Search

In this paper, we prove that there is no block-transitive 4-(v, k, 1) designs and 6-(v, k, 1) designs with k divides v. [ABSTRACT FROM AUTHOR]

Set-optimization has attracted increasing interest in the last years, as for instance uncertain multiobjective optimization problems lead to such problems with a set-valued objective function. Thereby, from a practical point of view, most of all the so-called set approach is of interest. However, optimality conditions for these problems, for instance using directional derivatives, are still very limited. The key aspect for a useful directional derivative is the definition of a useful set difference for the evaluation of the numerator in the difference quotient. We present here a new set difference which avoids the use of a convex hull and which applies to arbitrary convex sets, and not to strictly convex sets only. The new set difference is based on the new concept of generalized Steiner sets. We introduce the Banach space of generalized Steiner sets as well as an embedding of convex sets in this space using Steiner points. In this Banach space we can easily define a difference and a directional derivative. We use the latter for new optimality conditions for set optimization. Numerical examples illustrate the new concepts. [ABSTRACT FROM AUTHOR]

A novel triple-band frequency selective surface (FSS) as a band stop filter in Global System for Mobile communication (GSM) frequencies is presented. Unit cell of the FSS consists of two isolated resonators, one square loop resonating at 942 MHz and another synthetic resonator in the same layer having resonant frequencies of 1842 and 2142 MHz. The synthetic resonator consists of two similar geometries which are coupled to each other by slim gaps in a way that each resonance arises through the joint lengths of both of the geometries. Therefore, these dependent resonators simply provide frequency tuning ability in those very closely spaced frequencies. Moreover, very low-frequency response sensitivity to the oblique incidence angles is achieved by using a miniaturized single synthetic resonator for the two frequencies in a single layer. A desirable 20 dB attenuation in the transmission characteristics is achieved at all frequencies of the GSM system with stability for oblique incidence for both TE and TM polarizations. [ABSTRACT FROM AUTHOR]

Ferroelectric materials at morphotropic phase boundary (MPB) exhibit large piezoelectric coefficients and thus are widely used as piezoelectric actuators and sensors. Three different phase diagram topologies have been reported in various ferroelectric MPB systems: one with a cubic(C)-tetragonal(T)-orthorhombic(O)-rhombohedral(R) quadruple point; another with a C-T-R triple point and the other with a C-T-R along with a T-O-R triple point. However, it is unclear which phase diagram topology would give the best piezoelectric property. Here in this work, we obtain the above three different MPB phase diagram topologies by Landau free energy. It was found that among the three phase diagram topologies, the one with a T-O-R triple point exhibits superior piezoelectric property at the T-O-R triple point because of the small polarization anisotropy required by the simultaneous thermodynamic equilibrium of three ferroelectric phases. This work could guide the design of piezoelectric materials. [ABSTRACT FROM AUTHOR]

This paper studies the problem of sensor fault interval estimation for discrete-time linear system with unknown but bounded disturbances and noises. A descriptor system which is equivalent to the original system is constructed by considering the fault as an auxiliary state vector. Based on the augmented descriptor system, a zonotopic Kalman filter is designed to obtain the interval estimation of sensor fault. To improve estimation accuracy, we further propose a Frobenius norm minimisation method to design the gain matrix of zonotopic Kalman filter. Finally, numerical simulations of a quadruple-tank system are given to illustrate the effectiveness and superiority of the proposed approach. [ABSTRACT FROM AUTHOR]

This article investigates the robustness of binary incomplete block designs against giving rise to a disconnected design in the event of observation loss. A link is established between theE-value of a planned design and the extent of observation loss that can be experienced while still guaranteeing an eventual design from which all treatment contrasts can be estimated. Patterns of missing observations covered include loss of entire blocks and loss of individual observations. Simple bounds are provided enabling practitioners to easily assess the robustness of a planned design. [ABSTRACT FROM AUTHOR]

We formulate a definition of equilateral triangles in the complex line that makes sense over the field with seven elements. Adjacency of these abstract triangles gives rise to the Heawood graph, which is a way to encode the Fano plane. Through some reformulation, this gives a geometric construction of the Steiner systems S(2, 3, 7) and S(3, 4, 8). As a consequence, we embed the Heawood graph in a torus, and we derive the exceptional isomorphism PSL2(F7) ≃ GL3(F2). The study of equilateral triangles over other finite fields shows that seven is very specific. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the comparison results for solutions of a class of sublinear elliptic equations using Steiner symmetrization. [ABSTRACT FROM PUBLISHER]

An important manufacturing technology spectrum is to consider rapid and sensitive assemblies through convergent product (CP) in digital environment. We integrate functions and sub-functions using a comprehensive mathematical optimization process. To form the CP, a web-based fuzzy network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is to be a link between two nodes. The aim is to find an optimal tree of functionalities in the network adding value to the product in the web environment. First, a purification process is performed in the product network to assign the links among bases and sub-functions. Then, fuzzy numbers as benefits, costs and customers' value are determined. Next, the fuzzy Steiner tree methodology is adapted to a multi-objective model of the network to find the optimal tree determining the value adding sub-functions to bases in a CP. A new fuzzy multi-objective optimization is developed to work out the problem. Finally, an example is worked out to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

We propose several problems on the Fibonacci polytope. [ABSTRACT FROM AUTHOR]

The aim of this article is to answer a question posed by Merris in European Journal of Combinatorics, 24 (2003) pp. 413 - 430, about the possibility of finding split non-threshold graphs that are Laplacian integral, i.e. graphs for which the eigenvalues of the corresponding Laplacian matrix are integers. Using Kronecker products, balanced incomplete block designs, and solutions to certain Diophantine equations, we show how to build infinite families of these graphs. [ABSTRACT FROM AUTHOR]

In this article we give the classification of compact exceptional simple Kantor triple systems defined on tensor products of composition algebras A = 1⊗ 2 such that their Kantor algebras L(φ, A) are real forms of exceptional simple Lie algebras. [ABSTRACT FROM AUTHOR]

Several evolutionary algorithms (EAs) applied to a wide class of communication network design problems modelled under the generalized Steiner problem (GSP) are evaluated. In order to provide a fault-tolerant design, a solution to this problem consists of a preset number of independent paths linking each pair of potentially communicating terminal nodes. This usually requires considering intermediate non-terminal nodes (Steiner nodes), which are used to ensure path redundancy, while trying to minimize the overall cost. The GSP is an NP-hard problem for which few algorithms have been proposed. This article presents a comparative study of pure and hybrid EAs applied to the GSP, codified over MALLBA, a general purpose library for combinatorial optimization. The algorithms were tested on several GSPs, and asset efficient numerical results are reported for both serial and distributed models of the evaluated algorithms. [ABSTRACT FROM AUTHOR]

In this short review, the existence of third bodies in close binary systems is presented. Starting with the observational methods used to detect the tertiary component, we continue with the theoretical studies concerning the stability and evolution of triple systems and also of multiple systems in general. We next consider the type of tertiary component and give a list of catalogues for these systems; we end with a general discussion. [ABSTRACT FROM AUTHOR]

In this article the question of finding the best constant in a Hardy–Sobolev inequality is addressed. The inequality under investigation gives the possibility to bound a weighted norm of a function u , with a weight that depends only on a group of variables, in terms of the L p -norm of its gradient. A complete answer is obtained in a special case. [ABSTRACT FROM AUTHOR]

In the present paper we prove some comparison results via Steiner symmetrization for solutions to the Neumann problem where T > 0, Ω is a smooth connected open bounded subset of ℝ n , the coefficients a ij ( x , y ) and the datum f are smooth functions such that a ij ( x , y )ξ i ξ j ≥ |ξ| 2 , for any ( x , y ) ∈ G , for any ξ ∈ ℝ n and ∈ t G f dx dy = 0. [ABSTRACT FROM AUTHOR]

This paper presents an optimal sequential and an optimal parallel algorithm to compute a minimum cardinality Steiner set and a Steiner tree. The sequential algorithm takes O ( n ) time and parallel algorithm takes O (log n ) time and O ( n /log n ) processors on an EREW PRAM model. [ABSTRACT FROM AUTHOR]

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. [ABSTRACT FROM AUTHOR]

Freudenthal triple systems come in two flavors, degenerate and nondegenerate. The best criterion for distinguishing between the two which is available in the literature is by descent. We provide an identity which is satisfied only by nondegenerate triple systems. We then use this to define algebraic structures whose automorphism groups produce all adjoint algebraic groups of type E[SUB7] over an arbitrary field of characteristic ≠ 2, 3. The main advantage of these new structures is that they incorporate a previously unconsidered invariant (a symplectic involution) of these groups in a fundamental way. As an application, we give a construction of adjoint groups with Tits algebras of index 2 which provides a complete description of this involution and apply this to groups of type E[SUB7] over a real-closed field. [ABSTRACT FROM AUTHOR]