Elementary Parameter Research Articles

Frequency-Derivative Measurement Technique for Dispersive Effects in Single-Mode Fiber Systems

An optical dispersion analysis and measurement technique based on frequency derivatives of the Jones matrix is presented. This approach enables measurement of all scalar and polarization-dependent phase and amplitude dispersion effects over a broad wavelength range in a single sweep. Owing to its differential nature, it can be more accurate than techniques that calculate dispersion by comparing phase and amplitude measurements from adjacent wavelengths in a sweep. The method involves measuring eight elementary parameters related to the frequency derivative of the Jones matrix. An experimental setup and data analysis methods for measuring the elementary parameters are presented. Three optical devices exhibiting various dispersive effects are tested, and the ability to measure all the elementary parameters is demonstrated. Elementary parameter estimation error is 1-2 ps in this proof-of-concept experiment.

Model Checking Lower Bounds for Simple Graphs

A well-known result by Frick and Grohe shows that deciding FO logic on trees involves a parameter dependence that is a tower of exponentials. Though this lower bound is tight for Courcelle's theorem, it has been evaded by a series of recent meta-theorems for other graph classes. Here we provide some additional non-elementary lower bound results, which are in some senses stronger. Our goal is to explain common traits in these recent meta-theorems and identify barriers to further progress. More specifically, first, we show that on the class of threshold graphs, and therefore also on any union and complement-closed class, there is no model-checking algorithm with elementary parameter dependence even for FO logic. Second, we show that there is no model-checking algorithm with elementary parameter dependence for MSO logic even restricted to paths (or equivalently to unary strings), unless E=NE. As a corollary, we resolve an open problem on the complexity of MSO model-checking on graphs of bounded max-leaf number. Finally, we look at MSO on the class of colored trees of depth d. We show that, assuming the ETH, for every fixed d>=1 at least d+1 levels of exponentiation are necessary for this problem, thus showing that the (d+1)-fold exponential algorithm recently given by Gajarsk\`{y} and Hlin\u{e}n\`{y} is essentially optimal.

Measurement on physical parameters of raindrop energy

Rainfall erosivity factor (R) is one of the most commonly used factors in soil erosion models. While rainfall energy (E) is the most elementary physical parameter to predict R. Based on comparative analysis of previous soil erosion models and rainfall erosivity factor measuring methods, integrated application of modern photogrammetric techniques, image analytic methods and automatic control theories, this paper provided a new method based on image analytic to calculate the rainfall energy and R factor, which obtains raindrop's volume and velocity by means of modern photogrammetric technique. Results show that this method can improve both efficiency and accuracy of rainfall energy calculation and other rainfall physical parameters measurement.

Fractal Description of Rock Mass Structure Representative Elementary Volume

The mechanical parameters of the rock masses are scale dependent because of the existence of the discontinuities. The self-similarity of the discontinuities makes the application of fractal theory in the description of the rock mass structure possible. The novel point in this study is that the structure representative elementary volume (SREV) of rock mass is proposed. Rock mass structures were obtained through the two-dimensional discontinuity network simulation results, from which ten pieces of square rock mass specimens were chosen. The side lengths of the specimens were increased in turn from 1m to 10m. And the fractal dimension of each specimen with different sizes was calculated by the box-counting principal of the fractal geometry. The fractal dimensions of the rack mass structures became larger with their side lengths increasing, and finally stable. And the SREV of the rock mass was determined based on the variation rule of the fractal dimensions. Further, the relation between the structure representative elementary volume (SREV) and mechanical parameter representative elementary volume (REV) was qualitatively analyzed from the strength differences between the discontinuities and intact rock. And the conclusion was inferred that the size of the SREV was the upper limit of mechanical parameter REV. Meanwhile, the conclusion was verified by the results of the finite element method. This study can provided a referring value for the estimation of the mechanical parameter REV in future.

Physical properties of BaMg1/3Nb2/3O3–BaCo1/3Nb2/3O3 solid solutions

Abstract Structural, electric and magnetic properties of Ba 3 Mg 1− x Co x Nb 2 O 9 based dielectric ceramic compounds have been studied. The samples, prepared by a solid state reaction method, were characterised by X-ray powder diffraction (XRPD), electron microscopy (SEM), dielectric ( e ( T )) and magnetic measurements ( χ −1 ( T )). The XRPD analyses showed that the crystal structure of these compounds does change by the increase of substitution degree, passing from a superstructure hexagonal-type, P 3 ¯ m 1 (no. 164), space group (SG) to a simple structure cubic-type, P m 3 ¯ m (no. 221), SG. However, the evolution of the elementary unit cell lattice parameter can be followed and it exhibit a linear increasing tendency with increase in the substitution, indicating the existence of a solid solution through out the investigated range of substitution (0–1). The microstructure analysis shows a variation in the grain size and also the porosity of the samples with the degree of substitution. The results are in good agreement with that of dielectric measurements, which also showed that the dielectric constant ( e ) increases with the increase of cobalt content. The magnetic characterization of cobalt substituted samples showed an antiferromagnetic type super-exchange interaction between these magnetic ions. At the same time, the values of effective magnetic momentum ( μ eff ) are close to the value that corresponds to Co 2+ free ions. The study highlights the possibility of modelling these materials by substitutions, in order to improve properties of negative–positive–zero (NPO) type dielectric applications.

Quantifying macrophage defects in type 1 diabetes

Macrophages from animals prone to autoimmune (type 1) diabetes differ from those of diabetes-resistant animals in processing and clearing apoptotic cells. Using in vitro time-course assays of the number of engulfed apoptotic cells observed within macrophages, we quantified these differences in non-obese diabetic (NOD) versus Balb/c mice. Simple models lead to several elementary parameter estimation techniques. We used these to compute approximate rates of macrophage engulfment and digestion of apoptotic cells from basic features of the data (such as initial rise-times, phagocytic index and percent phagocytosis). Combining these estimates with full fitting of a sequence of model variants to the data, we find that macrophages from normal (Balb/c) mice engulf apoptotic cells up to four times faster than macrophages from the diabetes-prone (NOD) mice. Further, Balb/c macrophages appear to undergo an activation step before achieving their high engulfment rate. In NOD macrophages, we did not see evidence for this activation step. Rates of digestion of engulfed apoptotic cells by macrophages are similar in both types. Since macrophage clearance is an important mechanism of disposal of self-antigen, these macrophage defects could potentially be a factor in predisposition to type 1 diabetes.

Geometro-stochastic quantization of a theory for extended elementary objects

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space ℋ $$_{\bar \eta }^{(\rho )} $$ constructed in terms of generalized coherent states $$\bar \eta $$ ρ related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter ρ. The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from ℋ $$_{\bar \eta }^{(\rho )} $$ .

Quantitative analysis of recovery curves

It is assumed that recovery curves may be produced either by a dynamic process caused by a feedback mechanism or by a linear compensation process which is independent of previous compensation. Based on this assumption, 3 types of recovery functions are derived. Two behavior functions correspond to each of these types of recovery curves, one starting at a low level and the other at a high level. For each of the resulting 6 types of behavior curves, examples of real data have been reported in literature. Elementary parameter estimates are provided and substantial interpretations of the parameters are given. Behavior measures are derived for the data from an illustrative example, and 1 of the 6 behavior curves is fitted to this data. By additionally taking into account a physical repair function which is assumed to cause a certain delay in recovery, it is shown that an even better fit can be achieved.

The effective exchange energy of paramagnetic solid helium-3

An analysis is made of recent extensive National Bureau of Standards spin-pressure-modulation data, of increased accuracy and precision, along isochores of paramagnetic solid 3 He in the absence and presence of an externally applied constant and uniform magnetic field of strength up to 8 T. This leads to values of the exchange-energy parameterJ(V) and its derivativedJ(V)/dV along a set of isochores of molar volumeV within the formalism of the Heisenberg antiferromagnetic exchange-interaction model. To the order of the asymptotic product termJ(V)dJ(V)/dV and up to terms quartic in the magnetic field strength the validity of the model has been verified in the relevant temperature range along isochores of molar volumes between 22.5 and 24.4 cm 3 /mole. The termperature and field-strength independence of the elementary interaction parameter is further supported by control calculations of the temperature-dependent part of the isochoric pressures of the free and magnetized solid, ensuring the internal consistency of the formal approach to the stated order of approximation. These results strengthen the conclusion reached in previous work based on earlier initial isochoric solid 3 He pressure data of University of Florida investigators, namely, that over a range of temperatures and molar volumes the thermal and magnetic equation-of-state properties of paramagnetic solid 3 He can be quantitatively accounted for through the asymptotic formalism involving the Heisenberg exchange-energy function and its volume derivative.

A Case Study on the Measurement of Rate of Return on Investment in Joint Products: the Problem of m Products Made out of n Components on f Facilities

A particular joint products situation and the type of industry are first described. Since the measurement of rate of return on inventory investment assumes the knowledge of an inventory value structure, a section is devoted to the definition of a facility capital expense framework for production. The problem is formulated and the solution search technique briefly indicated. Results for a particular problem are presented together with the effects of some elementary parameter variations.