Integrability and singularity structure of predator‐prey system

The ‘‘extended’’ ARS (Ablowitz, Ramani, and Segur) algorithm is introduced to characterize a dynamical system as Painlevé or otherwise; to that end, it is required that the formal series—the Laurent series, logarithmic, algebraic psi series about a movable singularity—are shown to converge in the deleted neighborhood of the singularity. The determinations thus obtained are compared with those following from the α method of Painlevé. An attempt is made to relate the structure of solutions about a movable singularity with that of first integrals (when they exist). All these ideas are illustrated by a comprehensive analysis of the general two‐dimensional predator‐prey system.

The Commercial Structure of Pedestrian Streets and Shopping Districts - Three Cases from Finland

Kävelykadut ovat tunnustettu tapa elävöittää keskusta-alueiden kauppaa. Aluksi moni kauppias epäilee kävelykadun tuomia muutoksia, mutta kokemus osoittaa, että kävelykadut ovat olleet menestyksekkäitä ja nostavat siellä olevien yritysten myyntiä. Jotkut yritykset eivät kuitenkin hyödy kävelykaduista, kun taas toiset hyötyvät paljon kun katu muuttuu kävelykaduksi. Tämä pro gradu -tutkielma tutkii kävelykatujen kaupallista rakennetta, jotta saataisiin selville minkätyyppiset yritykset löytyvät kävelykadulta. Tuloksia verrataan sen kaupallisen keskusvyöhykkeen kaupalliseen rakenteeseen missä kävelykatu sijaitsee. Näin saadaan selville erot kaupallisessa rakenteessa. Pro gradu tutkii myös miten tavallisia ketjuyritykset ovat kävelykaduilla ja kaupallisissa keskusvyöhykkeissä. Tutkimusaineisto koottiin kaupallisen inventoinnin avulla, joka suoritettiin kolmessa suomalaisessa kaupungissa: Tammisaaressa, Keravalla ja Porissa. Saatu aineisto luokiteltiin ja tulokset piirrettiin kartalle. Perustilastollisia menetelmiä käytettiin tulosten analysoimisessa. Tulokset eriteltiin kävelykadun, kauppakeskusten ja muiden paikkojen osalta ja luokiteltiin yleisluokkiin vähittäiskauppa, ravintola ja muu palvelu. Tulokset näyttävät, että on olemassa selkeitä eroja kun vertaa kävelykatuja ja kaupallisia keskusvyöhykkeitä. Kävelykaduilla on paljon enemmän vähittäiskauppoja, etenkin muotikauppoja, kuin muilla kaduilla. Kauppakeskuksilla on samantapainen kaupallinen rakenne kuin kävelykaduilla kun taas muilla kaduilla esiintyy vähemmän vähittäiskauppoja ja enemmän palveluyrityksiä. Ravintolat ovat melkein yhtä tavallisia koko kaupallisessa keskusvyöhykkeessä. Ketjuyritysten osalta tulokset ovat epäselviä. On olemassa osviittaa siitä, että ne ovat tavallisempia kävelykaduilla, etenkin suurissa kaupungeissa. Saatua tulosta ei ole kuitenkin tarpeeksi, jotta varmaa tietoa olisi saatu. Viimeisten 10–15 vuoden ajan Suomen kävelykadut ovat muuttuneet enemmän ravintolavaltaisiksi muiden palveluiden kustannuksella. Vähittäiskauppojen määrä on pysynyt vakaana. Suomalaiset kävelykadut eroavat kaupalliselta rakenteeltaan pohjoismaisista kävelykaduista, joilla on enemmän vähittäiskauppoja ja vähemmän palveluyrityksiä. Tapauskohtaisissa tuloksissa esiintyy paljon eroavaisuuksia. Paikalliset tekijät ovat usein voimakkaampia kuin yleiset teoriat kauppojen sijainnista kävelykaduilla. Yleisesti ottaen tulokset tukevat teoreettista viitekehystä. Tulokset antavat tarkempaa tietoa kävelykatujen ja kaupallisten keskusvyöhykkeiden kaupallisesta rakenteesta ja siitä, mitkä tekijät tähän vaikuttaa.

Molecular structure of electron donor-acceptor complexes of metallotetraphenylporphyrins with trinitrobenzene

The metallotetraphenylporphyrins, MTPPs, where M=Co(II), Cu(II) and Ag(II) form one to one molecular complexes in solution with 1,3,5-trinitrobenzene (TNB). The crystal structure of CoTPP.TNB.2CH3OH revealed that the mean separation between the porphyrin and TNB planes is 3·27 Å and the centre of the aryl ring of TNB is displaced by 0·90 Å from the centre of the porphyrin plane. Extended Huckel molecular orbital calculations suggest that acceptor orbitals are predominantly nitro-group based rather than an aryl π framework. The contribution of the metal orbitals in the donation is also seen as predicted by the structural data. Electrochemical redox measurements in solution provide evidence for charge-transfer stabilisation in these complexes.

Molecular structure of Lantadene-B&C, triterpenoids ofantana camara, red variety: Lantadene-B, 22β-angeloyloxy-3-oxoolean-12-en-28-oic acid; Lantadene-C, 22 β-(S)-2′-methyl butanoyloxy-3-oxoolean-12-en-28-oic acid

(I)Lantadene-B: C35H52O5,M r =552.80, MonoclinicC2,a=25.65(1),b=6.819(9),c=18.75(1) Å,beta=100.61(9),V=3223(5) Å3,Z=4,D x =1.14 g cm–3 CuKagr (lambda=1.5418A),mgr=5.5 cm–1,F(000)=1208,R=0.118,wR=0.132 for 1527 observed reflections withF o ge2sgr(F o ). (II)Lantadene-C: C35H54O5·CH3OH,Mr=586.85, Monoclinic,P21,a=9.822(3),b=10.909(3),c=16.120(8)Å,beta=99.82(4),V=1702(1)Å3,Z=2,D x =1.145 g cm–3, MoKagr (lambda=0.7107Å), mgr=0.708 cm–1 F(000)=644,R=0.098, wR=0.094 for 1073 observed reflections. The rings A, B, C, D, and E aretrans, trans, trans, cis fused and are in chair, chair, sofa, half-chair, chair conformations, respectively, in both the structures. In the unit cell the molecules are stabilized by O-HctdotO hydrogen bonds in both the structures, however an additional C-HctdotO interaction is observed in the case of Lantadene-C.

Organometallic chemistry of diphosphazanes *1: VIII. Synthesis, spectroscopic studies and crystal structure of fac-[Mo(CO)3(MeCN)Ph2PN(iPr)P(Ph)(DMP)], and its reactions with tertiary phosphines

The reaction of fac-[Mo(CO)3(MeCN)3] with the unsymmetrical diphosphazane Ph2PN(iPr)P(Ph)(DMP) (L) gives the complex fac-[Mo(CO)3(MeCN)(L)] (2) in almost quantitative yield. The structure of the complex has been determined by an X-ray diffraction study. The compound reacts with PR3 (where R = Ph, OPh) to give fac-[Mo(CO)3(PR3)(L)] (3a, 4a), which undergoes an intramolecular isomerization to afford mer-[Mo(CO)3(PR3)(L)] (3b, 4b). Synthesis of cis-[Mo(CO)4(L)] (1) and fac-[MO(CO)3L] (2a) and their spectroscopic data are also reported.

Potassamide induced in situ alkylation of 5,6-dihydroisoquinolines: Structure of products

Potassamide induced in situ alkylation of 1-alkyl- 4-cyano-3-methoxy-5,6-dihydroisoquinolines (2a & 2b) with alkyl iodides (CH3I, CH3CH2I & cyclohexyl iodide) gave the 5-alkyl- and 5,9-dialkyl-5,6-dihydroisoquinolines (4–ad & 3a–e), isoquinoline derivatives, (5a–b) and diastereomeric mixture of 4- alkyl-1,2,3,4-tetrahydroisoquinolin-3(2H)-ones (6a–e & 6′a–e). Structures were assigned on the basis of spectral data [Mass, 1H & 13C NMR, 2D NOESY & HC-COLOC]. Amide induced in situ alkylation of compounds 3a and 4a with CH3I gave in almost quantitative yield the dimethylated compounds 3d and 3a respectively. While KNH2/liq.NH3 methylation of 1,2- dihydroisoquinoline, 1 with CH3I gave the mixture of compounds, 6a & 6′a and the isoquinoline derivative 5a, NaH/benzene reaction of 1 with CH3I gave exclusively 5a. N-methylation of the mixture of compounds 6a & 6′a with NaH/CH3I gave the methylated derivatives, 7 & 8. A suitable mechanism has been proposed for the formation of products.

Reaction of spironaphthalenones with hydroxylamine: Part II. Structure of product in the reaction of 1′-substituted spironaphthalenone.

Reaction of 1′-aryl substituted spironaphthalenones 1a–d with hydroxylamine hydrochloride in ethanol gave substituted cinnamic ester derivatives 4a–d. Similarly, reaction of spironaphthalenone 1a with different alcohols gave the corresponding esters 4i–m. Reaction of unsymmetrical spironaphthalenones 1e–h with hydroxylamine hydrochloride in presence of ethanol gave the respective esters 4e–h. All the esters were characterised by their spectral data.

Stereochemical properties and x-ray structure of a water-soluble diastereomeric (arene)ruthenium(II) Schiff-base complex: [Ru(.eta.-MeC6H4Pri-p)(H2O)(L*)](ClO4), containing a weakly bound aqua ligand [HL* = (S)-(.alpha.-methylbenzyl)salicylaldimine]

An air-stable and water-soluble diastereomeric half-sandwich ruthenium(I1) complex, [Ru(s-MeCsH4Pr'-p)(H*O)-(L*)] (C104) (l), has been isolated and structurally characterized [HL* = (27)-(a methylbenzyl)salicylaldimine,2-HOC6H4CH-NCHMePhI. Complex 1, Czd-I3oNO&lRu, crystallizes in the noncentric triclinic space group P1 with a = 9.885(1) A, b = 10.185(1) A, c = 14.187(2) A, a = 110.32(1)', 6 = 102.17(1)', y = 102.41(1)O, V=1243( 1) A3, and 2 = 2. The X-ray structure shows the presence of two diastereomers in a 1:l ratio having RR,,,SCand SR,,,&c onfigurations. The Ru-OHz bond distances are considerably long, and the values for RR, - a~n d SRu-1isomers are 2.1 19(5) and 2.203(5) A, respectively. The aqua complex (1) exists as a single diastereomer in solution,and it forms stable adducts with P-, N-, and halide-donor ligands. The stereochemical changes associated with adduct-forming reactions follow an inversion order: PPhs >> P(OMe)3 > pyridine bases >> halides (I, Br, Cl) >H20.

Stereochemistry of 2'-5' linked nucleic acids: crystal and molecular structure of ammonium adenylyl-2',5'-adenosine tetrahydrate: a core fragment of 2'-5' oligo A's produced by interferon induced adenylate synthetase

The preponderance of 3'-5' phosphodiester links in nucleic acids is well known. Albeit less prevalent, the 2'-5' links are specifically utilised in the formation of 'lariat' in group II introns and in the msDNA-RNA junction in myxobacterium. As a sequel to our earlier study on cytidylyl-2',5'-adenosine we have now obtained the crystal structure of adenylyl-2',5'-adenosine (A2'p5'A) at atomic resolution. This dinucleoside monophosphate crystallizes in the orthorhombic space group P2(1)2(1)2(1) with a = 7.956(3) A, b = 12.212(3) A and c = 36.654(3) A. CuK alpha intensity data were collected on a diffractometer. The structure was sloved by direct methods and refined by full matrix least squares methods to R = 10.8%. The 2' terminal adenine is in the commonly observed anti (chi 2 = 161 degrees) conformation and the 5' terminal base has a syn (chi 1 = 55 degrees) conformation more often seen in purine nucleotides. A noteworthy feature of A2'p5'A is the intranucleotide hydrogen bond between N3 and O5' atoms of the 5' adenine base. The two furanose rings in A2'p5'A show different conformations - C2' endo, C3' endo puckering for the 5' and 2' ends respectively. In this structure too there is a stacking of the purine base on the ribose O4' just as in other 2'-5' dinucleoside structures, a feature characteristically seen in the left handed Z DNA. In having syn, anti conformation about the glycosyl bonds, C2' endo, C3' endo mixed sugar puckering and N3-O5' intramolecular hydrogen bond A2'p5'A resembles its 3'-5' analogue and several other 2'-5' dinucleoside monophosphate structures solved so far. Striking similarities between the 2'-5' dinucleoside monophosphate structures suggest that the conformation of the 5'-end nucleoside dictates the conformation of the 2' end nucleoside. Also, the 2'-5' dimers do not favour formation of miniature classical double helical structures like the 3'-5' dimers. It is conceivable, 2-5(A) could be using the stereochemical features of A2'p5'A which accounts for its higher activity.

Structure of a steriod fungal metabolite

3a,7a, 14a-Trihydroxypregn-16-en-20-one, C21H3204, M r = 348.48, orthorhombic, P212121, a = 9.211 (1), b = 13.201 (1), c = 16.031 (1),~, V = 1949.28 (29)/~3, Z = 4, Dx = 1.187 g cm -3, A(Cu Ka), = 1.5418 ,~,/z = 6.07 cm-l, F(000) = 760, T= 293 K, R = 0.061 for 1337 observations. The A, B and C rings adopt normal chair conformations with the D ring in a 14a-envelope conformation. The molecules are held together by two hydrogen bonds [0(3)..'0(20) = 2.879 and O(7).--O(14)= 2.612 A,].

Structure of pregna-4,16-diene-7[alpha],14[alpha]-diol-3,20-dione

7a,14a-Dihydroxypregna-4,16-diene-3,20- dione, C21H2804, M r = 344.45, orthorhombic, P212121, a = 7.136 (1), b = 12.342 (1), c = 20.049 (3)/k, V= 1765.7 (3)/k 3, Z = 4, Dx = 1.295 g cm -3, A(Cu Kte) = 1.5418/k, /z = 6.7 cm- a, F(000) = 744, T = 293 K, R = 0.048 for 1345 observations. The A ring may be described as in a l a,2flhalf- chair conformation or a l a-sofa conformation. The B and C rings adopt normal chair conformations and the D ring has a 14a-envelope conforma tion. The molecules are held together by a hydrogen bond [0(3)...0(7)= 2.767 A].

Structure of Sesbania Mosaic Virus at 4·7 Å Resolution and Partial Sequence of the Coat Protein

Sesbania mosaic virus (SMV) is a plant virus infecting Sesbania grandiflora plants in Andhra Pradesh, India. Amino acid sequence of the tryptic peptides of SMV coat protein were determined using a gas phase sequenator. These sequences showed identical amino acids at 69% of the positions when aligned with the corresponding residues of southern bean mosaic virus (SBMV).Crystals diffracting to better than 3 Å resolution were obtained by precipitating the virus with ammonium sulphate. The crystals belonged to rhombohedral space group R3 with α = 291·4 Å and α = 61·9°. Three-dimensional X-ray diffraction data on these crystals were collected to a resolution of 4·7 Å, using a Siemens-Nicolet area detector system. Self-rotation function studies revealed the icosahedral symmetry of the virus particles, as well as their precise orientation in the unit cell. Cross-rotation function and modelling studies with SBMV showed that it is a valid starting model for SMV structure determination. Low resolution phases computed using a polyalanine model of SBMV were subjected to refinement and extension by real-space electron density averaging and solvent flattening. The final electron density map revealed a polypeptide fold similar to SBMV. The single disulphide bridge of SBMV coat protein is retained in SMV. Four icosahedrally independent cation binding sites have been tentatively identified. Three of these sites, related by a quasi threefold axis, are also found in SBMV. The fourth site is situated on the quasi threefold axis. Aspartic acid residues, which replace Ile218 of SBMV from the quasi threefold-related subunits are suitable ligands to the cation at this site

Synthesis, spectral characterisation and single-crystal structure of a bicyclic tetraphosphapentazane tetraoxide, N5P4ET5O4(OC6H3Me2-2,6)2

Reaction of the bicyclic phosphazane N5P4Et5Cl2 with 2,6-dimethylphenol and subsequent oxidation of the product by aqueous hydrogen peroxide yields N5P4Et5O4(OC6H3Me2-2,6)2 in 85% yield. Its structure has been established by NMR spectroscopy and single-crystal X-ray diffraction. The compound crystallises in the monoclinic space group C2/c with a= 21.245(5), b= 10.879(2), c= 16.450(6)Å, ?= 123.94(2)°, Z= 4, R= 0.066. The structural features are compared with those of bicyclic ?5-phosphazenes of type N5P4R3(NR1R2)5(NHR3)(R1,R3= Me or Et, R2= H or Me). The observed conformation of the N3P3 rings in the present compound is mainly dictated by the maximisation of the stabilising influence of �negative hyperconjugative interactions� between the nitrogen lone pairs and the adjacent P�X ?* orbitals.

Analysis of the effects of amino-acid-sequence on the structure of proteins

The conformation of amino acid side chains as observed in well-determined structures of globular proteins has earlier been extensively investigated. In contrast, the structural features of the polypeptide backbone that result from the occurrence of specific amino acids along the polypeptide have not been analysed. In this article, we present the statistically significant features in the backbone geometry that appear to be a consequence of the occurrence of rotamers of different amino acid side chains by analysing 102 well-refined structures that form a random collection of proteins. It is found that the persistence of helical segments around each residue is influenced by the residue type. Several residues exert asymmetrical influence between the carboxyl and amino terminal polypeptide segments. The degree to which secondary structures depart from an average geometry also appears to depend on residue type. These departures are correlated to the corresponding Chou and Fasman parameters of amino acid residues. The frequency distribution of the side chain rotamers is influenced by polypeptide secondary structure. In turn, the rotamer conformation of side chain affects the extension of the secondary structure of the backbone. The strongest correlation is found between the occurrence of g+ conformation and helix propagation on the carboxyl side of many residues.