scholarly journals Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology

2017 ◽  
Vol 468 (1) ◽  
pp. 927-930 ◽  
Author(s):  
Maarten Baes ◽  
Peter Camps ◽  
Dries Van De Putte
Keyword(s):  
Numerical Evaluation ◽  
Luminosity Distance ◽  
Analytical Expressions

NEGATIVE ELECTROMAGNETIC SCREENING BY A CYLINDRICAL CONDUCTING COVER

Geophysics ◽  
1969 ◽  
Vol 34 (6) ◽  
pp. 944-957 ◽  
Author(s):  
Janardan G. Negi ◽  
Upendra Raval
Keyword(s):  
Numerical Evaluation ◽  
Inner Core ◽  
Electromagnetic Response ◽  
Spherical Case ◽  
Cylindrical Model ◽  
Cylindrical System ◽  
Screening Factor ◽  
Analytical Expressions ◽  
Electromagnetic Screening

The paradoxical augmentation of the electromagnetic response of an inner core by a conducting cover is reexamined by investigating the behavior of a cylindrical model to establish the geometrical independence of the negative screening phenomenon. The theory is developed for the coaxial cylindrical system in analogy with the spherical case. Results of numerical evaluation of the analytical expressions for the screening factor prove the geometrical independence of the phenomenon of negative screening, as indicated in earlier studies.

The matrix M/M/∞ system: retrial models and Markov Modulated sources

1993 ◽  
Vol 25 (2) ◽  
pp. 453-471 ◽  
Author(s):  
J. Keilson ◽  
L. D. Servi
Keyword(s):  
Numerical Evaluation ◽  
Stability Conditions ◽  
Kummer Functions ◽  
The Matrix ◽  
Service Rates ◽  
System Properties ◽  
Markov Modulated ◽  
The Stability ◽  
Analytical Expressions

The matrix-geometric work of Neuts could be viewed as a matrix variant of M/M/1. A 2 × 2 matrix counterpart of Neuts for M/M/∞ is introduced, the stability conditions are identified, and the ergodic solution is solved analytically in terms of the ten parameters that define it. For several cases of interest, system properties can be found from simple analytical expressions or after easy numerical evaluation of Kummer functions. When the matrix of service rates is singular, a qualitatively different solution is derived. Applications to telecommunications include some retrial models and an M/M/∞ queue with Markov-modulated input.

scholarly journals THE CLASS OF NONLINEAR STOCHASTIC MODELS AS A BACKGROUND FOR THE BURSTY BEHAVIOR IN FINANCIAL MARKETS

2012 ◽  
Vol 15 (supp01) ◽  
pp. 1250071 ◽  
Author(s):  
VYGINTAS GONTIS ◽  
ALEKSEJUS KONONOVICIUS ◽  
STEFAN REIMANN
Keyword(s):  
Financial Markets ◽  
Stochastic Models ◽  
Numerical Evaluation ◽  
First Passage Time ◽  
Passage Time ◽  
Bessel Process ◽  
Proposed Model ◽  
Nonlinear Stochastic Model ◽  
Bursty Behavior ◽  
Analytical Expressions

We investigate behavior of the continuous stochastic signals above some threshold, bursts, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model applicable for the modeling of absolute return and trading activity in financial markets which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the proposed model. We confirm derived analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE.

The matrix M/M/∞ system: retrial models and Markov Modulated sources

1993 ◽  
Vol 25 (02) ◽  
pp. 453-471
Author(s):  
J. Keilson ◽  
L. D. Servi
Keyword(s):  
Numerical Evaluation ◽  
Stability Conditions ◽  
Kummer Functions ◽  
The Matrix ◽  
Service Rates ◽  
System Properties ◽  
Markov Modulated ◽  
The Stability ◽  
Analytical Expressions

The matrix-geometric work of Neuts could be viewed as a matrix variant of M/M/1. A 2 × 2 matrix counterpart of Neuts for M/M/∞ is introduced, the stability conditions are identified, and the ergodic solution is solved analytically in terms of the ten parameters that define it. For several cases of interest, system properties can be found from simple analytical expressions or after easy numerical evaluation of Kummer functions. When the matrix of service rates is singular, a qualitatively different solution is derived. Applications to telecommunications include some retrial models and an M/M/∞ queue with Markov-modulated input.

Layered and ion implantation specimens as possible reference materials for the electron-probe microanalysis

1992 ◽  
Vol 50 (2) ◽  
pp. 1652-1653
Author(s):  
G. Remond ◽  
R.H. Packwood ◽  
C. Gilles ◽  
S. Chryssoulis
Keyword(s):  
Ion Implantation ◽  
Reference Materials ◽  
Analytical Techniques ◽  
Thin Film Deposition ◽  
Film Deposition ◽  
X Ray ◽  
Spatially Resolved ◽  
Analytical Expressions ◽  
Original Approach ◽  
Depth Concentration

Merits and limitations of layered and ion implanted specimens as possible reference materials to calibrate spatially resolved analytical techniques are discussed and illustrated for the case of gold analysis in minerals by means of x-ray spectrometry with the EPMA. To overcome the random heterogeneities of minerals, thin film deposition and ion implantation may offer an original approach to the manufacture of controlled concentration/ distribution reference materials for quantification of trace elements with the same matrix as the unknown.In order to evaluate the accuracy of data obtained by EPMA we have compared measured and calculated x-ray intensities for homogeneous and heterogeneous specimens. Au Lα and Au Mα x-ray intensities were recorded at various electron beam energies, and hence at various sampling depths, for gold coated and gold implanted specimens. X-ray intensity calculations are based on the use of analytical expressions for both the depth ionization Φ (ρz) and the depth concentration C (ρz) distributions respectively.

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

1990 ◽  
Vol 48 (1) ◽  
pp. 64-65
Author(s):  
D. Van Dyck
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Direct Method ◽  
Real Space ◽  
Zone Axis ◽  
Phase Object ◽  
High Resolution Images ◽  
The Many ◽  
Analytical Expressions ◽  
Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

KINEMATIC FEATURES OF THE LAPPING PROCESS AND DETERMINATION OF ITS BASIC PARAMETERS

2020 ◽  
Vol 7 (3) ◽  
pp. 23-28
Author(s):  
EZIZ SARVAN SHIRVAN ◽  
Keyword(s):  
Dynamic Properties ◽  
Cutting Speed ◽  
Equilibrium System ◽  
Technological Parameters ◽  
Kinematic Characteristics ◽  
Angular Velocities ◽  
Basic Parameters ◽  
Grinding Tool ◽  
Mathematical Relationships ◽  
Analytical Expressions

This paper discusses the kinematic characteristics of lapping process and the main parameters of the process. It was determined that the influencing degree of technological parameters to the forming surface and processes. It was projected the construction of the lapping head for processing of internal cylindrical surfaces, scheme of the lapping operation and graphic description of the forces influencing. The relationships between the axial, radial and tangential cutting forces and the effect of the combined force thereof are determined in order to ensure the necessary surface pressure. During the analysis geometric and mathematical relationships were obtained. The extracted analytical expressions can be realized by further experimental researches and can be used in engineering calculations of technological parameters of processing by lapping. Angular velocity, friction force, linear velocity, also the length of the tactile curve and the radius of the part can be considered the main kinematic and dynamic parameters of the process that the formation of the surface, also the course of the process depends on these parameters. Depending on the kinematic parameters, the wear nature of the tool changes and this changes the linear and angular velocities, which have a significant impact on the accuracy, quality and productivity of processing. When examining the technological capabilities of the process, the nature of the movement between the part and the grinding tool, also changes in cutting speed are often considered as a main factor. Analytical expressions were obtained to determine the main parameters of the process, taking into account the kinematic characteristics of the friction process. These expressions can be used in engineering calculations and allow to determine the optimal values of the processing mode. In order to obtain the required micrometric surface cleanliness and measurement accuracy, correlation relationships were established between the main parameters of the process, equations of the equilibrium system of shear forces were compiled and analytical expressions were obtained based on the analysis of kinematic and dynamic properties of the system.

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