How Prime Numbers Are Interconnected and Built with Two Equations: Addition and Subtraction Rules the Function (6µ)

Are all prime numbers linked by four simple functions? Can we predict when a prime will appear in a sequence of primes? If we classify primes into two groups, Group 1 for all primes that appear before ζ (such that , for instance 5, ), an even number divisible by 3 and 2, and Group 2 for all primes that are after ζ (such that , for instance 7), then we find a simple function: for each prime in each group, , where n is any natural number. If we start a sequence of primes with 5 for Group 1 and 7 for Group 2, we can attribute a μ value for each prime. The μ value can be attributed to every prime greater than 7. Thus for Group 1, and . Using this formula, all the primes appear for , where μ is any natural number.

The 20 April 2013 Lushan, Sichuan, mainshock, and its aftershock sequence: tectonic implications

Using the double-difference relocation algo- rithm, we relocated the 20 April 2013 Lushan, Sichuan, earthquake （Ms 7.0）, and its 4,567 aftershocks recorded during the period between 20 April and May 3, 2013. Our results showed that most aftershocks are relocated between 10 and 20 km depths, but some large aftershocks were relocated around 30 krn depth and small events extended upward near the surface. Vertical cross sections illustrate a shovel-shaped fault plane with a variable dip angle from the southwest to northeast along the fault. Furthermore, the dip angle of the fault plane is smaller around the mainshock than that in the surrounding areas along the fault. These results suggest that it may be easy to generate the strong earthquake in the place having a small dip angle of the fault, which is somewhat similar to the genesis of the 2008 Wenchuan earthquake. The Lushan mainshock is underlain by the seismically anomalous layers with low-Vp, low-Vs, and high-Poisson＇s ratio anomalies, possibly suggesting that the fluid-filled fractured rock matrices might signifi- cantly reduce the effective normal stress on the fault plane to bring the brittle failure. The seismic gap between Lushan and Wenchuan aftershocks is suspected to be vulnerable to future seismic risks at greater depths, if any.

EFFECT OF SEQUENCE STRUCTURE ON THE THERMOTROPIC LIQUID CRYSTALLINE PROPERTIES OF POLYESTERAMIDES BASED ON DIMETHYLBENZIDINE, BISPHENOL-A AND ρ-TEREPHTHALYL CHLORIDE

A series of thermotropic liquid crystalline polyesteramides with differ-ent sequence structure based on dimethylbenzidine (DMBD), bisphenol-A(BPA) and p-terephthalyl chloride (TPC) was synthesized by changing the feeding order of monomers inlow temperature solution polycondensation system. By means of NMR and a computer pro-gram the sequence structure parameters were measured. The effect of sequence structureon liquid crystalline phase transition temperature of PEAs obtained was investigated.

STUDY ON THE SEQUENCE STRUCTURE OF BUTADIENE-STYRENE RUBBER BY ^(13)C-NMR METHOD Ⅲ. QUANTITATIVE CHARACTERIZATION OF SEQUENCE STRUCTURE

The quantitative description of the sequence structure of emulsion-processed SBR and solution-processed SBR (by lithium catalyst)was carried out based on their spectral data Of ^(13)C-NMR.The calculating formulae which could be used to obtain diad concentration from the peak intensifies of carbon spectra, average block length, average number of block, and the microstructure composition of the molecular chain were derived. The quantitative result showed that on the molecular chain styrene unit had the tendency to attach to trans-1,4 butadiene unit. The calculated result of the microstructure was in good agreement with that obtained through IR measurement.

STUDY ON THE SEQUENCE STRUCTURE OF BUTADIENE-STYRENE RUBBER BY ^(13)C-NMR METHOD V.CALCULATION METHOD OF DIAD COMPOSITION

The calculating equations which could be used to obtain diad composition from the peakintensities of carbon spectra were derived. The result of the microstructure calculated from thediad compositions was in good agreement with that obtained through IR or;H-NMR measurement.

STUDIES ON THE SEQUENCE STRUCTURE OF TPA/EG/PHB LIQUID CRYSTALLINE COPOLYESTERS

In this paper, the sequence structure of TPA/EG/PHB liquid crystalline copolyesters made from different synthetic methods has been studied by;H-NMR with the help of computer program of processing peaks. The results showed that the ether bonds were not observed in TPA./EG/PHB copolyesters and the synthetic process had a great effect on their sequence structure. Under certain conditions, the high,random TPA/EG/PHB copolyesters which were considered to have higher performances than PET/xPHB could be obtained.

Sequence Structure and Characteristics of Exon 1 of Mink MLPH Gene

[ Objective] To clone exon 1 and its flanking sequences of MLPH gene from minks raised in western Liaoning region and to predict its structure. The study will provide a theoretical basis for breeding of colored mink. [Method] The exon 1 and its 5＇-flanking sequences of MLPHgene were amplified from minks. SignalP 3.0 Server, ClustalX 1.83, Mega 4.1, TMHM 2.0, ProtComp v6.0 and other software were used for sequence analysis. [ Result] A 1 029-bp fragment was amplified with the expected size. As calculated with the Mega 4.1, the minks had the nearest genetic distance with rattus （0.540 5） and the farthest with human （0.655 2）. Phylogenetic tree of mink was constructed. [ Conclusion] The mink MLPH gene encodes a secretory protein.

SUBSTITUENT CHEMICAL SHIFT (SCS) AND THE SEQUENCE STRUCTURE OF ETHYLENE-VINYL ALCOHOL COPOLYMERS

Three ethylene-vinyl alcohol copolymers were studied by means of the substituent chemical shift (SCS) method. The SCS parameters of hydroxy (-OH) in two different solvents were obtained: in deuterium oxide/phenol (20/80 W/W ) the parameters are S_1 = 42.77±0.08ppm, S_2 = 7.15±0.06 ppm, S_3 (s)= -4.08±0.02ppm, S_3 (t) =-3.09±0.20ppm,S_4 = 0.48±0.03ppm, S_5 = 0.26±0.05ppm. In o-dichloro-benzen-d_4 S_1(s)=44.79±0.61ppm, S_2=7.40±0.00ppm, S_3(s)=-4.51±0.17ppm, S_3(t)=-3.13 ±0.00 ppm, S_4 =0.63±0.04ppm, S_5=0.36±0.00ppm.Simultaneously the ^(13)CNMR spectra of EVA copolymers were assigned by using the SCS parameters obtained.

Isolation and Identification of Staphylococcus chromogenes and 3 D Structural Analysis of the katA Gene

[Objective]Staphylococcus arthritis became an increasingly significant health problem in intensive chicken farming in China.[Method]In this study,a bacteria strain was isolated from the broiler chicken suffering from arthritis and named as the strain Gg1.[Result]It was then identified as Staphylococcus chromogenes by the biochemical tests and phylogenetic tree analysis based on 16S rDNA sequence.Furthermore,the catalase（katA）gene was amplified by PCR using the designed primers,and the expected fragment was 1 232 bp long encoding a protein of 410 amino acids that shares the conserved motifs including catalase,heme-binding ligand and active center motif.Six phosphorylation sites（Ser95,Thr96,Ser241,Ser242,Thr281,Ser338）,four conserved residues（Ser95,His216,Tyr281,Asp341）and two active sites（His56,Asn129）were demonstrated by multiple sequence alignment and homology comparisons.The homology modeling of 3D structure of katA protein was done by SWISSMODEL server based on the template retrieved from the catalase（PDB：2ISA_A）of Vibrio salmonicida.The katA protein represents a four-domain globular protein,the quality and reliability of the resulting protein structure was further verified by Ramachandran plot.[Conclusion]To our knowledge,this is the first report of S.chromogenes linked to arthritis in chicken and the bioinformatic characterization of its katA gene.

Genetic Diversity and Population Structure in Landraces and Improved Rice Varieties from India

A set of 50 rice genotypes comprising landraces, local selections, and improved varieties were characterized using simple sequence repeat（SSR） and inter simple sequence repeat（ISSR） markers to study genetic diversity and population structure. Following unweighted pair group method with arithmetic mean based clustering using binary data of polymorphic markers, the genotypes were grouped into 5 clusters and 11 sub-clusters, whereas population structure analysis separated 50 rice genotypes into 5 sub-populations. Grouping of rice genotypes showed better resemblance with the pedigree information of the genotypes. Both genetic diversity and population structure analysis separated majority of the improved varieties from landraces and local selections. Some of the SSR markers amplified unique alleles which were specific to a particular genotype and could distinguish them from the rest. The results indicate that these rice genotypes exhibit a higher genetic diversity and can be very useful in rice improvement program.

Informative ISSR Markers Help Identify Genetically Distinct Accessions of Oryza rufipogon in Yield Improvement

Inter simple sequence repeat（ISSR） polymorphism was used to determine genetic diversity and phylogenetic relationships in 90 genotypes of wild and cultivated species of Oryza from different geographical regions of the world. In all the 17 primers used in ISSR-PCR, a total of 11 464 bands were amplified at 253 band positions/loci. The primer UBC-809 amplified the maximum bands（1 059） at 21 band positions. UBC-810 and UBC-835 amplified the minimum of 391 bands each at 7 and 14 band positions, respectively. The mean polymorphism information content ranged from 0.44 to 0.84 and resolving power ranged from 8.69 to 23.53. Un-weighted pair group method with arithmetic mean dendrogram and population structure based on the 17 primers separated all genotypes into 4 major clusters with a genetic similarity of 53%–100%. The first two clusters consisted of 30 O. rufipogon accessions each. In the third cluster, O. nivara and O. longistaminata grouped as one sub-cluster and all other O. nivara accessions and cultivars grouped as another sub-cluster. The fourth cluster had only five O. rufipogon accessions which can be a source of new genes. Four sub-populations were identified within O. rufipogon and two sub-populations within O. nivara at K = 7. A subset of six primers with high resolving power values were the most informative and grouped all genotypes almost similarly as the 17 primers did. Use of these six highly informative primers in ISSR-PCR is a cost effective and robust method for assessing genetic diversity in large germplasm collections of wild rice species.

Knowledge-based potentials in bioinformatics: From a physicist's viewpoint

Biological raw data are growing exponentially, providing a large amount of information on what life is. It is believed that potential functions and the rules governing protein behaviors can be revealed from analysis on known native structures of proteins. Many knowledge-based potentials for proteins have been proposed. Contrary to most existing review articles which mainly describe technical details and applications of various potential models, the main foci for the discussion here are ideas and concepts involving the construction of potentials, including the relation between free energy and energy, the additivity of potentials of mean force and some key issues in potential construction. Sequence analysis is briefly viewed from an energetic viewpoint.

Synthesis and Structure of Butylene Terephthalate-ε-Caprolactone Copolyesters

A series of butylene terephthalate-E-caprolactone copolyesters (BCL) with different hard segment content were successfully synthesized and characterized by 1H-NMR. DSC. PLM and U viscometer, The sequence structure and crystallization characteristics of BCL copolyesters were carefully investigated.

Monte Carlo simulation of sequential structure control of AN-MA-IA aqueous copolymerization by different operation modes

The regulation of polyacrylonitrile(PAN)copolymer composition and sequence structure is the precondition for producing high-quality carbon fiber high quality.In this work,the sequential structure control of acrylonitrile(AN),methyl acrylate(MA)and itaconic acid(IA)aqueous copolymerization was investigated by Monte Carlo(MC)simulation.The parameters used in Monte Carlo were optimized via machine learning(ML)and genetic algorithms(GA)using the experimental data from batch copolymerization.The results reveal that it is difficult to control the aqueous copolymerization to obtain PAN copolymer with uniform sequence structure by batch polymerization with one-time feeding.By contrary,it is found that the PAN copolymer with uniform composition and sequence structure can be obtained by adjusting IA feeding quantity in each reactor of a train of five CSTRs.Hopefully,the results obtained in this work can provide valuable information for the understanding and optimization of AN copolymerization process to obtain high-quality PAN copolymer precursor.

Precise Synthesis of Acrylate Copolymer via RAFT Polymerization and Its Application

A series of different sequence structure containing stearyl acrylate (SA) and hydroxyethyl acrylate (HEA) copolymer were synthesized via reversible addition-fragmentation chain transfer (RAFT) polymerization. The crystallization property of PHEA-b-PSA, PHEA-b-PSA-b-PHEA, PSA-b-PHEA-b-PSA, PHEA-co-PSA, and PHEA-grad-b-PSA were characterized by Differential Scanning Calorimetry (DSC). The condensed structure of different sequence copolymers were investigated using small-angle X-ray scattering (SAXS). A series of copolymers with different sequence structure were coated on the surface of polyester fabric, which can be found that PHEA-b-PSA-b-PHEA block copolymer has good water repellency.

PERVAPORATION FOR SEPARATING BENZENE/CYCLOHEXANE MIXTURE BY P(AA-MA) COPOLYMER MEMBRANES

P（AA-MA） copolymers composed of acrylic acid and methyl acrylate with different molecular weights and sequence structures were synthesized by combination of ATRP and selective hydrolysis. These copolymers were used as membrane materials to separate benzene/cyclohexane mixture by pervaporation. The effects of molecular weight and sequence structure of the copolymers on the pervaporation performance were investigated in detail. For the random copolymers, the permeate flux decreased rapidly with the increasing of molecular weight. The separation factor was also influenced by the molecular weight, which was changed from no selectivity to cyclohexane selectivity with increasing the molecular weight. Contrarily, the block copolymer membrane showed good benzene selectivity with separation factor of 4.3 and permeate flux of 157 g/（m2h） to 50 wt% benzene/cyclohexane mixture.