Coordinate Coefficients Research Articles

Extension procedures for lattice Lipschitz operators on Euclidean spaces

We present a new class of Lipschitz operators on Euclidean lattices that we call lattice Lipschitz maps, and we prove that the associated McShane and Whitney formulas provide the same extension result that holds for the real valued case. Essentially, these maps satisfy a (vector-valued) Lipschitz inequality involving the order of the lattice, with the peculiarity that the usual Lipschitz constant becomes a positive real function. Our main result shows that, in the case of Euclidean space, being lattice Lipschitz is equivalent to having a diagonal representation, in which the coordinate coefficients are real-valued Lipschitz functions. We also show that in the linear case the extension of a diagonalizable operator from the values in their eigenvectors coincide with the operator obtained both from the McShane and the Whitney formulae. Our work on such extension/representation formulas is intended to follow current research on the design of machine learning algorithms based on the extension of Lipschitz functions.

Influence of the Dufour Effect on Shear Thermal Diffusion Flows

The article considers thermal diffusion shear flows of a viscous incompressible fluid with spatial acceleration. The simulation uses a system of thermal diffusion equations (in the Boussinesq approximation), taking into account the Dufour effect. This system makes it possible to describe incompressible gases, for which this effect prevails, from a unified standpoint. It is shown that for shear flows, the system of equations under study is nonlinear and overdetermined. In view of the absence of a theorem on the existence and smoothness of the solution of the Navier–Stokes equation, the integration of the existing system seems to be an extremely difficult task. The article studies the question of the existence of a solution in the class of functions represented as complete linear forms in two Cartesian coordinates with non-linear (with respect to the third Cartesian coordinate) coefficients. It is shown that the system is non-trivially solvable under a certain condition (compatibility condition) constructed by the authors. The corresponding theorem is formulated and proven. These conclusions are illustrated by a comparison with the previously obtained results.

Development of quality evaluation indicator system of midwifery care in Shanghai

Objective To develop a quality evaluation indicator system of midwifery care in line with the modern service concept in Shanghai area under the background of over-medicalization trend of midwifery services, and to guide the improvement direction of midwifery quality. Methods Guided by the evidence-based framework of midwifery quality and indicator selection principles, the indicators for evaluating midwifery quality were preliminarily selected by literature review and theoretical analysis. Two rounds of Delphi survey among 53 experts from Shanghai were conducted to decide the final quality evaluation indicator system of midwifery care. Analytic hierarchy process (AHP) and the importance′ sum average method were adopted to calculate weights coefficients of the indicators. Results 45 indicators for evaluating midwifery quality were preliminarily selected. The response rate of two rounds of Delphi survey were 76% and 100%, the authority coefficients were 0.90 and 0.89, expert opinion coordinate coefficients were 0.190 and 0.257, respectively. The final version of the indicator system consists of 11 structure quality indicators, 13 process quality indicators and 19 outcome quality indicators. The weight values of the three first-level indicators were 0.195 8, 0.310 8 and 0.493 4 respectively. The weight values of the 43 second-level indicators ranged from 0.016 1 to 0.028 6. Conclusions The quality evaluation indicator system of midwifery care developed fits evidence-based midwifery philosophy. It provides a scientific tool for midwifery quality evaluation in Shanghai, which can guide the improvement of midwifery quality. Key words: Midwifery; Quality; Evaluation Indicator; Weight; Shanghai city

Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys.

Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in the electrode. The structural changes to the lattice symmetry affect the host material's properties. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model, which describes the composition field of a diffusing species, with a phase-field crystal (PFC) model, which describes the host-material lattice symmetry. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a diffusion-induced phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process.

Quality Assessment of the Homogeneous Coordinate Time Series of Eastern European GNSS Stations in the IGS05 Reference Frame

Abstract For the first time, a homogeneous coordinate solution in the IGS05 reference frame and the values of the zenith tropospheric refraction for the GPS weeks 935-1399 (from December 12, 1997 to November 4, 2006) were obtained at the GNSS Data Center Analysis of the Main Astronomical Observatory NAS of Ukraine. The obtained solution is devoid of effects, brought by changes in the methods of processing models, a priori data and software (absolute phase center model combinations of antenna-dome instead of relative models, model of ocean loading FES2004 instead of GOT00.2_PP, the elevations cut-off angle 3° instead of 10°, etc. were used). To estimate the quality of the solution, a comparison with the international combined solutions using the Helmert transformation was carried out. The RMS of direct station coordinate differences and correlation coefficients between the solutions estimated by the Main Astronomical Observatory, European GNSS Permanent Network and International GNSS Service are presented. The obtained results allow making the conclusion that the solution obtained at the GNSS Data Center Analysis of the Main Astronomical Observatory shows a good quality and agrees well with other solutions.

Hyperspectral Data Transformation and Vegetation Index Performance Based on the Universal Pattern Decomposition Method

Traditional vegetation indices are based on only a few spectral bands. However, hyperspectral spectrometers, such as the airborne visible infrared imaging spectrometer (AVIRIS), collect data with 224 contiguous spectral bands. Traditional vegetation index extraction methods lose much of the information contained in hyperspectral data. The universal pattern decomposition method (UPDM) is tailored for hyperspectral data analysis. In this article, we consider the UPDM as a type of multivariate analysis; standard patterns are interpreted as an oblique coordinate system and coefficients are thought of as the coordinates of a pixel';s reflectance. This article describes UPDM hyperspectral data transformation of AVIRIS data, the performance of a vegetation index based on the universal pattern decomposition method (VIUPD), and the influences of a noise-to-vegetation index. The results demonstrate that the VIUPD is an effective vegetation information extraction approach for hyperspectral data. The VIUPD is more sensitive to vegetation conditions than the normalized difference vegetation index and enhanced vegetation index. Furthermore, noise influences can be neglected in VIUPD computations, with satisfactory accuracy. (c) 2007 Society for Imaging Science and Technology.

Three-dimensional modal transmission-line method for radio wave propagation through periodic building structures

The modal transmission-line (MTL) method is used to study the transmission and reflection characteristics of a periodic building structure under the most general condition of oblique incidence (three-dimensional incidence). The presented method extends a previous analysis for the two-dimensional incidence case. Using a coordinate transformation, the reflection and transmission coefficients for an electromagnetic plane wave obliquely incident onto a periodic building structure can be solved rigorously by combining the 2-D incidence result for TE and TM polarisation, respectively. The transmission and reflection properties of concrete block and reinforced concrete walls are also analysed. Simulation findings are compared with those obtained by other researchers and the good agreement validates the extended MTL method.

Nuclear spin–spin coupling in silane and its isotopomers: Ab initio calculation and experimental investigation

Ab initio calculated symmetry coordinate and internal valence coordinate coefficients for the two spin–spin coupling surfaces of the silane molecule—J1(Si, H) and J2(H,H)—are presented. Calculations were carried out at the level of the second-order polarization propagator approximation involving coupled-cluster singles and doubles amplitudes [SOPPA(CCSD)] using a large basis set for a total of 78 different geometries corresponding to 133 distinct points on the J1(Si, H) surface and 177 distinct points on the J2(H,H) surface. The results were fitted to fourth order in Taylor series expansions and are presented to second order in the coordinates. Both couplings are sensitive to geometry—more so than found for methane in earlier calculations. The surfaces are averaged over a very accurate, recent ab initio force field to give values for the couplings in silane and its variously deuterated isotopomers over a range of temperatures. For J(Si, H) in SiH429 both stretching and bending contribute to the nuclear motion effects with the former being considerably larger numerically. For J(H,D) in SiH328D the bending and stretching contributions are both substantial but, being of opposing sign, cancel each other out, leaving the bending–stretching cross terms to give most of the remaining contributions. The calculated values are in excellent agreement with new experimental values presented in this work; for J1(Si, H) in SiH429 and SiHD329 at 298 K we calculate −199.9 Hz and −198.5 Hz, respectively, to be compared with experimental values of −201.3 (±0.4) Hz and −199.9 (±0.4), Hz respectively. For (γH/γD) J(H,D) we predict a value of 2.58 Hz, to be compared with 2.61 (±0.08) Hz obtained by experiment at 298 K. Calculation of the tensor components of all parts of the one-bond and two-bond couplings are reported for equilibrium geometry and compared to newly calculated values of the corresponding components of methane. The principal finding for the one-bond coupling is that K∥>K⊥ for silane and K∥<K⊥ for methane. For J(H, H) each component of the contributory parts of the coupling is numerically smaller for silane than for methane.

Nuclear spin–spin coupling in the acetylene isotopomers calculated from ab initio correlated surfaces for 1J(C,H), 1J(C,C), 2J(C,H), and 3J(H,H)

Ab initio calculated coordinate and internal valence coordinate coefficients for each of the four spin–spin coupling surfaces of the acetylene molecule—1J(C,H), 1J(C,C), 2J(C,H), and 3J(H,H) are presented. Calculations were carried out at the SOPPA(CCSD) level using a large basis set. Couplings were calculated at 35 geometries (including equilibrium) giving 35 distinct sites on the 1J(C,C) and 3J(H,H) surfaces and 53 distinct sites on the 1J(C,H) and 2J(C,H) surfaces. The results were fitted to fourth order in Taylor series expansions and are presented to second order in the coordinates. All couplings are sensitive to geometry with the principal features being (a) an even steeper increase of J(C1, H1) with CC bond stretching than with CH bond stretching—an example of “unexpected differential sensitivity” (or UDS), (b) very opposite variations of 2J(C1,H2) with variations of the CC and C2H2 bond lengths, (c) very opposite variations of 1J(C,C) with a CC stretch and a CH stretch and (d) very opposite variations of 1J(C1,H1) with variations of the H1C1C2 and C1C2H2 angles with the latter variation being three times more effective (another example of UDS). The surfaces are averaged over a very accurate force field to give values of all couplings in the ten isotopomers containing all possible combinations of 12C, 13C, 1H, and 2H nuclei at 0 K and at a number of selected temperatures in the range accessible to experiment. The dominant nuclear motion effect comes from bending at the carbon atoms with stretching being of greater importance only for 1J(C,H). Agreement with recent experimental data both for the absolute values of the couplings and for isotope effects on them is generally very good although there are some disappointments for 1J(C,H). Values of the reduced coupling constants and their derivatives for the carbon–carbon and the one-bond carbon–proton coupling in acetylene are compared with recent results for some other molecules.

Large deflection analysis of space frames

Abstract A nonlinear finite element procedure for large deflection analysis of three dimensional frames is presented in this paper. On the basis of the beam‐column approach, the convected coordinate system is used in each element to separate the rigid‐body motions from the local deformations. In the derivation of the nonlinear stiffness matrix for the beam‐column element, the element axial shortening due to bowing is taken into account. With reference to a slightly deformed position of the beam column, the linearized coordinate transformation coefficients of the first and second orders are found and expressed explicitly by the member orientation matrix. The Newton‐Raphson method of iteration is adopted for solving the linearized system equation. Several selected examples are studied in detail. The numerical results indicate that the proposed procedure can be accurately and efficiently used to handle space frame problems with laige displacements and large rotations.

A mixed-variational approach for the analysis of circular plate-elastic halfspace interaction

The Hellinger-Reissner mixed-variational principle is used to study the flexural interaction of thin circular plates resting in smooth and continuous contact with an isotropic elastic halfspace. In this approach, both the plate deflection and the plate flexural moments are approximated independently by power series in terms of radial coordinate and unknown coefficients such that they satisfy the kinematic and force constraints at the boundary. The unknown coefficients are evaluated by utilizing the stationary property of the Hellinger-Reissner's mixed-variational functional. The proposed analysis technique can accurately predict the plate deflections as well as the flexural moments. Comparison of numerical results with those obtained by more rigorous techniques shows an excellent agreement.

Buchdahl’s glass dispersion coefficients calculated in the near infrared

Buchdahl's chromatic coordinate provides a rapidly converging polynomial form for describing the dispersion of glass. A method of generating Buchdahl's chromatic coordinate coefficients with a Code V sequence file is presented. The quadratic model coefficients for eighty-two glasses at a base wavelength of 0.830 microm are listed. When evaluating Buchdahl coefficients across different wavelength ranges (i.e., infrared or ultraviolet), the chromatic coordinate constant alpha can be changed to improve convergence of the refractive-index model.

Theory of the carbon-13 proton spin-spin coupling and the proton shielding surfaces of the methane molecule

The form of the carbon-13 proton spin-spin coupling surface of the methane molecule is investigated. The three first-order and twelve second-order independent symmetry coordinate coefficients required to determine the four distinct coupling constants for small but otherwise arbitary displacements from equilibrium are identified. Valence coordinate coefficients for the surface are also determined. The results will be of help in understanding the effects of temperature and of primary and secondary isotopic substitution on the observed coupling and also in simplifying ab initio calculations of the surface for methane and for 1 J(X, Y) in other XY 4 compounds of Td symmetry. The results are also applicable to the proton shielding surface of methane and the Y nuclear shielding surfaces in other XY 4 compounds of Td symmetry.

Similarity Principles and Intrinsic Geometries: Contrasting Approaches to Interspecies Scaling

We criticize standard allometric approaches on the grounds that they emphasize scaling to one variable at a time, whereas chemically reactive hydrodynamic systems involved in pharmacokinetic phenomena are of higher dimension. We show that attempts based on mechanical similitude to set a dosage that would be equivalent across species (for example, from mouse to humans) lead to ambiguous results. Another failing of standard allometry may be its incapability to accommodate the neoteny of Homo sapiens, even though it helped discover the phenomenon. The retarded development in our species implied by neoteny can most clearly be seen in the evidence that both our brain size and our lifespan lie well above the allometric curve for Class Mammalia for these features. In contrast to allometry, which proposes a search for scaling coefficients through invariant external measurement reference frames, we propose a search for transformations of coordinate space coefficients in an intrinsic geometry for the mammalian body plan.

Growing strain coefficients in metal powder rolling

1. In the study described, in which x-radiographs were taken of rolled porous powder strip incorporating a plane deformable coordinate grid, growing transverse and longitudinal strain coefficients were determined for powder rolled under conditions of narrow and wide deformation zones. 2. Growing height strain coefficients were calculated, starting with the law of conservation of mass, with allowance for growing transverse and longitudinal strain coefficients and strip porosity in various sections of the deformation zone. 3. The strained state of a powder body can be described in terms of appropriate total growing strain coefficients, as determined in this work, and principal strain schemes. 4. The shaping region is characterized by predominance of a uniaxial compression scheme. To describe the processes occurring in this region, it is permissible to employ the plane sections hypothesis.

Stochastic Frame Response using Modal Truncation

This paper describes a computationally simplified procedure for calculating the covariance matrix of building frame displacements when the structure is excited by multiple correlated stationary forcing functions. Normal mode truncation procedures are used to enable the analyst to obtain an approximate covariance matrix of response to any desired degree of accuracy. Plots are given for normal coordinate receptance coefficients with 2% and 5% critical damping. Comments are made with respect to the importance of auto-power and cross-power spectral densities and frequency bands in which their values must be accurately calculated.

On the generalized Karhunen-Loeve expansion (Corresp.)

In a recent paper Watanabe (1965) has established two useful theorems concerning the optimum properties of the Karhunen-Loeve expansion for the random functions of a stochastic process. The resulting coordinate system (Karhunen-Loeve system) was found to be optimum in the sense of i) minimizing the mean-square error committed by approximating the expansion of an infinite series by a finite number of terms, ii) minimizing the entropy function defined over the probability distribution of the coordinate coefficients for the entire ensemble. These optimum features were then effectively applied to the preprocessing of input data for the speech recognition problem. However, in the development of these properties considerations were only given to the situation where the random functions come from the same stochastic process, and consequently the coordinate coefficients in the expansion were treated to be nonrandom. The question then arises as to whether the optimum properties will hold if the random functions are realizations of more than one stochastic process as in the case of many preprocessing problems in pattern recognization and signal detection. The purpose of this correspondence is to show. that the cited optimum properties can be retained by defining a generalized Karhunen-Loeve expansion which considers the possibility of two or more stochastic processes generating the random functions. Necessary conditions are derived to assure the existence of such an expansion. Applications of these results are indicated in the ranking and selection of feature measurements for the sequential recognition (decision) problems.