Sharif Digital Repository

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... 

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... 

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... 

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... 

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... 

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  

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... 

Modeling and analysis of information system vulnerabilities helps us to predict possible attacks to networks using the network configuration and vulnerabilities information. As a fact, exploiting most of vulnerabilities result in access rights alteration. In this paper, we propose a new vulnerability analysis method based on the Take-Grant protection model. We extend the initial Take-Grant model to address the notion of vulnerabilities and introduce the vulnerabilities rewriting rules to specify how the protection state of the system can be changed by exploiting vulnerabilities. Our analysis is based on a bounded polynomial algorithm, which generates the closure of the Take-Grant graph... 

Combining the advection-diffusion equation approach with Monte Carlo simulations we study chaperone driven polymer translocation of a stiff polymer through a nanopore. We demonstrate that the probability density function of first passage times across the pore depends solely on the Péclet number, a dimensionless parameter comparing drift strength and diffusivity. Moreover it is shown that the characteristic exponent in the power-law dependence of the translocation time on the chain length, a function of the chaperone-polymer binding energy, the chaperone concentration, and the chain length, is also effectively determined by the Péclet number. We investigate the effect of the chaperone size on... 

We study the translocation of stiff polymers through a nanopore, driven by the chemical-potential gradient exerted by binding proteins (chaperones) on the trans side of the pore. Bound chaperones prevent backsliding through the pore and, therefore, partially rectify the polymer passage. We show that the sequence of chain monomers with different binding affinity for the chaperones significantly affects the translocation dynamics. In particular, we investigate the effect of the nearest-neighbor adjacency probability of the two monomer types. Depending on the magnitude of the involved binding energies, the translocation speed may either increase or decrease with the adjacency probability. We... 

The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may explain why one always observes a ripple structure on suspended graphene. We show that a compression-relaxation mechanism produces static ripples on graphene sheets and determine a peculiar temperature Tc, such that for T