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Let G be a simple graph of order n. A dominating set of G is a set S of vertices of G so that every vertex of G is either in S or adjacent to a vertex in 5. The domination polynomial of G is the polynomial D(G, x) = Σn i=1 d(G, i) xi, where d(G, i) is the number of dominating sets of G of size i. In this paper we show that cycles are determined by their domination polynomials  

Let G be a simple graph of order n and size m. An edge covering of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set. In this paper we introduce a new graph polynomial. The edge cover polynomial of G is the polynomial E(G,x)=∑i=1me(G,i)xi, where e (G, i) is the number of edge coverings of G of size i. Let G and H be two graphs of order n such that δ(G)≥n2, where δ (G) is the minimum degree of G. If E (G, x) = E (H, x) , then we show that the degree sequence of G and H are the same. We determine all graphs G for which E (G, x) = E (P n, x) , where P n is the path of order n. We show that if δ (G) ≥ 3, then E (G, x) has at least one... 

In conventional grinding of hard to cut materials such as Ti6Al4V alloys, surface burning, redeposition and adhesion of chips to the grinding wheel and workpeice occur visibly unless it is carried out at low speeds and with high volume of cutting fluid. Ultrasonic assisted grinding is an efficient machining process which improves the machinability of hard-to-cut materials by changing the kinematics of the process. In this research, the effect of imposition of ultrasonic vibration on the grinding of Ti6Al4V alloy is studied. Longitudinal vibration at ultrasonic frequency range (20 kHz) is applied on the workpiece and machining forces and surface roughness are compared between conventional... 

Let G be a graph and f: V (G) → ℕ be a function. An f-coloring of a graph G is an edge coloring such that each color appears at each vertex v ∈ V (G) at most f(v) times. The minimum number of colors needed to f-color G is called the f-chromatic index of G and is denoted by χʹf(G). It was shown that for every graph G, Δf(G) ≤ χʹf(G) ≤ Δf(G) + 1, where Δf(G) = maxv ∈V (G)(formula presented). A graph G is said to be f-Class 1 if χʹf(G) = Δf(G), and f-Class 2, otherwise. Also, GΔfis the induced subgraph of G on (formula presented). In this paper, we show that if G is a connected graph with Δ(GΔf) ≤ 2 and G has an edge cut of size at most Δf(G) − 2 which is a star, then G is f-Class 1. Also, we... 

In this paper, an algorithm has been developed to evaluate the performance of omni channel distribution network configurations based on data envelopment analysis (DEA) models and consensus formation. At first, bi-objective input- and output-oriented simultaneous DEA models are developed to evaluate the configurations with respect to two common criteria, i.e., the service and cost, and the transparency criterion which is defined based on the blockchain technology. Then, a consensus is formed on the evaluation results, based on a risk-based optimisation model. The proposed models are solved by fuzzy goal programming. In addition, the application of the proposed models is demonstrated through a... 

Location and allocation problems in supply chain networks are considered as strategic decisions; because they both require investment and have long-term effects. On the other hand, the supply chain network is not protected against disruptions in the real world. In this paper, a branch and efficiency (B&E) algorithm is developed which integrates a multi-objective optimization model used for designing the supply chain network with an extended data envelopment analysis (EDEA) model. Through this integration, efficient solutions are obtained that lead to minimization of the costs. The objective functions of the optimization model include the operational costs, resilience costs and inequality in... 

As an outcome of economies of scale, demand growth can benefit companies in various ways. However, demand fulfillment and management are just not possible in a supply chain whose managers focus only on cost minimization. For this reason, the present paper proposes a sustainable, efficient, customer-centered and resilient closed-loop supply chain network. Limited access to labor during the Covid-19 pandemic, traffic congestion due to transportation of products, as well as transparency through the Blockchain technology are some of the key considerations in our supply chain network design. To the best of our knowledge, this is the first attempt where such a supply chain network is designed,... 

The production and distribution planning problem, where incomplete information from the manufacturer factories is available to the distributor, is prevalent in the real world. Yet, researchers have not focused sufficiently on this field of research. Therefore, our paper offers a two-level multi-objective optimization of production and distribution planning for the two-stage supply chain based on the Data Envelopment Analysis method, which minimizes both the cost and the traffic congestion caused by the establishment of distributor warehouses. In addition, transparency through the blockchain technology and uncertain conditions through stochastic and fuzzy programming are considered in the... 

Packet loss recovery is an important part of P2P video streaming networks due to inevitable packet loss in today's internet and interdependency of data units in compressed video streams. In addition, the architecture of P2P streaming networks, in which the data delivered to the receivers through chain of peers, can intensify the impact of the internet packet loss on the quality of perceived video at the receivers. FEC and ARQ are the two most important techniques that can be used to overcome the side effect of the internet packet loss in P2P video streaming networks. Based on these two techniques, different packet loss recovery strategies can be applied in different overlay hops of a given... 

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... 

Let R be a ring with non-zero identity. The unit graph G(R) of R is a graph with elements of R as its vertices and two distinct vertices a and b are adjacent if and only if a + b is a unit element of R. It was proved that if R is a commutative ring and is a maximal ideal of R such that |R/| = 2, then G(R) is a complete bipartite graph if and only if (R, ) is a local ring. In this paper we generalize this result by showing that if R is a ring (not necessarily commutative), then G(R) is a complete r-partite graph if and only if (R, ) is a local ring and r = |R/| = 2n for some n ∞ N or R is a finite field. Among other results we show that if R is a left Artinian ring, 2 U(R) and the clique... 

Desktop and miniaturized machine tools are a new trend in small scale and customized manufacturing. The performance of these machines in terms of their energy consumption, machining fluid consumption and their precision have been investigated in the literature, but the effect of miniaturization on static deflection, stability against chatter and the resulting surface error has not been studied. In this paper, the performance of the desktop milling machine tool in terms of their static and dynamic form errors is studied. The performance of a miniature milling machine used for end milling of a typical workpiece is compared with a similar machine of conventional size through dimensional... 

A rapid wax injection tool of a gearbox shift fork was designed, simulated, and manufactured using rapid prototyping and rapid tooling technology to save time and cost of producing wax models used for the investment casting process. CAE simulation softwares, in particular, MoldFlow, are used to get wax injection moulding parameters such as filling parameters, temperature profiles, freeze time, speed, and pressure. The results of this research were compared with conventional wax model production methods. The criteria of such comparison were based upon parameters such as time, cost, and other related characteristics, which resulted in saving of 50% in time and 60% in cost. In this research,... 

The energy of a graph/matrix is the sum of the absolute values of its eigenvalues. We investigate the result of duplicating/removing an edge to the energy of a graph. We also deal with the problem that which graphs G have the property that if the edges of G are covered by some subgraphs, then the energy of G does not exceed the sum of the subgraphs' energies. The problems are addressed in the general setting of energy of matrices which leads us to consider the singular values too. Among the other results it is shown that the energy of a complete multipartite graph increases if a new edge added or an old edge is deleted. © 2008 Elsevier Inc. All rights reserved  

Abstract: Although the band-gap in pure graphene is zero, the oxygenated graphene could have a considerable band-gap. The D/G peak intensity ratio is known as a measure of the size of sp3∕sp2 domains in graphene oxide (GO) sheets and determines the band-gap in GO sheets. Characterization results showed that the photoluminescence (PL) spectra of GO suspensions has a peak at ~604 nm and also the I(D)/I(G) intensity ratio of GO suspensions is 1.73. After reduction, a redshift appeared at PL spectrum (at 650 nm) and the I(D)/I(G) intensity ratio decrease to 1.26. Our results showed that the band-gap in GO is related to the I(D)/I(G) intensity ratio of GO suspensions and offers a mechanism for... 

Peer-to-peer streaming has recently gained attention as an effective solution to support large scale media streaming applications over the Internet. One of the main challenges of peer-to-peer video streaming is the cumulative impact of the Internet packet loss due to the decoding dependency of the compressed video frames. In this paper we study the impact of the Internet packet loss on the performance of peer-to-peer video streaming systems, and analyze the efficiency of various packet loss recovery policies in such systems. Our analytical and simulation results show how the Internet packet loss can affect the performance of peer- to-peer video streaming systems and how different packet loss... 

In this paper we propose a rate-efficient peer-to-peer architecture for video multicasting over the Internet. The limited capacity of the Internet hosts and the heterogeneous property of their access links are the main challenges of the peer-to-peer video multicasting over the Internet. Although, the rate-optimized overlay tree construction is a NP-hard problem, we propose a number of distributed and efficient protocols for rate-efficient overlay tree construction. Our proposed protocols include efficient join, improvement, overlay tree refinement and an optimum rate allocation protocol. The simulation results show the efficiency of the proposed protocols in rate-efficient overlay tree... 

In this paper, a new dynamic proxy solution based on overlay multicasting network for layered video streaming is presented. In our proposed approach, all clients in an Internet service provider network interested in receiving a video stream, provided by a media server in the Internet, organize themselves into an overlay tree. The root of the overlay tree acts as a proxy and receives video stream from original server and distributes it in the local overlay tree. In addition to introducing a new architecture, our main contribution in this paper is proposing a number of distributed protocols for construction and improvement of local overlay tree in video streaming applications. The experimental... 

We develop an integrated vendor-buyer model for a two-stage supply chain. The vendor manufactures the product and delivers it in a number of equal-sized batches to the buyer. The items delivered are presented to the end customers in a display area. Demand is assumed to be positively dependent on the amount of items displayed. The objective is to maximize total supply chain profit. The numerical analysis shows that buyer-vendor coordination is more profitable in situations when demand is more stock dependent. It also shows that the effect of double marginalization provides a link between the non-coordinated and the coordinated case  

Facility layout problem is a well-known optimization problem which generally deals with the arrangement of the facilities required in an organization. This problem has received much attention during the past decades. However, the researchers have mainly focused on the case where a single floor is available. While, in the competitive world, it is clear that using multi-floor structure layouts are much more efficient and in some cases necessary due to the nature of the functions and activities performed in the firms. Hence, this issue has recently attracted much attention and is becoming increasingly popular. Nevertheless, the lack of a review study on this subject for directing the new...