Minimality considerations for graph energy over a class of graphs

Let G be a graph on n vertices, and let CHP(G;λ) be the characteristic polynomial of its adjacency matrix A(G). All n roots of CHP(G;λ), denoted by , are called to be its eigenvalues. The energy E(G) of a graph G, is the sum of absolute values of all eigenvalues, namely, . Let be the set of n-vertex unicyclic graphs, the graphs with n vertices and n edges. A fully loaded unicyclic graph is a unicyclic graph taken from with the property that there exists no vertex with degree less than 3 in its unique cycle. Let be the set of fully loaded unicyclic graphs. In this article, the graphs in with minimal and second-minimal energies are uniquely determined, respectively.     

Rewrite-Based Decision Procedures

The rewrite-based approach to satisfiability modulo theories consists of using generic theorem-proving strategies for first-order logic with equality. If one can prove that an inference system generates finitely many clauses from the presentation of a theory and a finite set of ground unit clauses, then any fair strategy based on that system can be used as a -satisfiability procedure. In this paper, we introduce a set of sufficient conditions to generalize the entire framework of rewrite-based -satisfiability procedures to rewrite-based -decision procedures. These conditions, collectively termed subterm-inactivity, will allow us to obtain rewrite-based -decision procedures for several theories, namely those of equality with uninterpreted functions, arrays with or without extensionality and two of its extensions, finite sets with extensionality and recursive data structures.     

-admissibility of the right-shift semigroup on

It is shown that the right-shift semigroup on does not satisfy the weighted Weiss conjecture for α(0,1). In other words, α-admissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition. This result is in contrast to the unweighted case, where 0-admissibility can be characterised by a simple growth bound. The result is proved by providing a link between discrete and continuous α-admissibility and then translating a counterexample for the unilateral shift on to continuous time systems.     

Full-rank representation of generalized inverse AT,S and its application

In this paper, we introduce a full-rank representation of the generalized inverse of a given complex matrix A, which is based on an arbitrary full-rank decomposition of G, where G is a matrix such that R(G)=T and N(G)=S. Using this representation, we introduce the minor of the generalized inverse ; as a special case of the minor, a determinantal representation of the generalized inverse is obtained. As an application, we use an example to demonstrate that this representation is correct.     

Output feedback control of a class of stochastic hybrid systems

This paper deals with static output feedback control of a class of reconfigurable systems with Markovian Parameters and state-dependent noise. The main contribution is to formulate conditions for multi-performance design related to this class of stochastic hybrid systems. The specifications and objectives under consideration include stochastic stability, and performances. Another problem related to a more general class of stochastic hybrid systems, known as Markovian Jump Linear Systems (MJLS), is also addressed. This problem concerns the mode-independent output feedback control of MJLS. The obtained results are illustrated on a numerical example.     

A simple derivation of ARE solutions to the standard control problem based on LMI solution

In this note, a simple derivation of the Riccati equation based solutions to the standard control problem, namely the well-known Glover–Doyle solution and DGKF solution is given based on LMI solution. It is hoped that this will be helpful in deepening the understanding of Riccati equation solutions.     

An LMI approach to boundary control of semilinear parabolic and hyperbolic systems

Exponential stability analysis and L₂-gain analysis are developed for scalar uncertain distributed parameter systems, governed by semilinear partial differential equations of parabolic and hyperbolic types. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for both systems. These conditions are then utilized to synthesize  static output feedback boundary controllers of the systems in question.     

Ab initio calculations of NO2 and SO2 chemisorption onto non-polar ZnO surfaces

The authors present an ab initio study of NO₂ and SO₂ chemisorption onto non-polar ZnO and ZnO surfaces with the aim of providing theoretical hints for further developments in gas sensors. From first principles calculations (DFT-GGA approximation), the most relevant surface reduction scenarios are analyzed and, subsequently, considered in the chemisorption study. First, calculations indicate that NO₂ adsorbs avidly onto Zn surface atoms. This is compatible with the oxidizing character of NO₂. Second, results also explain the sensor poisoning by SO₂ adsorption (since this molecule competes with NO₂ for the same adsorption sites) and indicate that poisoning can only be reverted at typical operation temperatures (T ≤ 700 °C) in the case of stoichiometric ZnO surfaces.     

An algorithm to generate all upper boundary points for in terms of minimal cuts

This paper discusses a stochastic-flow network from single-commodity case to multicommodity case. We propose a performance index, namely the probability that the upper bound of the system capacity is a given vector subject to the budget constraint, to evaluate the quality level for such a network. A simple approach based on minimal cuts is presented to generate the all upper boundary points for the demand subject to the budget B in order to evaluate the performance index.     

Controller synthesis with guaranteed closed-loop phase constraints

In this paper, we present an analysis and synthesis approach for guaranteeing that the phase of a single-input, single-output closed-loop transfer function is contained in the interval [−α,α] for a given α>0 at all frequencies. Specifically, we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint. Next, we use the Kalman–Yakubovich–Popov theorem to derive an equivalent time domain condition. In the case where , we show that frequency and time domain sufficient conditions specialize to the positivity theorem. Furthermore, using linear matrix inequalities, we develop a controller synthesis approach for guaranteeing a phase constraint on the closed-loop transfer function. Finally, we extend this synthesis approach to address mixed gain and phase constraints on the closed-loop transfer function.     

First-principles study of ground-state properties and phase stability of vanadium nitrides

Using a series of density functional electronic structure total energy calculations, we have systematically studied the ground-state properties and phase stability of vanadium nitrides. Comparison of enthalpy of formation shows that V ₂N is equally stable (polymorphic) in , and Fe₂C phases within a few meV. Formation enthalpy of the various phases considered for perfect stoichiometric V N_1.0 shows that it has enhanced stability in hexagonal WC and NiAs structures in relation to NaCl-type δ-phase. The TiAs phase of VN has nearly same energy as NaCl structure. Comparison of energetics of -type , for x=0 and 0.3333 and of , for x=0, 0.0625, 0.125 and 0.25 shows that vacancies on the nitrogen sublattice lowers the formation enthalpy in relation to respective stoichiometric phases which is in agreement with experiments, as bulk vanadium nitrides are known to be generally non-stoichiometric. The calculated dilute heat of solution for the interstitial nitrogen is found to be in good agreement with experimental values and shows that nitrogen prefers to occupy the octahedral sites in bcc vanadium. The α^′-FeN and martensite structures, considered for the metastable phases of vanadium nitrides, have higher formation enthalpy in relation to equilibrium phases. Analysis of electronic density of states of V ₂N shows that the low energy , and Fe₂C phases are characterized by broad V 3d-N 2p and V 3d bonding bands. Density of states of VN shows that in the low energy WC and NiAs phases some of the antibonding states are made empty, leading to a minimum near the Fermi level. For and , density of states shows that vacancies on the nitrogen sublattice introduce additional filled states in the 3d band below Fermi level enabling enhanced bonding. Comparison between bulk moduli and atomic volumes for the various phases of vanadium nitrides shows that higher bulk moduli are dominated by increased V–N bonds combined with low atomic volumes.     

A Hybridization of Irreflexive Modal Logics

This paper discusses a bimodal hybrid language with a sub-modality (called the irreflexive modality) associated with the intersection of the accessibility relation R and the inequality ≠. First, we provide the Hilbert-style axiomatizations (with and without the COV-rule) for logics of our language, and prove the Kripke completeness and the finite frame property for them. Second, with respect to the frame expressive power, we compare our language containing the irreflexive modality with the hybrid languages and . Finally, we establish the Goldblatt-Thomason-style characterization for our language.     

Delay-dependent filtering for time-delayed LPV systems

The present paper addresses the parameter-dependent filter design problem for output estimation in linear parameter varying (LPV) plants that include constant delays in the state. We develop LMI-based delay-dependent conditions to guarantee stability and an induced gain bound performance for the filtering error system. An explicit characterization of the filters’ state–space representation is given in terms of the solutions to a convex optimization problem associated with the synthesis conditions. By taking the output estimation error into account as the criterion, the developed filters are shown to be capable of tracking the desired outputs of the time-delayed parameter varying system in the presence of external disturbances. Two families of filters are examined: memoryless and state-delayed filters. The latter one which involves a delay term in its dynamics has the benefit of reducing the conservatism in the design and improving performance. Illustrative examples are provided to demonstrate the feasibility and advantages of the proposed methodologies for memoryless and state-delayed filter design and to validate the superiority of using the state-delayed configuration compared to the conventional memoryless filters.     

Reconstruction of a word from a multiset of its factors

Let be the multiset containing all factors of w of length k including repetitions. One of the main results is that if for all , then w=v. The bound is optimal; however we will also show that if for all , then w and v are structurally similar.     

The global existence of nonlinear observers with linear error dynamics: A topological point of view

In this paper we show that under suitable assumptions, there exists a global homeomorphism Ψ(=Φ^-1) of which maps a nonlinear system onto a linear system with output injection . Thus, an observer for state x can be directly constructed as , which is a generalized version of Luenberger observer. An important feature of the obtained result is that there is no need to find the corresponding change of coordinates Ψ explicitly, which is different from current various existing approaches.     

H2 sensing characteristics of highly textured Pd-doped SnO2 thin films

The effects of the crystallographic orientation on the H₂ gas sensing properties were investigated in highly oriented polycrystalline Pd-doped SnO₂ films, which were obtained using rf magnetron sputtering of a Pd (0.5 wt%)-SnO₂ target on various substrates (a-, m-, r-, and c-cut sapphire and quartz). All the films had a similar thickness (110 nm), root-mean-square (rms) roughness (1.3 nm), surface area, and chemical status (O, Sn, and Pd). However, the orientation of the films was strongly affected by the orientation of the substrates. The (1 0 1), (0 0 2), and (1 0 1) oriented films were grown on (a-cut), (m-cut), and (r-cut) Al₂O₃ substrates, respectively, and rather randomly oriented films were deposited on (0 0 0 1) (c-cut) Al₂O₃ and quartz substrates. In addition, the oriented Pd-doped SnO₂ films were highly textured and had in-plane orientation relationships with the substrates similar to the epitaxial films. The (1 0 1) Pd-doped SnO₂ films on and Al₂O₃ showed a considerably higher H₂ sensitivity, and their gas response decreased with increasing sensing temperature (400–550 °C). The films deposited on and (0 0 0 1) Al₂O₃ showed the maximum sensitivity at 500 °C. The comparison of the H₂ gas response between undoped and Pd-doped SnO₂ films revealed that the Pd-doping shifted the optimum sensing temperature to a lower value instead of improving the gas sensitivity.     

Robust PID controller tuning based on the heuristic Kalman algorithm

This paper presents a simple but effective tuning strategy for robust PID controllers satisfying multiple performance criteria. Finding such a controller is known to be computationally intractable via the conventional techniques. This is mainly due to the non-convexity of the resulting control problem which is of the fixed order/structure type. To solve this kind of control problem easily and directly, without using any complicated mathematical manipulations and without using too many “user defined” parameters, we utilize the heuristic Kalman algorithm (HKA) for the resolution of the underlying constrained non-convex optimization problem. The resulting tuning strategy is applicable both to stable and unstable systems, without any limitation concerning the order of the process to be controlled. Various numerical studies are conducted to demonstrate the validity of the proposed tuning procedure. Comparisons with previously published works are also given.     

Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay

We regard the stochastic functional differential equation with infinite delay as the result of the effects of stochastic perturbation to the deterministic functional differential equation , where is defined by x_t(θ)=x(t+θ),θ(−∞,0]. We assume that the deterministic system with infinite delay is exponentially stable. In this paper, we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable.     

Chaos synchronization for a class of discrete dynamical systems on the N-dimensional torus

In this paper, a class of dynamical systems on (the N-dimensional torus) is investigated. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that the sequences produced are equidistributed for almost every initial data. The above results are then extended to switched affine transformations of . Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup.     

How many servers are best in a dual-priority system?

We ask the question, “for minimizing mean response time (sojourn time), which is preferable: one fast server of speed 1, or k slow servers each of speed 1/k?” Our setting is the system with two priority classes of customers, high priority and low priority, where PH is a phase-type distribution. We find that multiple slow servers are often preferable, and we demonstrate exactly how many servers are preferable as a function of the load and service time distribution. In addition, we find that the optimal number of servers with respect to the high priority jobs may be very different from that preferred by low priority jobs, and we characterize these preferences. We also study the optimal number of servers with respect to overall mean response time, averaged over high and low priority jobs. Lastly, we ascertain the effect of the service demand variability of high priority jobs on low priority jobs.