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In this note, bounded-input bounded-output (BIBO)-stability of a large class of neutral type fractional delay systems is investigated. Necessary and sufficient conditions of BIBO-stability are presented for the intended class of systems (the sufficient conditions have been provided for a more general case in the previous studies). Two lemmas are provided for checking a prerequisite imposed on the considered class of systems. Finally, two numerical examples are given to illustrate the obtained results  

This paper considers a closed-loop system consisting of a fractional/integer order system and a fractional PID controller. Assuming that the uncertain coefficients of the fractional PID controller lie in some known intervals independently (i.e. that controller is a member of an interval family), the paper presents some easy to use theorems to investigate the robust bounded-input bounded-output stability of the resultant closed-loop system. Moreover, a finite frequency bound required in drawing the related graphs has also been provided. Finally, some numerical examples are presented to illustrate the results  

In this paper, the computation of robustness margin for linear time invariant fractional order systems is studied. For the definition of robustness margin, we employ the one introduced for polynomials (i.e. integer order) and extend it to fractional order functions. Using the well known concept of the value set and knowing its shape for the intended functions, this paper presents an easy way to obtain the robustness margin for fractional order systems. To illustrate the results, a numerical example is provided  

This paper deals with the analysis of robust BIBO-stability of LTI fractional order delay systems in the presence of real parametric uncertainties. Two large classes of these systems, namely retarded and neutral types, are considered. Two theorems are given to check the robust BIBO-stability of these two families of fractional order systems. One of these theorems provides necessary and sufficient conditions for the case of retarded type and another one presents only sufficient conditions for the case of neutral type. Furthermore, upper and lower bounds (cutoff frequencies) are provided for drawing the value sets. To illustrate the results, two numerical examples are presented  

Robustness of a fractional proportional-integral-derivative (PID)-based control system is investigated. At first the largest pathwise connected region subset of a box in three-dimensional space of the parameters of the model is determined such that the closed-loop system is bounded-input bounded-output stable for any point inside it. Then a value that represents the size (in a specified sense) of the calculated region in the first stage and can be considered as a margin for the robustness of the closed-loop system is computed. Furthermore, lower and upper frequency bounds required in depiction of boundaries of the region and computing the mentioned margin are provided. Some special cases in... 

This study deals with the subject of robust bounded-input bounded-output (BIBO)-stability of a family of fractional order interval systems. Employing the idea of'robust stability testing function'and extending it to the case of intended systems, a simple graphical procedure for checking the robust BIBO-stability applicable to both commensurate and incommensurate orders is developed. Moreover, a Kharitonov-like theorem is provided that presents necessary and sufficient conditions for checking the mentioned stability of the fractional order interval systems with commensurate order α belonging to [1,2), but only sufficient conditions for commensurate order α in interval (0,1). Besides, lower... 

In this paper, the robust bounded-input bounded-output stability of a large class of linear time invariant fractional order families of systems with real parametric uncertainties is analyzed. The transfer functions contain polynomials in fractional powers of the Laplace variable s, possibly in combination with exponentials of fractional powers of s. Using the concept of the value set and a generalization of the zero exclusion condition theorem, a theorem to check the robust bounded-input bounded-output stability of these families of systems is presented. An upper cutoff frequency for drawing the value sets is provided as well. Finally, two numerical examples are given to illustrate results... 

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. 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  

The current research aims to implement a reliable analytical model in order to scrutinize the transient behavior of a counter-flow non-premixed combustion system fueled by wet porous biomass particles under non-adiabatic conditions, including several processes such as phase change and dehumidification. A special term is added to the heat equation based on the law of conservation of energy as a means to assess the convective heat loss impacts. In order to analyze the structure of the diffusion flame and predict the time-dependent temperature and mass fractions of reactants distributions, transient forms of energy and mass equations are solved through the asymptotic method. Eventually, the...