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A critical set in an n×n array is a set C of given entries, such that there exists a unique extension of C to an n×n Latin square and no proper subset of C has this property. For a Latin square L, scs(L) denotes the size of the smallest critical set of L, and scs(n) is the minimum of scs(L) over all Latin squares L of order n. We find an upper bound for the number of partial Latin squares of size k and prove thatn2-(e+o(1))n10/6≤maxscs(L)≤n2- π2n9/6.This improves on a result of Cavenagh (Ph.D. Thesis, The University of Queensland, 2003) and disproves one of his conjectures. Also it improves the previously known lower bound for the size of the largest critical set of any Latin square of order... 

In the present study, titanium nano-particles have been synthesized using chemical vapor condensation (CVC) process. Reaction of sodium and titanium tetrachloride vapors in the tube furnace resulted in the production of titanium nano-particles that were encapsulated in sodium chloride. Dried Argon gas was employed as a carrying agent. Titanium nano-particles were contained in an ethanol bath. Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM) and X-ray Diffraction (XRD) were employed for analysis and characterization of nano-particles. The size of primary particles was smaller than 100 nm and secondary particles were submicron agglomerations  

In this paper, a new algorithm for solving the shortest loop design problem is presented. The shortest loop design problem is to find the shortest loop for an automated guided vehicle covering at least one edge of each department of a block layout. In this paper, first it is shown that this problem can be represented as a graph model. The properties of the presented model enable us to design a meta-heuristic based on ant colony system algorithm for solving the shortest loop design problem. Computational results show the efficiency of our algorithm in compare to the other techniques  

Using software products as engineering artifacts is becoming more widespread in industry. It leads to increasing the need for training students and experts in the academic centers with software developing skills in accordance with the engineering principles and disciplines. However, one of the main challenges in the software engineering education is how to teach engineering disciplines to the students so that we can inspire the engineering concept to them. To do so if we use educational methods for teaching this course, which can show the usage of engineering disciplines to the students in practice and demonstrate the impact of their application on creating the engineered software products,... 

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χc′(G) ≤ 11/3 provided that G does not contain H1 or H2 as a subgraph, where H1 and H2 are obtained by subdividing one edge of K23 (the graph with three parallel edges between two vertices) and K4, respectively. As χc′(H1) = χ c′(H2) = 4, our result implies that there is no graph G with 11/3 < χc′(G) < 4. It also implies that if G is a 2-edge connected cubic graph, then χc′(G) ≤ 11/3. © 2005 Wiley Periodicals, inc