Sharif Digital Repository

In this study, the effects of stress-assisted heat treatment on the microstructure and phase transformation of a Ti-rich (Ti-49.52 at.% Ni) shape memory alloy were investigated. For this purpose, the alloy was heat treated at temperature of 500 °C for 10 h under applied stresses of 100 and 200 MPa. XRD, TEM, and repeated thermal cycling were employed to study the microstructure and transformation behavior of the heat-treated materials. Room temperature XRD diffractogram of the stress-free heat-treated material showed a weak reflection of austenite (B2), while that for the stress-assisted heat-treated materials had a high intensity implying the presence of residual austenite in the... 

A proper orientation of a graph G=(V,E) is an orientation D of E(G) such that for every two adjacent vertices v and u, dD -(v) ≠ dD -(u) where dD -(v) is the number of edges with head v in D. The proper orientation number of G is defined as χ→(G)=minD∈Γmaxv∈V(G)d D -(v) where Γ is the set of proper orientations of G. We have χ(G)-1≤χ→(G)≤Δ(G), where χ(G) and Δ(G) denote the chromatic number and the maximum degree of G, respectively. We show that, it is NP-complete to decide whether χ→(G)=2, for a given planar graph G. Also, we prove that there is a polynomial time algorithm for determining the proper orientation number of 3-regular graphs. In sharp contrast, we will prove that this problem... 

An additive labeling of a graph G is a function H: V(G)→ N, such that for every two adjacent vertices v and u of G, Σw∼v l(w) = Σw∼vl(w) (x ∼ y means that x is joined to y). The additive number of G, denoted by η(G), is the minimum number k such that G has a additive labeling l: V(G)→ Nk. The additive choosability of a graph G, denoted by ηl(G), is the smallest number k such that G has an additive labeling for any assignment of lists of size k to the vertices of G, such that the label of each vertex belongs to its own list. Seamone in his PhD thesis conjectured that for every graph G, η(G) = ηe(G). We give a negative answer to this conjecture and we show that for every k there is a graph G... 

“How many guards are required to cover an art gallery?” asked Victor Klee in 1973, initiated a deep and interesting research area in computational geometry. This problem, referred to as the Art Gallery Problem, has been considered thoroughly in the literature. A recent version of this problem, introduced by Sadhu et al. in CCCG'10, is related to the connectivity of the guards. In this version, for a given set of initial guards inside a given simple polygon, the goal is to obtain a minimum set of new guards, such that the new guards alongside the initial ones have a connected visibility graph. The visibility graph of a set of points inside a simple polygon is a graph whose vertices correspond... 

A simple and straight forward method for acoustic impedance measurement is presented and evaluated. In this method a speaker is used as the signal source. The relationship between the electrical impedance of the speaker and its acoustical load is developed and studied. It is shown that the electrical current and voltage of the speaker relate to the acoustical pressure and volume velocity. The mechanical and acoustical impedances are therefore easily derived by measuring the electrical current and voltage of the circuit. The proposed method yield itself to the automatic computer measurement and can be used for the field and in situ measurements. Comparison of the measurement data with those... 

A new method to detect leakage in a water-filled plastic pipe is proposed. In this method, a leakage signal-signature in time domain is first captured by monitoring the Short Time Fourier Transforms (STFT) of AE (Acoustic Emission) signals over a relatively long time-interval. The captured signal is then used to find a mother wavelet (tuned wavelet) for the best signal localization in time and frequency domains. The technique for AE signal detection using tuned wavelet is then described. Practical application of the method proposed herein is then presented using a water-filled plastic pipe as a case study. Signals generated from this experimental setup are collected to identify leakage... 

In the Touring Polygons Problem (TPP) there is a start point s, a sequence of simple polygons P = (P1,...,Pk) and a target point t in the plane. The goal is to obtain a path of minimum possible length that starts from s, visits in order each of the polygons in P and ends at t. This problem has a polynomial time algorithm when the polygons in P are convex and is NP-hard in general case. But, it has been open whether the problem is NP-hard when the polygons are pairwise disjoint. In this paper, we prove that TPP is also NP-hard when the polygons are pairwise disjoint in any Lp norm even if each polygon consists of at most two line segments. This result solves an open problem from STOC '03 and... 

In the Touring Polygons Problem (TPP) there is a start point s, a sequence of simple polygons P=(P1,. . .,Pk) and a target point t in the plane. The goal is to obtain a path of minimum possible length that starts from s, visits in order each of the polygons in P and ends at t. This problem was introduced by Dror, Efrat, Lubiw and Mitchell in STOC '03. They proposed a polynomial time algorithm for the problem when the polygons in P are convex and proved its NP-hardness for intersecting and non-convex polygons. They asked as an open problem whether TPP is NP-hard when the polygons are pairwise disjoint. In this paper, we prove that TPP is also NP-hard when the polygons are pairwise disjoint in... 

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation (Formula presented.) of G for every two adjacent vertices v and u, the sum of incoming edges of v and u in the oriented graph are different from each other. The universal labeling number of a graph G is the minimum number k such that G has universal labeling from (Formula presented.) denoted it by (Formula presented.). We have (Formula presented.), where (Formula presented.) denotes the maximum degree of G. In this work, we offer a provocative question that is: “Is there any polynomial function f such that for every graph G, (Formula presented.)?”. Towards this question, we introduce some... 

A graph G is weakly semiregular if there are two numbers a,b, such that the degree of every vertex is a or b. The weakly semiregular number of a graph G, denoted by wr(G), is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is a weakly semiregular graph. We present a polynomial time algorithm to determine whether the weakly semiregular number of a given tree is two. On the other hand, we show that determining whether wr(G)=2 for a given bipartite graph G with at most three numbers in its degree set is NP-complete. Among other results, for every tree T, we show that wr(T)≤2log2 δ(T)+O(1), where δ(T) denotes the maximum... 

A graph G is weakly semiregular if there are two numbers a,b, such that the degree of every vertex is a or b. The weakly semiregular number of a graph G, denoted by wr(G), is the minimum number of subsets into which the edge set of G can be partitioned so that the subgraph induced by each subset is a weakly semiregular graph. We present a polynomial time algorithm to determine whether the weakly semiregular number of a given tree is two. On the other hand, we show that determining whether wr(G)=2 for a given bipartite graph G with at most three numbers in its degree set is NP-complete. Among other results, for every tree T, we show that wr(T)≤2log2⁡Δ(T)+O(1), where Δ(T) denotes the maximum... 

In the touring polygons problem (TPP), for a given sequence (s= P0, P1, ⋯, Pk, t = Pk+1) of polygons in the plane, where s and t are two points, the goal is to find a shortest path that starts from s, visits each of the polygons in order and ends at t. In the constrained version of TPP, there is another sequence (F0, ⋯, Fk) of polygons called fences, and the portion of the path from Pi to Pi+1 must lie inside the fence Fi. TPP is NP-hard for disjoint non-convex polygons, while TPP and constrained TPP are polynomially solvable when the polygons are convex and the fences are simple polygons. In this work, we present the first polynomial time algorithm for solving constrained TPP when the...