On reliability of the folded hypercubes

In this paper, we explore the 2-extra connectivity and 2-extra-edge-connectivity of the folded hypercube FQ_n. We show that κ₂(FQ_n) = 3n − 2 for n ⩾ 8; and λ₂(FQ_n) = 3n − 1 for n ⩾ 5. That is, for n ⩾ 8 (resp. n ⩾ 5), at least 3n − 2 vertices (resp. 3n − 1 edges) of FQ_n are removed to get a disconnected graph that contains no isolated vertices (resp. edges). When the folded hypercube is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system.     

Dielectric and piezoelectric properties of [0 0 1] and [0 1 1]-poled relaxor ferroelectric PZN–PT and PMN–PT single crystals

The properties of PZN–PT and PMN–PT single crystals of varying compositions and orientations have been investigated. Among the various compositions studied, [0 0 1]-optimally poled PZN-(6–7)%PT and PMN-30%PT exhibit superior dielectric and piezoelectric properties, with K^T ≈ 6800–8000, d₃₃ ≈ 2800 pC/N, d₃₁ ≈ −(1200–1800) pC/N for PZN-(6–7)%PT; and K^T = 7500–9000, d₃₃ = 2200–2500 pC/N and d₃₁ = −(1100–1400) pC/N for PMN-30%PT. These two compositions are also fairly resistant to over-poling. The [0 0 1]-poled electromechanical coupling factors (k₃₃, k₃₁ and k_t) are relatively insensitive to crystal composition. [0 1 1]-optimally poled PZN-7%PT single crystal also exhibits extremely high d₃₁ values of up to −4000 pC/N with k₃₁ ≈ 0.90–0.96. While [0 1 1]-poled PZN-7%PT single crystal becomes over-poled with much degraded properties when poled at and above 0.6 kV/mm, PZN-6%PT crystal shows no signs of over-poling even when poled to 2.0 kV/mm. The presence of a certain amount (i.e., 10–15%) of orthorhombic phase in a rhombohedral matrix has been found to be responsible for the superior transverse piezoelectric properties of [0 1 1]-optimally poled PZN-(6–7)%PT. The present work shows that flux-grown PZN–PT crystals exhibit superior and consistent properties and improved over-poling resistance to flux-grown PMN–PT crystals and that, for or a given crystal composition, flux-grown PMN–PT crystals exhibit superior over-poling resistance to their melt-grown counterparts.     

Finite-state dimension and real arithmetic

We use entropy rates and Schur concavity to prove that, for every integer k ⩾ 2, every nonzero rational number q, and every real number α, the base-k expansions of α, q + α, and qα all have the same finite-state dimension and the same finite-state strong dimension. This extends, and gives a new proof of, Wall’s 1949 theorem stating that the sum or product of a nonzero rational number and a Borel normal number is always Borel normal.     

Computing Modular Invariants of p-groups

Let V be a finite dimensional representation of a p -group, G, over a field,k , of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k [ V ]^G, has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k [ V ] G. We use these methods to analyse k [2V₃ ]^U₃where U₃is the p -Sylow subgroup ofGL₃ (F_p) and 2 V₃is the sum of two copies of the canonical representation. We give a generating set for k [2 V₃]^U₃forp =  3 and prove that the invariants fail to be Cohen–Macaulay forp >  2. We also give a minimal generating set for k [mV₂ ]^Z / pwere V₂is the two-dimensional indecomposable representation of the cyclic group Z / p.     

Modal analysis and modified cascade neural networks in identification of geometrical parameters of circular arches

A hybrid computational system, composed of the finite element method (FEM) and cascade neural network system (CNNs), is applied to the identification of three geometrical parameters of elastic arches, i.e. span l, height f and cross-sectional thickness h. FEM is used in the direct (forward) analysis, which corresponds to the mapping α = {l, f, h} → {ω_j}, where: α – vector of control parameters, ω_j – arch eigenfrequencies. The reverse analysis is related to the identification procedure in which the reverse mapping is performed {ω_j} → {α_i}. For the identification purposes a recurrent, three level CNNs of structure (D^k-H^k-1)_s was formulated, where: k – recurrence step, s = I, II, III-levels of cascade system. The Semi-Bayesian approach is introduced for the design of CNNs applying the MML Maximum Marginal Likelihood) criterion. The computation of hyperparameters is performed by means of the Bayesian procedure evidence. The numerical analysis proves a great numerical efficiency of the proposed hybrid approach for both the perfect (noiseless) values of eigenfrequencies and noisy ones simulated by an added artificial noise.     

Taylor approximation for hybrid systems

We propose a new approximation technique for Hybrid Automata. Given any Hybrid Automaton H, we call Approx(H, k) the Polynomial Hybrid Automaton obtained by approximating each formula ϕ in H with the formulae ϕ_k obtained by replacing the functions in ϕ with their Taylor polynomial of degree k. We prove that Approx(H, k) is an over-approximation of H. We study the conditions ensuring that, given any ϵ > 0, some k₀ exists such that, for all k > k₀, the “distance” between any vector satisfying ϕ_k and at least one vector satisfying ϕ is less than ϵ. We study also conditions ensuring that, given any ϵ > 0, some k₀ exists such that, for all k > k₀, the “distance” between any configuration reached by Approx(H, k) in n steps and at least one configuration reached by H in n steps is less than ϵ.     

Linear Differential Operators for Polynomial Equations

Given a squarefree polynomial P ∈ k₀[ x,y ], k₀a number field, we construct a linear differential operator that allows one to calculate the genus of the complex curve defined by P =  0 (when P is absolutely irreducible), the absolute factorization of P over the algebraic closure of k₀, and calculate information concerning the Galois group of P over ___ k₀(x) as well as overk₀ (x).     

Coarse-Grained Parallel Geometric Search

We present a parallel algorithm for solving thenext element search problemon a set of line segments, using a BSP-like model referred to as thecoarse grained multicomputer(CGM). The algorithm requiresO(1) communication rounds (h-relations withh=O(n/p)),O((n/p) log n) local computation, andO((n/p) log p) memory per processor, assumingn/p⩾p. Our result implies solutions to the point location, trapezoidal decomposition, and polygon triangulation problems. A simplified version for axis-parallel segments requires onlyO(n/p) memory per processor, and we discuss an implementation of this version. As in a previous paper by Develliers and Fabri (Int. J. Comput. Geom. Appl.6(1996), 487–506), our algorithm is based on a distributed implementation of segment trees which are of sizeO(n log n). This paper improves onop. cit.in several ways: (1) It studies the more general next element search problem which also solves, e.g., planar point location. (2) The algorithms require onlyO((n/p) log n) local computation instead ofO(log p*(n/p) log n). (3) The algorithms require onlyO((n/p) log p) local memory instead ofO((n/p) log n).     

Calibration and validation of hyperspectral indices for the estimation of broadleaved forest leaf chlorophyll content,leaf mass per area,leaf area index and leaf canopy biomass

This article aims at finding efficient hyperspectral indices for the estimation of forest sun leaf chlorophyll content (CHL, µg cm_leaf^? 2), sun leaf mass per area (LMA, g_{dry matter} m_leaf^? 2), canopy leaf area index (LAI, m²_leaf m_soil^? 2) and leaf canopy biomass (B_leaf, g_{dry matter} m_soil^? 2). These parameters are useful inputs for forest ecosystem simulations at landscape scale. The method is based on the determination of the best vegetation indices (index form and wavelengths) using the radiative transfer model PROSAIL (formed by the newly-calibrated leaf reflectance model PROSPECT coupled with the multi-layer version of the canopy radiative transfer model SAIL). The results are tested on experimental measurements at both leaf and canopy scales. At the leaf scale, it is possible to estimate CHL with high precision using a two wavelength vegetation index after a simulation based calibration. At the leaf scale, the LMA is more difficult to estimate with indices. At the canopy scale, efficient indices were determined on a generic simulated database to estimate CHL, LMA, LAI and Bleaf in a general way. These indices were then applied to two Hyperion images (50 plots) on the Fontainebleau and Fougères forests and portable spectroradiometer measurements. They showed good results with an RMSE of 8.2 µg cm^? 2 for CHL, 9.1 g m^? 2 for LMA, 1.7 m² m^? 2 for LAI and 50.6 g m^? 2 for Bleaf. However, at the canopy scale, even if the wavelengths of the calibrated indices were accurately determined with the simulated database, the regressions between the indices and the biophysical characteristics still had to be calibrated on measurements. At the canopy scale, the best indices were: for leaf chlorophyll content: ND_chl = (ρ₉₂₅ ? ρ₇₁₀)/(ρ₉₂₅ + ρ₇₁₀), for leaf mass per area: ND_LMA = (ρ₂₂₆₀ ? ρ₁₄₉₀)/(ρ₂₂₆₀ + ρ₁₄₉₀), for leaf area index: D_LAI = ρ₁₇₂₅ ? ρ₉₇₀, and for canopy leaf biomass: ND_Bleaf = (ρ₂₁₆₀ ? ρ₁₅₄₀)/(ρ₂₁₆₀ + ρ₁₅₄₀).     

Bounds for the Roots of Lacunary Polynomials

A polynomial P(X)  = X^d + a_d − 1X^d − 1 + ⋯ is called lacunary when a_d − 1 =  0. We give bounds for the roots of such polynomials with complex coefficients. These bounds are much smaller than for general polynomials.     

Curves of Genus 2 with (N,N) Decomposable Jacobians

Let C be a curve of genus 2 and ψ₁: C  −  → E ₁  a map of degree n, from C to an elliptic curveE₁ , both curves defined over C. This map induces a degree n map φ₁:P¹  −  → P ¹  which we call a Frey–Kani covering. We determine all possible ramifications for φ₁. If ψ₁:C  −  → E ₁  is maximal then there exists a maximal map ψ₂: C  −  → E ₂  , of degree n, to some elliptic curveE₂ such that there is an isogeny of degree n²from the JacobianJ_C to E₁ × E₂. We say thatJ_C is (n, n)-decomposable. If the degree n is odd the pair (ψ₂, E₂) is canonically determined. For n =  3, 5, and 7, we give arithmetic examples of curves whose Jacobians are (n, n)-decomposable.     

Evolution of structure,stability, and nonlinear optical properties of the heterodinuclear CNLin (n = 1–10) clusters

The lowest-energy structures and stabilities of the heterodinuclear clusters, CNLi_n (n = 1–10) and relevant CNLi_n⁺ (n = 1–10) cations, are studied using the density functional theory with the 6-311 + G(3df) basis set. The CNLi₆ and CNLi₅⁺ clusters are the first three-dimensional ones in the CNLi_n^0/+ series, respectively, and the CN group always caps the Li_n^0/+ moiety in the CNLi_n^0/+ (n = 1–9) configurations. The CN triple bond is found to be completely cleaved in the CNLi₁₀^0/+ clusters where the C and N atoms are bridged by two Li atoms. The CNLi_n (n = 2–10) clusters are hyperlithiated molecules with delocalized valence electrons and consequently possess low VIP values of 3.780–5.674 eV. Especially, the CNLi₈ and CNLi₁₀ molecules exhibit lower VIPs than that of Cs atom and can be regarded as heterobinuclear superalkali species. Furthermore, these two superalkali clusters show extraordinarily large first hyperpolarizabilities of 19,423 and 42,658 au, respectively. For the CNLi_n⁺ cationic species, the evolution of the energetic and electronic properties with the cluster size shows a special stability for CNLi₂⁺.     

Performance analysis of networks of queues under active queue management scheme

Analysis of networks of queues under repetitive service blocking mechanism has been presented in this paper. Nodes are connected according to an arbitrary configuration and each node in the networks employs an active queue management (AQM) based queueing policy to guarantee certain quality of service for multiple class external traffic. This buffer management scheme has been implemented using queue thresholds. The use of queue thresholds is a well known technique for network traffic congestion control. The analysis is based on a queue-by-queue decomposition technique where each queue is modelled as a GE/GE/1/N queue with single server, R (R ⩾ 2) distinct traffic classes and {N = N₁, N₂, … , N_R} buffer threshold values per class under first-come-first-serve (FCFS) service rule. The external traffic is modelled using the generalised exponential (GE) distribution which can capture the bursty property of network traffic. The analytical solution is obtained using the maximum entropy (ME) principle. The forms of the state and blocking probabilities are analytically established at equilibrium via appropriate mean value constraints. The initial numerical results demonstrate the credibility of the proposed analytical solution.     

The possibility of using C20 fullerene and graphene as semiconductor segments for detection,and destruction of cyanogen-chloride chemical agent

Detection of hazardous chemical species by changing the electrical conductivity of a semiconductor matter is a proposed and applied way for decreasing their subsequent unpleasant effects. Recently, many examples of using inorganic or organic materials, polymeric, and also nano-sized species as sensors were reported in which, in some cases, those matters were strongly affective and suitable.In this project, we have made an assessment on whether the graphene segment or C₂₀ fullerene, able to sense the existence of cyanogen chloride NCCl? In order to gain trustable results, the possible reaction pathways along with the adsorption kinetics were investigated. Moreover, the electronic density of states DOS showed that C₂₀ fullerene senses the existence of cyanogen chloride agent with a clearer signal (ΔE_g = 0.0110 eV) compared to the graphene segment (ΔE_g = 0.0001 eV). Also the adsorption energy calculations showed that cyanogen chloride could be adsorbed by the fullerene in a multi-step process (E_ads1 = −0.852 kcal mol⁻¹; E_ads2 = −0.446 kcal mol⁻¹; E_ads3 = −2.330 kcal mol⁻¹).     

An Algorithm for the Quillen–Suslin Theorem for Quotients of Polynomial Rings by Monomial Ideals

This paper presents an algorithm for the Quillen–Suslin Theorem for quotients of polynomial rings by monomial ideals, that is, quotients of the form A = k [ x₀, . . . ,x_n ] / I, with I a monomial ideal and k a field. Vorst proved that finitely generated projective modules over such algebras are free. Given a finitely generated module P, described by generators and relations, the algorithm tests whether P is projective, in which case it computes a free basis forP .     

Some Applications of Magma in Designs and Codes: Oval Designs,Hermitian Unitals and Generalized Reed–Muller Codes

We describe three applications of Magma to problems in the area of designs and the associated codes:  •  Steiner systems, Hadamard designs and symmetric designs arising from an oval in an even-order plane, leading in the classical case to bent functions and difference-set designs;  •  the Hermitian unital as a 2-(q³ +  1, q +  1, 1) design, and the code overF_p where p divides q +  1;  •  a basis of minimum-weight vectors for the code over F_pof the design of points and hyperplanes of the affine geometry AG_d(F_p), where p is a prime.     

Scalable 2D Convex Hull and Triangulation Algorithms for Coarse Grained Multicomputers

In this paper we describe scalable parallel algorithms for building the convex hull and a triangulation ofncoplanar points. These algorithms are designed for thecoarse grained multicomputermodel:pprocessors withO(n/p)⪢O(1) local memory each, connected to some arbitrary interconnection network. They scale over a large range of values ofnandp, assuming only thatn⩾p^1+ε(ε>0) and require timeO((T_sequential/p)+T_s(n, p)), whereT_s(n, p) refers to the time of a global sort ofndata on approcessor machine. Furthermore, they involve only a constant number of global communication rounds. Since computing either 2D convex hull or triangulation requires timeT_sequential=Θ(n log n) these algorithms either run in optimal time,Θ((n log n)/p), or in sort time,T_s(n, p), for the interconnection network in question. These results become optimal whenT_sequential/pdominatesT_s(n, p) or for interconnection networks like the mesh for which optimal sorting algorithms exist.