Spectrum of the density matrix of a large block of spins of the XY model in one dimension

We consider reduced density matrix of a large block of consecutive spins in the ground states of the XY spin chain on an infinite lattice. We derive the spectrum of the density matrix using expression of Rényi entropy in terms of modular functions. The eigenvalues λ _n form exact geometric sequence. For example, for strong magnetic field λ _n = C exp(−π τ ₀ n), here τ ₀ > 0 and C > 0 depend on anisotropy and magnetic field. Different eigenvalues are degenerated differently. The largest eigenvalue is unique, but degeneracy g _n increases sub-exponentially as eigenvalues diminish: g_n ~ exp(p?{n/3}){g_{n}\sim \exp{(\pi \sqrt{n/3})}}. For weak magnetic field expressions are similar.     

Calculating optimal addition chains

An addition chain is a finite sequence of positive integers 1 = a ₀ ≤ a ₁ ≤ · · · ≤ a _r = n with the property that for all i > 0 there exists a j, k with a _i = a _j + a _k and r ≥ i > j ≥ k ≥ 0. An optimal addition chain is one of shortest possible length r denoted l(n). A new algorithm for calculating optimal addition chains is described. This algorithm is far faster than the best known methods when used to calculate ranges of optimal addition chains. When used for single values the algorithm is slower than the best known methods but does not require the use of tables of pre-computed values. Hence it is suitable for calculating optimal addition chains for point values above currently calculated chain limits. The lengths of all optimal addition chains for n ≤ 2³² were calculated and the conjecture that l(2n) ≥ l(n) was disproved. Exact equality in the Scholz–Brauer conjecture l(2 ⁿ − 1) = l(n) + n − 1 was confirmed for many new values.     

Structural and electrical properties of mixed oxides of manganese and vanadium: A new semiconductor oxide thermistor material

Binary oxides of manganese and vanadium have been synthesized by solid state sintering, in which the mass ratio of the individual components Mn₂O₃ and VO₂ have been varied from 90:10 to 5:95. The bulk ceramic samples were characterized by X-ray diffraction and scanning electron microscopy with energy dispersive X-ray analysis. The initial compositions either rich in Mn₂O₃ or in equi-proportion by mass with VO₂ yield β-Mn₂V₂O₇ or a new crystalline form of Mn₂V₂O₇, with unit cell parameters: a = 7.73091 Å, b = 6.640788 Å, c = 6.70779 Å α = γ = 90° and β = 98.7086° which is designated as γ-Mn₂V₂O₇. The compositions, richer in VO₂ produce MnV₂O₆ co-existing with V₂O₅ the proportion of which increases with increase in VO₂. The surface microanalysis shows a spherical-granular morphology in Mn₂V₂O₇ structure and plate/rod-like structures co-existing with granular morphology in case of MnV₂O₆ together with V₂O₅. The electrical parameters of the negative temperature coefficient thermistors were determined. Depending on the constituent oxide composition, the NTC thermistors showed room temperature resistivity in the range of 6.52 × 10² to 6.1 × 10⁶ Ω-cm. The thermistor constant and activation energy are in the range of 0.12–0.458 eV and 1393–4801 K, respectively.     

Direct electrochemistry of cytochrome c and biosensing for hydrogen peroxide on polyaniline grafted multi-walled carbon nanotube electrode

Cytochrome c (cyt c) was immobilized into a matrix consisting of polyaniline (PANI) and multi-walled carbon nanotubes (MWNT) by a new strategy. First, PANI chains were grafted onto MWNT through electropolymerization. Second, the amine groups in PANI chains were oxidized at an applied potential of +0.80 V to acquire positive charges that would effectively immobilize negatively charged cyt C. The ITO/MWNT-g-PANI(O)/cyt c electrode exhibited a pair of redox peaks with a peak potential separation (anodic to cathodic) of 0.25 V (vs Ag/AgCl) in 0.1 M phosphate buffer (pH 7.0). The results demonstrated that ITO/MWNT-g-PANI(O)/cyt c promoted direct electron transfer between cyt c and electrode with a high electron transfer rate constant (17 s⁻¹). The ITO/MWNT-g-PANI(O)/cyt c electrode catalyzes the reduction of H₂O₂. The ITO/MWNT-g-PANI(O)/cyt c biosensor displays an amperometric response to H₂O₂ with a linear concentration range from 0.5 μM to 1.5 mM (r = 0.99, n = 12), a high sensitivity (32.2 μAm M⁻¹) and fast response (9 s) and detection limit of 0.3 μM (S/N = 3).     

Viscous heating in nanoscale shear driven liquid flows

Three-dimensional Molecular Dynamics (MD) simulations of heat and momentum transport in liquid Argon filled shear-driven nano-channels are performed using 6–12 Lennard–Jones potential interactions. Work done by the viscous stresses heats the fluid, which is dissipated through the channel walls, maintained at isothermal conditions through a recently developed interactive thermal wall model. Shear driven nano-flows for weak wetting surfaces (ε _wf /ε ≤ 0.6) are investigated. Spatial variations in the fluid density, kinematic viscosity, shear- and energy dissipation rates are presented. Temperature profiles in the nano-channel are obtained as a function of the surface wettability, shear rate and the intermolecular stiffness of wall molecules. The energy dissipation rate is almost a constant for ε _wf /ε ≤ 0.6, which results in parabolic temperature profiles in the domain with temperature jumps due to the well known Kapitza resistance at the liquid/solid interfaces. Using the energy dissipation rates predicted by MD simulations and the continuum energy equation subjected to the temperature jump boundary conditions developed in [Kim et al. Journal of Chemical Physics, 129, 174701, 2008b], we obtain analytical solutions for the temperature profiles, which agree well with the MD results.     

Asymmetric quantum Reed-Solomon and generalized Reed-Solomon codes

Two new families of asymmetric quantum codes are constructed in this paper. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to classical Reed-Solomon (RS) codes, providing quantum codes with parameters [[N = l(q ^l −1), K = l(q ^l −2d + c + 1), d _z ≥ d/d _x ≥ (d−c)]] _q , where q is a prime power and d > c + 1, c ≥ 1, l ≥ 1 are integers. The second family is derived from the CSS construction applied to classical generalized RS codes, generating quantum codes with parameters [[N = mn, K = m(2k−n + c), d _z ≥ d/d _x ≥ (d−c)]] _q , where q is a prime power, 1 < k < n < 2k + c ≤ q ^m , k = n − d + 1, and n, d > c + 1, c ≥ 1, m ≥ 1 are integers. Although the second proposed construction generalizes the first one, the techniques developed in both constructions are slightly different. These new codes have parameters better than or comparable to the ones available in the literature. Additionally, the proposed codes can be utilized in quantum channels having great asymmetry, that is, quantum channels in which the probability of occurrence of phase-shift errors is large when compared to the probability of occurrence of qudit-flip errors.     

Investigation of laminar flow in microtubes with random rough surfaces

A new approach of numerically generating a microtube with three-dimensional random surface roughness is presented. In this approach, we combined a bi-cubic Coons patch with Gaussian distributed roughness heights. Two random roughness generation methods are studied. A computational fluid dynamic solver is used to solve the 3-D N–S equations for the flow through the generated rough microtubes with D = 50 μm and L = 100 μm. The effects of the peak roughness height, H, asperities spacing in the θ direction, S _θ , and Z direction, S _Z , standard deviation of the Gaussian distribution, σ, arithmetical mean roughness, R _a, on the Poiseuille number, Po are investigated. It is found that when H/D < 5% the Po number can still be predicted by the conventional flow theory if the mean diameter of rough microtubes, D _m, is used to be the hydraulic diameter D _h. When H/D = 10%, the main flow is strongly affected by the roughness at Reynolds number Re = 1,500. The Po number increases with Re and deviates from the prediction up to 11.9%. The Po number does not change a lot with S _θ and S _Z because D _m almost keeps constant when the spacing is changed. For the rough microtubes with different R _a values, the Po numbers can be almost the same, which prove that only with the R _a value we can not determine the friction in the rough microtube. The mean value μ, the maximum and minimum values of the random roughness are found to be critical to determine the Po number.     

Electrochemical DNA biosensor for the detection of interaction between di[azino-di(5,6-azafluorene)-κ-NN′]dichlormanganous and DNA

A new Mn(II) complex of MnL₂Cl₂ (L = azino-di(5,6-azafluorene)-κ²-NN′) was synthesized and utilized as an electrochemical indicator for the determination of hepatitis B virus (HBV) based on its interaction with MnL₂Cl₂. The electrochemical behavior of interaction of MnL₂Cl₂ with salmon sperm DNA was investigated on glassy carbon electrode (GCE). In the presence of salmon sperm DNA, the peak current of [MnL₂]²⁺ was decreased and the peak potential was shifted positively without appearance of new peaks. The binding ratio between [MnL₂]²⁺ and salmon sperm DNA was calculated to be 2:1 and the binding constant was 3.72 × 10⁸ mol² L⁻². The extent of hybridization was evaluated on the basis of the difference between signals of [MnL₂]²⁺ with probe DNA before and after hybridization with complementary sequence. Control experiments performed with non-complementary and mismatch sequence demonstrated the good selectivity of the biosensor. With this approach, a sequence of the HBV could be quantified over the range from 1.76 × 10⁻⁸ to 1.07 × 10⁻⁶ mol L⁻¹, with a linear correlation of r = 0.9904 and a detection limit of 6.80 × 10⁻⁹ mol L⁻¹. Additionally, the binding mechanism was preliminarily discussed. The mode of interaction between MnL₂Cl₂ and DNA was found to be primary intercalation binding.     

Pivot language approach for phrase-based statistical machine translation

This paper proposes a novel method for phrase-based statistical machine translation based on the use of a pivot language. To translate between languages L _s and L _t with limited bilingual resources, we bring in a third language, L _p , called the pivot language. For the language pairs L _s  − L _p and L _p  − L _t , there exist large bilingual corpora. Using only L _s  − L _p and L _p  − L _t bilingual corpora, we can build a translation model for L _s  − L _t . The advantage of this method lies in the fact that we can perform translation between L _s and L _t even if there is no bilingual corpus available for this language pair. Using BLEU as a metric, our pivot language approach significantly outperforms the standard model trained on a small bilingual corpus. Moreover, with a small L _s  − L _t bilingual corpus available, our method can further improve translation quality by using the additional L _s  − L _p and L _p  − L _t bilingual corpora.     

Quantum algorithm for the asymmetric weight decision problem and its generalization to multiple weights

As one of the applications of Grover search, an exact quantum algorithm for the symmetric weight decision problem of a Boolean function has been proposed recently. Although the proposed method shows a quadratic speedup over the classical approach, it only applies to the symmetric case of a Boolean function whose weight is one of the pair {0 < w ₁ < w ₂ < 1, w ₁ + w ₂ = 1}. In this article, we generalize this algorithm in two ways. Firstly, we propose a quantum algorithm for the more general asymmetric case where {0 < w ₁ < w ₂ < 1}. This algorithm is exact and computationally optimal. Secondly, we build on this to exactly solve the multiple weight decision problem for a Boolean function whose weight as one of {0 < w ₁ < w ₂ < · · · < w _m  < 1}. This extended algorithm continues to show a quantum advantage over classical methods. Thirdly, we compare the proposed algorithm with the quantum counting method. For the case with two weights, the proposed algorithm shows slightly lower complexity. For the multiple weight case, the two approaches show different performance depending on the number of weights and the number of solutions. For smaller number of weights and larger number of solutions, the weight decision algorithm can show better performance than the quantum counting method. Finally, we discuss the relationship between the weight decision problem and the quantum state discrimination problem.     

Constructive approximation to real function by wavelet neural networks

We present a type of single-hidden layer feed-forward wavelet neural networks. First, we give a new and quantitative proof of the fact that a single-hidden layer wavelet neural network with n + 1 hidden neurons can interpolate n + 1 distinct samples with zero error. Then, without training, we constructed a wavelet neural network X _a (x, A), which can approximately interpolate, with arbitrary precision, any set of distinct data in one or several dimensions. The given wavelet neural network can uniformly approximate any continuous function of one variable.     

A high-efficiency planar micromixer with convection and diffusion mixing over a wide Reynolds number range

Over a wide Reynolds number range (0.1 ≤ Re ≤ 40), the new planar obstacle micromixer has been demonstrated over 85% mixing efficiency covering the mixing improvement in both convection-enhanced (higher Re flow) and diffusion-enhanced (lower Re flow) mechanisms. Mixing behavior between two operation windows was investigated by numerical simulations and experiments. For the adaptive design, numerical simulations and Taguchi method were used to study the effect of four geometrical factors on sensitivity of mixing. The factors are gap ratio (H/W), number of mixing units, baffle width (W _b) and chamber ratio (W _m /W). The degree of sensitivity using the Taguchi method can be ranked as: Gap ratio > Number of mixing units > Baffle width > Chamber ratio. Micromixer performance is greatly influenced by the gap ratio and Reynolds number. Beside the wide Reynolds number range, good mixing efficiency can be obtained at short distance of a mixing channel and relatively low-pressure drop. This micromixer had improved both complex fabrication process of multi-layer or 3D micromixers and low mixing efficiency of planar micromixer at Re < 100. The trend of the verified experimental results is in agreement with the simulate results.     

Application of m-CNTs/NaClO4/Ppy to a fast response, room working temperature ethanol sensor

A new blended material, m-CNTs/NaClO₄/Ppy, was developed as a gas sensor to detect ethanol concentrations at room temperature. The sensing material polypyrrole (Ppy) was synthesized in situ by UV-photo-polymerization. The multiwall carbon nanotubes (m-CNTs) added enhanced the short-term repeatability of the Ppy-sensing material. The relative resistance variation (R_ethanol/R_air) of m-CNTs/NaClO₄/Ppy was 1.193 when exposed to ethanol of 30,000 ppm. The sensor response and recovery times (both 20 s) were very short to this concentration. An unstable baseline of the sensor was explained by theoretical calculation of molecular dynamics made for ethanol adsorption on polypyrrole, which revealed formation of a new bond, N–HO. Adsorption energy decreased with increasing the number of ethanol molecules adsorbed and was 0.8 kcal/mol at eight adsorbed molecules. Sensor responses of three different Ppy samples were measured to ethanol concentrations of 18,000–40,000 ppm.     

New gas sensitive MIS structures Pt/Al2O3(M = Pt, Rh)/Si with a granular dielectric layer

New gas sensitive MIS structures Pt/Al₂O₃(M)/p-Si, where M = Pt, Rh, with granular dielectric Al₂O₃ layers doped with noble metals were obtained by an aerosol pyrolysis method. Surface morphology and composition of the structures were studied by TEM, AFM and EPMA. Sensor properties of the MIS structures were studied towards reducing gases (1000 ppm H₂, 300 ppm CO, 1000 ppm CH₄ in air) at 100 and 200 °C. The Pt/Al₂O₃(M = Pt, Rh)/Si structures showed a very high sensor response to reducing gases. A shift of C–V characteristics was up to 2.5 V under CO, 2.2 V under hydrogen and 0.7 V under methane. High values of shift of C–V curves can be related with cooperative influence of a change of surface state density in dielectric layer, reduction of platinum electrode and dipole layer formation.     

Editing Graphs into Disjoint Unions of Dense Clusters

In the Π-Cluster Editing problem, one is given an undirected graph G, a density measure Π, and an integer k≥0, and needs to decide whether it is possible to transform G by editing (deleting and inserting) at most k edges into a dense cluster graph. Herein, a dense cluster graph is a graph in which every connected component K=(V _K ,E _K ) satisfies Π. The well-studied Cluster Editing problem is a special case of this problem with Π:=“being a clique”. In this work, we consider three other density measures that generalize cliques: (1) having at most s missing edges (s-defective cliques), (2) having average degree at least |V _K |−s (average-s-plexes), and (3) having average degree at least μ⋅(|V _K |−1) (μ-cliques), where s and μ are a fixed integer and a fixed rational number, respectively. We first show that the Π-Cluster Editing problem is NP-complete for all three density measures. Then, we study the fixed-parameter tractability of the three clustering problems, showing that the first two problems are fixed-parameter tractable with respect to the parameter (s,k) and that the third problem is W[1]-hard with respect to the parameter k for 0<μ<1.     

A technique for monitoring SO2 in combustion exhausts: Use of a non-Nernstian sensing element in combination with an upstream catalytic filter

Detection of sulfur dioxide (SO₂) at high temperature (600–750 °C) in the presence of some interferents found in combustion exhausts (NO₂, NO, CO₂, CO, and hydrocarbon (C₃H₆)) is described. The detection scheme involves use of a catalytic filter in front of a non-Nernstian (mixed-potential) sensing element. The catalytic filter was a Ni:Cr powder bed operating at 850 °C, and the sensing elements were pairs of platinum (Pt) and oxide (Ba-promoted copper chromite ((Ba,Cu)_xCr_yO_z) or Sr-modified lanthanum ferrite (LSF)) electrodes on yttria-stabilized zirconia. The Ni:Cr powder bed was capable of reducing the sensing element response to NO₂, NO, CO, and C₃H₆, but the presence of NO₂ or NO (“NO_x”, at 100 ppm by volume) still interfered with the SO₂ response of the Pt–(Ba,Cu)_xCr_yO_z sensing element at 600 °C, causing approximately a 7 mV (20%) reduction in the response to 120 ppm SO₂ and a response equivalent to about 20 ppm SO₂ in the absence of SO₂. The Pt–LSF sensing element, operated at 750 °C, did not suffer from this NO_x interference but at the cost of a reduced SO₂ response magnitude (120 ppm SO₂ yielded 10 mV, in contrast to 30 mV for the Pt-(Ba,Cu)_xCr_yO_z sensing element). The powder bed and Pt–LSF sensing element were operated continuously over approximately 350 h, and the response to SO₂ drifted downward by about 7%, with most of this change occurring during the initial 100 h of operation.     

Decomposition of Polynomials with Respect to the Cyclic Group of Orderm

Given a polynomial solution of a differential equation, its m -ary decomposition, i.e. its decomposition as a sum of m polynomials P^{[ j ]}(x)  = ∑_kα_j,kx^{λ_{j, k}}containing only exponentsλ_{j, k} with λ_{j,k  + 1} − λ_j,k = m, is considered. A general algorithm is proposed in order to build holonomic equations for the m -ary parts P^{[ j ]}(x) starting from the initial one, which, in addition, provides a factorized form of them. Moreover, these differential equations are used to compute expansions of the m -ary parts of a given polynomial in terms of classical orthogonal polynomials. As illustration, binary and ternary decomposition of these classical families are worked out in detail.     

Uq(sl(2)) Satisfies a Bernstein Duality

It is well known that in some cases the functorExt_R^μ( − , R) defines a duality between module categories. In earlier papers we studied when this duality can be represented by a bimodule and have characterized when this happens. In this paper, using some computational methods of noncommutative Gröbner bases in the construction of projective resolutions of irreducible finite-dimensional representations, we show new examples of algebras satisfying this property.     

Whole-body vibration exposure experienced by motorcycle riders – An evaluation according to ISO 2631-1 and ISO 2631-5 standards

Riders of twelve motorcycles, comprising 6 full-scale motorbikes and 6 motor-scooters, and 5 sedan vehicles, performed test runs on a 20.6 km paved road composed of 5 km, 5 km, and 10.6 km of rural, provincial and urban routes, respectively. Each test run of motorcycle was separately performed under speed limits of 55 km/h and 40 km/h. Tri-axial accelerations of whole-body vibration (WBV) were obtained by using a seat pad and a portable data logger, and the driver's view was videotaped with a portable media recorder. Root mean square (RMS) acceleration, 8-h estimated vibration dose value (VDV₍₈₎) and 8-h estimated daily dose of static compression dose (S_ed) were determined from the collected data in accordance with ISO 2631-1 and ISO 2631-5 standards. Experimental results indicate that the WBV values of the sedan vehicle drivers have low RMS, VDV₍₈₎ and S_ed values (RMS 0.27–0.32 m/s²; VDV₍₈₎ 6.3–8.3 m/s^1.75; S_ed 0.21–0.26 MPa). However, over 90% of the motorcycle riders had VDV₍₈₎ (mean 23.5 m/s^1.75) exceeding the upper boundary of health guidance caution zone (17 m/s^1.75) recommended by ISO 2631-1, or had S_ed (mean 1.17 MPa) exceeding the value associated with a high probability of adverse health effects (0.8 MPa) recommended by ISO 2631-5. Over 50% of the motorcycle riders reached these boundary values for VDV and S_e in less than 2 h. The WBV exposure levels of the full-scale motorbikes riders and motor-scooter riders were not significantly different. However, the RMS and VDV₍₈₎ values of motorcycle riders indicate significant roadway effect (p < 0.001), while their S_ed values indicate significant speed limit effect (p < 0.05). This study concludes that the WBV exposure levels of common motorcycle riders are distinctively higher than those of sedans, even on a regular paved road. The impact on health of WBV exposure in motorcycle riders should be carefully addressed with reference to ISO 2631-1 and ISO 2631-5.

Relevance to industry

This study compares the predicted health risks of motorcycle riders according to ISO 2631-1 and ISO 2631-5 standards. Experimental data suggest that the vibration dose value of ISO 2631-1 and daily dose of equivalent static compression stress of ISO 2631-5 have roughly equivalent boundaries for probable health effects.     

Enhanced H2S sensing characteristics of SnO2 nanowires functionalized with CuO

The CuO-functionalized SnO₂ nanowire (NW) sensors were fabricated by depositing a slurry containing SnO₂ NWs on a polydimethylsiloxane (PDMS)-guided substrate and subsequently dropping Cu nitrate aqueous solution. The CuO coating increased the gas responses to 20 ppm H₂S up to 74-fold. The R_a/R_g value of the CuO-doped SnO₂ NWs to 20 ppm H₂S was as high as 809 at 300 °C, while the cross-gas responses to 5 ppm NO₂, 100 ppm CO, 200 ppm C₂H₅OH, and 100 ppm C₃H₈ were negligibly low (1.5–4.0). Moreover, the 90% response times to H₂S were as short as 1–2 s at 300–400 °C. The selective detection of H₂S and enhancement of the gas response were attributed to the uniform distribution of the sensitizer (CuO) on the surface of the less agglomerated network of the SnO₂ NWs.