On the complete weight distributions of quantum error-correcting codes

In a recent paper, Hu et al. defined the complete weight distributions of quantum codes and proved the Mac Williams identities, and as applications they showed how such weight distributions may be used to obtain the singleton-type and hamming-type bounds for asymmetric quantum codes. In this paper we extend their study much further and obtain several new results concerning the complete weight distributions of quantum codes and applications. In particular, we provide a new proof of the Mac Williams identities of the complete weight distributions of quantum codes. We obtain new information about the weight distributions of quantum MDS codes and the double weight distribution of asymmetric quantum MDS codes. We get new identities involving the complete weight distributions of two different quantum codes. We estimate the complete weight distributions of quantum codes under special conditions and show that quantum BCH codes by the Hermitian construction from primitive, narrow-sense BCH codes satisfy these conditions and hence these estimate applies.

Construction and Weight Distributions of Binary Linear Codes Based on Deep Holes

Deep holes are very important in the decoding of generalized RS codes, and deep holes of RS codes have been widely studied, but there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with binary BCH codes. In this article, we consider the 2-error-correcting binary primitive BCH codes and the extended codes to construct new binary linear codes by combining them with deep holes, respectively. Furthermore, three classes of binary linear codes are constructed, and then we determine the parameters and the weight distributions of these new binary linear codes.

Distribution and Length-weight Relationships of Glyptosternoid Fishes in the Drung River Basin, Yunnan

Glyptosternoid fishes are a group of sisorid catfishes living in torrents of rivers mainly originating from the Qinghai-Tibet Plateau. Based on our survey in the Drung River Basin, seven collecting sites were investigated and 271 glyptosternoid fishes caught belong to three species （Pareuchiloglanis kamengensis, Exostoma labiatum and Oreoglanis mocropterus）. Features of the distribution of the three catfishes were assessed. More individuals of E. labiatum were caught in the lower reaches of the Drung River with fast water velocity and it might be more adapted to a torrent habitat. The relationships between standard length （L） and weight （W） for P. kamengensis, E. labiatum and O. macropterus were also studied, and the parameter b of the L-W relationship （W = aL^b） ranged between 2. 8201 and 3. 0131. From the present study, all the three catfish species grow allometrically and the growth type of E. labiatum is the closest to a symmetrical one.

Analysis of Molecular Weight Distribution and Antioxidant Activities of Cirrhinus molitorella Skin Collagen Hydrolysates

[Objective] The aim of this work was to identify molecular weight （MW） distribution and antioxidant activity of fish skin col agen hydrolysates. [Method] The MW distribution of hydrolysates was determined using both size exclusion chromatography and matrix-assisted laser desorption ionization time-of-flight mass spec-trometry （MALDI-TOF-MS）. Fish skin were treated by the alkaline protease 2709. [Result] The optional conditions for hyerolysis were time 3 h, temperature 55 ℃, pH 10.0, substrate concentration 80 g/L and E/S 4%. The results of both methods indi-cated that the molecular weight of col agen hydrolysates was from 400 to 1 800 Da, and the peptides’ molecular weight was less than 1 400 Da mostly. The reducing power and antioxidant/radical scavenging activity [1, 1-diphenyl-2-picryl-hydrazyl （DPPH） free radical scavenging activity] were determined. [Conclusion] The results reveal that the fishskin hydrolysate is a potential source of antioxidants.

Study on Enzymatic Hydrolysis of Gadus morrhua Skin Collagen and Molecular Weight Distribution of Hydrolysates

Process parameters on enzymatic hydrolysis and molecular weight （MW） distribution of collagen hydrolysates from Gadus morrhua skin were investigated. The optimal process parameters were obtained by the single-factor and orthogonal experiments. The molecular weight distribution of hydrolysates was determined using both Sephadex G25 partition and high speed liquid chromatography electricity spray mass spectrum （HPLC-ESI-MS）. Collagen hydrolysates were first gained by an alkaline protease ＂alcalase＂ for 3 h at temperature （50~C）, pH （10.0）, substrate concentration （75 g L-~）, and E/S （3%）. The molecular weight distribution of collagen hydrolysates ranged from 300 to 1 500 Da, and most of peptides were under 1 200 Da. Sephadex G25 partition and HPLC-ESI-MS should be successfully employed to determine the molecular weight distribution of collagen hydrolysates.

A HIGHLY ACTIVE NEODYMIUM CHLORIDE ISOPROPANOL COMPLEX/MODIFIED METHYLALUMINOXANE CATALYST FOR PREPARING POLYISOPRENE WITH HIGH CIS-1,4 STEREOSPECIFICITY AND NARROW MOLECULAR WEIGHT DISTRIBUTION

Neodymium chloride isopropanol complex （NdCl3.3＇prOH） activated by modified methylaluminoxane （MMAO） was examined in isoprene polymerization in hexane, with regards to Nd compounds, aluminum （Al） compounds, [Al]/[Nd] ratio, polymerization temperature and time. NdCl3＇3iprOH exhibited high activity producing polymers feasting high cis-l,4 stereospecificity （〉 96%）, very high molecular weight （Mn 〉 1.0 × 10^6） and fairly narrow molecular weight distribution （MWD, Mw/Mn 〈 2.0） simultaneously. In comparison, neodymium isopropoxide also showed high activity providing polymers with narrow MWD （Mw/Mn = 2.07）, but somewhat low cis-1,4 content （ca. 92%）, while neodymium chloride had no activity under present polymerization conditions. The Al compounds affected the polymer yield in the order of Al（i-Bu）3 〉 MMAO 〉 Al（i-Bu）2H. MMAO as cocatalyst afforded polyisoprene with high Mn over 1.0 × 10^6, whereas as stronger chain transfer agent than MMAO, AI（i-Bu）3 and AI（i-Bu）EH yielded polymers with low Mn （1.0 × 10^5-8.0 × 10^5）. NdCl3·3＇PrOH/MMAO catalyst showed a fairly good catalytic activity even at relatively low [Al]/[Nd] ratio of 30, and the produced polymer remained high cis-1,4 content of 95.8% along with high Mn over 1.0× 10^6 even at elevated temperatures up to 70℃. The polymerization rate is of the first order with respect to the concentration of isoprene. The mechanism of active species formation was discussed preliminarily.

Influences of Rifle Weight,Weight Distribution and Layout on Aiming Comfort

A rifle in a soldier’s system is often equipped with a grenade launcher,aiming device,etc.,which increases the weight of the rifle and changes its center of gravity.This study explores how the rifle weight,weight distribution and layout(e.g.stock length,position of grip and forestock)affect aiming comfort.In the paper,the upper extremity muscle activity was used to characterize the aiming comfort.A human-rifle musculoskeletal model was developed,which was validated by the surface electromyography(EMG)data.The results showed that the design parameters of rifle(weight,distance of gravity center to body and layout)had a significant influence on aiming comfort.The greater the weight was,the stronger the muscle activity was.With the distance increasing,first the muscle activity decreased,and then increased when the distance is exceeding a certain value.In addition,the combined influences of weight and distance illustrated that there was an optimal distance to make the slightest muscle movements for certain weight.For designing a rifle’s layout,more muscular exertions were required to maintain the holding posture with the stock length increasing,which was suggested to be in the range of 0.1 8 m to 0.2 7 m.Results can be used to optimize the ergonomics design of rifle,improving the comfort of the rifle aiming process and the shooting accuracy.

Spatial distribution and potential poverty-returning factors of former poverty-stricken villages in the Liangshan Mountains,China

Remote mountainous villages are at risk of falling back into poverty,despite having been lifted out of extreme poverty.However,there has been a lack of focus on the factors contributing to povertyreturn in these villages,which making it difficult to understand the risks and their underlying causes.This study investigates the spatial distribution of 546 key assistance villages(KAVs)in the Liangshan mountainous region,a former poverty-stricken area,using the average nearest neighbor(ANN)and kernel density estimation(KDE)methods.Linear regression and geographically weighted regression(GWR)models are then employed to analyze the relationship between the KAVs'economy and potential povertyreturning factors.The results show that KAVs are primarily located in elevation ranges of 1800-2500 m(31.87%),with slopes of 6°-15°(42.67%)and 2-3 km from the township(28.94%).The distribution of KAVs exhibits distinct spatial clustering,forming four gathering areas.Several factors impact the KAVs'economy positively,including the normalized difference vegetation index(NDVI),built-up area,grassland,and education facilities,while elevation has a negative effect.The built-up area has the most critical impact on the rural economy,followed by NDVI and elevation.Additionally,education facilities and grassland areas also have significant effects.The study suggests promoting the Ex-situ Poverty Alleviation Relocation Program(ESPARP)and increasing rural built-up areas,grasslands,and educational facilities as practical measures for preventing poverty return and promoting economic development promotion in remote mountain villages.

Molecular Weight and Distribution of Cellulose and Cellulose Microspheres

[ Objective ] This study aimed to provide basic data for studying the relationship between structure and property of cellulose microspheres by measuring molecular weight of cellulose and cellulose microspheres with viscosity method and gel permeation chromatography （GPC） method. [ Method] In viscosity method, cadmium ethylenediamine was used as the solvent, intrinsic viscosity η of the solution was determined at 25 ℃ by using a Ubbelohde viscometer, to calculate the molecular weight of cellulose; in GPC method, 8% LiC1 / N, N-dimethylacetamide （LiC1/DMAc） was used as the solvent and 0.5% LiC1/DMAc was used as the mobile phase to determine the relative molecular weight and distribution of cellulose and cellulose microspheres. In addition, the determination results were analyzed to compare these two methods. [ Result ] Viscosity-average molecular weight Mr/ of cellulose and cellulose microspheres determined with viscosity method were 224,532 and 16,686, respectively; weight-average molecular weight Mw of cellulose and cellulose microspheres determined with GPC method were 284,196 and 22,345, respectively. [ Conclusion] The determination results of （;PC method are relatively close to the actual value and could truly reflect the characteristics of molecular weialat distribution of eellulose and cellulose mierosr, heres.

Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr TypeⅫdistribution

Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.

Wavelet Density Estimation and Statistical Evidences Role for a GARCH Model in the Weighted Distribution

We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.

GIS Mapping, Biomonitoring and Distribution of Heavy Metal Concentrations Using Neem (Azadirachta indica) Bark in Makurdi Town, Benue State, Nigeria

The present work determined the concentration and spatial distribution of heavy metals (As, Hg, Cr, Cd and Pb) in soil samples from Makurdi and its environs using geographic information system (GIS). The specific objective is to produce the spatial distribution maps showing the spatial distribution of toxic heavy metals in the study area. Inverse Distance Weighting (IDW), a GIS technique was used to produce dotted maps showing the spatial distribution of heavy metals in neem bark for better visualization of contamination zones and non-contamination zones. The map reveals few hotspot areas showing areas of high concentrations of the heavy metals investigated which were identified in red colours, the following concentration ranges were obtained;As (4.71 - 6.43 mg/kg), Cd (13.9 - 16.84 mg/kg), Cr (46.3 - 60.84 mg/kg), Hg (3.70 - 5.05 mg/kg) and Pb (24.02 - 31.34 mg/kg). These hotspot areas were found close to business outlets, fuel filling and service stations, farm sites where the application of fertilizers and pesticides were persistent coupled with heavy traffic of vehicles and other machinery which was associated with As, Hg, Cd, Pb and Cr been released into the environment thus, suggesting anthropogenic activities controlling the concentration of these heavy metals in the study areas. The cumulative effect of these heavy metals into the barks of neem could pose as danger, because this plant is used as herbs in folk medicine.

SUPPORTED ZIEGLER-NATTA CATALYSTS FOR ETHYLENE SLURRY POLYMERIZATION AND CONTROL OF MOLECULAR WEIGHT DISTRIBUTION OF POLYETHYLENE

The effect of chemical composition of highly active supported Ziegler-Natta catalysts with controlled morphology on the MWD of PE has been studied.It was shown the variation of transition metal compound in the MgCl_2-supported catalyst affect of MWD of PE produced in broad range:Vanadium-magnesium catalyst(VMC)produce PE with broad and bimodal MWD(M_w/M_n=14-21).MWD of PE,produced over titanium-magnesium catalyst(TMC)is narrow or medium depending on Ti content in the catalyst(M_w/M_n=3.1-4.8).The oxidation ...

Spatial distribution of snow depth based on geographically weighted regression kriging in the Bayanbulak Basin of the Tianshan Mountains, China

Snow depth is a general input variable in many models of agriculture,hydrology,climate and ecology.This study makes use of observational data of snow depth and explanatory variables to compare the accuracy and effect of geographically weighted regression kriging(GWRK)and regression kriging(RK)in a spatial interpolation of regional snow depth.The auxiliary variables are analyzed using correlation coefficients and the variance inflation factor(VIF).Three variables,Height,topographic ruggedness index(TRI),and land surface temperature(LST),are used as explanatory variables to establish a regression model for snow depth.The estimated spatial distribution of snow depth in the Bayanbulak Basin of the Tianshan Mountains in China with a spatial resolution of 1 km is obtained.The results indicate that 1)the result of GWRK's accuracy is slightly higher than that of RK(R^2=0.55 vs.R^2=0.50,RMSE(root mean square error)=0.102 m vs.RMSE=0.077 m);2)for the subareas,GWRK and RK exhibit similar estimation results of snow depth.Areas in the Bayanbulak Basin with a snow depth greater than 0.15m are mainly distributed in an elevation range of 2632.00–3269.00 m and the snow in this area comprises 45.00–46.00% of the total amount of snow in this basin.However,the GWRK resulted in more detailed information on snow depth distribution than the RK.The final conclusion is that GWRK is better suited for estimating regional snow depth distribution.

Development of a mass model in estimating weight-wise particle size distribution using digital image processing

Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But digital image processing generated size distribution of particles, while being fast and accurate, is often expressed in terms of area function or number of particles. In this paper, a mass model is developed which converts the image obtained size distribution to mass-wise distribution, mak- ing it readily comparable to mechanical sieving data. The concept of weight/particle ratio is introduced for mass reconstruction from 2D images of particle aggregates. Using this mass model, the effects of several particle shape parameters （such as major axis, minor axis, and equivalent diameter） on sieve-size of the particles is studied. It is shown that the sieve-size of a particle strongly depend upon the shape param- eters, 91% of its variation being explained by major axis, minor axis, bounding box length and equivalent diameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size （D-50） being just 0.4%. However, sieve-size of smaller particles （〈20 ram） strongly depends upon the length of the smaller arm of the bounding box enclosing them and sieve-sizes of larger particles （〉20 mm） are highly correlated to their equivalent diameters. Multiple linear regression analysis has been used to generate overall mass-wise particle size distribution, considering the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated overall mass-wise particle size distribution shows a strong correlation with sieve generated data. The adjusted R-square value of the regression analysis is found to be 99 percent （w.r,t cumulative frequency）. The method proposed in this paper provides a time-efficient way of producing accurate （up to 99%） mass-wise PSD using digital image processing and it can be used effectively to renlace the mechanical sieving.

Properties, Inference and Applications of Inverse Power Two-Parameter Weighted Lindley Distribution

We proposed “a new extension of three-parametric distribution” called the inverse power two-parameter weighted Lindley (IPWL) distribution capable of modeling a upside-down bathtub hazard rate function. This distribution is studied to get basic structural properties such as reliability measures, moments, inverse moments and its related measures. Simulation studies are done to present the performance and behavior of maximum likelihood estimates of the IPWL distribution parameters. Finally, we perform goodness of fit measures and test statistics using a real data set to show the performance of the new distribution.

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.

Molecular Weight Distribution of Dissolved Organic Matter in Lake Hongfeng Determined by High Performance Size Exclusion Chromatography (HPSEC) With On-Line UV-Vis Absorbance and Fluorescence Detection

The molecular weight distribution (MWD) of dissolved organic matter (DOM) in lake waters from Lake Hongfeng was examined using high performance size exclusion chromatography (HPSEC) with UV-vis absorbance and fluorescence detection. The elution curves obtained by absorbance and fluorescence techniques expressed similar patterns, with the exception of diminishing of large fraction and the peaks behind several seconds in fluorescence chromatograms. According to its molecular weight (MW), DOM in water samples is divided into several fractions: large ({>3.5} kDa); medium-large ({3.5}-{2.0} kDa); medium ({2.0}-{1.0} kDa) and small ({<1.0} kDa). The average molecular weight was calculated using the elution curve detected by UV-vis absorbance and fluorescence detection techniques. The results showed that the weight-average molecular weight (Mw) and number-average molecular weight (Mn) calculated by UV-vis absorbance techniques range from 1750 to 2050 Dalton and from 1450 to 1850 Dalton, respectively. And the Mw and Mn obtained by fluorescence detection are lower by 50 to 400 Dalton. As a reference, the molecular weight of Fluka humic acid (FHA) is larger than that of water samples by about 200 Dalton. The average molecular weight of DOM for water samples collected in March and July was compared. The results revealed that the molecular weight is lower for water samples obtained in July than that obtained in March, indicating the ambient environment has an influence on the molecular weight, including photo-degradation and biological activity.

THE RELATION OF SEQUENCE DISTRIBUTIONS OF S-SBR TO ITS MOLECULAR WEIGHT DISTRIBUTIONS

The relationship between sequence distributions and molecular weight distributions of S-SBR, obtained from styrene and butadiene anionic copolymerization at various conversions with THF/Li^+ as an initiator has been studied by ^(13)C-NMR,GPC. The results showed that the molecular weight distributions of the copolymer couldbe correlated sophisticatedly to the binary sequcne distributions or the monomer unit distributions of the copolymer in a corrected Poisson's distribution from.

Tide forecasting method based on dynamic weight distribution for operational evaluation

Through analysis of operational evaluation factors for tide forecasting, the relationship between the evaluation factors and the weights of forecasters was examined. A tide forecasting method based on dynamic weight distribution for operational evaluation was developed, and multiple-forecaster synchronous forecasting was realized while avoiding the instability cased by only one forecaster. Weights were distributed to the forecasters according to each one＇s forecast precision. An evaluation criterion for the professional level of the forecasters was also built. The eligibility rates of forecast results demonstrate the skill of the forecasters and the stability of their forecasts. With the developed tide forecasting method, the precision and reasonableness of tide forecasting are improved. The application of the present method to tide forecasting at the Huangpu Park tidal station demonstrates the validity of the method.