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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... 

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... 

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... 

This paper presents a novel method fortuning the parameters of an sliding mode (SM) controller to obtain near-optimal performance. In order to do so the Linear Quadratic Regulator (LQR) was implemented on a linearized system. The input history of the LQR was used as a reference to obtain an optimal space for sliding mode controller parameters. Afterwards, the optimal space boundaries were dedicated to Genetic Algorithm (GA) to search for the optimal parameter for the nonlinear model. Also, the center of the obtained optimal space was used as an initial guess to the Particle Swarm Optimization (PSO) Algorithm. The proposed algorithm was implemented to regulate SM controller for the attitude... 

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... 

A universal labeling of a graph G is a labeling of the edge set in G such that in every orientation ℓ 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 { 1 , 2 , … , k} denoted it by χu→ (G). We have 2 Δ (G) - 2 ≤ χu→ (G) ≤ 2 Δ ( G ), where Δ (G) 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, χu→ (G) ≤ f(Δ (G)) ?”. Towards this question, we introduce some lower and upper bounds on their parameter... 

Electrical properties and electronic structure of Bi1-xCa xFe1-yMnyO3-δ grown by pulsed-laser deposition on BaTiO3/SiO2/Si substrate were investigated. Results showed that Ca has drastic effect on symmetry of crystal and electrical poperties of BiFeO3. On the other hand, Mn revealed to have more radical effect on optical properties and energy gap of the compound. XPS results represented that although Ca tend to decrease Fe valence state, Mn tends to stabilize it at 3+ (at least in this concentrations). UV-visible study yielded bandgap of 2.51-2.81 eV (at 300 K) for different concentrations of Ca and Mn. UV-visible spectra also revealed sub-bandgap defect transitions at 2.2 and 2.4 eV.... 

The regular number of a graph (Formula presented.) denoted by (Formula presented.) is the minimum number of subsets into which the edge set of (Formula presented.) can be partitioned so that the subgraph induced by each subset is regular. In this work we answer to the problem posed as an open problem in Ganesan et al. (J Discrete Math Sci Cryptogr 15(2-3):49-157, 2012) about the complexity of determining the regular number of graphs. We show that computation of the regular number for connected bipartite graphs is NP-hard. Furthermore, we show that, determining whether (Formula presented.) for a given connected (Formula presented.)-colorable graph (Formula presented.) is NP-complete. Also, we... 

The electronic conductor-insulator transition in Ca-doped BiFeO 3 films grown by pulsed-laser deposition technique has been investigated. Nature of the transition is resolved to be Mott type through the control of band-filling. Calcium resolved to have colossal effect on enhancing the electrical conductivity of BiFeO 3, but it did not affect band gap of the mother phase perceptibly. UV-visible study yielded band gap of 2.72-2.81 eV (at 300 K) for different concentrations of calcium. Both UV-visible and photoluminescence spectra revealed sub-band gap transitions at 2.17 and 2.38 eV, of which the latter might be ascribed to the oxygen vacancies  

The morphological characteristics as well the optical properties of Ca-doped BiFeO3 films grown by pulsed-laser deposition technique have been investigated. AFM images revealed that calcium has a radical effect on the surface features of BiFeO3 films. By utilizing spectrophotometer, transmission behaviour of the films was investigated. Local IV characteristics of the films disclosed about three orders of magnitude enhancement concerning electrical conductivity through Ca doping. X-ray photoelectron spectroscopy results revealed that Ca can reduce the valence state of iron in the compound  

In this study, a near equiatomic NiTi shape memory alloy was hot rolled at 800°C using thethickness reductions of 30 and 50%. Optical and transmission electron microscopy, together withX-ray diffraction were used to demonstrate the microstructural changes associated with the hotrolling at different thickness reductions. Repeated transformation cycling was employed toinvestigate the evolution of R phase during cycling. Microstructural observations revealed thepresence of deformation twins embedded in an elongated grain matrix in the hot rolled material.Moreover, it was found that with increasing degree of thickness reduction, the size and number ofdeformation twins increased throughout the... 

A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The problem of proper labeling offers many variants and received a great interest during recent years. We consider the algorithmic complexity of some variants of the proper labeling problems, we present some polynomial time algorithms and NP-completeness results for them  

A Not-All-Equal decomposition of a graph G is a decomposition of the vertices of G into two parts such that each vertex in G has at least one neighbor in each part. Also, a 1-in-Degree decomposition of a graph G is a decomposition of the vertices of G into two parts A and B such that each vertex in the graph G has exactly one neighbor in part A. Among our results, we show that for a given graph G, if G does not have any cycle of length congruent to 2 mod 4, then there is a polynomial time algorithm to decide whether G has a 1-in-Degree decomposition. In sharp contrast, we prove that for every r, r≥ 3 , for a given r-regular bipartite graph G determining whether G has a 1-in-Degree... 

E-commerce is one of the industries most affected by big data, from collection to analytics in the highly competitive market. Previous research on big data analytics in E-commerce focused only on particular applications, and there is still a gap in presenting a framework to evaluate big data applications from a challenges-values point of view. This study employs a three-phase methodology to evaluate big data applications in E-commerce with respect to big data challenges and values using a hybrid multi-criteria decision-making technique that combines BWM and fuzzy TOPSIS. The results showed process challenge and the strategic value obtained the highest weight for challenges and values... 

A lucky labeling of a graph G is a function l:V(G)→N, such that for every two adjacent vertices v and u of G, σ w∼vl(w)≠ σ w∼ul(w) (x∼y means that x is joined to y). A lucky number of G, denoted by η(G), is the minimum number k such that G has a lucky labeling l:V(G)→{1,⋯,k}. We prove that for a given planar 3-colorable graph G determining whether η(G)=2 is NP-complete. Also for every k≥2, it is NP-complete to decide whether η(G)=k for a given graph G