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.     

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).     

DFT study on X−·(H2O)n=1-10 (X = OH,NO2, NO3, CO3) anionic water cluster

A theoretical study to understand the interaction between anion and the water molecules through the hydration (X⁻·(H₂O)_n (X = OH, NO₂, NO₃, CO₃), where n = 1–10), using the density functional theory method with B3LYP functional and 6-311++G(d,p) basis set has been carried out systematically. In these hydrated clusters we notice three different cases of bond arrangements, namely, symmetrical double hydrogen bond, single hydrogen bond and inter-water hydrogen bond. All the complexes are dominated by the OH⋯O hydrogen bond, in which the anion act as a proton acceptor, while the water molecule act as a proton donor. A linear correlation is obtained between the solvent stabilization energy and the size (n) of the hydrated cluster for all the anions. The weighted average interaction energy values, shows that the water molecules strongly bind with the OH⁻ anion. Besides, the solvation of the OH⁻ anion requires less number of water molecules when compared with the other anions. Energy decomposition analysis (EDA) shows the strong dominance of the electrostatic energy component within the interaction energy. The total NPA charges on the anions indicate an increase in the solvation due to hydration. From AIM analysis, excellent linear inverse correlation is observed for both the electron density and Laplacian of the electron density with respect to the hydrogen bond length. Natural bonding orbital analysis (NBO) predicts large charge transfer between the OH⁻ anion and the water molecules.     

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⁺.     

Approximate Solutions of Polynomial Equations

In this paper, we introduce “approximate solutions" to solve the following problem: given a polynomial F(x, y) over Q, where x represents an n -tuple of variables, can we find all the polynomials G(x) such that F(x, G(x)) is identically equal to a constant c in Q ? We have the following: let F(x, y) be a polynomial over Q and the degree of y in F(x, y) be n. Either there is a unique polynomial g(x)  ∈ Q [ x ], with its constant term equal to 0, such that F(x, y)  = ∑_j = 0ⁿc_j(y − g(x))^jfor some rational numbers c_j, hence, F(x, g(x)  + a)  ∈ Q for all a ∈ Q, or there are at most t distinct polynomials g₁(x),⋯ , g_t(x), t ≤ n, such that F(x, g_i(x))  ∈ Q for 1  ≤ i ≤ t. Suppose that F(x, y) is a polynomial of two variables. The polynomial g(x) for the first case, or g₁(x),⋯ , g_t(x) for the second case, are approximate solutions of F(x, y), respectively. There is also a polynomial time algorithm to find all of these approximate solutions. We then use Kronecker’s substitution to solve the case of F(x, y).     

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.     

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.     

Electrochemical determination of ascorbic acid in fruits on a vanadium oxide polypropylene carbonate modified electrode

A novel vanadium oxide polypropylene carbonate modified glassy carbon electrode was developed and used for the measurement of ascorbic acid (AA). The electrode was prepared by casting a mixture of vanadium tri(isopropoxide) oxide (VO(OC₃H₇)₃) and poly(propylene carbonate) (PPC) onto the surface of a glassy carbon electrode. The electrochemical behavior of the VO(OC₃H₇)₃–PPC film modified glassy carbon electrode was investigated by cyclic voltammetry and amperometry. This modified electrode exhibited electrocatalytic response to the oxidation of ascorbic acid. Compared with a bare glassy carbon electrode, the modified electrode exhibits a 220 mV shift of the oxidation potential of ascorbic acid in the cathodic direction and a marked enhancement of the current response. The response current revealed a good linear relationship with the concentration of ascorbic acid in the range of 4 × 10⁻⁸ and 1 × 10⁻⁴ mol L⁻¹ and the detection limit of 1.5 × 10⁻⁸ mol L⁻¹ (S/N = 3) in the pH 8.06 Britton–Robinson solution. Quantitative recovery of the ascorbic acid in synthetic samples has been obtained and the interferences from different species have been studied. The method has been successfully applied to the determination of ascorbic acid in fruits. The concentrations of ascorbic acid measured by this method are in good agreement with the literature value. It is much promising for the modified films to be used as an electrochemical sensor for the detection of ascorbic acid.     

A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: Validation

Accurate assessment of phytoplankton chlorophyll-a (chla) concentrations in turbid waters by means of remote sensing is challenging due to the optical complexity of case 2 waters. We have applied a recently developed model of the form [R_rs^? 1(λ₁) ? R_rs^? 1(λ₂)] × R_rs(λ₃) where R_rs(λ_i) is the remote-sensing reflectance at the wavelength λ_i, for the estimation of chla concentrations in turbid waters. The objectives of this paper are (a) to validate the three-band model as well as its special case, the two-band model R_rs^? 1(λ₁) × R_rs(λ₃), using datasets collected over a considerable range of optical properties, trophic status, and geographical locations in turbid lakes, reservoirs, estuaries, and coastal waters, and (b) to evaluate the extent to which the three-band model could be applied to the Medium Resolution Imaging Spectrometer (MERIS) and two-band model could be applied to the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate chla in turbid waters.The three-band model was calibrated and validated using three MERIS spectral bands (660–670 nm, 703.75–713.75 nm, and 750?757.5 nm), and the 2-band model was tested using two MODIS spectral bands (λ₁ = 662–672, λ₃ = 743–753 nm). We assessed the accuracy of chla prediction in four independent datasets without re-parameterization (adjustment of the coefficients) after initial calibration elsewhere. Although the validation data set contained widely variable chla (1.2 to 236 mg m^? 3), Secchi disk depth (0.18 to 4.1 m), and turbidity (1.3 to 78 NTU), chla predicted by the three-band algorithm was strongly correlated with observed chla (r² > 0.96), with a precision of 32% and average bias across data sets of ? 4.9% to 11%. Chla predicted by the two-band algorithm was also closely correlated with observed chla (r² > 0.92); however, the precision declined to 57%, and average bias across the data sets was 18% to 50.3%. These findings imply that, provided that an atmospheric correction scheme for the red and NIR bands is available, the extensive database of MERIS and MODIS imagery could be used for quantitative monitoring of chla in turbid waters.     

Simulation of solid thermal explosion and liquid thermal explosion of dicumyl peroxide using calorimetric technique

Dicumyl peroxide (DCPO), is produced by cumene hydroperoxide (CHP) process, is utilized as an initiator for polymerization, a prevailing source of free radicals, a hardener, and a linking agent. DCPO has caused several thermal explosion and runaway reaction accidents in reaction and storage zone in Taiwan because of its unstable reactive property. Differential scanning calorimetry (DSC) was used to determine thermokinetic parameters including 700 J g^–1 of heat of decomposition (ΔH_d), 110 °C of exothermic onset temperature (T₀), 130 kJ mol^–1 of activation energy (E_a), etc., and to analyze the runaway behavior of DCPO in a reaction and storage zone. To evaluate thermal explosion of DCPO with storage equipment, solid thermal explosion (STE) and liquid thermal explosion (LTE) of thermal safety software (TSS) were applied to simulate storage tank under various environmental temperatures (T_e). T_e exceeding the T₀ of DCPO can be discovered as a liquid thermal explosion situation. DCPO was stored under room temperature without sunshine and was prohibited exceeding 67 °C of self-accelerating decomposition temperature (SADT) for a tank (radius = 1 m and height = 2 m). SADT of DCPO in a box (width, length and height = 1 m, respectively) was determined to be 60 °C. The TSS was employed to simulate the fundamental thermal explosion behavior in a large tank or a drum. Results from curve fitting demonstrated that, even at the earlier stage of the reaction in the experiments, ambient temperature could elicit exothermic reactions of DCPO. To curtail the extent of the risk, relevant hazard information is quite significant and must be provided in the manufacturing process.     

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.     

Qualitatively different cognitive processing during online reading primed by different study activities

This article uses eye-tracking technology to examine how study activities such as taking notes or filling in a graphic organizer affect cognitive processing during learning. College students read a computer-presented passage that compared the characteristics of eastern steamboats (top section) and western steamboats (bottom section), either by reading it twice (read-only group), typing notes into a textbox on the right side of the screen (note-taking group), or typing characteristics of the two types of steamboats into a compare-and-contrast graphic organizer on the right side of the screen (graphic organizer group). Compared to the note-taking group, the graphic organizer group displayed more eye movements between the top and bottom of the passage (i.e., integrative saccades, d = 1.03), more eye movements between the text and the type-in window on the right side (i.e., constructive saccades, d = 0.79), fewer constructive saccades during initial reading (d = −0.64), and less time looking to the right side during initial reading (d = −0.81); and scored higher on a comprehension test given afterwards (d = 1.17), although both study groups outscored the read-only group. Results suggest that students in the note-taking group (and read-only group) tended to use a linear learning strategy in which their eyes followed the text in the order presented whereas students in the graphic organizer group tended to use a generative learning strategy in which their eyes searched for connections between specific information across the passage required to make comparisons.     

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).     

Cationic P⋯N interaction in XH3P+⋯NCY complexes (X = H,F, CN,NH2, OH; Y = H,Li, F,Cl) and its cooperativity with hydrogen/lithium/halogen bond

The geometries, interaction energies and bonding properties of cationic pnicogen bond (CPB) interactions are studied in binary XH₃P⁺⋯NCY (X = H, F, CN, NH₂, OH; Y = H, Li, F, Cl) complexes by means of MP2/aug-cc-pVTZ calculations. Interaction energies of these binary complexes span a large range, from −16.36 kcal/mol in (NH₂)H₃P⁺⋯NCF to −71.36 kcal/mol in FH₃P⁺⋯NCLi complex. The spin–spin coupling constant across P⋯N interaction depends considerably on the nature of X and Y substituents. The characteristic of CPB interactions is analyzed in terms of parameters derived from quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses. The charge transfer from the nitrogen base to the cationic acid stabilizes these pnicogen–bonded complexes. For a given XH₃P⁺, the net charge transfer value increases as the interaction energy of the complex becomes more negative, i.e., NCLi > NCCl > NCH > NCF. Moreover, mutual influence between the CPB and hydrogen/halogen/lithium bond is studied in the ternary XH₃P⁺⋯NCY⋯NCH complexes. The results indicate that the formation of a Y⋯N interaction tends to strengthen CPB in the ternary systems.     

Hyperspectral remote sensing of cyanobacteria in turbid productive water using optically active pigments,chlorophyll a and phycocyanin

Nuisance blue-green algal blooms contribute to aesthetic degradation of water resources by means of accelerated eutrophication, taste and odor problems, and the production of toxins that can have serious adverse human health effects. Current field-based methods for detecting blooms are costly and time consuming, delaying management decisions. Methods have been developed for estimating phycocyanin concentration, the accessory pigment unique to freshwater blue-green algae, in productive inland water. By employing the known optical properties of phycocyanin, researchers have evaluated the utility of field-collected spectral response patterns for determining concentrations of phycocyanin pigments and ultimately blue-green algal abundance. The purpose of this research was to evaluate field spectroscopy as a rapid cyanobacteria bloom assessment method. In-situ field reflectance spectra were collected at 54 sampling sites on two turbid reservoirs on September 6th and 7th in Indianapolis, Indiana using ASD Fieldspec (UV/VNIR) spectroradiometers. Surface water samples were analyzed for in-vitro pigment concentrations and other physical and chemical water quality parameters. Semi-empirical algorithms by Simis et al. [Simis, S., Peters, S., Gons, H. (2005). Remote sensing of the cyanobacterial pigment phycocyanin in turbid inland water. American Society of Limnology and Oceanography 50(11): 237–245] were applied to the field spectra to predict chlorophyll a and phycocyanin absorption at 665 nm and 620 nm, respectively. For estimation of phycocyanin concentration, a specific absorption coefficient of 0.0070 m² mg PC^-1 for phycocyanin at 620 nm, a_PC^?(620), was employed, yielding an r² value of 0.85 (n = 48, p < 0.0001), mean relative residual value of 0.51 (σ = 1.41) and root mean square error (RMSE) of 19.54 ppb. Results suggest this algorithm could be a robust model for estimating phycocyanin. Error is highest in water with phycocyanin concentrations of less than 10 ppb and where phycocyanin abundance is low relative to chlorophyll a. A strong correlation between measured phycocyanin concentrations and biovolume measurements of cyanobacteria was also observed (r = 0.89), while a weaker relationship (r = 0.66) resulted between chlorophyll a concentration and cyanobacterial biovolume.     

Evaluation of a non-point source pollution model,AnnAGNPS, in a tropical watershed

Impaired water quality caused by human activity and the spread of invasive plant and animal species has been identified as a major factor of degradation of coastal ecosystems in the tropics. The main goal of this study was to evaluate the performance of AnnAGNPS (Annualized Non-Point Source Pollution Model), in simulating runoff and soil erosion in a 48 km² watershed located on the Island of Kauai, Hawaii. The model was calibrated and validated using 2 years of observed stream flow and sediment load data. Alternative scenarios of spatial rainfall distribution and canopy interception were evaluated. Monthly runoff volumes predicted by AnnAGNPS compared well with the measured data (R² = 0.90, P < 0.05); however, up to 60% difference between the actual and simulated runoff were observed during the driest months (May and July). Prediction of daily runoff was less accurate (R² = 0.55, P < 0.05). Predicted and observed sediment yield on a daily basis was poorly correlated (R² = 0.5, P < 0.05). For the events of small magnitude, the model generally overestimated sediment yield, while the opposite was true for larger events. Total monthly sediment yield varied within 50% of the observed values, except for May 2004. Among the input parameters the model was most sensitive to the values of ground residue cover and canopy cover. It was found that approximately one third of the watershed area had low sediment yield (0–1 t ha⁻¹ y⁻¹), and presented limited erosion threat. However, 5% of the area had sediment yields in excess of 5 t ha⁻¹ y⁻¹. Overall, the model performed reasonably well, and it can be used as a management tool on tropical watersheds to estimate and compare sediment loads, and identify “hot spots” on the landscape.     

A New Algorithm for Discussing Gröbner Bases with Parameters

Let F be a set of polynomials in the variables __x = x₁, . . . , x_nwith coefficients in R [__ a ], where R is a UFD and __ a = a₁, . . . ,a_m a set of parameters. In this paper we present a new algorithm for discussing Gröbner bases with parameters. The algorithm obtains all the cases over the parameters leading to different reduced Gröbner basis, when the parameters in F are substituted in an extension field K of R. This new algorithm improves Weispfenning’s comprehensive Gröbner basis CGB algorithm, obtaining a reduced complete set of compatible and disjoint cases. A final improvement determines the minimal singular variety outside of which the Gröbner basis of the generic case specializes properly. These constructive methods provide a very satisfactory discussion and rich geometrical interpretation in the applications.