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Let G = (V,E) be a simple undirected graph. For a given set L ⊂ ℝ, a function ω: E → L is called an L-flow. Given a vector γ ∈ ℝv, ω is a γ-L-flow if for each υ ∈ V, the sum of the values on the edges incident to υ is γ(υ). If γ(υ) = c, for all υ ∈ V, then the γ-L-flow is called a c-sum L-flow. In this paper, the existence of γ-L-flows for various choices of sets L of real numbers is studied, with an emphasis on 1-sum flows. Let L be a subset of real numbers containing 0 and denote L*:= L {0}. Answering a question from [S. Akbari, M. Kano, and S. Zare. A generalization of 0-sum flows in graphs. Linear Algebra Appl., 438:3629-3634, 2013.], the bipartite graphs which admit a 1-sum ℝ*-flow or... 

For every h ∈ ℕ, a graph G with the vertex set V (G) and the edge set E(G) is said to be h-magic if there exists a labeling l: E(G) → ℤh{0} such that the induced vertex labeling s: V (G) → ℤh, defined by s(v) = Puv∈E(G) l(uv) is a constant map. When this constant is zero, we say that G admits a zero-sum h-magic labeling. The null set of a graph G, denoted by N(G), is the set of all natural numbers h ∈ ℕ such that G admits a zero-sum h-magic labeling. In 2012, the null sets of 3-regular graphs were determined. In this paper we show that if G is an r-regular graph, then for even r (r > 2), N(G) = ℕ and for odd r (r ≠ 5), ℕ {2, 4} ⊆ N(G). Moreover, we prove that if r is odd and G is a 2-edge... 

Single-rate synchronous digital hierarchy (SDH) networks contain one master block and several slave blocks and the slaves will synchronize themselves by the master clock frequency. However, the clock frequencies of master and slaves are different in multi-rate SDH networks and hence, the slaves require a synchronization circuit to match their clock frequencies with the master clock frequency. This research presents an efficient synchronization circuit for such networks. The proposed circuit occupies smaller area than the prior circuit and requires no clock alignment for its implementation. The circuit constraints are described and the maximum clock frequencies of master and slaves are... 

Latency-insensitive design (LID) is a correct by-construction methodology for system on chip design that prevents multiple iterations in synchronous system design. However, one problem in the LID is system throughput reduction. In this study, a protocol is proposed to increase the throughput of internal cores in the latency-insensitive systems when there are several repetitive structures. The validation of the protocol is checked for latency equivalency in various system graphs. A shell wrapper to implement the protocol is described and superimposed logic gates for the shell wrapper are formulated. Simulation is performed for 12 randomly generated systems and four actual systems. The... 

Let G be a graph and H be an abelian group. For every subset SH a map φ:E(G)→S is called an S-flow. For a given S-flow of G, and every v∈V(G), define s(v)=∑uv∈E(G)φ(uv). Let k∈H. We say that a graph G admits a k-sum S-flow if there is an S-flow such that for each vertex v,s(v)=k. We prove that if G is a connected bipartite graph with two parts X={x1,⋯,xr}, Y={y1,⋯, ys} and c1,⋯,cr,d1,⋯, ds are real numbers, then there is an R-flow such that s( xi)=ci and s(yj)=dj, for 1≤i≤r,1≤j≤s if and only if ∑i=1rci=∑j=1s dj. Also, it is shown that if G is a connected non-bipartite graph and c1,⋯,cn are arbitrary integers, then there is a Z-flow such that s(vi)=ci, for i=1, ⋯,n if and only if the number... 

Communication wire delay between multiple blocks is becoming a critical issue in System on Chip (SoC) design. Scheduling-based Latency-Insensitive Design (LID) is a method to alleviate wire delays by utilizing a central scheduling scheme for periodic clock gating of the blocks. The scheduling scheme resides in shift registers as sequences of '1' and '0' bits. In many systems, these sequences are too long, and have large area overhead. This problem indisposes the implementation of the scheduling based protocol. This paper proposes an algorithm that finds sequences with shorter lengths in comparison with the prior algorithm. On synthetic/random test cases, the algorithm gives 45% reduction on... 

Delay in communication wires causes design iterations in system-on-chip. Latency-insensitive design copes with this issue by encapsulating each core in a shell wrapper and inserting buffers in the wires to separate the design of core from that of communication wires. Scheduling-based latency-insensitive protocol is a methodology which employs shift registers for periodic clock gating of blocks instead of the shell wrappers. In many cases, the bit sequences inside the shift registers are too long and therefore consume a large area. This study presents a heuristic algorithm that optimises the bit sequences and produces them with shorter lengths compared with the existing method. The algorithm... 

The energy of a graph G, denoted by E (G), is defined as the sum of the absolute values of all eigenvalues of G. Let G be a graph of order n and rank (G) be the rank of the adjacency matrix of G. In this paper we characterize all graphs with E (G) = rank (G). Among other results we show that apart from a few families of graphs, E (G) ≥ 2 max (χ (G), n - χ (over(G, -))), where n is the number of vertices of G, over(G, -) and χ (G) are the complement and the chromatic number of G, respectively. Moreover some new lower bounds for E (G) in terms of rank (G) are given. © 2008 Elsevier B.V. All rights reserved  

A graph G of order n is called hyperenergetic if E(G) > 2n -2, where E(G) is the energy of G. In this paper it is shown that Kneser graph K n:r is hyperenergetic for any naturals n and r > 2 with n > 2r + 1. Also we prove that for r > 2, the complement of Kneser graph, E(K n.r), is hyperenergetic  

Let G be a graph. Assume that l and k are two natural numbers. An l-sum flow on a graph G is an assignment of non-zero real numbers to the edges of G such that for every vertex v of G the sum of values of all edges incident with v equals l. An l-sum k-flow is an l-sum flow with values from the set {±1,…, ±(k — 1)}. Recently, it was proved that for every r, r ≥ 3, r ≠ 5, every r-regular graph admits a 0-sum 5-flow. In this paper we settle a conjecture by showing that every 5-regular graph admits a 0-sum 5-flow. Moreover, we prove that every r-regular graph of even order admits a 1-sum 5-flow  

Optimal Reactive Power Dispatch (ORPD) has a salient impact on decreasing the power loss of transmission lines and adjusting the voltage deviation. The parameters that are used for the ORPD are tap settings of transformers, voltages of generating plants and the output of compensating device such as capacitor banks and synchronous condensors. In this paper settings of FACTS devices are considered as additional parameters in solving the ORPD problem. Also the genetic algorithm has been used to find the optimal settings of the controlling parameters. The results of the ORPD have been obtained on a 30 bus IEEE network. © 2009 IEEE  

The structural dynamics (SD) behavior of Elastic Flapping Wings (EFWs) is investigated analytically as a novel approach in EFWs analysis. In this regard an analytical SD solution of EFW undergoing a prescribed rigid body motion is initially derived, where the governing equations are expressed in modal space. The inertial forces are also analytically computed utilizing the actuator induced acceleration effects on the wing structure, while due to importance of analytical solution the linearity assumption is also considered. The formulated initial-value problem is solved analytically to study the EFW structural responses, where the effect of structure-actuator frequency ratio,... 

The effect of inertial forces on the Structural Dynamics (SD) behaviour of Elastic Flapping Wings (EFWs) is investigated. In this regard, an analytical modal-based SD solution of EFW undergoing a prescribed rigid body motion is initially derived. The formulated initial-value problem is solved analytically to study the EFW structural responses, and sensitivity with respect to EFWs' key parameters. As a case study, a rectangular wing undergoing a prescribed sinusoidal motion is simulated. The analytical solution is derived for the first time and helps towards a conceptual understanding of the overall EFW's SD behaviour and its analysis required in their designs. Specifically, the EFW transient... 

Relativistic electrons, generated in the interaction of an ultra-intense laser pulse with plasma in front of a high-Z solid target, when passing near the nuclei of the solid target produce several MeV highly collimated Bremsstrahlung gamma beam, which can be used to induce photo-nuclear reactions. In this work the possibility of photo-induced transmutation (γn) of a nuclear waste of 126Sn with a half-life of 100,000 years into 125Sn with a half-life of 9.64 days was investigated for the first time. Calculations based on the available experimental data show that the Bremsstrahlung γ beam generated by irradiating a 2 mm thick tantalum target as a converter with 1020Wcm-2μm2 and 10 Hz table-top... 

Molybdenum(VI)–oxodiperoxo complex containing an oxazine ligand, ([MoO(O2)2(phox)], phox: 2-(2′-hydroxyphenyl)-5,6-dihydro-1,3-oxazine) was conveniently synthesized and immobilized onto chloro-functionalized mesoporous silica SBA-15 by covalent bonding between the chloropropyl group on the internal surface of the pores and the nitrogen atom of oxazine ligand yielding [MoO(O2)2(phox)]/SBA-15. The resulting material was characterized by FT-IR, TGA, XRD, SEM, TEM, EDX, ICP-AES, BET and UV–vis spectroscopy. The heterogeneous catalyst [MoO(O2)2(phox)]/SBA-15 was employed in the epoxidation of alkenes, exhibiting high catalytic performance and selectivity for epoxide similar to that of homogeneous... 

Suppose that G is a graph and f: V (G) → ℕ is a labeling of the vertices of G. Let S(v) denote the sum of labels over all neighbors of the vertex v in G. A labeling f of G is called lucky if S(u) ≠ S(v) for every pair of adjacent vertices u and v. Also, for each vertex v ∈ V(G), let L(v) denote a list of natural numbers available at v. A list lucky labeling, is a lucky labeling f such that f(v) ∈ L(v) for each v ∈ V(G). A graph G is said to be lucky k-choosable if every k-list assignment of natural numbers to the vertices of G permits a list lucky labeling of G. The lucky choice number of G, ηl(G), is the minimum natural number k such that G is lucky k-choosable. In this paper, we prove that... 

Let G be a graph. The minimum number of colors needed to color the edges of G is called the chromatic index of G and is denoted by x0(G). It is well known that δ(G) ≤ x0(G) ≤ δ(G) + 1, for any graph G, whereδ(G) denotes the maximum degree of G. A graph G is said to be class 1 if x0(G) = δ(G) and class 2 if x0(G) = δ(G)+1. Also, Gδ is the induced subgraph on all vertices of degreeδ(G). Let f : V(G) ! N be a function. An f -coloring of a graph G is a coloring of the edges of E(G) such that each color appears at each vertex v 2 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 x0f (G). It was shown that for every... 

Novel organic-inorganic hybrid heterogeneous nanocatalysts were obtained by covalent anchoring of a molybdenum(vi) complex of salicylidene 2-picoloyl hydrazine, MoO2(sal-phz)(CH3OH), (1) on the surface of magnetic nanoparticles functionalized by one of two routes: in the first method, the surface of magnetic nanoparticles is directly modified with 3-chloropropyltrimethoxysilane yielding 1A. In the second method, magnetic nanoparticles were silica-coated with tetraethoxysilane and then with 3-chloropropyltrimethoxysilane yielding the intermediate 2B. Then complex 1 was grafted on the surface of 1A or 2B through covalent interaction yielding 2A or 3B, respectively. The nanocatalysts 2A and 3B... 

The cryptocurrency industry has changed the human life and accelerated financial exchange in this decade. Many investors want to invest in this industry and establish cryptocurrency farms. This research sets up a CryptoCurrency Farm Location (CCFL) as a facility location that supplies energy by Renewable Energy (RE). We presented a new robust optimization with the stochastic approach for tackling uncertainty in CCFL and compared it with stochastic CCFL. Our objective function includes maximizing the mean and minimum profits coefficient under different scenarios by adding an energy-aware constraint. Our model enables us to select supply energy by RE or power network country. The results show...