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.

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.

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 ...

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.

The Relationship between Bulk Property and Property Distribution in Thin-Wall Injection Molded PP at Different Molecular Weight and Molecular Weight Distribution

Thin-wall injection molded parts have been paid much attention to the lightweight saving from viewpoints of natural resources saving. In the injection molding, skin-core structure can be found in the parts. This skin-core structure affects the property of completed injection molding parts (bulk property) even if in thin-wall injection molding. However, there is a few research about the relationship between bulk property and internal property distribution in the injection molding specimen. In this study, thin-wall injection molded parts of polypropylene (PP) were prepared by 4 different molecular weight and molecular weight distribution to reveal the relationship between bulk property and property distribution. These characteristics were investigated by using tensile test, fracture toughness characterized by Essential Work of Fracture (EWF) method for bulk property and film tensile test by sliced sample for tensile property distribution. The property distribution test results revealed that the highly bulk property sample had thicker highly mechanical property layer on its surface.

Tuning Polymer Molecular Weight Distribution in Cationic RAFT Polymerization by Mixing Chain Transfer Agents

Polymer dispersity (Đ) or molecular weight distribution (MWD) is a basic but vital parameter for the properties of polymeric materials. Developing new methodologies for controlling polymer MWD is emerging as a research hotspot. However, the methods to tune polymer MWD in cationic polymerization are still not well explored. Herein, we present a simple method to control the dispersity of poly(isobutyl vinyl ether) (PIBVE) by mixing two different chain transfer agents in batch visible light induced cationic RAFT polymerization. A broad dispersity range (Đ ≈ 1.16—1.80) was successfully achieved while maintaining monomodal MWD. Moreover, chain extension of PIBVE through both cationic polymerization and radical polymerization has been studied, which also provides a method to tune polymer MWD in mechanism transformation polymerization.

Characteristics of molecular weight distribution of dissolved organic matter in bromide-containing water and disinfection by-product formation properties during treatment processes

The characteristics of dissolved organic matter（DOM） and bromide ion concentration have a significant influence on the formation of disinfection by-products（DBPs）. In order to identify the main DBP precursors, DOM was divided into five fractions based on molecular weight（MW）, trihalomethane formation potential and haloacetic acid formation potential were determined for fractions, and the change in contents of different fractions and total DBPs during treatment processes（pre-chlorination, coagulation, sand filtration,disinfection） were studied. Moreover, the relationship between bromide concentration and DBP generation characteristics in processes was also analyzed. The results showed that the main DBP precursors were the fraction with MW 1 k Da and fraction with MW 3-10 k Da, and the DBP＇s generation ability of lower molecular weight DOM（ 10 k Da） was higher than that of higher molecular weight DOM. During different processes,pre-chlorination and disinfection had limited effect on removing organics but could alter the MW distribution, and coagulation and filtration could effectively remove organics with higher MW. For DBPs, trihalomethanes（THMs） were mainly generated in pre-chlorination and disinfection, while haloacetic acids（HAAs） were mostly generated during pre-chlorination; coagulation and sand filtration had little effect on THMs but resulted in a slight removal of HAAs. In addition, the results of ANOVA tests suggested that molecular sizes and treatment processes have significant influence on DBP formation. With increasing bromide concentration, the brominated DBPs significantly increased, but the bromine incorporation factor in the processes was basically consistent at each concentration.

STUDIES ON MOLECULAR WEIGHT DISTRIBUTION OF CARBON FIBER POLYMER PRECURSORS SYNTHESIZED USING MIXED SOLVENTS

The molecular weight distributions were estimated for carbon fiber polymer precursors such as poly（acrylonitrile-co-itaconic acid） synthesized by semi batch solution polymerization in mixed solvents media with the azonitrile compounds as initiator under the different ratios of solvent and non solvent from 0.75 to 2.5 in weight. The copolymer was characterized by using Fourier transform infrared spectroscopy （FTIR） and nuclear magnetic resonance （1H-NMR） analyses. The molecular weight distributions were evaluated by Mv/Mn ratios estimated from viscosity and osmotic measurements, and Mw/Mn estimated from size exclusion chromatography. The molecular weight distributions of these polymers as determined from M, JMn and Mw/Mn are 2.9 to 3,2 and 2.0 to 2.5 respectively. The molecular distributions were close to a narrow distribution of 2.0 when the solvent/non-solvent ratio was varied between 1.4 and 2.0. Intrinsic viscosity [η] as a function of molecular weight of poly（acrylonitrile-co-itaconic acid） was evaluated by means of low angle laser light scattering with size exclusion chromatography （SEC-LALLS） and viscometry with SEC （SEC-VISCO）. The relationship between [η] and Mw for poly（acrylonitrile-co-itaconic acid） in DMF at 50℃ was [q] = 1.1×10-5 Mw0.79, where [η] is obtained in dL/g.

Facile Control of Molecular Weight Distribution via Droplet-Flow Light-Driven Reversible-Deactivation Radical Polymerization

Molecular weight distribution(MWD)is fundamental for polymer analysis,which influences many important properties of polymeric materials.In this work,we demonstrate the development of a computer-aided droplet-flow system that combines photo-mediated reversible-deactivation radical polymerization(RDRP)and chain transfer agent(CTA)diffusion strategy to enable facile MWD control for the first time.Synthetic advantages of this photo-flow polymerization allow controlled chain-growth to yield a variety of polymers of tunable MWDs in a broad range(Ð≈1.1—1.9)with predetermined molecular weights(Mn≈4—30 kDa)and good chain-end fidelity.Notably,the computer-aided platform has streamlined an automatic and high-throughput pathway to prepare polymer libraries of tunable MWDs.For copolymers,chemical compositions could be readily regulated besides MWDs with the droplet-flow platform.We believe that this work should be attractive for polymer engineering,and informative to create more flow polymerization techniques toward on-demand control of diverse polymer characters.

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.

A GENERAL APPROACH TO DETERMINING THE EVOLUTION OF MOLECULAR WEIGHT DISTRIBUTION CURVES OF LINEAR POLYMERS UNDERGOING CHAIN SCISSION

A numerical method is developed to compute the development of molecular weight distribution （MWD） curves of linear polymers undergoing chain scission. The method can be applied to complex chain scission kinetics and for arbitrarily complex initial MWD curves. Our method is based on the method of lines （MoL）. Different from the existing numerical scheme, we propose the use of logarithmically spaced points. This development ensures the accuracy of the computed MWD curves at low molecular weights, and it does not require a very fine discretization to produce an accurate result.

Effect of Molecular Weight and Molecular Distribution on Skin Structure and Shear Strength Distribution near the Surface of Thin-Wall Injection Molded Polypropylene

In this study, the relationship between skin structure and shear strength distribution of thin-wall injection molded polypropylene (PP) molded at different molecular weight and molecular distribution was investigated. Skin-core structure, cross-sectional morphology, crystallinity, crystal orientation, crystal morphology and molecular orientation were evaluated by using polarized optical microscope, differential scanning calorimeter, X-ray spectroscopic analyzer and laser Raman spectroscopy, respectively, while the shear strength distribution was investigated using a micro cutting method called SAICAS (Surface And Interfacial Cutting Analysis System). The results indicated that the difference of molecular weight and molecular weight distribution showed own skin layer thickness. Especially, high molecular weight sample showed thicker layer of the lamellar orientation and molecular orientation than low molecular weight sample. In addition, wide molecular distribution sample showed large crystal orientation layer.

Purification and molecular weight distribution of a key exopolysaccharide component of Bacillus megaterium TF10

Extracellular polymeric substances（EPS） are organic metabolic compounds excreted by microorganisms. They largely impact microbial aggregate structures and functions.Extracellular polysaccharides（EP） in EPS are responsible for the formation of microbial aggregates. In this work, we successfully separated and characterized EP from EPS of the bacterium Bacillus megaterium TF10. Extraction of EP from EPS was optimized using Sevag＇s reagent. Chemical characteristics, functional groups, and molecular weight（MW） distribution of EP were compared with the harvested EPS and soluble microbial products（SMP）. We found that the polymers of lower MW and free proteins were successfully removed by Sevag＇s reagent. The higher MW components of EPS were predominantly polysaccharides,while the polymers of lower MW tended to secrete to the supernatant and were described as SMP. A part of the proteins in the EP was polysaccharide-bonded. Our results can be further used in elucidating the complex flocculation mechanisms in which EP play a major role.

Stability of weighted spectral distribution in a pseudo tree-like network model

The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distribution（i.e., a spectral graph feature） as the network order increases. First, we use deterministic scale-free networks generated by a pseudo treelike model to derive the precise formula of the spectral feature, and then analyze the stability of the spectral feature based on the precise formula. Except for the scale-free feature, the pseudo tree-like model exhibits the hierarchical and small-world structures of complex networks. The stability analysis is useful for the classification of networks with different orders and the similarity analysis of networks that may belong to the same evolving system.

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.

A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data

High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.

Scaling of weighted spectral distribution in weighted small-world networks

Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution（W SD） have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the W SD in a deterministic weighted scale-free small-world network model and find that the W SD grows sublinearly with increasing network order（i.e., the number of nodes） and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the W SD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents.