Centralized multivariable control by simplified decoupling

This paper presents a generalized formulation of simplified decoupling to n × n processes that allows for different configurations depending on the decoupler elements set to unity. To apply this decoupling method, the realizability conditions are stated. Then, from the previous decoupling in combination with a decentralized control, the formulation of a centralized control by simplified decoupling is developed. After reducing the controller, this last proposed method is modified to a multivariable PID control. From an implementation point of view, the windup problem is addressed for these methods, and an anti-windup scheme for multivariable PID controllers is proposed. Comparisons with other works demonstrate the effectiveness of these methodologies, through the use of several simulation examples and an experimental lab process.     

Fast Constructive Recognition of a Black Box Group Isomorphic toSnorAnusing Goldbach’s Conjecture

The well-known Goldbach Conjecture (GC) states that any sufficiently large even number can be represented as a sum of two odd primes. Although not yet demonstrated, it has been checked for integers up to 10¹⁴. Using two stronger versions of the conjecture, we offer a simple and fast method for recognition of a gray box group G known to be isomorphic to S_n(or A_n) with knownn ≥  20, i.e. for construction1of an isomorphism from G toS_n (or A_n). Correctness and rigorous worst case complexity estimates rely heavily on the conjectures, and yield times of O([ρ + ν + μ ] n log²n) or O([ ρ + ν + μ ] n logn / loglog n) depending on which of the stronger versions of the GC is assumed to hold. Here,ρ is the complexity of generating a uniform random element of G, ν is the complexity of finding the order of a group element in G, and μ is the time necessary for group multiplication in G. Rigorous lower bound and probabilistic approach to the time complexity of the algorithm are discussed in the Appendix.     

Highly fault-tolerant cycle embeddings of hypercubes

The hypercube Q_n is one of the most popular networks. In this paper, we first prove that the n-dimensional hypercube is 2n − 5 conditional fault-bipancyclic. That is, an injured hypercube with up to 2n − 5 faulty links has a cycle of length l for every even 4 ⩽ l ⩽ 2ⁿ when each node of the hypercube is incident with at least two healthy links. In addition, if a certain node is incident with less than two healthy links, we show that an injured hypercube contains cycles of all even lengths except hamiltonian cycles with up to 2n − 3 faulty links. Furthermore, the above two results are optimal. In conclusion, we find cycles of all possible lengths in injured hypercubes with up to 2n − 5 faulty links under all possible fault distributions.     

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⁺.     

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.     

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.     

A study of nonlinear dispersive equations with solitary-wave solutions having compact support

With the use of Adomian decomposition method, the prototypical, genuinely nonlinear K(m,n) equation, u_t+(u^m)_x+(uⁿ)_xxx=0, which exhibits compactons — solitons with finite wavelength — is solved exactly. Two numerical illustrations, K(2,2) and K(3,3), are investigated to illustrate the pertinent features of the proposed scheme. The technique is presented in a general way so that it can be used in nonlinear dispersive equations.     

Generalized Strong Pseudoprime Tests and Applications

We describe probabilistic primality tests applicable to integers whose prime factors are all congruent to 1 mod r where r is a positive integer;r =  2 is the Miller–Rabin test. We show that if ν rounds of our test do not find n ≠  =  (r +  1)²composite, then n is prime with probability of error less than (2 r) ^− ν. Applications are given, first to provide a probabilistic primality test applicable to all integers, and second, to give a test for values of cyclotomic polynomials.     

Fast LLL-type lattice reduction

We modify the concept of LLL-reduction of lattice bases in the sense of Lenstra, Lenstra, Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982) 515–534 towards a faster reduction algorithm. We organize LLL-reduction in segments of the basis. Our SLLL-bases approximate the successive minima of the lattice in nearly the same way as LLL-bases. For integer lattices of dimension n given by a basis of length 2^O(n), SLLL-reduction runs in O (n^{5 +ε}) bit operations for every ε > 0, compared to O (n^{7 +ε}) for the original LLL and to O (n^{6 +ε}) for the LLL-algorithms of Schnorr, A more efficient algorithm for lattice reduction, Journal of Algorithm, 9 (1988) 47–62 and Storjohann, Faster Algorithms for Integer Lattice Basis Reduction. TR 249, Swiss Federal Institute of Technology, ETH-Zurich, Department of Computer Science, Zurich, Switzerland, July 1996. We present an even faster algorithm for SLLL-reduction via iterated subsegments running in O (n³log n) arithmetic steps. Householder reflections are shown to provide better accuracy than Gram–Schmidt for orthogonalizing LLL-bases in floating point arithmetic.     

Evaluation of response characteristics of resistive oxygen sensors based on porous cerium oxide thick film using pressure modulation method

In order to reduce the response time of resistive oxygen sensors using porous cerium oxide thick film, it is important to ascertain the factors controlling response. Pressure modulation method (PMM) was used to find the rate-limiting step of sensor response. This useful method measures the amplitude of sensor output (H(f)) for the sine wave modulation of oxygen partial pressure at constant frequency (f). In PMM, “break” response time, which is minimum period in which the sensor responds precisely, can be measured. Three points were examined: (1) simulated calculations of PMM were carried out using a model of porous thick film in which spherical particles are connected in a three-dimensional network; (2) sensor response speed was experimentally measured using PMM; and (3) the diffusion coefficient and surface reaction coefficient were estimated by comparison between experiment and calculation. The plot of log f versus log H(f) in the high f region was found to have a slope of approximately −0.5 for both porous thick film and non-porous thin film, when the rate-limiting step was diffusion. Calculations showed the response time of porous thick film was 1/20 that of non-porous thin film when the grain diameter of the porous thick film was the same as the thickness of non-porous thin film. At 973 K, “break” response time (t_b) of the resistive oxygen sensor was found by experiment to be 109 ms. It was concluded that the response of the resistive oxygen sensor prepared in this study was strongly controlled by diffusion at 923–1023 K, since the experiment revealed that the slope of plot of log f versus log H(f) in the high f region was approximately −0.5. At 923–1023 K, the diffusion coefficient of oxygen vacancy in porous ceria (D_V) was expressed as follows: D_V (m²s⁻¹) = 5.78 × 10⁻⁴ exp(−1.94 eV/kT). At 1023 K, the surface reaction coefficient (K) was found to exceed 10⁻⁴ m/s.     

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.     

Composing Power Series Over a Finite Ring in Essentially Linear Time

Fix a finite commutative ringR. Letuandvbe power series overR, withv(0) = 0. This paper presents an algorithm that computes the firstnterms of the compositionu(v), given the firstnterms ofuandv, inn^1 + o(1)ring operations. The algorithm is very fast in practice whenRhas small characteristic.     

On the influence of the number of algorithms,problems, and independent runs in the comparison of evolutionary algorithms

When conducting a comparison between multiple algorithms on multiple optimisation problems it is expected that the number of algorithms, problems and even the number of independent runs will affect the final conclusions. Our question in this research was to what extent do these three factors affect the conclusions of standard Null Hypothesis Significance Testing (NHST) and the conclusions of our novel method for comparison and ranking the Chess Rating System for Evolutionary Algorithms (CRS4EAs). An extensive experiment was conducted and the results were gathered and saved of k = 16 algorithms on N = 40 optimisation problems over n = 100 runs. These results were then analysed in a way that shows how these three values affect the final results, how they affect ranking and which values provide unreliable results. The influence of the number of algorithms was examined for values k = {4, 8, 12, 16}, number of problems for values N = {5, 10, 20, 40}, and number of independent runs for values n = {10, 30, 50, 100}. We were also interested in the comparison between both methods – NHST's Friedman test with post-hoc Nemenyi test and CRS4EAs – to see if one of them has advantages over the other. Whilst the conclusions after analysing the values of k were pretty similar, this research showed that the wrong value of N can give unreliable results when analysing with the Friedman test. The Friedman test does not detect any or detects only a small number of significant differences for small values of N and the CRS4EAs does not have a problem with that. We have also shown that CRS4EAs is an appropriate method when only a small number of independent runs n are available.     

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).     

A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations

We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier–Stokes equations. The main originality of the method consists of using the operator (I ? ?_xx)(I ? ?_yy)(I ? ?_zz) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2 × 10⁹ points.     

Stability and convergence of sequential methods for coupled flow and geomechanics: Fixed-stress and fixed-strain splits

We analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics, in which the flow problem is solved first. We employ the von Neumann and energy methods for linear and nonlinear problems, respectively. We consider two sequential methods with the generalized midpoint rule for t_n+α, where α is the parameter of time discretization: namely, the fixed-strain and fixed-stress splits. The von Neumann method indicates that the fixed-strain split is only conditionally stable, and that its stability limit is a coupling strength less than unity if α ? 0.5. On the other hand, the fixed-stress split is unconditionally stable when α ? 0.5, the amplification factors of the fixed-stress split are different from those of the undrained split and are identical to the fully coupled method. Unconditional stability of the fixed-stress split is also obtained from the energy method for poroelastoplasticity. We show that the fixed-stress split is contractive and B-stable when α ? 0.5.We also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward Euler method in time. From the estimates, the fixed-strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable. The fixed-stress split, however, is convergent for a fixed number of iterations, showing better accuracy than the undrained split. Even when we cannot obtain the exact local bulk modulus (or exact rock compressibility) at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials, the fixed-stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus, such as the dimension-based estimation, by which the employed local bulk modulus is less stiff than the exact local bulk modulus.We provide numerical examples supporting all the estimates of stability and convergence for the fixed-strain and fixed-stress splits.     

Single-phase Ce3+–Mn2+–Tb3+ tri–codoped barium–yttrium–silicate phosphors

Ce³⁺–Mn²⁺–Tb³⁺ cooperative barium–yttrium-orthosilicate phosphors composed of Ba_{9-3m/2-n-3p/2}Ce_mMn_nTb_pY₂Si₆O₂₄ (m = 0.005–0.4, n = 0–0.5, p = 0–0.5) were prepared using a solid-state reaction. The X-ray diffraction patterns of the resultant phosphors were examined to index the peak positions. The photoluminescence (PL) excitation and emission spectra of the Ce³⁺–Mn²⁺–Tb³⁺ activated phosphors were clearly monitored. The dependence of the luminescent intensity of the Mn²⁺–Tb³⁺ co-doped Ba_9-3m/2Ce_mY₂Si₆O₂₄ host lattices on Ce³⁺ content (m = 0.025, 0.1) was also investigated. Co-doping Mn²⁺ into the Ce³⁺–Tb³⁺ co-doped host structure enabled energy transfer from Ce³⁺ to Mn²⁺; this energy transfer mechanism is discussed. The phosphors of Ce³⁺–Mn²⁺–Tb³⁺ doped Ba₉Y₂Si₆O₂₄ host lattice were prepared for efficient white-light emission under NUV excitation. With these phosphors, the desired CIE values including white region of the emission spectra were achieved.     

Conditional fault-tolerant hamiltonicity of star graphs

The star graph possesses many nice topological properties. In this study, we show that for any n-dimensional star graph (n ⩾ 4) with ⩽2n − 7 edge faults in which each node is incident to at least two non-faulty edges, there exists a fault-free Hamiltonian cycle. Compared with the corresponding study in hypercube, our method is rather succinct. Additionally, we also show the probability that an n dimensional star graph with arbitrary 2n − 7 faulty edges at most is Hamiltonian is very close to one.     

Evaluation of three methodologies to estimate the VO2max in people of different ages

Aging and gender are factors that affect the variation of physical work capacity. The present paper highlights the importance of the metabolism used by ergonomics to establish the appropriate limits of loads at work. This study compares the aerobic capacity of people from 20 to 71 years old split in 5 different groups. The laboratory experiment tested 33 volunteers (19 women and 14 men). A submaximal step test was used to measure the VO₂ using a portable breath by breath metabolic system and a telemetric heart rate monitor. Three methods to estimate the VO_2max were compared: 1) a direct measurement of VO₂, 2) estimation by heart rate, and 3) a step test method using predetermined charts. Significant difference was encountered among the estimation methods as well as among the age ranges (F_2,92 = 6.43, p < 0.05 y F_4,92 = 7.18, p < 0.05 respectively). The method of direct measurement and the method of predetermined charts were different for the estimation of the VO_2max with a confidence level of 95%. The method of predetermined charts is better adapted for males and people younger than 30 years. The estimation through non invasive heart rate apparatus was a good appraiser of the maximal oxygen consumption considering both genders and all the age groups.     

Efficient and exact quantum compression

We present a divide and conquer based algorithm for optimal quantum compression/decompression, using O(n(log⁴n)log log n) elementary quantum operations. Our result provides the first quasi-linear time algorithm for asymptotically optimal (in size and fidelity) quantum compression and decompression. We also outline the quantum gate array model to bring about this compression in a quantum computer. Our method uses various classical algorithmic tools to significantly improve the bound from the previous best known bound of O(n³) for this operation.