An Explicit Difference Scheme with High Accuracy and Branching Stability for Solving Parabolic Partial Differential Equation

This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.

A High-order Accuracy Explicit Difference Scheme with Branching Stability for Solving Higher-dimensional Heat-conduction Equation

A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncation error is O（△t^2 ＋ △x^4）.

Engineering high amylose and resistant starch in maize by CRISPR/Cas9-mediated editing of starch branching enzymes

To improve the amylose content(AC)and resistant starch content(RSC)of maize kernel starch,we employed the CRISPR/Cas9 system to create mutants of starch branching enzyme I(SBEI)and starch branching enzyme IIb(SBEIIb).A frameshift mutation in SBEI(E1,a nucleotide insertion in exon 6)led to plants with higher RSC(1.07%),lower hundred-kernel weight(HKW,24.71±0.14 g),and lower plant height(PH,218.50±9.42 cm)compared to the wild type(WT).Like the WT,E1 kernel starch had irregular,polygonal shapes with sharp edges.A frameshift mutation in SBEIIb(E2,a four-nucleotide deletion in exon 8)led to higher AC(53.48%)and higher RSC(26.93%)than that for the WT.E2 kernel starch was significantly different from the WT regarding granule morphology,chain length distribution pattern,X-ray diffraction pattern,and thermal characteristics;the starch granules were more irregular in shape and comprised typical B-type crystals.Mutating SBEI and SBEIIb(E12)had a synergistic effect on RSC,HKW,PH,starch properties,and starch biosynthesis-associated gene expression.SBEIIa,SS1,SSIIa,SSIIIa,and SSIIIb were upregulated in E12 endosperm compared to WT endosperm.This study lays the foundation for rapidly improving the starch properties of elite maize lines.

ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK

Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈R^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Z_(n).In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∞.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

A FAMILY OF HIGH-ORDER ACCURACY EXPLICIT DIFFERENCE SCHEMES WITH BRANCHING STABILITY FOR SOLVING 3-D PARABOLIC PARTIAL DIFFERENTIAL EQUATION

A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).

Branching and growth of plantings in fifth year of a seedling seed orchard of Masson pine (Pinus massoniana Lamb.)

The features of branching and growth studied included height, diameter at breast height (DBH), total number of branches, annual height growth, annual branch elongation in the year of elongating, annual branch number for four consecutive years, diameter of branches of different ages, and diameter of stem where branch-whorl originates. For features of total growth and overall branching, no significant differences were found between families, except for DBH. For annual features, no significant differences were found in annual stem height growth, annual branch elongation in the year of elongation and diameter of branches. In the last four years, differences in number of branches were not significant in the first two years but were significant in the last two year; differences in stem diameter where branch-whorls grow were significant for the four consecutive years. Trend of annual growth and branching features of families can be divided into three types as increasing type, stable type and fluctuating type. Most of families have an increasing type with respect of annual height growth and annual branch elongation, while most families belong to a fluctuating type with annual branch number. The results indicated that in the fifth year after planted in seedling seed orchard, differences between families were mostly insignificant. This result may have two main explanations: one is the growth rhyme in early ages of Masson pine, the other one is the complex paternal components to form the open-pollinated families. Family selection seemed to be not useful based on the result. It is suggested to select some of families in the nursery instead of to use all the families when establishing seedling seed orchards with open-pollinated families from plus-trees.

Cloning and Expression of the Promoter of Maize Starch-Branching Enzyme sbeⅡb Gene

[Objective] The aim was to construct promoter of maize starch-branching enzyme sbe Ⅱb gene specifically expressed in seed.[Method] The promoter sequence of maize starch-branching enzyme sbe Ⅱb gene was amplified by LA-PCR and then cloned into pMD18-T vector.Subsequently,the promoter was cloned into pBI121 vector to construct plant expression vector pBI121-sbe Ⅱb.Recombinant plasmid pSBE-GUS was constructed by connecting GUS gene into pBI121-sbe Ⅱb and transformed into tobacco mediated by Agrobacterium tumefaciens,before detection by PCR and Southern blot.The biochemical analysis and fluorescence detection of GUS activity were performed in different parts of the tobacco by Gene Gun Method and Agrobacterium tumefaciens transformation respectively.[Result] The homology between promoter sequence cloned in this experiment and the corresponding sequence announced in the GenBank reached 98.52%.Four transformed tobaccos were obtained by PCR and Southern blot after co-culture and selective culture.A small number of blue spots appeared in leaves,and the spots could barely been seen in the stems and roots,while a large number of blue spots were found in seeds.So,it could be concluded that the promoter of sbeⅡb gene was specifically expressed in seeds.[Conclusion] Promoter of maize starch branching enzyme sbe Ⅱb specifically expressed in seeds was successfully cloned.

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.

Analysis of the Flow Rate Characteristics of Valveless Piezoelectric Pump with Fractal-like Y-shape Branching Tubes

Microchannel heat sink with high heat transfer coefficients has been extensively investigated due to its wide application prospective in electronic cooling. However, this cooling system requires a separate pump to drive the fluid transfer, which is uneasy to minimize and reduces their reliability and applicability of the whole system. In order to avoid these problems, valveless piezoelectric pump with fractal-like Y-shape branching tubes is proposed. Fractal-like Y-shape branching tube used in microchannel heat sinks is exploited as no-moving-part valve of the valveless piezoelectric pump. In order to obtain flow characteristics of the pump, the relationship between tube structure and flow rate of the pump is studied. Specifically, the flow resistances of fractal-like Y-shape branching tubes and flow rate of the pump are analyzed by using fractal theory. Then, finite element software is employed to simulate the flow field of the tube, and the relationships between pressure drop and flow rate along merging and dividing flows are obtained. Finally, valveless piezoelectric pumps with fractal-like Y-shape branching tubes with different fractal dimensions of diameter distribution are fabricated, and flow rate experiment is conducted. The experimental results show that the flow rate of the pump increases with the rise of fractal dimension of the tube diameter. When fractal dimension is 3, the maximum flow rate of the valveless pump is 29.16 mL/min under 100 V peak to peak （13 Hz） power supply, which reveals the relationship between flow rate and fractal dimensions of tube diameter distribution. This paper investigates the flow characteristics of valveless piezoelectric pump with fractal-like Y-shape branching tubes, which provides certain references for valveless piezoelectric pump with fractal-like Y-shape branching tubes in application on electronic chip cooling.

ASYMPTOTIC PROPERTIES OF A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.

CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.

Characterization and Expression Analysis of Starch Branching Enzymes in Sweet Potato

Spatial and temporal expression patterns of Sbel and Sbe2 that encode starch branching enzyme （SBE） Ⅰ and Ⅱ, respectively, in sweet potato （Ipomoea batatas L.） were analyzed. Expression of both genes in Escherichia coli indicate that both genes encoded active SBE. Analysis with real-time quantitative polymerase chain reaction technique indicates that IbSbel mRNA was expressed at very low levels in leaves but was the predominant isoform in tuberous root while the reverse case was found for lbSbe2. The expression pattern of IbSbel, closely resembles that of AGPase S, a gene coding for one of the subunits ofADP-glucose pyrophosphorylase, which is the key regulatory enzyme in the starch biosynthetic pathway. Western analysis detected at least two isoforms of SBE I in tuberous roots, those two isoforms showed adverse expression patterns with the development of the tuberous roots. Expression of the two IbSbe genes exhibited a diurnal rhythm during a 12-h cycle when fed a continuous solution of sucrose. Abscisic acid （ABA） was aother potent inducer of IbSbe expression, but bypassed the semidian oscillator.

Photodissociation of HOD via the C1B1 State： OD/OH Branching Ratio and OD Bond Dissociation Energy

Photodissociation of jet-cooled HOD via the C state around 124 nm has been studied using the H（D）-atom Rydberg tagging time-of-flight technique. Rotational state resolved action spectrum and the product translational energy distribution spectra have been recorded for both D＋OH and H＋OD dissociation channels. Product channel OH/OD branching ratios for the individual C-X rotational transition have been determined. A comparison is also given with the B-X and A-X transitions. In addition, the dissociation energy of the OD bond in HOD has been determined accurately to be 41751.3±5 cm-1.

Dendritic branching patterns in platforms of complex Ni-based single crystal castings

Dendritic branching patterns at variable cross-sections in Ni-based single crystal(SX) castings of different generations were investigated using optical microscope(OM), electro probe microanalyzer(EPMA),differential scanning calorimeter(DSC), Thermo-Cal software and Pro-CAST software. Results show that the dendritic branching patterns are similar in outward platform in SXs of different generations. That is, the primary dendrites(PDs) are introduced into the platform by developing a series of secondary dendrites(SDs) to occupy the bottom of the platform, and the ternary dendrites(TDs) originating from these SDs grow upward to fill up the platform. With the SX generation increasing, the undercooling of melts in the inward platform increases significantly due to the increasing alloying elements and the segregation in the directional solidification(DS)process, and the growth velocity of the dendrite tip increases according to the dynamic model of dendrite growth,which is beneficial for the high-order dendrite development. The stronger dendritic branching ability is shown in the inward platform of the higher generation Ni-based SX.

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.

Branching ratios of autoionization from Eu 4f^76p_(1/2)6d [J] autoionizing states

The autoionization branching ratios from Eu 4f76p1/26 d [J] autoionizing states to its 4f76s+(9So), 4f76s+(7So), and4f75d+(9Do) final ionic states are investigated with the combination of the three-step laser excitation and the velocity-map imaging technique. These different autoionizing states are excited via 4f76s6d8 DJ [J = 5/2, 7/2, and 9/2] intermediate states, respectively. The experimental photoelectron images are obtained, from which energy distributions of ejected electrons are achieved with the mathematical transformation. Furthermore, the energy dependence of the branching ratio is investigated within the autoionization resonance, by which population inversion is observed as an important characteristic.The J-dependence is also studied systematically. The validity of the well-known isolated core excitation technique used for obtaining the autoionization spectrum is also studied.

Crack branching mechanism of rock-like quasi-brittle materials under dynamic stress

The cracking patterns of a thin sheet with a pre-existing crack subjected to dynamic loading are numerically simulated to investigate the mechanism of crack branching by using the FEM method.Six numerical models were set up to study the effects of load,tensile strength and heterogeneity on crack branching.The crack propagation is affected by the applied loads,tensile strength and heterogeneity.Before crack branching,the crack propagates by some distance along the direction of the pre-existing crack.For the materials with low heterogeneity,the higher the applied stress level is and the lower the tensile strength of the material is,the shorter the propagation distance is.Moreover,the branching angle becomes larger and the number of branching cracks increases.In the case of the materials with high heterogeneity,a lot of disordered voids and microcracks randomly occur along the main crack,so the former law is not obvious.The numerical results not only are in good agreement with the experimental observations in laboratory,but also can be extended to heterogeneity media.The work can provide a good approach to model the cracking and fracturing of heterogeneous quasi-brittle materials,such as rock,under dynamic loading.

Isolation and Functional Analysis of the Regulation of Branching by Isopentenyl Transferase Gene CmIPT1 in <i>Chrysanthemum morifolium </i>cv. ‘Jinba’

Today’s chrysanthemums are highly evolved flowering plants and they are considered as one of the most important ornamental cut flowers. In this research an isopentenyl transferase gene named CmIPT1 was isolated from Chrysanthemum morifolium cv. ‘Jinba’ using RACE and RT-PCR methods. The full cDNA sequence of CmIPT1 was 873 bp which encoded a deduced protein of 290 amino acids. It contained GxxGxGKS which is a conserved sequence of the typical domain of IPT family. The phylogenetic tree analysis of CmIPT1 in Chrysanthemum morifolium cv. ‘Jinba’ shows that it has the closest relationship with CcIPT1 in Cynara cardunculus var. scolymus. Expression of CmIPT1 was higher in stems and apex, whereas it was lower in leaves and roots. And the overexpression of CmIPT1 obviously increased the number of rosette branches in Arabidopsis. Here, in our study, we showed that CmIPT1 is a positive regulator of branch development in Chrysanthemum and may play a key role in regulating lateral branch formation of Chrysanthemum plants.

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.

Numerical prediction of fiber motion in a branching channel flow of fiber suspensions

Fiber orientation and dispersion in the dilute fiber suspension that flows through a T-shaped branching channel are simulated numerically based on the slender-body theory. The simulated results are consistent qualitatively with the experimental data available in the literature. The results show that the spatial distribution of fibers is dependent on the fiber aspect ratio, but has no relation with the volume fraction of fiber. The content ratio of fibers near the upper wall increases monotonically with an increasing Re number, and the situation is reverse for the region near the bottom wall. The orientation of fibers depends on Re number, however, the function of fiber volume fraction and aspect ratio is negligible. The fibers near the wall and in the central region of the channel align along the flow direction at all times, but the fibers in the other parts of the channel tend to align along the flow direction only in the downstream region.