Approximate solutions for the structure of shock waves

Approximate solutions of the B-G-K model equation are obtained for the structure of a plane shock, using various moment methods and a least squares technique. Comparison with available exact solution shows that while none of the methods is uniformly satisfactory, some of them can provide accurate values for the density slope shock thickness delta n . A detailed error analysis provides explanations for this result. An asymptotic analysis of delta n for largeMach numbers shows that it scales with theMaxwell mean free path on the hot side of the shock, and that their ratio is relatively insensitive to the viscosity law for the gas.

Suomenlinnan Kustaanmiekan ketokasvillisuus ja siihen vaikuttavat tekijät

Suomenlinna on yksi Helsingin suosituimmista matkailu- ja kulttuurinähtävyyksistä. Kustaanmiekan, samoin kuin koko Suomenlinnan luonto on muodostunut perinteisestä suomalaisesta saaristoluonnosta ja vuosisatojen saatossa paikalle tulleista linnoituksien kasvistosta. Saaren vaihtelevien elinympäristöjen johdosta alueen kasvillisuus on hyvin rikasta. Linnoituksien monet kasvilajit ovat tulleet tulokaskasveina eri puolilta Eurooppaa sekä Venäjältä. Suurin osa Suomenlinnan alueesta on kallioketoa ja tämän lisäksi myös valliketoa, joista molemmat kuuluvat suojeltaviin alueisiin. Kustaanmiekan niityillä kasvaa keto- ja paahdelajeja, kuten harvinaista ketonoidanlukkoa (Botrychium lunaria L.) sekä ketoneilikkaa (Dianthus deltoides L.). Tämän tutkimuksen ensisijaisena tarkoituksena oli kartoittaa Kustaanmiekan alueen kesäkauden 2009 ketokasvilajisto ja eri putkilokasvilajien runsaus. Tutkimuksessa selvitettiin myös maaperätekijöiden ja alueen hoitohistorian mahdollista vaikutusta ketokasvilajistoon. Tutkimuksessa kartoitettiin kymmenen eri kedon kasvillisuus Suomenlinnan Kustaanmiekan linnoitusalueella. Kedot sijaitsivat eri puolilla Kustaanmiekkaa, sellaisilla paikoilla, missä ketokasvillisuus oli runsainta. Maastotyöt suoritettiin kesä- ja heinäkuussa laskemalla jokaisen kedon ruutujen putkilokasvien peittävyydet sekä listaamalla ylös myös ruutujen ulkopuoliset kevät- ja loppukesän kukkijat touko- ja elokuussa. Maaperän ominaisuuksien määrittämiseksi otettiin kultakin kedolta pintamaanäytteet elokuussa. Muita tutkittuja muuttujia olivat maapinnan kaltevuus sekä sammalen, karikkeen, paljaan maan, kenttäkasvillisuuden pohjakerros ja kallion osuus tutkimusruuduilla. Ketojen kasvillisuuden keskimääräinen korkeus mitattiin kesä- ja heinäkuussa. Kasvistossa oli selviä eroavaisuuksia ketojen välillä. Kasvilajien määrä vaihteli ketojen kokonaislajimäärän ollessa 40-60 kasvilajia. Yhteensä kedoilta löytyi 120 eri putkilokasvilajia, joista useimmat kukkivat sekä kesä- että heinäkuussa. Ketojen kasvilajimäärä vaihteli yhdellä neliömetrillä 6,3-13,6 kasvilajiin, minkä lisäksi Shannon-Wienerin diversiteetti-indeksi vaihteli 1,4-2,3 arvon välillä. Yleisimpiä lajeja, joita kedoilla tavattiin, olivat muun muassa siankärsämö (Achillea millefolium L.), koiranheinä (Dactylis glomerata L.), juolavehnä (Elymus repens L.) ja hopeahanhikki (Potentilla argentea L.). Alueella kasvoi myös muutamia sotatulokaslajeja kuten harmiota (Berteroa incana L.), ukonpalkoa (Bunias orientalis L.) ja karvahorsmaa (Epilobium hirsutum L.). Maaperätekijöillä, kuten suurella fosforin pitoisuudella ei ollut vaikutusta kasvilajien määrään kedoilla. Vain maan pH ja johtoluku korreloivat positiivisesti ketojen kasvillisuuden korkeuden kanssa. Vaikka tulosten perusteella ketojen hoidolla ei ollut vaikutusta ketojen kasvillisuuden määrään, voidaan kuitenkin olettaa oikeanlaisen hoidon parantavan tyypillisten ketokasvien kilpailukykyä muita niittykasveja kohtaan.

Flow of non-newtonian fluid between torsionally oscillating discs

The flow of an incompressible non-Newtonian viscous fluid contained between two torsionally oscillating infinite parallel discs is investigated. The two specific cases studied are (i) one disc only oscillates while the other is at rest and (ii) both discs oscillate with the same frequency and amplitude but in opposite directions. Assuming that the amplitude of oscillation,Ω/n, is small and neglecting the squares and higher powers ofΩ/n, the equations of motion have been solved exactly for velocity and pressure satisfying all the boundary conditions. The effect of both positive and negative coefficients of cross-viscosity on the steady components of the flow has been represented graphically.

Crystal And Molecular-Structure Of 8-Acetoxy-6-(2,4-Dimethoxy-5-Bromophenyl)-3-Methyl-Tricyclo[5,2,1,03,8 ]Decan-2-One

The crystal and molecular structure has been determined by the heavy-atom method and refined by the least-squares procedure to R= 8"3 % for 2033 photographically observed reflexions. The compound crystallizes in the space group P]" with two molecules in a unit cell of dimensions a = 11"68 + 0-02, b = 12"91 +0"02, c= 10"43+0"02/~, e= 114"7+ 1, fl=90-2+ 1 and 7,= 118.3+ 1 °. The unit cell also contains one molecule of the solvent, benzene. The 'cage' part of the molecule exhibits a large number of elongated bonds and strained internal valency angles. The bridgehead angle in the bicyclic heptane ring system is 89 °. The acetate group at C(16) and the methyl group at C(15) are cis to each other.

Crystal And Molecular Structure Of A Dimethyl Sulphoxide Complex With Lanthanum Nitrate, La(No3)34.(Ch3)2so

The crystal structure of the complex La(NO3)3.4(CH3)2SO has been solved by the heavy-atom method. The complex crystallizes in the monoclinic space group C2/e with four formula units in a unit cell of dimensions a= 14.94, b= 11.04, c= 15.54 A and fl= 109 ° 10'. The parameters have been refined by threedimensional least-squares procedures with anisotropic thermal parameters for all atoms except hydrogen. The final R index for 1257 observed reflexions is 0.094. The La 3 + ion is coordinated by ten oxygen atoms with La-O distances varying from 2.47 to 2.71 A. The geometry of the coordination polyhedron is described.

Inference on Cointegration in Vector Autoregressive Models (summary section only)

In the thesis we consider inference for cointegration in vector autoregressive (VAR) models. The thesis consists of an introduction and four papers. The first paper proposes a new test for cointegration in VAR models that is directly based on the eigenvalues of the least squares (LS) estimate of the autoregressive matrix. In the second paper we compare a small sample correction for the likelihood ratio (LR) test of cointegrating rank and the bootstrap. The simulation experiments show that the bootstrap works very well in practice and dominates the correction factor. The tests are applied to international stock prices data, and the .nite sample performance of the tests are investigated by simulating the data. The third paper studies the demand for money in Sweden 1970—2000 using the I(2) model. In the fourth paper we re-examine the evidence of cointegration between international stock prices. The paper shows that some of the previous empirical results can be explained by the small-sample bias and size distortion of Johansen’s LR tests for cointegration. In all papers we work with two data sets. The first data set is a Swedish money demand data set with observations on the money stock, the consumer price index, gross domestic product (GDP), the short-term interest rate and the long-term interest rate. The data are quarterly and the sample period is 1970(1)—2000(1). The second data set consists of month-end stock market index observations for Finland, France, Germany, Sweden, the United Kingdom and the United States from 1980(1) to 1997(2). Both data sets are typical of the sample sizes encountered in economic data, and the applications illustrate the usefulness of the models and tests discussed in the thesis.

Monetary Policy, Stock Price Misalignments and Macroeconomic Instability

Perhaps the most fundamental prediction of financial theory is that the expected returns on financial assets are determined by the amount of risk contained in their payoffs. Assets with a riskier payoff pattern should provide higher expected returns than assets that are otherwise similar but provide payoffs that contain less risk. Financial theory also predicts that not all types of risks should be compensated with higher expected returns. It is well-known that the asset-specific risk can be diversified away, whereas the systematic component of risk that affects all assets remains even in large portfolios. Thus, the asset-specific risk that the investor can easily get rid of by diversification should not lead to higher expected returns, and only the shared movement of individual asset returns – the sensitivity of these assets to a set of systematic risk factors – should matter for asset pricing. It is within this framework that this thesis is situated. The first essay proposes a new systematic risk factor, hypothesized to be correlated with changes in investor risk aversion, which manages to explain a large fraction of the return variation in the cross-section of stock returns. The second and third essays investigate the pricing of asset-specific risk, uncorrelated with commonly used risk factors, in the cross-section of stock returns. The three essays mentioned above use stock market data from the U.S. The fourth essay presents a new total return stock market index for the Finnish stock market beginning from the opening of the Helsinki Stock Exchange in 1912 and ending in 1969 when other total return indices become available. Because a total return stock market index for the period prior to 1970 has not been available before, academics and stock market participants have not known the historical return that stock market investors in Finland could have achieved on their investments. The new stock market index presented in essay 4 makes it possible, for the first time, to calculate the historical average return on the Finnish stock market and to conduct further studies that require long time-series of data.

Viscous flow computations using a meshless solver, LSFD-U

The Upwind-Least Squares Finite Difference (LSFD-U) scheme has been successfully applied for inviscid flow computations. In the present work, we extend the procedure for computing viscous flows. Different ways of discretizing the viscous fluxes are analysed for the positivity, which determines the robustness of the solution procedure. The scheme which is found to be more positive is employed for viscous flux computation. The numerical results for validating the procedure are presented.

X-Ray structure of a ternary complex, copper(II)–lnosine 5-monophosphate–benzimidazole. The first example for the absence of direct metal–nucleotide interaction

The unprecedented absence of direct metal–nucleotide interaction has been observed in the X-ray structure of the ternary metal nucleotide system [Cu(bzim)(H2O)5]2+[IMP]2–·3H2O [IMP = inosine 5-monophosphate(2–), bzim = benzimidazole). The complex crystallizes in the space group P21 with a= 7.013(2), b= 13.179(9), c= 14.565(9)Å, = 94.82(4)°, and Z= 2. The structure was solved by the heavy-atom method and refined by full-matrix least squares on the basis of 1 761 observed (I? 3i) reflections to final R and R values of 0.034 and 0.036 respectively. The CuII has a distorted octahedral co-ordination with a nitrogen of the bzim ligand [Cu–N 1.947(5)Å] and three oxygens of water molecules in the basal plane [mean Cu–O 2.017(3)Å] and two more water oxygens at axial positions [Cu–O 2.194(6) and 2.732(5)Å]. The nucleotide base stacks with the bzim ligand at an average distance of 3.5 Å and an angle of 22°. In the lattice, N(7) of the base is linked to a lattice water through a hydrogen bond, while all the phosphate oxygens are involved in hydrogen bonds with co-ordinated as well as lattice water molecules. The co-ordination behaviour of IMP to CuII is compared in structures containing different -aromatic amines in order to assess the influence of the ternary ligand in complex formation. The present results indicate that, apart from the commonly observed phosphate binding, other modes of co-ordination are possible, these being influenced mainly by the -accepting properties of the ternary ligand.

On-board correction of systematic error of Earth sensors

Infrared Earth sensors are used in spacecraft for attitude sensing. Their accuracy is limited by systematic and random errors. Dominant sources of systematic errors are analyzed for a typical scanning infrared Earth sensor used in a remote-sensing satellite in a 900-km sun-synchronous orbit. The errors considered arise from 1) seasonable variation of infrared radiation, 2) oblate shape of the Earth, 3) ambient temperature of sensors, 4) changes in spin/scan period, and 5) misalignment of the axis of the sensors. Simple relations are derived using least-squares curve fitting for onboard correction of these errors. With these, it is possible to improve the accuracy of attitude determination by eight fold and achieve performance comparable to ground-based post-facto attitude computation.

Crystal structure of L-lysyl-L-glutamic acid dihydrate

L-Lysyl-L-glutamic acid dihydrate, C11N3O5H21·2H2O, crystallizes in the monoclinic space group P21 with a = 12.474(2), b = 5.020(1), c = 13.157(2) Å, β= 114.69(1)° and Z = 2. The crystal structure was solved by direct methods and refined to an R value of 0.037 using full matrix least-squares method. The molecule exists as a double zwitterion with both the amino and carboxyl groups ionised. The peptide has a folded conformation with its Lys residue trans and Glu residue gauche−gauche+. The side chains of the Lys and Glu residues correspond to all trans and folded (g−g−g−) conformations respectively. The terminal carboxyl group forms hydrogen bonds with the ξ-amino group of the lysine side chain. The head-to-tail interaction often seen in peptide crystals is absent in the present structure. In the extended crystal structure water molecules form channels along the b direction and are enclosed within helically arranged hydrogen bonds formed by the lysine side chain and the peptide backbone.

Modified linear prediction method for directions of arrival estimation of narrow-band plane waves

A modified linear prediction (MLP) method is proposed in which the reference sensor is optimally located on the extended line of the array. The criterion of optimality is the minimization of the prediction error power, where the prediction error is defined as the difference between the reference sensor and the weighted array outputs. It is shown that the L2-norm of the least-squares array weights attains a minimum value for the optimum spacing of the reference sensor, subject to some soft constraint on signal-to-noise ratio (SNR). How this minimum norm property can be used for finding the optimum spacing of the reference sensor is described. The performance of the MLP method is studied and compared with that of the linear prediction (LP) method using resolution, detection bias, and variance as the performance measures. The study reveals that the MLP method performs much better than the LP technique.

Chemical-shift of the X-ray K-absorption edge of Co in some compounds, complexes and minerals

The chemical-shift of the X-ray K-absorption edge of Co was studied in a large number of compounds, complexes (spinels) and minerals of Co in its different oxidation states having widely different crystal structures and containing different types of bonding and various types of ligands, and were reported collectively, for the first time, in a single paper. A quadratic relationship was established on the basis of least-squares regression analysis to hold between the chemical-shift and the effective charge on the absorbing atom, but the dominance of the linear term was shown. This relation was utilized in evaluating the charge on the Co-ion in a number of minerals. The effect on chemical-shift of oxidation states of the absorbing atom, of the bond length, crystal structure and higher shell atoms of the molecule, and of electronegativity, atomic number and ionic radius of the ligand was discussed.

Interaction of metal ions with 6-oxopurine nucleotides. Part 2. X-Ray structures of ternary nickel(II) complexes with 2'-deoxyguanosine 5'-monophosphate or guanosine 5'-monophosphate

The ternary metal nucleotide complexes [Ni(en)1.3(H2O)1.4(H2O)2][Ni(5?-dGMP)2(en)0.7-(H2O)0.6(H2O)2]·7H2O (1) and [Ni(en)2(H2O)2][Ni(5?-GMP)2(H2O)4]·6H2O (2)(en = ethylenediamine, 5?-dGMP = 2?-deoxyguanosine 5?-monophosphate, 5?-GMP = guanosine 5?-monophosphate) have been prepared and their structures analyzed by X-ray diffraction methods. Both compounds crystallise in the space group C2221 with a= 8.810(1), b= 25.090(4), c= 21.084(1)Å, and Z= 4 for (1) and a= 8.730(1), b= 25.691(4), c= 21.313(5)Å, and Z= 4 for (2). The structures were deduced from the analogous CoIII complexes and refined by full-matrix least-squares methods to final R values of 0.087 and 0.131 for 1 211 and 954 reflections for (1) and (2) respectively. An interesting feature of the deoxyribonucleotide complex (1) is that en is not totally labilized from the metal centre on nucleotide co-ordination, as observed in corresponding ribonucleotide complexes. Apart from extensive intra- and inter-molecular hydrogen bonding, the structures are stabilized by significant intracomplex base�base and base�sugar interactions. The nucleotides in both complexes have an anti base, C(2?)-endo sugar pucker, and gauche�gauche conformation about the C(4?)�C(5?) bond.

Successive refinement of structures with data of increasing resolution: a theoretical study for triclinic space groups

The method of least squares could be used to refine an imperfectly related trial structure by adoption of one of the following two procedures: (i) using all the observed at one time or (ii) successive refinement in stages with data of increasing resolution. While the former procedure is successful in the case of trial structures which are sufficiently accurate, only the latter has been found to be successful when the mean positional error (i.e.<|[Delta]r|>) for the atoms in the trial structure is large. This paper makes a theoretical study of the variation of the R index, mean phase-angle error, etc. as a function of <|[Delta]r|> for data corresponding to different esolutions in order to find the best refinement procedure [i.e. (i) or (ii)] which could be successfully employed for refining trial structures in which <|[Delta]r|> has large, medium and low values. It is found that a trial structure for which the mean positional error is large could be refined only by the method of successive refinement with data of increasing resolution.