Sharif Digital Repository

Let be a ring and be the set of all non-trivial left ideals of. The intersection graph of ideals of, denoted by, is a graph with the vertex set and two distinct vertices and are adjacent if and only if. In this paper, we classify all rings (not necessarily commutative) whose domination number of the intersection graph of ideals is at least 2. Moreover, some results on the intersection graphs of ideals of matrix algebras over a finite field are given. For instance, we determine the domination number, the clique number and the independence number of. We prove that if is a positive integer and, then the domination number of is. Among other results, we show that if, where is a positive integer... 

Determining an object location in a specific region is an important task in many machine vision applications. Different parameters affect the accuracy of the localization process. The quantization process in charge-coupled device of a camera is one of the sources of error that causes estimation rather than identifying the exact position of the observed object. A cluster of points, in the field of view of a camera are mapped into a pixel. These points form an uncertainty region. In this paper, we present a geometrical model to analyze the volume of this uncertainty region as a criterion for object localization error. The proposed approach models the field of view of each pixel as an oblique... 

For a block design D, a series of block intersection graphs G i, or i-BIG(D), i = 0,..., k is defined in which the vertices are the blocks of D, with two vertices adjacent if and only if the corresponding blocks intersect in exactly i elements. A silver graph G is defined with respect to a maximum independent set of G, called an α-set. Let G be an r-regular graph and c be a proper (r + 1)-coloring of G. A vertex x in G is said to be rainbow with respect to c if every color appears in the closed neighborhood N[x] = N(x) ∪ {x}. Given an α-set I of G, a coloring c is said to be silver with respect to I if every x ∈ I is rainbow with respect to c. We say G is silver if it admits a silver... 

Let R be a ring with unity and I(R)* be the set of all nontrivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R)* and two distinct vertices I and J are adjacent if and only if I ∩ J ≠ 0. In this paper, we study some connections between the graph-theoretic properties of this graph and some algebraic properties of rings. We characterize all rings whose intersection graphs of ideals are not connected. Also we determine all rings whose clique number of the intersection graphs of ideals is finite. Among other results, it is shown that for a ring R, if the clique number of G(R) is finite, then the chromatic number is finite and if R is... 

The Local Binary Patterns (LBP) feature extraction method is a theoretically and computationally simple and efficient methodology for texture analysis. The LBP operator is used in many applications such as facial expression recognition and face recognition. The original LBP is based on hard thresholding the neighborhood of each pixel, which makes texture representation sensitive to noise. In addition, LBP cannot distinguish between a strong and a weak pattern. In order to enhance the LBP approach, Fuzzy Local Binary Patterns (FLBP) is proposed. In FLBP, any neighborhood does not represented only by one code, but, it is represented by all existing codes with different degrees. In FLBP, any... 

Water impact phenomenon in the case of a circular cylinder is an important issue in offshore industry where cross members may be in the splash zone of the incident wave. An analytical method as well as a numerical solution are employed to study the water entry problem of a circular section. The procedure for derivation of the analytical formulas is demonstrated step by step. The volume of fluid (VOF) simulation of the water entry problem is also performed to offer comparison of the results of the linearized analytical solution with a fully nonlinear and viscous fluid flow solution. To achieve this, the FLOW- 3D code is utilized. Some consideration has also been given to the points of... 

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of an R-module M, denoted by G(M), is defined to be the undirected simple graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have nonzero intersection. We investigate the interplay between the module-theoretic properties of M and the graph-theoretic properties of G(M). We characterize all modules for which the intersection graph of submodules is connected. Also the diameter and the girth of G(M) are determined. We study the clique number and the chromatic number of G(M). Among... 

This paper develops a model for estimating unsignalized intersection delays which can be applied to traffic assignment (TA) models. Current unsignalized intersection delay models have been developed mostly for operational purposes, and demand detailed geometric data and complicated procedures to estimate delay. These difficulties result in unsignalized intersection delays being ignored or assumed as a constant in TA models. Video and vehicle license plate number recognition methods are used to collect traffic volume data and to measure delays during peak and off-peak traffic periods at four unsignalized intersections in the city of Tehran, Iran. Data on geometric design elements are measured... 

We study here the algorithmic analysis of systems modeled in terms of availability languages. Our first main result is a positive answer to the emptiness problem: it is decidable whether a given availability language contains a word. The key idea is an inductive construction that replaces availability languages with Parikh-equivalent regular languages. As a second contribution, we solve the intersection problem modulo bounded languages: given availability languages and a bounded language, it is decidable whether the intersection of the former contains a word from the bounded language. We show that the problem is NP-complete. The idea is to reduce to satisfiability of existential Presburger... 

We develop accurate analytical relations for the droplet volume ratio, droplet length during breakup process, and pressure drop of asymmetric T junctions with a valve in each of the branches for producing unequal-sized droplets. An important advantage of this system is that after manufacturing the system, the size of the generated droplets can be changed simply by adjusting the valves. The results indicate that if the valve ratio is smaller than 0.65, the system enters a nonbreakup regime. Also the pressure drop does not depend on the time and decreases by increasing the valve ratio, namely, opening the degree of valve 1 to valve 2. In addition, the results reveal that by decreasing... 

The performance and the buzz onset of a supersonic mixed-compression axisymmetric intake are experimentally investigated. Effectsof the slot bleed position, angle, and width onthe intake performance and onthe buzz initiation at three different Mach numbers of 1.8, 2.0, and 2.2 and at a zero degree angle of attack are studied. The intake performance is assessed using the total pressure recovery, mass flow ratio, flow distortion, and bleed mass flow ratio. The results show that applying the bleed at a position near the intake entrance and reducing the bleed entrance slant angle and width all improve the intake performance considerably. Moreover, these parameters postpone the buzz onset. In... 

Let G be a group. The intersection graph of G, denoted by Γ(G), is the graph whose vertex set is the set of all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent if and only if H ∩ K ≠= 1. In this paper, we show that the girth of Γ(G) is contained in the set {3,∞ }. We characterize all solvable groups whose intersection graphs are triangle-free. Moreover, we show that if G is finite and Γ (G) is triangle-free, then G is solvable. Also, we prove that if Γ (G) is a triangle-free graph, then it is a disjoint union of some stars. Among other results, we classify all abelian groups whose intersection graphs are complete. Finally, we study the intersection graphs of... 

Let R be a ring with identity and M be a unitary left R-module. The complement of the intersection graph of submodules of M, denoted by Γ(M), is defined to be a graph whose vertices are in one-to-one correspondence with all nontrivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have zero intersection. In this paper, we consider the complement of the intersection graph of submodules of a module. We prove that, if Γ(M) is connected and Δ(Γ(M)) < ∞, then M is semisimple, where Δ(Γ(M)) is the maximum degree of Γ(M). We show that, if Γ(M) is a forest, then each component of Γ(M) is a star graph. Moreover, it is proved that, if Γ(M) is a... 

Let Δ be a simplicial complex and χ be an s-coloring of Δ. Biermann and Van Tuyl have introduced the simplicial complex Δχ. As a corollary of Theorems 5 and 7 in their 2013 article, we obtain that the Stanley–Reisner ring of Δχ over a field is Cohen–Macaulay. In this note, we generalize this corollary by proving that the Stanley–Reisner ideal of Δχ over a field is set-theoretic complete intersection. This also generalizes a result of Macchia  

In this study, the Lattice Boltzmann Method (LBM) is used to investigate the deformation of two droplets within microfluidic T-junctions (MFTD). In order to increase the accuracy the two immiscible fluids are modeled using the He-Chen-Zhang model. First, this model is applied to ensure that the surface tension effect existing between the droplets and the continuous fluid is properly implemented in the model. Then the collision and merging of the two droplets within the intersection of a T-shaped microchannel is investigated. For generating droplet formation the effects of relevant dimensionless parameters such as the Reynolds, the Weber numbers as well as a collision parameter affecting the...