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This paper is concerned with the global exponential synchronization issues for variable-order fractional complex dynamic networks (FCDNs). Firstly, a new derivative operator, which is called as the generalized Caputo variable-order fractional derivative, is developed, and some properties and lemmas are rigorous proved. Secondly, a new dynamic event-triggered control mechanism is designed to realize the synchronization objective, where the generalized Caputo variable-order fractional derivative is applied to characterize the evolution state of internal dynamic variable. And the exclusion for Zeno behavior is verified by contradiction analysis method. Thirdly, a class of functions, which is an extension of the Lipschitz function, is introduced to model the nonlinear dynamics for the considered system. With the aid of fractional Lyapunov functional method, some auxiliary functions and advanced mathematical analysis techniques, the global exponential synchronization conditions are established in terms of linear matrix inequalities (LMIs). Finally, the correctness of the theoretical results and the feasibility of the designed controller in this paper are confirmed by applying a numerical simulation example. [ABSTRACT FROM AUTHOR]

In their recent paper 'Do Accelerating Turing Machines Compute the Uncomputable?' Copeland and Shagrir (Minds Mach 21:221-239, 2011) draw a distinction between a purist conception of Turing machines, according to which these machines are purely abstract, and Turing machine realism according to which Turing machines are spatio-temporal and causal 'notional" machines. In the present response to that paper we concede the realistic aspects of Turing's own presentation of his machines, pointed out by Copeland and Shagrir, but argue that Turing's treatment of symbols in the course of that presentation opens the door for later purist conceptions. Also, we argue that a purist conception of Turing machines (as well as other computational models) plays an important role not only in the analysis of the computational properties of Turing machines, but also in the philosophical debates over the nature of their realization. [ABSTRACT FROM AUTHOR]

In this paper, we study the L p -boundedness of the commutator [ b , S R δ (H) ] (f) = b S R δ (H) f - S R δ (H) (b f) of a BMO function b and the Bochner–Riesz means S R δ (H) for Hermite operator H = - Δ + | x | 2 on R n , n ≥ 2 . We show that if δ > δ (q) = n (1 / q - 1 / 2) - 1 / 2 , the commutator [ b , S R δ (H) ] is bounded on L p (R n) whenever q < p < q ′ and 1 ≤ q ≤ 2 n / (n + 2) . [ABSTRACT FROM AUTHOR]

The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose that a non-negative monotone submodular function f:Z+n→R+ is given via an evaluation oracle. Assume further that f satisfies the diminishing return property, which is not an immediate consequence of submodularity when the domain is the integer lattice. Given this, we design polynomial-time (1-1/e-ϵ)-approximation algorithms for a cardinality constraint, a polymatroid constraint, and a knapsack constraint. For a cardinality constraint, we also provide a (1-1/e-ϵ)-approximation algorithm with slightly worse time complexity that does not rely on the diminishing return property. [ABSTRACT FROM AUTHOR]

The paper is concerned with a new way of deriving computable estimates for the difference between the exact solutions of elliptic variational inequalities and arbitrary functions in the corresponding energy space that satisfy the main (Dirichlét) boundary conditions. Unlike the method derived earlier, the estimates are obtained by certain transformations of variational inequalities without using duality arguments. For linear elliptic and parabolic problems, this method was suggested by the author in previous papers. The present paper deals with two different types of variational inequalities (also called variational inequalities of the first and second kind). The techniques discussed can be applied to other nonlinear problems related to variational inequalities. Bibliography: 20 titles. [ABSTRACT FROM AUTHOR]

By employing a certain multiplicative group in the rational function field and places of degree one and two, we present a construction of binary linear codes in this paper. One feature is that the minimum distance of the code is bounded via the Hurwitz genus formula of function fields. It turns out that many optimal and best-known binary linear codes are obtained through our construction. [ABSTRACT FROM AUTHOR]

This paper is a continuation and wide extension of (Ann. Glob. Anal. Geom., doi:, ). In the first part of the present paper, we give a unified geometric proof that both focal submanifolds of every isoparametric hypersurface in spheres with four distinct principal curvatures are Willmore. In the second part, we completely determine which focal submanifolds are Einstein except one case. [ABSTRACT FROM AUTHOR]

In this paper, we make several observations on cellular-Lindelöf spaces. We prove that in perfect spaces, the property of being cellular-Lindelöf is equivalent to the countable chain condition. Using this result, we prove that every cellular-Lindelöf first-countable perfect space has cardinality at most c and obtain a regular example of a weakly Lindelöf non-cellular-Lindelöf space. We also prove that if X is a cellular-Lindelöf space then every discrete family of non-empty open subsets of X is countable. Finally, we prove that if X is a cellular-Lindelöf space with a symmetric g-function such that ∩{g2(n,x):n∈ω}={x} for each x∈X then |X|≤2c. [ABSTRACT FROM AUTHOR]

Effective dimension, an indicator for the difficulty of high-dimensional integration, describes whether a function can be well approximated by low-dimensional terms or sums of low-order terms. Some problems in option pricing are believed to have low effective dimensions, which help explain the success of quasi-Monte Carlo (QMC) methods recently observed in financial engineering. This paper provides a way of studying the structure of effective dimensions by finding a proper space the function of interest belongs to and then determining the effective dimension of that space. To this end, we extend the definitions of effective dimensions to weighted function spaces with product-order-dependent weights and give bounds on norms and variances. Furthermore, we show that the proposed method is applicable to functions arising in option pricing and consequently offers some hints on the performance of QMC methods. [ABSTRACT FROM AUTHOR]

In multiple-objective optimization literature, a properly efficient solution has been interpreted as a point in which the trade-offs between all objectives are bounded. In this paper, it is shown that this boundedness does not necessarily hold for problems with three or more objective functions. It is possible that in a properly efficient solution the trade-offs between some objectives are unbounded. To overcome this, in this paper strongly proper efficient solutions are introduced, in which the trade-offs between all objectives are bounded. This notion is defined in different senses, and the relationships between them are investigated. In addition to theoretical discussions, some clarifying examples are given. [ABSTRACT FROM AUTHOR]

When are so happy in a vector lattice that all band preserving linear operators turn out to be in the ideal centre? This question was raised by Wickstead (Representation and duality in Representation and duality Riesz spaces. Compos Math 35(3):225-238, ) (though not explicitly stated) and by the first author and Chil and Meyer (On the centre of a vector lattice. Indag Math 23:167-183, ). The answer depends on the vector lattice in which the operator in question acts. However, in this article we focus our attention on this question. First, we give a complete description of those vector lattices $$E$$ with the property that every orthomorphism on $$E$$ is a central operator. Secondly, we provide a counterexample to the main result, about Wickstead's question, in a recent paper of Toumi [see Theorem 3, When orthomorphisms are in the ideal center, in Positivity (, in press). (Published online: 11 Dec 2013)]. [ABSTRACT FROM AUTHOR]

Via a general construction, we are able to establish a quite general and comprehensive stability theory for Feynman's operational calculus in the time independent setting. In particular, we are able to establish stability of the operational calculus with respect to general types of the time-ordering measures. While the domain of the operational calculus is somewhat restricted as compared to the 'standard' version of the operational calculus (established by Jefferies and Johnson (Russ. J. Math. Phys. 8:153-171, ; Mat. Zametki 70:815-838, ; Adv. Appl. Clifford Algebras 11:239-264, ; Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5:171-199, ), the advantages of this relatively minor domain restriction are significant in that the stability theory (with respect to the time-ordering measures) as it stands to this time is contained, essentially in its entirety, in the principle result of this paper, Theorem 2. Moreover, Theorem 2 allows immediate, and rather far-reaching extensions of the stability theory that, until now, have not been possible. [ABSTRACT FROM AUTHOR]

Möbius monoids are Möbius categories in the sense of Leroux having a single object. The paper explores several properties of Möbius monoids and inverse monoids as well as the links between them. The right cancellative, left rigid Möbius monoids have a special place in our study. The paper has two goals: first, an examination of Möbius functions and Möbius inversion under suitable conditions, and second, a development of special inverse monoids and inverse submonoids which arise from Möbius monoids and Möbius categories. The prototype of this development is the polycyclic monoid, more precisely the free monoid as a Möbius monoid. This leads us to the generalization of some significant results on polycyclic monoids as Meakin-Sapir's result involving self-conjugate inverse submonoids, or as Jones-Lawson's results involving gauge inverse submonoids of the polycyclic monoids. Regarding Möbius functions we create links between several types of these functions. [ABSTRACT FROM AUTHOR]

Let $$G$$ be a graph of order $$n$$ and size $$m$$ . Suppose that $$f:V(G)\rightarrow {\mathbb {N}}$$ is a function such that $$\sum _{v\in V(G)}f(v)=m+n$$ . In this paper we provide a criterion for $$f$$ -choosability of $$G$$ . Using this criterion, it is shown that the choice number of the complete $$k$$ -partite graph $$K_{2,2,\ldots ,2}$$ is $$k$$ , which is a well-known result due to Erdös, Rubin and Taylor. Among other results we study the $$f$$ -choosability of the complete $$k$$ -partite graphs with part sizes at most $$2$$ , when $$f(v)\in \{k-1,k\}$$ , for every vertex $$v\in V(G)$$ . [ABSTRACT FROM AUTHOR]

University and older school students following scientific courses now use complex calculators with graphical, numerical and symbolic capabilities. In this context, the design of lessons for 11th grade pre-calculus students was a stimulating challenge. In the design of lessons, emphasising the role of mediation of calculators and the development of schemes of use in an 'instrumental genesis' was productive. Techniques, often discarded in teaching with technology, were viewed as a means to connect task to theories. Teaching techniques of use of a complex calculator in relation with 'traditional' techniques was considered to help students to develop instrumental and paper/pencil schemes, rich in mathematical meanings and to give sense to symbolic calculations as well as graphical and numerical approaches. The paper looks at tasks and techniques to help students to develop an appropriate instrumental genesis for algebra and functions, and to prepare for calculus. It then focuses on the potential of the calculator for connecting enactive representations and theoretical calculus. Finally, it looks at strategies to help students to experiment with symbolic concepts in calculus. [ABSTRACT FROM AUTHOR]

In this paper the inequality (∫0∞(∫x∞(∫t∞h)qw(t)dt)r/qu(x)ds)1/r≤C∫0∞hv,h∈M+(0,∞)is characterized. Here 0 and u,v,w are weight functions on (0,∞). [ABSTRACT FROM AUTHOR]

The paper deals with the question of the solvability of inclusions F(x, σ) ∈ Q for mappings F close, in some metrics, to a given mapping ̂F. [ABSTRACT FROM AUTHOR]

In this paper, using the algebraic structure of the Abelian group, we introduce the concept of a matched space for time scales, and we construct the algebraic structure of matched spaces to solve the closedness of time scales under non-translational shifts. Using a matched space for time scales, a new concept of periodic time scales is introduced. Based on it, new concepts of periodic functions, almost periodic functions and almost automorphic functions whose concepts were defined on translations of their arguments are proposed through non-translational shifts. The results in this paper provide new methods to consider periodic solution, almost periodic solution and almost automorphic solutions for q-difference equations and others on irregular time scales via the background of the algebraic structure. [ABSTRACT FROM AUTHOR]

F-test is the most popular test in the general linear model. However, there is few discussions on the robustness of F-test under the singular linear model. In this paper, the necessary and sufficient conditions of robust F-test statistic are given under the general linear models or their partition models, which allows that the design matrix has deficient rank and the covariance matrix of error is a nonnegative definite matrix with parameters. The main results obtained in this paper include the existing findings of the general linear model under the definite covariance matrix. The usage of the theorems is illustrated by an example. [ABSTRACT FROM AUTHOR]

In the present paper, we study the nature of LP-Sasakian manifolds admitting the M-projective curvature tensor. It is examined whether this manifold satisfies the condition W( X, Y ) .R = 0 . Moreover, it is proved that, in the M-projectively flat LP-Sasakian manifolds, the conditions R( X, Y ) .R = 0 and R( X, Y ) .S = 0 are satisfied. In the last part of the paper, an M-projectively flat space-time is introduced, and some properties of this space are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce fractional number-theoretic transforms (FrNTT) based on matrix functions. In contrast to previously proposed FrNTT, our approach does not require the construction of any number-theoretic transform (NTT) eigenvectors set. This allows us to obtain an FrNTT matrix by means of a closed-form expression corresponding to a linear combination of integer powers of the respective NTT matrix. Fractional Fourier, Hartley, cosine and sine number-theoretic transforms are developed. We show that fast algorithms applicable to ordinary NTT can also be used to compute the proposed FrNTT. Furthermore, we investigate the relationship between fractional Fourier and Hartley number-theoretic transforms, and demonstrate the applicability of the proposed FrNTT to a recently introduced image encryption scheme. [ABSTRACT FROM AUTHOR]

In the paper, we introduce a notion of a key relation, which is similar to the notion of a critical relation introduced by Keith A. Kearnes and Ágnes Szendrei. All clones on finite sets can be defined by only key relations. In addition, there is a nice description of all key relations on 2 elements. These are exactly the relations that can be defined as a disjunction of linear equations. In the paper, we show that in general, key relations do not have such a nice description. Nevertheless, we obtain a nice characterization of all key relations preserved by a weak near-unanimity function. This characterization is presented in the paper. [ABSTRACT FROM AUTHOR]

We are concerned with the following class of equations with exponential nonlinearities: which is related to the Tzitzéica equation. Here $$h_1, h_2$$ are two smooth positive functions. The purpose of the paper is to initiate the analytical study of the above equation and to give a quite complete picture both for what concerns the blow-up phenomena and the existence issue. In the first part of the paper we provide a quantization of local blow-up masses associated to a blowing-up sequence of solutions. Next we exclude the presence of blow-up points on the boundary under the Dirichlet boundary conditions. In the second part of the paper we consider the Tzitzéica equation on compact surfaces: we start by proving a sharp Moser-Trudinger inequality related to this problem. Finally, we give a general existence result. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy numbers (IFNs) are a useful tool to depict the uncertain information in real life. Based on IFNs, the intuitionistic fuzzy calculus (IFC) has been put forward recently. To further develop the IFC theory, in this paper, we investigate the limit properties of IFCs, and study the intuitionistic fuzzy infinitesimals and their orders. We also discuss the continuity, the derivatives and the differentials of intuitionistic fuzzy functions in detail, and reveal their relationships. Additionally, we define the metric space of the IFNs, based on which, a series of desirable results are obtained. These results are similar to the ones in the classical calculus. [ABSTRACT FROM AUTHOR]

This paper proves that the nearby cycles complexes on a certain family of PEL local models are central with respect to the convolution product of sheaves on the corresponding affine flag varieties. As a corollary, the semisimple trace functions defined using the action of Frobenius on those nearby cycles complexes are, via the sheaf-function dictionary, in the centers of the corresponding Iwahori-Hecke algebras. This is commonly referred to as Kottwitz's conjecture. The reductive groups associated with the PEL local models under consideration are unramified unitary similitude groups with even dimension. The proof follows the method of Haines and Ngô (Compos Math 133:117-150, 2002). Upon completion of the first version of this paper, Pappas and Zhu released a preprint (now published as Pappas and Zhu in Invent Math 194(1):147-254, 2013) which contained within its scope the main theorem of this paper. However, the methods of Pappas and Zhu (2013) are very different, and some of the proofs from this paper have been useful in forthcoming work of Haines-Stroh. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of positive solutions for a Kirchhoff-type fractional equation involving a positive potential function that is asymptotically linear at infinity. [ABSTRACT FROM AUTHOR]

Penalty function is an important tool in solving many constrained optimization problems in areas such as industrial design and management. In this paper, we study exactness and algorithm of an objective penalty function for inequality constrained optimization. In terms of exactness, this objective penalty function is at least as good as traditional exact penalty functions. Especially, in the case of a global solution, the exactness of the proposed objective penalty function shows a significant advantage. The sufficient and necessary stability condition used to determine whether the objective penalty function is exact for a global solution is proved. Based on the objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions. Furthermore, the sufficient and necessary calmness condition on the exactness of the objective penalty function is proved for a local solution. An algorithm is presented in the paper in finding a local solution, with its convergence proved under some conditions. Finally, numerical experiments show that a satisfactory approximate optimal solution can be obtained by the proposed algorithm. [ABSTRACT FROM AUTHOR]

It is known that the Clarke generalized directional derivative is nonnegative along the limit directions generated by directional direct-search methods at a limit point of certain subsequences of unsuccessful iterates, if the function being minimized is Lipschitz continuous near the limit point. In this paper we generalize this result for discontinuous functions using Rockafellar generalized directional derivatives (upper subderivatives). We show that Rockafellar derivatives are also nonnegative along the limit directions of those subsequences of unsuccessful iterates when the function values converge to the function value at the limit point. This result is obtained assuming that the function is directionally Lipschitz with respect to the limit direction. It is also possible under appropriate conditions to establish more insightful results by showing that the sequence of points generated by these methods eventually approaches the limit point along the locally best branch or step function (when the number of steps is equal to two). The results of this paper are presented for constrained optimization and illustrated numerically. [ABSTRACT FROM AUTHOR]

The classical criterion of asymptotic stability of the zero solution of equations x′ = f( t, x) is that there exists a function V ( t, x), a(∥ x∥) ≤ V ( t, x) ≤ b(∥ x∥) for some a, b ∈ K such that $$ \dot{V} $$( t, x) ≤ −c(∥ x∥) for some c ∈ K. In this paper, we prove that if $$ \mathop {V}\limits^{(m + {1})} $$( t, x) is bounded on some set [ tk − T, tk + T] × BH( tk → + ∞ as k → ∞), then the condition that $$ \dot{V} $$( t, x) ≤ −c(∥ x∥) can be weakened and replaced by that $$ \dot{V} $$( t, x) ≤ 0 and − (− $$ \dot{V} $$( tk, x)| + − $$ \ddot{V} $$( tk, x)| + ⋯ + − $$ \mathop {V}\limits^{(m)} $$( tk, x)|) ≤ −c′(∥ x∥) for some c′ ∈ K. Moreover, the author also presents a corresponding instability criterion. [-] [ABSTRACT FROM AUTHOR]

The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various classes of mathematical programs with equilibrium constraints (MPECs), whose principal role has been well recognized in optimization theory and its applications. Based on robust generalized differential calculus, we derive new results giving pointwise necessary and sufficient conditions for linear suboptimality in general MPECs and its important specifications involving variational and quasivariational inequalities, implicit complementarity problems, etc. [ABSTRACT FROM AUTHOR]

Abstract  This paper is concerned with the study of the delay-dependent stability of Runge–Kutta methods for delay differential equations. First, a new sufficient and necessary condition is given for the asymptotic stability of analytical solution. Then, based on this condition, we establish a relationship between τ(0)-stability and the boundary locus of the stability region of numerical methods for ordinary differential equations. Consequently, a class of high order Runge–Kutta methods are proved to be τ(0)-stable. In particular, the τ(0)-stability of the Radau IIA methods is proved. [ABSTRACT FROM AUTHOR]

There have been lots of papers on the uniqueness theory of entire functions concerning shared-sets in the whole complex plane. However, it seems that the uniqueness theory in an angular domain is not widely investigated. In this paper, we study the uniqueness of entire functions concerning shared-sets in an angular domain instead of the whole complex plane, and we supply examples to show that Theorem 1 is sharp. [ABSTRACT FROM AUTHOR]

A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of the Fejér (or ( C, 1)) means of functions on unbounded Vilenkin groups. There are several papers of the author of this paper concerning this. That is, we know the a.e. convergence σ n f → f ( n → ∞) for functions f ∈ L p , where p > 1 ( Journal of Approximation Theory, 101(1), 1–36, (1999)) and also the a.e. convergence σ M n f → f ( n → ∞) for functions f ∈ L 1 ( Journal of Approximation Theory, 124(1), 25–43, (2003)). The aim of this paper is to prove the a.e. relation lim n → σ n f = f for each integrable function f on any rarely unbounded Vilenkin group. The concept of the rarely unbounded Vilenkin group is discussed in the paper. Basically, it means that the generating sequence m may be an unbounded one, but its "big elements" are not "too dense". [ABSTRACT FROM AUTHOR]

In this paper, we first define a kind of pseudo-distance function and annulus domain on Riemann surfaces, then prove the Hadamard Theorem and the Borel-Carathéodory Theorem on any Riemann surfaces. [ABSTRACT FROM AUTHOR]

Several recent papers have proposed the use of grids for solving unconstrained optimisation problems. Grid-based methods typically generate a sequence of grid local minimisers which converges to stationary points under mild conditions. In this paper the location and number of grid local minimisers is calculated for strictly convex quadratic functions in two dimensions with certain types of grids. These calculations show it is possible to construct a grid with an arbitrary number of grid local minimisers. The furthest of these can be an arbitrary distance from the quadratic's minimiser. These results have important implications for the design of practical grid-based algorithms. Grids based on conjugate directions do not suffer from these problems. For such grids only the grid points closest (depending on the choice of metric) to the minimiser are grid local minimisers. Furthermore, conjugate grids are shown to be reasonably stable under mild perturbations so that in practice, only approximately conjugate grids are required. [ABSTRACT FROM AUTHOR]

The classical results by Kräuter and Seifter concerning the divisibility of permanents for (±1)-matrices by large powers of 2 are useful in testing whether the permanent function is nonvanishing. This paper suggests a new approach to this problem, allowing one to obtain a short combinatorial proof of the results by Kräuter and Seifter. [ABSTRACT FROM AUTHOR]

In this paper, we obtain generating functions of three-variable Chebyshev polynomials (of the first as well as of the second type) associated with the root system of the A Lie algebra. Bibliography: 21 titles. [ABSTRACT FROM AUTHOR]

Abstract. The remarkable class of measurable functions was introduced by classics of function theory. It has found different applications in various branches of mathematics. However this class turned out too restrictive for solving some natural mathematical problems because it is essentially connected with the property of countability. Therefore, along with it another remarkable class, essentially connected with the property of finiteness, was introduced. It is the class of uniform functions. Measurable functions are described both in the classical Lebesgue-Borel language of preimages and in the quite new language of covers. Uniform functions are described in the language of covers exclusively. Both the families of measurable functions and the families of uniform functions are determined by the rigid structure of their supports (descriptive spaces). For this reason, mathematicians weakened more that once the rigidity of the structure of descriptive spaces at the expense of using the additional property of negligence. The present paper is devoted to a contemporary formalization of the indicated ideas. Some applications of the introduced classes of functions to solving a number of known mathematical problems is traced in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore, hence all focal submanifolds of isoparametric hypersurfaces in the sphere are Willmore. [ABSTRACT FROM AUTHOR]

In this paper, we study an optimal portfolio, consumption-leisure and retirement choice problem for an infinitely lived economic agent with a CES utility function. Using the dynamic programming method, we obtain the value function and optimal investment, consumption, leisure, and retirement strategies in analytic form. Numerically we observe that the threshold retirement wealth level is an increasing function with respect to the elasticity of substitution. [ABSTRACT FROM AUTHOR]

An example of solving a boundary-value problem for a homogeneous Monge-Ampère equation is given, which produces a Bellman function for an extremal problem on the space BMO. The paper contains a step-by-step instruction for calculation of this function. Cases of rather complicated foliations are considered. This illustrates the technique elaborated in a paper by Ivanishvili, Stolyarov, Vasyunin, and Zatitskiy. Bibliography: 6 titles. [ABSTRACT FROM AUTHOR]

In this paper, we consider the setting of multiplicative metric spaces to establish results regarding the common fixed points of four mappings, using a contraction condition defined by means of a comparison function. Also, we provide illustrative examples in support of our new results. The results obtained in this paper extend and improve some well-known comparable results in the literature due to He et al. (Fixed Point Theory and Appl. 2013:48, 2013). [ABSTRACT FROM AUTHOR]

In this paper we investigate the bilinear versions of Swartz's theorem. Thus we characterize the nuclear and the multiple 1-summing operators on a cartesian product of $$c_{0}\left( \mathcal {X}\right) $$ . As applications we give the necessary and sufficient conditions for some natural operators on a cartesian product of $$c_{0}\left( \mathcal {X}\right) $$ to be multiple 1-summing and nuclear operators. By an example, we show that the natural bilinear version of Swartz's theorem is not necessarily true. [ABSTRACT FROM AUTHOR]

The maximal covering location problem has been shown to be a useful tool in siting emergency services. In this paper we expand the model along two dimensions - workload capacities on facilities and the allocation or multiple levels of backup or prioritized service for all demand points. In emergency service facility location decisions such as ambulance sitting, when all of a facility's resources are needed to meet each call for service and the demand cannot be queued, the need for a backup unit may be required. This need is especially significant in areas of high demand. These areas also will often result in excessive workload for some facilities. Effective siting decisions, therefore, must address both the need for a backup response facility for each demand point and a reasonable limit on each facility's workload. In this paper, we develop a model which captures these concerns as well as present an efficient solution procedure using Lagrangian relaxation. Results of extensive computational experiments are presented to demonstrate the viability of the approach. [ABSTRACT FROM AUTHOR]

This paper presents a simple way for diagonalization of matrices in an arbitrary field, with which one can calculate functions of matrices. [ABSTRACT FROM AUTHOR]

In 1936 Zygmunt Zalcwasser asked, with respect to the trigonometric system, how "rare" can a sequence of strictly monotone increasing integers (nj) be such that the almost everywhere relation 1N∑j=1NSnjf→f is fulfilled for each integrable function f. In this paper, we give an answer to this question. It follows from the main result that this a.e. relation holds for every integrable function f and lacunary sequence (nj) of natural numbers. [ABSTRACT FROM AUTHOR]

Let $${K_n^{(k)}}$$ be the complete k-uniform hypergraph, $${k\ge3}$$ , and let ℓ be an integer such that 1 ≤ ℓ ≤ k−1 and k−ℓ divides n. An ℓ-overlapping Hamilton cycle in $${K_n^{(k)}}$$ is a spanning subhypergraph C of $${K_n^{(k)}}$$ with n/( k−ℓ) edges and such that for some cyclic ordering of the vertices each edge of C consists of k consecutive vertices and every pair of consecutive edges in C intersects in precisely ℓ vertices. An edge-coloring of $${K_n^{(k)}}$$ is ( a, r)-bounded if every subset of a vertices of $${K_n^{(k)}}$$ is contained in at most r edges of the same color. In this paper, we refine recent results of the first author, Frieze and Ruciński by proving that there is a constant c = c( k, ℓ) such that every $${(\ell, cn^{k-\ell})}$$ -bounded edge-colored $${K_n^{(k)}}$$ in which no color appears more that cn times contains a rainbow ℓ-overlapping Hamilton cycle. We also show that there is a constant c′ = c′( k, ℓ) such that every (ℓ, c′ n)-bounded edge-colored $${K_n^{(k)}}$$ contains a properly colored ℓ-overlapping Hamilton cycle. [ABSTRACT FROM AUTHOR]

A periodic linear chain consists of a weighted $$2n$$ -path where new edges have been added following a certain periodicity. In this paper, we obtain the effective resistance and the Kirchhoff index of a periodic linear chain as non trivial functions of the corresponding expressions for the path. We compute the expression of the Kirchhoff index of any homogeneous and periodic linear chain which generalizes the previously known results for ladder-like and hexagonal chains, that correspond to periods one and two respectively. [ABSTRACT FROM AUTHOR]

A dynamic domain consists of a set of legal states and a transition function that maps states to states. AI formalisms for specifying dynamic domains have so far focused on describing the effects of actions, that is, the transition functions. In this paper we propose a notion of characteristic set of position systems for the purpose of describing legal states. A position system for a type of objects is a set of properties that are mutually exclusive, and that in each state, every object of the type must satisfy exactly one of these properties called its position under the position system. A set of position systems, one for each type of objects in the domain, is characteristic if there is a one-to-one mapping between legal states and sets of objects' positions under these position systems. These position systems are useful for reasoning about these dynamic systems including planning. In particular, we show that once we have characteristic sets of position systems for a dynamic domain, planning can be done by writing rules about when to move objects from one position to another. [ABSTRACT FROM AUTHOR]

We consider the so-called Encrypted Davies-Meyer (EDM) construction, which turns a permutation P on {0,1}n into a function from {0,1}n to {0,1}n defined as P(P(x)⊕x). A similar construction using two independent permutations, namely P′(P(x)⊕x), was previously analyzed by Cogliati and Seurin (Advances in cryptology—CRYPTO 2016 (Proceedings, Part I). LNCS, vol 9814, pp. 121-149, 2016) who showed that when P and P′ are secret and random, then any black-box adversary needs at least roughly 22n/3 queries to distinguish the construction from a uniformly random function from {0,1}n to {0,1}n. In this paper, we focus on the single-permutation variant of the construction. Our main result is that the PRF-security of the single-permutation EDM construction is also (at least) roughly 22n/3, in the sense that any black-box adversary needs at least this number of queries to distinguish the construction from a uniformly random function. This yields the first PRP-to-PRF conversion method which uses a single permutation, does not shrink the original domain nor range of the permutation, and provides security beyond the birthday bound. [ABSTRACT FROM AUTHOR]