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This paper presents a new three-dimensional autonomous chaotic system with only one positive term. Basic dynamical properties of the new attractor are demonstrated in terms of phase portraits, equilibria, Lyapunov exponents, Poincare mapping, bifurcation diagram. Furthermore, we derive a three-dimensional spheriform ultimate bound and positively invariant set for all the positive values of its parameters a , b , c . At last, the horseshoe chaos in this system is investigated based on the topological theory. [ABSTRACT FROM AUTHOR]

Solvent extracted sediments from El Junco Lake, Galápagos were sequentially hydrolyzed with base and acid. Some of the “bound” lipids thus generated were not detected among the “free” lipids obtained from the initial solvent extract of the freeze dried sediment. These include α-hydroxy acids, β-hydroxy acids, methyl β-hydroxy acids and cutin acids. Other bound lipids differed from the free lipids in their chain length, such as alkanols, sterols, ω-hydroxy acids and (ω-1)-hydroxy acids. A suite of biomarkers with unique ions of m / z 341 were identified in the acid hydrolysates that are most likely C 40 cyclic biomarkers derived from the L race of Botryococcus braunii . Free lipids and their isotopic composition are likely to be sufficient for the purpose of paleoenvironmental reconstructions, and therefore base or acid hydrolysis of solvent extracted sediment is not necessary. Nevertheless, the additional lipid biomarkers liberated by base and acid hydrolysis can provide information on microbial inputs to the sediment. [ABSTRACT FROM AUTHOR]

Let G be a simple graph of order N. The normalized Laplacian Estrada index of G is defined as NEE(G) = ∑Ni=1eλi-1, where λ1, λ2 ⋯, λN the normalized Laplacian eigenvalues of G. In this paper, we give a tight lower bound for NEE of general graphs. We also calculate NEE for a class of treelike fractals, which contains T fractal and Peano basin fractal as its limiting cases. It is shown that NEE scales linearly with the order of the fractal, in line with a best possible lower bound for connected bipartite graphs. [ABSTRACT FROM AUTHOR]

The nonlinear aeroelastic system of an airfoil with an external store was investigated, with emphasis on the bounds of limit cycle oscillations (LCOs). Based on the equivalent linearization, an approach was proposed to calculate the bounds on LCOs over the full flight envelope. The bounds are determined directly without solving LCOs one by one as the flow speed varies. The presented approach can provide us with the maximal LCO amplitudes and the lower threshold for flow speed beyond which LCOs may arise. Numerical examples show that the obtained bounds are in nice agreement with numerical simulation results. The speed threshold can be predicted to a relative error less than 0.1%, and the maximal LCO amplitude to about 3%. The influences of the system parameters on the speed threshold for speed were investigated efficiently by the proposed approach. [ABSTRACT FROM AUTHOR]

Although randomized experiments are widely regarded as the gold standard for estimating causal effects, missing data of the pretreatment covariates makes it challenging to estimate the subgroup causal effects. When the missing data mechanism of the covariates is nonignorable, the parameters of interest are generally not pointly identifiable, and we can only get bounds for the parameters of interest, which may be too wide for practical use. In some real cases, we have prior knowledge that some restrictions may be plausible. We show the identifiability of the causal effects and joint distributions for four interpretable missing data mechanisms and evaluate the performance of the statistical inference via simulation studies. One application of our methods to a real data set from a randomized clinical trial shows that one of the nonignorable missing data mechanisms fits better than the ignorable missing data mechanism, and the results conform to the study's original expert opinions. We also illustrate the potential applications of our methods to observational studies using a data set from a job-training program. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In a mixed model assembly line, the demands for products are usually uncertain. When the actual demands are larger than expectation, capacity adjustments should be made. The difficulty and cost of these adjustments rely heavily on the initial balancing. To the best of knowledge, the convenience of future adjustment and corresponding cost have not been considered in literature. This paper investigates the line balancing problem in a mixed model assembly system which faces uncertain demand and makes use of overtime work to meet unexpected demands. The objective is to minimize the expected labor cost, including cost for normal operation and overtime work. A mathematical model is built and a method is proposed to estimate the cost lower bound, based on which a single pass heuristic is designed. The numerical experiment shows that the algorithm is effective and efficient. [ABSTRACT FROM AUTHOR]

What the comparison between event nominalizations in French and Modem Standard Arabic reveals, is a fundamental similarity concerning the concept of what an event is, and what the result of an event can be. In this article, we show first that the two syntactic types of nominalizations described in the literature exist in Arabic as well as in French with parametric differences, mainly due to the fact that Arabic deverbal nouns retain more and stronger verbal features than their French counterparts. Nevertheless, the conceptual distinction between what we call "bound" and "free" event is made in the two languages. Our decision to treat result nominals at the end of the article relies on the fact we establish, that they are built on complex (and not simple, as often argued in the literature) event nominals, in the same way in the two languages, and with the same two possible interpretations (creation by modification or representation vs. "pure" creation) depending on the meaning of the verbal root. [ABSTRACT FROM AUTHOR]

SUMMARY We generalize the signless Laplacian matrices for graphs to the signless Laplacian tensors for even uniform hypergraphs and set some fundamental properties for the spectral hypergraph theory based upon the signless Laplacian tensors. In particular, the smallest and the largest Z-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are studied, and as an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving these two Z-eigenvalues are presented. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Let be the graph obtained from by adding a new vertex corresponding to each edge of and by joining each new vertex to the end vertices of the corresponding edge, and be the graph obtained from by inserting a new vertex into every edge of and by joining by edges those pairs of these new vertices which lie on adjacent edges of . In this paper, we determine the Laplacian polynomials of and of a regular graph ; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs. [Copyright &y& Elsevier]

Abstract: The adjacency matrices for graphs are generalized to the adjacency tensors for uniform hypergraphs, and some fundamental properties for the adjacency tensor and its Z-eigenvalues of a uniform hypergraph are obtained. In particular, some bounds on the smallest and the largest Z-eigenvalues of the adjacency tensors for uniform hypergraphs are presented. [Copyright &y& Elsevier]

Abstract: We derive a generalized matrix version of Pellet’s theorem, itself based on a generalized Rouché theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of the theorem are suggested to try and overcome situations where Pellet’s theorem cannot be applied. [Copyright &y& Elsevier]

Abstract: The spectral radius of a matrix A is the maximum modulus of its eigenvalues. We present bounds on that are often tighter and are applicable to a larger class of nonnegative matrices than previously reported. The bounds are particularly suited to matrices which are sparse. We complete the paper by applying these bounds to digraphs, deriving the associated equality conditions which relate to the outdegree regularity of the digraph. Finally, we show that the equality conditions may be achieved only for very specific values of the digraph’s spectral radius. [Copyright &y& Elsevier]

Abstract: Dynamic systems described by f c(z)= z 2 + c is called Mandelbrot set (M-set), which is important for fractal and chaos theories due to its simple expression and complex structure. f c(z)= zk + c is called generalized M set (k–M set). This paper proposes a new theory to compute the higher and lower bounds of generalized M set while exponent k is rational, and proves relevant properties, such as that generalized M set could cover whole complex number plane when k <1, and that boundary of generalized M set ranges from complex number plane to circle with radius 1 when k ranges from 1 to infinite large. This paper explores fractal characteristics of generalized M set, such as that the boundary of k–M set is determined by k, when k = p/q, where p and q are irreducible integers, (GCD(p, q)=1, k >1), and that k–M set can be divided into |p–q| isomorphic parts. [Copyright &y& Elsevier]

According to some identities and inequalities about the intermediate weights and control points of the de Casteljau algorithm for rational Bézier curve, we derive a new bound of the derivative of rational Bézier curves. The comparison of the new bounds with some existing ones is also presented. Based on some previous bounds, the bound presented in this paper and many numerical examples, we propose a conjecture of the bound for the derivative of rational Bézier curves. [ABSTRACT FROM AUTHOR]

The object of this paper is the uniform torsion of inhomogeneous, isotropic, linearly elastic cylindrical bar. The aim is to give lower and upper bounds for the torsional rigidity of the bar with doubly connected cross section. The outer and inner boundary curves of cross section are similar curves. The level lines of the function which gives the change of the shear rigidity on the cross section are also similar curves to the boundary curves. The application of derived bounding formulae is illustrated by examples. An approximated formula to determine the shear stresses is also presented. [ABSTRACT FROM AUTHOR]

In this paper, various modifications of a connected graph G are regarded as perturbations of its signless Laplacian matrix. Several results concerning the resulting changes to the signless Laplacian spectral radius of G are obtained by solving intermediate eigenvalue problems of the second type. AMS subject classifications: 05C50. [ABSTRACT FROM AUTHOR]

We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface. Both the local bounds and the global bounds are given by the maximum norm of the first differences or second differences or mixed differences of the control points of the surface patch. [ABSTRACT FROM AUTHOR]

Le but de ce papier est d'établir des bornes indépendantes du nombre de variables dans certains cas quadratiques. D'une part nous considérons k formes quadratiques Q, i = 1, . . . , k, en n + 1 variables à coefficients dans $${{\mathbb{R}}}$$ . Nous supposons que ces formes quadratiques ont une base orthogonale commune. Alors nous montrons que le nombre de composantes connexes du complémentaire de la réunion des quadriques { Q = 0}, i = 1, . . . , k dans l'espace projectif réel $${\mathbb{P}^{n}(\mathbb{R})}$$, est borné par 2, indépendamment du nombre de variables. D'autre part nous considérons un polynôme quadratique Q défini sur $${{\mathbb{R}}^n}$$. Soit B la boule unité ouverte de $${{\mathbb{R}}^n}$$. Nous montrons que la somme des diamètres géodésiques des composantes connexes de $${\{Q >0 \}\cap B^{n}}$$ est majorée par 2π, une constante indépendante de n. [ABSTRACT FROM AUTHOR]

In this paper, a MIMO system with finite-bit feedback based on fixed constellations is considered. Based on performance analysis of the system, an optimal operating system with maximum-likelihood decoding is demonstrated. Surprisingly, this operation reveals that the optimal way for the system to transmit signals needs to invoke the multimode scheme. We propose designing criteria for this scheme and methods for pre-codebooks, and a method to determine the number of modes for any specific channel. Furthermore, to reduce encoding complexity at the receiver side, we also develop a fast encoding algorithm. Theoretical analysis and simulations show that the proposed systems offer considerable gain over existing systems. Moreover, these systems also have much lower encoding complexity. Indeed, for the case of a MIMO system with two pairs of transmitting and receiving antennas, a properly designed system with a transmission rate of 8 bits per channel use and with 6-bit feedback can provide about a 1.5 dB performance gain over a beamforming system. [ABSTRACT FROM AUTHOR]

We consider the clustered travelling salesman problem in which vertices (except the starting vertex) of the network are divided into some prespecified clusters. The problem is to find a least cost Hamiltonian cycle (tour) in which vertices of any cluster are visited contiguously and the clusters are visited in the prespecified order. The problem is NP-hard and it arises in practical transportation and sequencing problems. This paper develops a lexisearch algorithm for obtaining exact optimal solution to the problem. The efficiency of the algorithm against an existing algorithm to the problem has been examined for asymmetric TSPLIB instances of various sizes and clusters. Finally, we present solutions to some symmetric TSPLIB instances. [ABSTRACT FROM AUTHOR]

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The signless Laplacian tensor and its H-eigenvalues for an even uniform hypergraph are introduced in this paper. Some fundamental properties of them for an even uniform hypergraph are obtained. In particular, the smallest and the largest H-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are discussed, and their relationships to hypergraph bipartition, minimum degree, and maximum degree are described. As an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving the smallest and the largest H-eigenvalues are presented. [ABSTRACT FROM AUTHOR]

The majority of papers on resilience deal with fast and resource-saving mechanisms that are typically taylored to a certain networking technology or to a certain protocol. The aim of this paper is rather to turn attention to some interesting aspects of resilience including multi-domain and multi-cast scenarios as well as handling physical impairments and obeying green networking requirements. [ABSTRACT FROM AUTHOR]

Abstract: The Randić index of a graph is defined by , where is the degree of a vertex in and the summation extends over all edges of . In this work, we give a sharp upper bound and a lower bound of the Randić index among connected -vertex graphs with girth . [Copyright &y& Elsevier]

The problem of finding bounds of time-averaged characteristics of dynamical systems, such as the bound on the mean energy dissipation rate in a turbulent flow governed by incompressible Navier-Stokes equations, is considered. It is shown that the direct method described by Seis (2015 J. Fluid Mech. 777 , 591-603. (doi:10.1017/jfm.2015.384)) and the auxiliary functional method by Chernyshenko et al. , 20130350. (doi:10.1098/rsta.2013.0350)) are related and can lead to the same bound. The well-known background flow method of Doering and Constantin is equivalent to the auxiliary functional method with a quadratic auxiliary functional. The known implementations of the direct method apparently also correspond to quadratic auxiliary functionals. The findings are illustrated by the analysis of the plane Couette flow. Three routes of further progress using non-quadratic auxiliary functionals and at the same time allowing to use the experience accumulated with the background flow method are proposed: making the balance parameter dependent on the energy, making the background flow time-dependent in a specific way and adding helicity to the auxiliary functional. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.Phil. Trans. R. Soc. B 372 , 20130350. (doi:10.1098/rsta.2013.0350)) are related and can lead to the same bound. The well-known background flow method of Doering and Constantin is equivalent to the auxiliary functional method with a quadratic auxiliary functional. The known implementations of the direct method apparently also correspond to quadratic auxiliary functionals. The findings are illustrated by the analysis of the plane Couette flow. Three routes of further progress using non-quadratic auxiliary functionals and at the same time allowing to use the experience accumulated with the background flow method are proposed: making the balance parameter dependent on the energy, making the background flow time-dependent in a specific way and adding helicity to the auxiliary functional. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

abstract: Let be a digraph with vertices and arcs without loops and multiarcs, . Denote by the largest eigenvalue of its adjacency matrix, the number of -walks from vertex . In this paper, we prove that the inequalities hold for every integers . If is strongly connected, then each equality holds iff . Furthermore, we have for every integers and each vertex . [Copyright &y& Elsevier]

This study sought to determine the distribution of free and bound phenolics in some Nigerian citrus peels [orange ( Citrus sinensis), grapefruit ( Citrus paradisii) and shaddock ( Citrus maxima)] and characterize the antioxidant properties. The free phenolics were extracted with 80% acetone, while the bound phenolics were extracted from the alkaline and acid hydrolyzed residue with ethyl acetate. Free phenolic extracts had significantly higher ( P < 0.05) DPPH* scavenging ability than the bound phenolic extracts, except in orange peels where the bound phenolic extracts had significantly higher ( P < 0.05) DPPH* scavenging ability. Bound phenolics from orange peels had the highest ABTS* scavenging ability (6.09 mmol./TEAC g) and ferric reducing antioxidant properties (FRAP) (71.99 mg/GAE 100 g), while bound phenolics from shaddock peels had the least ABTS* scavenging ability (1.35 mmol./TEAC g) and FRAP (2.58 mg/GAE 100 g) . Bound phenolics from grapefruit peels had the highest OH* scavenging ability (EC = 3.8 mg/ml), while bound phenolics from shaddock peels had the least (EC = 16.1 mg/ml). The phenolics chelated Fe and inhibited malondialdehyde production in rat's pancreas in a dose-dependent manner. The additive and/or synergistic action of the free and bound phenolics could have contributed to the observed medicinal properties of the peels; therefore, the high antioxidant properties of the free and bound phenolic extracts from orange peels could be harness in the formulation of nutraceuticals and food preservatives. [ABSTRACT FROM AUTHOR]

Abstract: Let denote the distance matrix of a connected graph with order , where is equal to the distance between vertices and in . The value () is called the distance degree of vertex . Denote by the largest eigenvalue and the smallest eigenvalue of respectively. The distance spectral spread of a graph is defined to be . In this paper, some lower bounds on are given in terms of distance degrees, the largest vertex degree and clique number; the spreads of , , , are proved to be the least among all connected graphs with vertices, all bipartite graphs with vertices, all the graphs with both vertices and independent number , all trees with vertices respectively. [Copyright &y& Elsevier]

Abstract: Let be a simple graph of order , and let be the Laplacian spectrum of . The Laplacian-energy-like invariant of ( for short) is defined as . In this paper, a new lower bound for of graphs in terms of the maximum degree is given. Meanwhile, an upper bound and a lower bound for of the line graph (resp., the subdivision graph and the total graph) of a regular graph are obtained. [Copyright &y& Elsevier]

The atom-bond connectivity ( ABC) index provides a good model for the stability of linear and branched alkanes as well as the strain energy of cycloalkanes, which is defined as $$ABC(G) = \sum\limits_{uv \in E(G)} {\sqrt {\frac{{d_u + d_v - 2}} {{d_u d_v }}} } $$, where d denotes the degree of a vertex u in G. A chemical graph is a graph in which no vertex has degree greater than 4. In this paper, we obtain the sharp upper and lower bounds on ABC index of chemical bicyclic graphs. [ABSTRACT FROM AUTHOR]

To construct a lager graphs from two smaller ones that have same order, one can add an arbitrary perfect matching between their vertex-sets, permutation graphs (or generalized prisms) are special cases of these graphs. This work presents bounds on the 3-restricted edge connectivity of these graphs. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph of order n with degree sequence ( d, d, ..., d). Denote ( t) = Σ d, ( m) = ( t)/ d and ( N) = Σ ( t), where α is a real number. Denote by λ( G) and µ( G) the spectral radius of the adjacency matrix and the Laplacian matrix of G, respectively. In this paper, we present some upper and lower bounds of λ( G) and µ( G) in terms of ( t), ( m) and ( N). Furthermore, we also characterize some extreme graphs which attain these upper bounds. These results theoretically improve and generalize some known results. [ABSTRACT FROM AUTHOR]

Abstract: Several exceptions are provided for a theorem in Cauchy’s Cours d’Analyse in the proof of which the need for uniform convergence has been ignored. A reconstruction of this theorem is offered. [Copyright &y& Elsevier]

Abstract: We apply several matrix inequalities to the derivative companion matrices of complex polynomials to establish new bounds and majorization relations for the critical points of these polynomials in terms of their zeros. [Copyright &y& Elsevier]

We give a definition of a bounded edge within the causal directed acyclic graph framework. A bounded edge generalizes the notion of a signed edge and is defined in terms of bounds on a ratio of survivor probabilities. We derive rules concerning the propagation of bounds. Bounds on causal effects in the presence of unmeasured confounding are also derived using bounds related to specific edges on a graph. We illustrate the theory developed by an example concerning estimating the effect of antihistamine treatment on asthma in the presence of unmeasured confounding. [ABSTRACT FROM PUBLISHER]

The purpose of this article is to discuss the conjecture on the Frobenius norm of matrices. The conjecture on the Frobenius norm of matrices proposed by Sloane and Harwit is proved for a class of special matrices. [ABSTRACT FROM PUBLISHER]

Locating arrays are of interest in generating software test suites to cover all t-way component interactions and locate interaction faults in component-based systems. Recently, Tang, Colbourn and Yin made an investigation into optimal locating arrays in the case where a single fault is to be located. They pointed out that when two or more faults were considered, matters would become rather complicated. To handle those cases generally seems challenging, but is well worth further research. In this paper, we establish a lower bound on the size of locating arrays with at most two faults, and then prove that optimal locating arrays meeting this bound can be equivalently characterized in terms of orthogonal arrays with prescribed properties. Using this characterization, we develop a number of constructions of optimal locating arrays. Two infinite series of optimal locating arrays are then obtained. [ABSTRACT FROM AUTHOR]

Abstract: A very important problem in many wireless ad-hoc networks, including wireless sensor networks, is positioning or the determination of geographical locations of the wireless nodes. Positioning is used both in infrastructural aspects of sensor networks, like geographic routing and topology maintenance, and in applications like wildlife tracking. Connectivity-based positioning algorithms in mobile wireless systems are studied in this work. These algorithms compute node positions based only on the connectivity, i.e. the neighborhood information of each node. Many algorithms have been proposed for positioning in stationary node systems and bounds on positional error of algorithms have been derived. The design and analysis of positioning algorithms for mobile node systems is a more challenging problem. Node mobility increases the amount of positional information available to a positioning algorithm. The work in this paper establishes a bound on the positional error for connectivity-based algorithms in mobile systems. The formulation from the analysis is used to investigate the benefit of this additional positional information on reducing positional error. There is a limit to the usefulness of positional information from previous node positions due to movement. This captures an important performance tradeoff: historical positional information can yield reduced positional error but requires more connectivity information from the network which requires greater computational resources. [Copyright &y& Elsevier]

Abstract: In this paper we study the maximal operators and the convolution operators associated with multipliers of the form We prove that satisfies the sharp weak type inequality on when and , or when and . We also obtain that is bounded from to for and . The indicated ranges of parameters p and δ cannot be improved. [Copyright &y& Elsevier]