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The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. A graph of order n, whose energy is less than n, i.e., E(G) < n, is said to be hypoenergetic. Graphs for which E(G) ≥ n are called non-hypoenergetic. A graph of order n is said to be orderenergetic, if its energy and its order are equal, i.e., E(G) = n. In this paper, we characterize non-hypoenergetic graphs with nullity 2. It is proved that except two graphs, every connected graph with nullity 2 is non-hypoenergetic. © 2021 University of Kragujevac, Faculty of Science. All rights reserved  

The energy of a graph G, denoted by E(G), is defined as the sum of absolute values of all eigenvalues of G. A graph of order n, whose energy is less than n, i.e., E(G) < n, is said to be hypoenergetic. Graphs for which E(G) ≥ n are called non-hypoenergetic. A graph of order n is said to be orderenergetic, if its energy and its order are equal, i.e., E(G) = n. In this paper, we characterize non-hypoenergetic graphs with nullity 2. It is proved that except two graphs, every connected graph with nullity 2 is non-hypoenergetic. © 2021 University of Kragujevac, Faculty of Science. All rights reserved  

A tunable IIR microwave-photonic filter (MPF) with controllable selectivity is implemented using an electrically tunable delay line. The proposed method has been experimentally tested and verified. An IIR Microwave-Photonic filter with variable Q factor in the range of 238 - 257 is realized  

Let $$G$$G be a graph. The core of $$G$$G, denoted by $$G_{Delta }$$GΔ, is the subgraph of $$G$$G induced by the vertices of degree $$Delta (G)$$Δ(G), where $$Delta (G)$$Δ(G) denotes the maximum degree of $$G$$G. A $$k$$k-edge coloring of $$G$$G is a function $$f:E(G)ightarrow L$$f:E(G)→L such that $$|L| = k$$|L|=k and $$f(e_1)e f(e_2)$$f(e1)≠f(e2), for any two adjacent edges $$e_1$$e1 and $$e_2$$e2 of $$G$$G. The chromatic index of $$G$$G, denoted by $$chi '(G)$$χ′(G), is the minimum number $$k$$k for which $$G$$G has a $$k$$k-edge coloring. A graph $$G$$G is said to be Class $$1$$1 if $$chi '(G) = Delta (G)$$χ′(G)=Δ(G) and Class $$2$$2 if $$chi '(G) = Delta (G) + 1$$χ′(G)=Δ(G)+1. Hilton... 

Let G be a 2k-edge-connected graph with 𝑘 ≥ 0 and let 𝐿(𝑣) ⊆ {𝑘,…, 𝑑𝐺(𝑣)} for every 𝑣 ∈ 𝑉 (𝐺). A spanning subgraph F of G is called an L-factor, if 𝑑𝐹 (𝑣) ∈ 𝐿(𝑣) for every 𝑣 ∈ 𝑉 (𝐺). In this article, we show that if (Formula presented.) for every 𝑣 ∈ 𝑉 (𝐺), then G has a k-edge-connected L-factor. We also show that if 𝑘 ≥ 1 and (Formula presented.) for every 𝑣 ∈ 𝑉 (𝐺), then G has a k-edge-connected L-factor. © 2018 Wiley Periodicals, Inc  

Let G be a graph. The energy of G, (Formula presented.), is defined as the sum of absolute values of its eigenvalues. Here, it is shown that if G is a graph and (Formula presented.) is an edge partition of G, such that (Formula presented.) are spanning; then (Formula presented.) if and only if (Formula presented.), for every (Formula presented.) and (Formula presented.), where (Formula presented.) is the adjacency matrix of (Formula presented.). It was proved that if G is a graph and (Formula presented.) are subgraphs of G which partition edges of G, then (Formula presented.). In this paper we show that if G is connected, then the equality is strict, that is (Formula presented.). © 2022... 

Let G be a graph and F: V(G) → 2N be a mapping. The graph G is said to be F- avoiding if there exists an orientation O of G such that do +(v)∉ F (v) for every v ∈ V (G), where do +(v) denotes the out-degree of v in the directed graph G with respect to O. In this paper it is shown that if G is bipartite and |F (v)| ≤ dG (v)/2 for every v ∈ V (G), then G is F-avoiding. The bound |F (v)| ≤ dG (v)/2 is best possible. For every graph G, we conjecture that if |F (v)| ≤ 1/2 dG (v)-1) for every v ∈ V (G), then G is F-avoiding. We also argue about this conjecture for the best possibility of the conditions and also show some partial solutions. © 2019 Wiley Periodicals, Inc  

The present work developed a mixed-mode cohesive zone model (CZM) with a mode I failure criterion to predict the delamination bending loads of multilayer, composite printed circuit boards (PCBs) assembled with soldered ball grid array (BGA) components that were reinforced with an underfill epoxy adhesive. Two different delamination modes were observed in these microelectronic assemblies: delamination at the interface between the solder mask and the first conducting layer of the PCB, and PCB subsurface delamination at the interface between the epoxy and glass fibers of one of the prepreg layers. The cohesive parameters for each of the two crack paths were obtained from fracture tests of... 

The present work developed a mixed-mode cohesive zone model (CZM) with a mode I failure criterion to predict the delamination bending loads of multilayer, composite printed circuit boards (PCBs) assembled with soldered ball grid array (BGA) components that were reinforced with an underfill epoxy adhesive. Two different delamination modes were observed in these microelectronic assemblies: delamination at the interface between the solder mask and the first conducting layer of the PCB, and PCB subsurface delamination at the interface between the epoxy and glass fibers of one of the prepreg layers. The cohesive parameters for each of the two crack paths were obtained from fracture tests of... 

Let μm be the group of mth roots of unity. In this paper it is shown that if m is a prime power, then the number of all square matrices (of any order) over μm with non-zero constant determinant or permanent is finite. If m is not a prime power, we construct an infinite family of matrices over μm with determinant one. Also we prove that there is no n×n matrix over μp with vanishing permanent, where p is a prime and n = pα-1. © 2003 Elsevier Inc. All rights reserved  

Let R be a ring with identity and M be a unitary left R-module. The intersection graph of an R-module M, denoted by G(M), is defined to be the undirected simple graph whose vertices are in one to one correspondence with all non-trivial submodules of M and two distinct vertices are adjacent if and only if the corresponding submodules of M have nonzero intersection. We investigate the interplay between the module-theoretic properties of M and the graph-theoretic properties of G(M). We characterize all modules for which the intersection graph of submodules is connected. Also the diameter and the girth of G(M) are determined. We study the clique number and the chromatic number of G(M). Among... 

In this paper, we introduce a new class of codes for overloaded synchronous wireless and optical code-division multiple-access (CDMA) systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary overloaded CDMA are derived that can predict the existence of such overloaded codes. We also propose a simplified maximum likelihood method for decoding these types of... 

Let G be a graph of order n. For every v ∈ V (G), let EG(v) denote the set of all edges incident with v. A signed k-matching of G is a function f : E(G) −→ {−1, 1}, satisfying f(EG(v)) ≤ 1 for at least k vertices, where f(S) = ∑e∈S f(e), for each S ⊆ E(G). The maximum of the values of f(E(G)), taken over all signed k-matchings f of G, is called the signed k-matching number and is denoted by βk S (G). In this paper, we prove that for every graph G of order n and for any positive integer k ≤ n, βk S (G) ≥ n −k −ω(G), where w(G) is the number of components of G. This settles a conjecture proposed by Wang. Also, we present a formula for the computation of βn S(G)  

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... 

In this research, the samples of a low carbon steel sheet were rolled up to a thickness prestrain of 67% at three different temperatures consisted of room, blue brittleness, and subzero temperature. Microhardness, SEM, and tensile tests were carried out to evaluate the static recrystallization kinetics defined by the Avrami equation, microstructural evolution, and mechanical properties. It was found that the Avrami exponent is altered with change in prestrain temperature and it achieves the value of 1 to 1. 5. Moreover, it was indicated that prestraining at subzero temperature followed by annealing at 600 °C leads to considerable enhancement in tensile properties and kinetics of static... 

A weighted graph Gω consists of a simple graph G with a weight ω, which is a mapping, ω: E(G)→Z∖{0}. A signed graph is a graph whose edges are labelled with −1 or 1. In this paper, we characterize graphs which have a sign such that their signed adjacency matrix has full rank, and graphs which have a weight such that their weighted adjacency matrix does not have full rank. We show that for any arbitrary simple graph G, there is a sign σ so that Gσ has full rank if and only if G has a {1,2}-factor. We also show that for a graph G, there is a weight ω so that Gω does not have full rank if and only if G has at least two {1,2}-factors. © 2020 Elsevier B.V  

In this paper optical filters based on photonic resonant tunneling effect are analyzed by using the polynomial expansion method. Amplitude and phase response together with their dependency on the physical parameters of the filters are also investigated. These steep-edge filters show low insertion loss amplitude response, and linear phase variation in their passband, a suitable feature for WDM and DWDM applications where constant time delay and dispersion free devices are needed. Two kinds of filters, namely discrete level and continuous profile filters are introduced. These structures can be analyzed and designed by using Transfer Matrix Method. However, this approach suffers from inaccuracy... 

The surface plasmon effect of Au nanostructures placed on the surface of hematite has recently been used to enhance light absorption within its carrier collection distance of 10 nm from the water-hematite interface. Despite significant narrow band absorption enhancements in the visible region, the reported enhancements in the overall performance of the cell under standard AM1.5 sunlight illumination are not significant. We numerically design an array of Au stripes on the surface of an extremely thin layer of hematite to maximize the number of charge carriers that can reach the hematite-water interface and explore the optical processes involved. The lateral dimensions and in particular the... 

We develop the real space quantum renormalization group (QRG) approach for majorana fermions. As an example we focus on the Kitaev chain to investigate the topological quantum phase transition (TQPT) in the one-dimensional spinless p-wave superconductor. Studying the behaviour of local compressibility and ground-state fidelity, show that the TQPT is signalled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point are used as proper indicators for the TQPT, which signals the appearance of Majorana fermions.... 

A fully electrically tunable microwave photonic filter is realized by the implementation of delay lines based on frequency-Time conversion. The frequency response and free spectral range (FSR) of the filter can be engineered by a simple electrical tuning of the delay lines. The method has the capability of being integrated on a silicon photonic platform. In the experiment, a 2-Tap tunable microwave photonic filter with a 3-dB bandwidth of 2.55 GHz, a FSR of 4.016 GHz, a FSR maximum tuning range from -354 MHz to 354 MHz and a full FSR translation range is achieved