this paper, it is shown that for n ≥ 3, [Kn, n] has size two. We conjecture that the complete bipartite graph Km,n for n - m ≥ 2, is uniquely determined by its domination polynomial  

Let R be a commutative ring with identity, and let A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R) {0}, and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study some connections between the graph theoretic properties of this graph and some algebraic properties of a commutative ring. We prove that if AG(R) is a tree, then either AG(R) is a star graph or a path of order 4 and, in the latter case, R = F × S, where F is a field and S is a ring with a unique non-trivial ideal. Moreover, we prove that if R has at least three minimal prime ideals, then AG(R) is... 

Suppose that R is a commutative ring with identity. Let A(R) be the set of all ideals of R with non-zero annihilators. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A( R)*=A(R)(0) and two distinct vertices I and J are adjacent if and only if IJ=(0). In Behboodi and Rakeei (2011) [8], it was conjectured that for a reduced ring R with more than two minimal prime ideals, girth(AG(R))=3. Here, we prove that for every (not necessarily reduced) ring R, ω(AG(R))<|Min(R)|, which shows that the conjecture is true. Also in this paper, we present some results on the clique number and the chromatic number of the annihilating-ideal graph of a commutative ring. Among... 

In this research, a modified, cost effective sol-gel procedure applied to synthesize BaTiO3 nanoparticles. XRD and electron microscopy (SEM and TEM) applied for microstructural characterization of powders. The obtained results showed that the type of precursors, their ratio and the hydrolysis conditions had a great effect on time, temperature and therefore the costs of the synthesis process. By selection, utilization of optimized precursor's type, hydrolysis conditions, fine cubic BaTiO3 nanoparticles were synthesized at low temperature and in short time span (1 h calcination at 800 °C). The proposed procedure seems to be more preferable for mass production. The result indicated that the... 

Let G be a group. The power graph of G is a graph with the vertex set G, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique/chromatic number. Furthermore, it is proved that for every group G, the clique number of the power graph of G is at most countably infinite. We also measure how close the power graph is to the commuting graph by introducing a new graph which lies in between. We call this new graph the enhanced power graph. For an arbitrary pair of these three graphs we... 

Inclusion of nano-clays into hydrogels is an efficient approach to produce nanocomposite hydrogels. The introduction of nano-clay into hydrogels causes an increase in water absorbency. In the present work, Nanocomposite hydro-gels based on kappa-carrageenan were synthesized using sodium montmorillonite as nano-clay. Acrylamide and meth-ylenebisacrylamide were used as monomer and crosslinker, respectively. The structure of nanocomposite hydrogels was investigated by XRD and SEM techniques. Swelling behavior of nanocomposite hydrogels was studied by varying clay and carrageenan contents as well as methylenebisacrylamide concentration. An optimum swelling capacity was achieved at 12% of sodium... 

In the present study, the out-of-phase thermomechanical fatigue (OP-TMF) behavior of a cast aluminum-silicon-magnesium alloy, the A356.0 alloy which has been widely used in diesel engine cylinder heads, is compared to room-temperature and high-temperature low cycle fatigue (RT-, HT-LCF) behaviors. For this purpose, strain/temperature-controlled isothermal and non-isothermal fatigue tests were performed based on realistic loading conditions in cylinder heads. Fatigue tests results showed that the plastic strain increased during cycles under constant mechanical strain amplitude, while the specimen failed. Under LCF loadings, the cyclic hardening occurred at low temperatures for the A356.0... 

Machine learning (ML) is generating new opportunities for innovative research in energy economics and finance. We critically review the burgeoning literature dedicated to Energy Economics/Finance applications of ML. Our review identifies applications in areas such as predicting energy prices (e.g. crude oil, natural gas, and power), demand forecasting, risk management, trading strategies, data processing, and analyzing macro/energy trends. We critically review the content (methods and findings) of more than 130 articles published between 2005 and 2018. Our analysis suggests that Support Vector Machine (SVM), Artificial Neural Network (ANN), and Genetic Algorithms (GAs) are among the most... 

The general approach to fault tolerance in uniprocessor systems is to maintain enough time redundancy in the schedule so that any task instance can be re-executed in presence of faults during the execution. In this paper a scheme is presented to add enough and efficient time redundancy to the Earliest-Deadline-First (EDF) scheduling policy for periodic real-time tasks. This scheme can be used to tolerate transient faults during the execution of tasks. We describe a recovery scheme which can be used to re-execute tasks in the event of transient faults and discuss conditions that must be met by any such recovery scheme. For performance evaluation of this idea a tool is developed. © 2007 IEEE  

The reliable transfer in Network on Chips (NoCs) can be threatened by crosstalk fault occurring in wires. Crossstalk fault is due to inter-wire coupling capacitance that based on the patterns of transitions appearing on the wires, significantly limits the reliability of NoCs. Among these transitions, 101 and 010 bit patterns impose the worst crosstalk effects to wires. This work intends to increase the reliability of NoCs against crosstalk faults by applying an improved Fibonacci-based numeral system, called Doubled-Penultimate Fibonacci (DP-Fibo). In the DP-Fibo coding algorithm, code words without ‘101’ and ‘010’ bit patterns are produced to reduce crosstalk faults. Experimental results... 

In the present work, specimens were cut out from St-37 plates with 19 mm thickness. The thickness of plates was reduced to 12.5 mm by milling and grinding operations. Then a standard V-shaped fillet was made on one edge of the plates. Two plates were butt-welded by standard metal arc gas (MAG) welding process. Residual stresses induced by welding were measured on 20 specimens by centre hole drilling. Load controlled axial fatigue tests were carried out to determine the fatigue life of specimens. Crack growth rates were obtained from experiment. Fractography of specimens was performed. Genetic Algorithm (GA) was employed for prediction of residual stress value in weldments using the crack... 

In this work, we implement some analytical techniques such as the Exp-function, Tanh, and extended Tanh methods for solving nonlinear partial differential equation, which contains sine terms, its name Double Sine-Gordon equation. These methods obtain exact solutions of different types of differential equations in engineering mathematics  

The qualitative effects of residual stress parameters on fatigue crack growth are investigated using Monte Carlo probabilistic analysis technique. These parameters include the maximum residual stress,σ0, half-width of the tensile residual stress region, b, and the redistribution of residual stress parameter, β. A normal distribution is assumed for all parameters considered in the investigation and fatigue life is determined using Forman equation. The results indicate that: (i) fatigue life decreases nonlinearly if the mean of random maximum residual stress and the half-width of tensile residual stress region increases; (ii) fatigue life increases nonlinearly if the rate of residual stress... 

In this paper residual stresses induced by butt metal arc gas welding (MAGW), in accordance with ASTM E837, are determined by hole drilling. The results are analyzed by probabilistic methods. Also, the effect of fatigue life on relaxation of welding residual stress is investigated. The specimens are tested to measure fatigue life and crack growth rates in accordance with ASTM E466 for force controlled amplitude axial fatigue testing. © 2008 Verlag Stahleisen GmbH, Düsseldorf