Small Absolute Values Research Articles

Electronic and vibrational properties of implanted silver deuteride

Resistivity measurements were performed on deuterium-implanted silver films. They provide evidence that the deuterium atoms occupy the octahedral sites of the silver lattice and show that the electron-optic phonon coupling parameter λ op is of the same order as its electron-acoustic phonon counterpart. The absence of superconductivity can be explained by a small absolute value of λ ac in agreement with recent band structure calculations which show that AgD should have a very small conduction electron density.

The human erythrocyte membrane skeleton may be an ionic gel. II. Numerical analyses of cell shapes and shape transformations.

In the first paper in this series (Stokke et al. Eur Biophys J 1986, 13:203-218) we developed the general theory of the mechanochemical properties and the elastic free energy of the protein gel--lipid bilayer membrane model. Here we report on an extensive numerical analysis of the human erythrocyte shapes and shape transformations predicted by this new cell membrane model. We have calculated the total elastic free energy of deformation of four different cell shape classes: disc-shaped cells, cup-shaped cells, crenated cells, and cells with membrane invaginations. We find that which of these shape classes is favoured depends strongly on the spectrin gel osmotic tension, IIGu, and the surface tensions, IIEu and IIPu, of the extracellular and protoplasmic halves of the membrane lipid bilayer, respectively. For constant ratio IIEu/IIPu greater than O large negative or positive values of IIGu favour respectively the crenated and invaginated cell shape classes. For small absolute values of IIGu, IIEu, and IIPu, biconcave or cup-shaped cells are the stable ones. Our numerical analysis shows that the higher the membrane skeleton compressibility is, the smaller are the values of IIGu needed to induce cell shape transformation. We find that the stable and metastable shapes of discocytes and stomatocytes generally depend both on the shape of the stressfree membrane skeleton and the membrane skeleton compressibility.

A new vibration mode for medical imaging arrays

Abstract The possibility of designing medical imaging arrays using a new transducer vibration mode is analyzed. The vibration mode, that we call ‘‘width mode'', is studied theoretically and experimentally and compared to the classical ‘‘array mode''. Starting from the constitutive equations for piezoelectric materials and with proper boundary conditions, the propagation velocity for the new mode is first found for the case of mono-dimensional propagation approximation. Then an approximate theory for vibrating systems which possess only two degrees of freedom is used in order to express dispersion curves for the propagation velocity for the two modes of interest. Theoretical results are then compared with experimental data obtained for PZT5-A and PZT4 ceramic materials. The new oscillation mode shows some advantages such as a smaller degree of wave velocity dispersion, a smaller absolute value of wave velocity propagation and a lower electrical impedance. Plots of input electrical admittance show that with...

Studies of molecular orbital momentum distributions by (e, 2e) spectroscopy

Binary electron impact ionization or (e, 2e) spectroscopy has recently been employed to measure molecular orbital momentum distributions in a variety of molecules. Interpretation of the momentum distributions ρ(q) has been facilitated by the use of the wave-function autocorrelation function B(r). In some cases differences in the autocorrelation function of two orbitals may be semiquantitatively interpreted in terms of contour plots of the average and difference of their position-space orbital amplitudes. The σg and σu orbitals of a homonuclear diatomic provide a simple illustration of this point. Calculated and experimental spherically averaged ρ(q) for the predominantly N 2p lone-pair HOMOs of NH3 and CH3NH2 are shown using a ΔB(r) analysis to indicate significant participation of the CH3 hydrogens in the lone-pair orbital of CH3NH2. Although the difference in ρ(q) between the lone pairs of NH3 and CH3NH2 is adequately reproduced by split valence (SV) level ab initio SCFMO calculations the experimental ρ(q) have their maxima at considerably smaller absolute values of q then that obtained from either SV or near Hartree–Fock SCFMO calculations. Experimental and calculated momentum distributions are also presented for the 2t2g HOMO of Cr(CO)6. A ΔB(r) analysis of ρ(q) for this orbital confirms that it has mixed Cr 3d and CO 2π character.

On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields

A new method of determining algebraic number fields with discriminants of small absolute value is developed that avoids lengthy considerations of subfields. As an application all minimum discriminants of sixth degree fields are computed.

A robust/resistant technique for crystal structure refinement

A refinement technique is robust if it works well over a broad class of error distributions in the data, and resistant if it is not strongly influenced by any small subset of the data. Least squares possesses neither property. A more robust/resistant procedure is to minimize, instead of a simple sum of squared differences, a sum of terms of the form (x/sup 2//2)(1 - (x/a)/sup 2/ + (1/3) (x/a)/sup 4/) for absolute value x absolute value less than or equal to a and a/sup 2//6 for absolute value x absolute value > a. Here x = w/sup 1/2/(absolute value F/sub 0/ absolute value - absolute value F/sub c/ absolute value)/S. S is a measure of the width of the error distribution based on the results of the previous cycle, and a is a constant chosen so that extreme data do not influence the solution. This function behaves like the sum of squares for small absolute value x absolute value, but is constant for large abolute value x absolute value, so that the effect of large differences is deemphasized. A least-squares program can easily be modified to perform this more robust/resistant procedure. The modified procedure has been used in a reanalysismore » of D(+)-tartaric acid data. Results show that the technique provides an efficient means for automatic screening of least-squares results for good data sets. If the results don't agree with least squares it suggests systematic effects.« less

Phloretin-sensitive lithium transport in erythrocytes of affectively ill patients: Intra-individual reproducibility

1. 1. The phloretin-sensitive component of lithium (Li +) efflux from erythrocytes has been reported to be significantly reduced in patients with bipolar affective disorders. The value of this finding depends on how reproducible the efflux measurements are. We have therefore investigated the intra-individual day-to-day reproducibility of this parameter, and total erythrocyte Li + efflux in patients with bipolar affective disorders and in age and sex matched healthy controls. 2. 2. Six carefully selected, typical bipolar patients and age and sex matched healthy volunteers were studied. These experiments were repeated under identical conditions on 3 occasions within a brief time period (21 days). 3. 3. We have found that both the total erythrocyte Li + efflux and the phloretin-sensitive Li + efflux exhibited considerable day-to-day intra-individual variability in both patients and healthy controls. The standard deviation of total efflux values was as large as ± 31.1% of the mean in some subjects. Mean phloretin-sensitive Li + efflux for patients was found to be 0.066 ± 0.02 mEq/1 RBC, and for controls 0.048 ± 0.01 mEq/1 RBC, in agreement with values reported in the literature. However, in some individuals standard deviation of this parameter, was as high as ± 50% of the mean. This variation was not the result of the biochemical technique, since all measurements were carried out in duplicate, and these differed less than 5%. 4. 4. These findings suggest, that in view of the small absolute values of the phloretin-sensitive Li + efflux, and its considerable day-to-day variation, the relevance of this biochemical parameter to the postulated cell membrane defect in affective disorders should be interpreted with some caution and needs further evaluation.

Analysis of linkage disequilibria between allozyme loci in natural populations of Drosophila melanogaster.

SUMMARYLinkage disequilibria between pairs of 8 polymorphic enzyme loci (αGpdh, Mdh, Adh, Est-6, Pgm, Odh, Est-CandAcph) in some 100 natural population samples ofDrosophila melanogasterwere examined. The estimates of linkage disequilibrium were made from zygotic frequencies. The magnitude of linkage disequilibria are small and similar to those in previous reports. Variation in linkage disequilibrium among related subpopulations was analysed by analysis of variance of the correlation coefficients. Despite the small absolute value of linkage disequilibrium there is a suggestion of a correlation among related subpopulations. The magnitude of linkage disequilibrium was observed to be positively correlated with linkage. Two cage populations were observed to demonstrate large amounts of linkage disequilibrium between closely linked loci in contrast to the situation in natural populations. This is attributable to the finite sizes of these cage populations.

Die zersetzung von intermetallphasen des platins mit erdalkalien und lanthaniden bei hohen temperaturen

The thermal decomposition of intermetallic compounds of platinum with alkaline earth ( A = Mg, Ca, Ba) and lanthanide ( A = Sm, Eu, Gd, Dy, Yb) elements obtained by the coupled reduction method, was investigated by using the Knudsen effusion technique. It was demonstrated that the APt 2 ( APt 3 ) intermetallic compounds are thermally decomposed to yield APt 5 ( APt 7 ) and A ( g ) , the condensation of which may be used to prepare pure metal A . Furthermore, it was shown, that the free molar solution enthalpy of A in APt x :Δ 1 G A → APt x has smaller absolute values for the alkaline earth compounds than for the lanthanide compounds, europium, however, showing a behaviour more characteristic for divalent metals. Data for the free molar solution enthalpy and the vapour pressure of A over APt x for temperatures up to 2000°C are given together with the melting points of the compounds investigated and a critical description for the procedure to prepare the metal A by hydrogen reduction of the oxide AO y vs APt x -compounds as intermediates.

Classical one-dimensional Heisenberg model with an interaction of finite range

It is shown that the thermodynamic quantities and spin correlation functions of the classical Heisenberg model on a linear chain are expressed in terms of the eigenvalue with the smallest absolute value and the corresponding eigenfunction of a homogeneous linear integral equation, where the range of the interaction is assumed to be finite. The magnetization and susceptibility at nonzero external magnetic fields are given as a function of temperature, for the case of the nearest neighbour ferromagnetic and antiferromagnetic interaction. Efforts are paid to determine the properties near zero temperature.

Liner-Medium Interaction in Tunnels

Results from a number of elastic finite element solutions for determination of forces and deformations in tunnel liners are presented. The effect on forces and deformations in the liner of the properties of the medium, loading conditions, and the extension of the tunnel longitudinally are examined. Several loadings were assumed in the solutions. The results indicate that small absolute values of the coefficients of moment, shear, and deflection are obtained irrespective of the loading condition assumed.

Numerical evaluation for classical one-dimensional gas of hard rods with an interaction of finite range

Abstract In a recent formulation of the theory of the classical one-dimensional gas of hard rods with an interaction of finite range, the Gibbs potential and distribution functions are expressed in terms of the eigenvalue with the smallest absolute value and the corresponding eigenfunction of the homogeneous linear integral equation. The description is given of a practical numerical procedure for obtaining those eigenvalue and eigenfunction. As an illustration, the procedure is applied to the system with the square-well potential, for the cases where the range of the interaction is three times and four times, respectively, the hard-core diameter. The equation of state and the pair distribution function are then calculated for this system.

Classical one-dimensional gas of hard rods with an interaction of finite range

The classical one-dimensional gas of hard rods with an interaction of finite range is investigated. The Gibbs potential, the distribution function of a finite number of successive particles, and the average length per particle of that system are shown to be expressed in terms of the eigenvalue with the smallest absolute value and the corresponding eigenfunction of a homogeneous linear integral equation. Byckling's equation is criticized.

The Influence of the Dipole-Dipole Interactions on the Phonon Induction

Abstract It is shown that the none quilibrium state of the dipole-dipole reservoir in paramagnetic and paraelectric systems can stimulate the generation of the coherent spontaneous radiation essentially. At the same time the uncoherent spontaneous radiation and coherent induced (in the Einstein sense) radiation canN′t be amplified in this conditions essentially. Moreover the electromagnetic and acoustic maser-effects and uncoherent apontaneous radiation completely disappear in the limit case of enough small absolute values of the dipole-dipole system (DDS) temperature. The nuclear polarization is also absent at enough low absolute electron-nuclear and nuclear-nuclear DDS temperatures. All of these consequences follow from the obvious trace property of the product of n-particle density matrix operators and operators of observable quantities constituted from m-particle operators: this trace is identically equal to zero if m > n (all n or m particles are different).

A heavy traffic result for the finite dam

The steady state content Z of a finite dam in discrete time is investigated for small absolute values of the expected net input and correspondingly large values of the dam capacity. It is shown that under general conditions Z has, asymptotically, a truncated exponential distribution, a result that supplements previous knowledge in queueing theory.

A heavy traffic result for the finite dam

The steady state content Z of a finite dam in discrete time is investigated for small absolute values of the expected net input and correspondingly large values of the dam capacity. It is shown that under general conditions Z has, asymptotically, a truncated exponential distribution, a result that supplements previous knowledge in queueing theory.

Variance of the Bearing Angle of a Discrete Linear-Difference Array in a Random Transmission Medium

An approximate expression has been derived for the variance of the bearing angle, about the central null point, of a discrete linear-difference array. The Chernov formulation for plane-wave propagation in a random medium, restricted to small absolute values of the phase and amplitude fluctuations, is used as a basis for the derivation. It is further assumed that the phase and amplitude fluctuations are zero-mean normal random variables. A special case is considered in detail for large values of the wave parameter D = 4R/ka2, where R is the range, k is the wavenumber, and a is a characteristic correlation distance. For this case, the variance of bearing angle with range is linear and is nearly independent of the frequency.

Natural selection in a population with annual breeding but overlapping generations

Dr. Bria n Clarke, of the Deparn:aent of Zoology, Edinburgh University, has presented mewi th a problem which may be generalized as follows. A large population of diploid organisms has an annual breeding season. The organisms become mature at m years. After this.a fraction s survives in each consecutive year. The mortality before maturigy is irrelevant. *Fertility-does not atter with age. t f it does so this could be at least part ly allowed for by changing the value ofs. Atl mature organisms mate at random. Dr. Clarke was concerned with a pop\clarion of Cepea nemoralis in which m was 2, and s about 0.5. Irl birds m varies from 1 to 5 or more in different species, and s f romlabout 0-3 ~o about 0"9. However when s is large I monogamy appears to be frequent. The population is polDr~orphic for a pair ofautosomal alIeles A and a. The mortal i ty of AA and Aa is the same. However for each AA or Aa which survives to matur i ty , 1-K a a surviv% arid for each AA or Aa which survives during a subsequent year, I -k aa survive. 37 and ~: are riot necessarily positive, nor o f the same sign. The3r are however supposed to have small absolute values, so that their squares or product may be neglected. The gametes produced in the year n are p= A+q~ a, where p~@q,~= t. I t is required to find art approxima~e functional relation between q+, and n. Dr. Clarke believed that in his snail populations k was about 1-02, and K 2 k , that is to say the annual diffez:entiaI mortality was constant. Idowever C give the solution for the more general casea So long as [K[ and l kl are small, while 1-s is not small, we can treat the finite difference equations as differential equations, as was done by H a l d a n e (1924) and most later

On the Nucleon-Nucleon Scattering Phase Shifts and the High Energy Nucleons Elastically Scattered from Light Nuclei

The polarizations and triple scattering parameters of the nucleons elastically scattered from light nuclei are explained with the optical model potential by the use of the nucleon-nucleon scattering phase shifts. The set of the two-body scattering phase shifts meson-theoretically derived gives a small magnitude of the parameter of optical model potential V SR. The small value of V iW is mainly caused by the large positive 3Po state phase shift of the two-body scattering. The small value of V SN gives a small polarization and a small absolute value of the triple scattering parameter for the nucleon scattered from the potential. Furthermore the value of i:;i ChjjJ.c) 2 calculated by the use of the meson-theoretical phase shifts is smaller than the ones based on the Gammel-Thaler and Signell-Marshak phase shifts. This difference is mainly due to the difference of 3PO state phase shifts in the two-body scattering. polarizations of the high energy nucleons elastically scattered from light nuclei, using the impulse approximation with the nucleon-nucleon scattering amplitude, for the impulse approximation is equivalent to the use of the optical model potential in the first Born approximation which may be justified for the small angle scatter­ ing from light nuclei. 4 ),5) The ordinary procedure is that, given several alternative sets of the nucleon-nucleon scattering phase shifts, the optical model potentials cor­ responding to the sets of the phase shifts are derived, and then the differential cross Sections and polarizations of the nucleons scattered in small angles are calcu­ lated. The comparison of the results with the observed differential cross sections and polarizations may distinguish the various sets of the nuclear phase shifts re­ jecting some of them. ,_ The best way of studying the nucleon-nucleon interactions by the use of these optical model potential is to investigate the polarizations and triple scattering pa­ rameters of the nucleons elastically scattered from light nuclei, because when one calculates the polarizations and triple scattering parameters of these nucleons through the optical model potentials, the final results are independent of the detailed structure of the target nucleus and to a certain extent free from the limitation of the Born approximation. That is, the expressions for the polarization and triple Bcattering parameter do not contain the nuclear form factors~ i.e. the Fourier trans

Coexistence Curve of the Triethylamine-Water System

The coexistence curve of the system triethylamine-water has been determined near its lower critical point. The observed critical temperature Tc is 18.33°C. There is evidence of a small horizontal portion of the coexistence curve, which extends from 0.559 to 0.657 volume fraction water, or from 0.907 to 0.936 mole fraction water, though the evidence is not absolutely certain. On the other hand, our results exclude the possibility of an anomalous phase transition in the concentration interval from 0.35 to 0.90 mole fraction water where, according to a report by J. E. Mayer, such an anomalous transition may occur. Outside the small horizontal portion the coexistence curve shows the same cubic behavior [(T–Tc)⅓, or better (T–Tc+0.007)⅓, proportional to the difference of the volume fractions of the phases in equilibrium] as do coexistence curves of systems with upper critical points, but is much flatter, the proportionality factor having a smaller absolute value.