THE EXISTENCE AND MOMENTS OF CANONICAL BRANCHING CHAIN IN RANDOM ENVIRONMENT

The concepts of branching chain in random environmnet and canonical branching chain in random environment are introduced. Moreover the existence of these chains is proved. Finally the exact formulas of mathematical expectation and variance of branching chain in random environment are also given.

THE CONSTRUCTION OF MULTITYPE CANONICAL MARKOV BRANCHING CHAINS IN RANDOM ENVIRONMENTS

The investigation for branching processes has a long history by their strong physics background, but only a few authors have investigated the branching processes in random environments. First of all, the author introduces the concepts of the multitype canonical Markov branching chain in random environment （CMBCRE） and multitype Markov branching chain in random environment （MBCRE） and proved that CMBCRE must be MBCRE, and any MBCRE must be equivalent to another CMBCRE in distribution. The main results of this article are the construction of CMBCRE and some of its probability properties.

The Laplace Functional and Moments for Markov Branching Chains in Random Environments

The concepts of random Markov matrix, Markov branching chain in randomenvironment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE)are introduced. The properties of LFMBCRE and the explicit formulas of momentsof MBCRE are given.

THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT(I):MODEL,MARKOV PROPERTY,MOMENTS

There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment （BCDSTRE）, i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.

EXTINCTION OF POPULATION-SIZE-DEPENDENT BRANCHING CHAINS IN RANDOM ENVIRONMENTS

We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.

The Rheological Property and Foam Morphology of Linear Polypropylene and Long Chain Branching Polypropylene

The rheological behavior, thermal properties and foam morphology of linear polypropylene and long chain branching polypropylene prepared through UV irradiation reactive extrusion were studied by rheological test, melt index test, DSC and supercritical carbon dioxide foaming technology. Rheological test and melt index test confirmed that under UV irradiation and extrusion, adding photo-initiator and cross- linking agent could achieve the purpose of branching, thus improved the melt strength of polypropylene effectively. The DSC results revealed that with the introducing of long chain branching, the melting range of the polypropylene broadened and the crystallization temperature increased. Owing to the introduction of long chain branches, polypropylene exhibited higher melt strength and strain hardening behavior. Compared with linear polypropylene, the foam morphologies of long chain branching polypropylene were more uniform.

ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS

In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...

Synthesis of Branched Chains with Actuation Redundancy for Eliminating Interior Singularities of 3T1R Parallel Mechanisms

Although it is common to eliminate the singularity of parallel mechanism by adding the branched chain with actuation redundancy, there is no theory and method for the configuration synthesis of the branched chain with actuation redundancy in parallel mechanism. Branched chains with actuation redundancy are synthesized for eliminating interior singularity of 3-translational and 1-rotational（3T1R） parallel mechanisms. Guided by the discriminance method of hybrid screw group according to Grassmann line geometry, all the possibilities are listed for the occurrence of interior singularities in 3T1R parallel mechanism. Based on the linear relevance of screw system and the principles of eliminating parallel mechanism singularity with actuation redundancy, different types of branched chains with actuation redundancy are synthesized systematically to indicate the layout and the number of the branched chainsinterior with actuation redundancy. A general method is proposed for the configuration synthesis of the branched chains with actuation redundancy of the redundant parallel mechanism, and it builds a solid foundation for the subsequent performance optimization of the redundant actuation parallel mechanism.

Synergistic renoprotective effect of a compiled branched-chain amino acids and Cymbopogon schoenanthus extract against experimentally induced oxido-nitrosative renal insult

Objective: To better investigate the protective role of branched-chain amino acids(BCAAs)and Cymbopogon schoenanthus(CS) extract against the potassium dichromate(PDC)-induced oxido-nitrosative nephrotoxic insult in the experimental rat model. Methods: Thirty male rats were randomly divided into five equal groups: The 1 st group served as control; the 2^(nd)was injected with a single dose of PDC(15 mg/kg b.w i.p.);the 3^(rd), 4^(th), and 5^(th) groups were respectively treated with BCAAs, CS, and their combination for 15 d prior to induction of renal insult via PDC single dose(15 mg/kg b.w s.c.). The experimental period was terminated in all groups 2 d after induction of renal insult. The harvested kdney samples were divided for biochemical assays and histological examination. Results: The PDC-induced nephrotoxic effect caused a depletion of renal oxidative scavengers glutathione, superoxide dismutase with consequent lipo-oxidative cellular membrane deterioration manifested by a rise in malonaldehyde, oxidized glutathione, myeloperoxidase and the concomitant increase in inflammatory response elements tumor necrosis factor α, nitric oxide, and interleukin 1 β.Moreover, the comet assay and increased 8-hydroxy-2-deoxyguanosine proved an accelerated apoptotic DNA fragmentation. These local renal changes were met with global altered blood biochemistry. The BCAAs and CS or their compiled administration showed an ameliorative effect against PDC-induced nephrotoxic in a synergistic pattern. Conclusions: Both BCAAs and CS or their combined administration afford potential competitors against renal insult induced by polyvalent anion pollutants in experimentally studied animals model. As a route for novel drug discovery, further investigation should be attempted to optimize their augmenting reno-protecting potential.

Diagnostic value of methylated branched chain amino acid transaminase 1/IKAROS family zinc finger 1 for colorectal cancer

BACKGROUND The diagnostic value of combined methylated branched chain amino acid transaminase 1(BCAT1)/IKAROS family zinc finger 1(IKZF1)in plasma for colorectal cancer(CRC)has been explored since 2015.Recently,several related studies have published their results and showed its diagnostic efficacy.AIM To analyze the diagnostic value of methylated BCAT1/IKZF1 in plasma for screening and postoperative follow-up of CRC.METHODS The candidate studies were identified by searching the PubMed,Embase,Cochrane Library,CNKI,and Wanfang databases from May 31,2003 to June 1,2023.Sensitivity,specificity,and diagnostic accuracy were calculated by merging ratios or means.RESULTS Twelve eligible studies were included in the analysis,involving 6561 participants.The sensitivity of methylated BCAT1/IKZF1 in plasma for CRC diagnosis was 60%[95%confidence interval(CI)53-67]and specificity was 92%(95%CI:90-94).The positive and negative likelihood ratios were 8.0(95%CI:5.8-11.0)and 0.43(95%CI:0.36-0.52),respectively.Diagnostic odds ratio was 19(95%CI:11-30)and area under the curve was 0.88(95%CI:0.85-0.91).The sensitivity and specificity for CRC screening were 64%(95%CI:59-69)and 92%(95%CI:91-93),respectively.The sensitivity and specificity for recurrence detection during follow-up were 54%CONCLUSION The detection of methylated BCAT1/IKZF1 in plasma,as a non-invasive detection method of circulating tumor DNA,has potential CRC diagnosis,but the clinical application prospect needs to be further explored.

ANALYSIS OF BRANCHING DISTRIBUTION IN POLYETHYLENES BY DIFFERENTIAL SCANNING CALORIMETRY

Short chain branching has been characterized using thermal fractionation, a stepwise isothermal crystallizationtechnique, followed by a melting analysis scan using differential scanning calorimetry. Short chain branching distributionwas also characterized by a continuous slow cooling crystallization, followed by a melting analysis scan. Four differentpolyethylenes were studied: Ziegler-Natta gas phase, Ziegler-Natta solution, metallocene, constrained-geometry single sitecatalyzed polyethylenes. The branching distribution was calculated from a calibration of branch content with meltingtemperature. The lamellar thickness was calculated based on the thermodynamic melting temperature of each polyethyleneand the surface free energy of the crystal face. The branching distribution and lamellar thickness distribution were used tocalculate weight average branch content, mean lamellar thickness, and a branch dispersity index. The results for the branchcontent were in good agreement with the known comonomer content of the polyethylenes. A limitation was that high branchcontent polyethylenes did not reach their potential crystallization at ambient temperatures. Cooling to sub-ambient wasnecessary to equilibrate the crystallization, but melting temperature versus branch content was not applicable after cooling tobelow ambient because the calibration data were not performed in this way.

Structure influence of alkyl chains of thienothiophene-porphyrins on the performance of organic solar cells

Two new A-D-A porphyrin derivatives,denoted as XLP-I and XLP-II,were prepared through extending theπ-conjugation of thienothiophene-porphyrin center with phenylethynyl bridges and electron-deficient ethylrhodanine terminal units,and varying the structures of alkyl chain(linear vs branched)on peripheral thienothiophene substitutions of porphyrin rings.Both molecules show strong absorption in UV–visible–near-infrared region,good thermal stability,suitable energy levels,and ordered molecular packing in solid state.In organic solar cells,PC71BM was used as electron acceptor,and porphyrin small molecules were used as electron donors.The device based on XLP-I exhibits a power conversion efficiency(PCE)of 8.30%,an open circuit voltage(Voc)of 0.894 eV,and a fill factor(FF)of 62.1%.In contrast,the device based on XLP-II presents an inferior performance with a PCE of 3.14%,a Voc of 0.847 eV,and a FF of 49.3%.The better performance of XLP-I based device is mainly attributed to its optimized film morphology,excellent absorption,and well-balanced charge transport properties.

OPTICALLY ACTIVE AMINO ACIDS WITH HIGHLY BRANCHED SIDE CHAIN (I) SYNTHESIS OF D- AND L- 2-AMINO-5,5-DIMETHYLHEXANOIC ACID AND 2-AMINO-6,6-DIMETHYLHEPTANOIC ACID

The title compounds were prepared by the enzymatic resolution of the corresponding N-acetylated DL-amino acids methyl esters, which were obtained from t-butyl chloride via an 8-step synthesis.

Determining Role of the Branched-Chain Reaction Mechanism in Combustion, Explosion and Detonation of Gases

The role of branching-chain mechanism in gas phase combustion is considered. The results of experimental and theoretical investigations show that contrary the accepted for a long time views, branching-chain mechanism of the reaction, competition of chain branching and termination determine the origin and features of gas phase combustion of almost all compounds not only at pressures below atmospheric dozen times, but also at atmospheric and elevated pressures, in conditions of any self-heating. The latter becomes important in the course of developing chain combustion and enhances the chain avalanche. Kinetic methods for controlling combustion, explosion and detonation of gases have been developed by taking into account the decisive role of chain avalanche in these processes. The approach is based on purposeful variation of the rates of the competing reactions of chain branching and termination by means of special small additives. Suggested methods enable not only prevent combustion and explosion, but also adjust the intensity of the process, deflagration to detonation transition and destroy stationary detonation wave at a given distance from the place of its origin.

Preparation and Rheological Characterization of Long Chain Branching Polyglycolide

The long chain branching(LCB)polyglycolide(PGA)was successfully prepared by the successive reactions of the terminal hydroxyl groups of PGA with triglycidyl isocyanurate(TGIC)and pyromellitic dianhydride(PMDA).The influence of LCB produced by functional group reaction on rheological and crystallization behavior was studied and discussed through linear rheology,uniaxial elongation and DSC(differential scanning calorimetry).The much higher viscosity and the more notable strain hardening behavior of modified PGA indicates the LCB with high degree of entanglements are created.The melt strength of PGA is finally improved greatly and can make su re that the supercritical CO_(2)foaming can be carried out successfully.

Double Conditional Expectation

The concept of double conditional expectation is introduced. A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved. Finally we discuss the special cases and application for double conditional expectation. Key words double conditional expectation - covergence theorem - Jensen inequality - branching chain in random environment CLC number O 211.6 Foundation item: Supported by the National Science Foundation of China (10371092) and the Foundation of Wuhan UniversityBiography: HU Di-he (1935-), male, Professor, research direction: stochastic processes and random fractals.

Effect of Long Chain Branching on the Rheological Behavior,Crystallization and Mechanical Properties of Polypropylene Random Copolymer

Long chain branched polypropylene random copolymers （LCB-PPRs） were prepared via reactive extrusion with the addition of dicumyl peroxide （DCP） and various amounts of 1,6-hexanediol diacrylate （HDDA） into PPR. Fourier transform infrared spectrometer （FTIR） was applied to confirm the existence of branching and（ investigate the grafting degree for the modified PPRs. Melt flow index （MFI） and oscillatory shear rheological properties including complex viscosity, storage modulus, loss tangent and the Cole-Cole plots were studied to differentiate the LCB-PPRs from linear PPR. Differential scanning calorimetry （DSC） and polarized light microscopy （PLM） were used to study the melting and crystallization behavior and the spherulite morphology, respectively. Qualitative and quantitative analyses of rheological curves demonstrated the existence of LCB. The effect of the LCB on crystalline morphology, crystallization behavior and molecular mobility, and, thereby, the mechanical properties were studied and analyzed. Due to the entanglements between molecular chains and the nucleating effect of LCB, LCB-PPRs showed higher crystallization temperature and crystallinity, higher crystallization rate, more uniformly dispersed and much smaller crystallite compared with virgin PPR, thus giving rise to significantly improve impact strength. Moreover, the LCB-PPRs exhibited the improved yield strength. The mobility of the molecular chain segments, as demonstrated by dynamic mechanical analysis （DMA）, was improved for the modified PPRs, which also contributed to the improvement of their mechanical properties.

Protein tolerance to standard and high protein meals in patients with liver cirrhosis

To investigate the plasma amino acid response and tolerance to normal or high protein meals in patients with cirrhosis. METHODSThe plasma amino acid response to a 20 g mixed protein meal was compared in 8 biopsy-proven compensated cirrhotic patients and 6 healthy subjects. In addition the response to a high protein meal (1 g/kg body weight) was studied in 6 decompensated biopsy-proven cirrhotics in order to evaluate their protein tolerance and the likelihood of developing hepatic encephalopathy (HE) following a porto-caval shunt procedure. To test for covert HE, the “number connection test” (NCT) was done on all patients, and an electroencephalogram was recorded in patients considered to be at Child-Pugh C stage. RESULTSThe changes in plasma amino acids after a 20 g protein meal were similar in healthy subjects and in cirrhotics except for a significantly greater increase (P < 0.05) in isoleucine, leucine and tyrosine concentrations in the cirrhotics. The baseline branched chain amino acids/aromatic amino acids (BCAA/AAA) ratio was higher in the healthy persons and remained stable-but it decreased significantly after the meal in the cirrhotic group. After the high protein meal there was a marked increase in the levels of most amino acids, but only small changes occurred in the levels of taurine, citrulline, cysteine and histidine.The BCAA/AAA ratio was significantly higher 180 and 240 min after the meal. Slightly elevated basal plasma ammonia levels showed no particular pattern. Overt HE was not observed in any patients. CONCLUSIONPatients with stable liver disease tolerate natural mixed meals with a standard protein content. The response to a high protein meal in decompensated cirrhotics suggests accumulation of some amino acids but it did not precipitate HE. These results support current nutritional guidelines that recommend a protein intake of 1.2-1.5 g/kg body weight/day for patients with cirrhosis.

Serial therapies oriented by surgery for large primary liver carcinoma

Objective: To discuss the methods and effects of serial therapies oriented by surgery in the treatment of pri- mary large liver cancers. Methods: From January 1993 to June 1999, 191 pa- tients with large liver carcinoma were treated surgi- cally. The size of tumors varied from 5.2 to 19.7 cm (mean 9.4 cm). Several types of liver resections were made in 121 patients and as a supplement, cry- osurgery was carried out for the remaining 70 pa- tients. Importable drug delivery system was institu- ted intraoperatively. Transcatheter arterial chemo- embolization (THP 30-60 mg, E-ADM 20-40 mg, CDDP 40-80 mg, MMC 10-20 mg, iodin oil 5-30 ml), percutaneous ethanol injection, bioimmunother- apy and traditional Chinese medicine were used pre- and post-operatively. CT angiography and CT dur- ing arterial portography were used to find satellite nodules. Early stage recurrences were predicted by AFPmRNA in peripheral blood. Child-Pugh's classi- fication plus branch chain amino acid/aromatic ami- no acid ratio (BCAA/AAA) was adopted in evalua- ting pre-operative liver functions. Results: Marked results were observed after serial treatments oriented by surgery. The 1-, 3- and 5- year survival rates in resection group were 75.8 %, 45.6% and 30.4%. respectively. The 1- and 3-year survival rates in cryosurgery group were 63.2 % and 37.0 %. The operative mortality was 1.57 %. Recur- rence rates were 69.2 % in AFPmRNA positive group and 33.3% in AFPmRNA negative group (P< 0.05). The BCAA/AAA ratio was lower than 1.5 in two patients who died of hepatic failure after resec- tion. Conclusions: Serial treatments with surgery as the chief modality gives satisfactory results in patients with large primary liver carcinoma. This regimen should be regarded as a main strategy to deal with large liver carcinoma. AFPmRNA in the peripheral blood, signifying a recurrence, may become a new clinical parameter. The BCAA/AAA ratio plus Child-Pugh's classification is able to evaluate more accurately liver function reserve before surgery.

Impaired gluconeogenesis in a porcine model of paracetamol induced acute liver failure

AIM:To investigate glucose homeostasis and in particular gluconeogenesis in a large animal model of acute liver failure(ALF).METHODS:Six pigs with paracetamol induced ALF under general anaesthesia were studied over 25 h.Plasma samples were withdrawn every five hours from a central vein.Three animals were used as controls and were maintained under anaesthesia only.Using 1 H NMR spectroscopy we identified most gluconeogenic amino acids along with lactate and pyruvate in the animal plasma samples.RESULTS:No significant changes were observed in the concentrations of the amino acids studied in the animals maintained under anaesthesia only.If we look at the ALF animals,we observed a statistically significant rise of lactate(P<0.003)and pyruvate(P<0.018) at the end of the experiments.We also observed statistically significant rises in the concentrations of alanine(P<0.002),glycine(P<0.005),threonine(P< 0.048),tyrosine(P<0.000),phenylalanine(P<0.000) and isoleucine(P<0.01).Valine levels decreased significantly(P<0.05).CONCLUSION:Our pig model of ALF is characterized by an altered gluconeogenetic capacity,an impaired tricarboxylic acid(TCA)cycle and a glycolytic state.