Using the Huygens and Babinet principles van de Hulst [ 11 ] considered the problem of light scattering and extinction by a particle having the size and the refractive index . ... The absorption cross-section is . ... The range of applicability of the anomalous diffraction theory for the scattering amplitude is limited by small angles, however the formules for the cross-sections became good approximations for a wide class of particles. ... This problem for spherical particles was solved by A.Ya. ...

... N.A.Bobylev, Yu.M.Burman, Morse lemmas for functionals of the variational calculus, Func.Anal.Appl., ... N.A.Bobylev, Yu.M.Burman. ... N.A.Bobylev, Yu.M.Burman, A.B.Shubin, Algorithms for control with a minimal number of switchings, Automation and remote control , V.53, 5:619, 1992. ... TeX file ) . ... Quadratic Poisson brackets compatible with an algebra structure . ... Yu.M.Burman. ... Yu.M.Burman, Whitney's index formula in higher dimensions and Laplace integrals , Preprint math.DG/9801044 . ...

QED calculations of H2 molecule Vladimir A. Yerokhin St. Petersburg State Polytechnical University in collaboration with Krzysztof Pachucki Warsaw University FFK 2013, Pulkovo, St. Petersburg, October 7-11 Do we need QED for H2? ... 150, 51 (2011) An order of magnitude in precision every 14 years QED : -0.1964 (9) 5, 3039 (2009) Theory: J. Chem. ... Wave function is represented by a linear combination of basis functions Choice of the basis functions: · · Explicitly correlated basis set. ...

We now consider estimation of count rates for objects with stellar, power law, and emission line spectra. To estimate the number of electrons collected from a point source of apparent visual magnitude V, one can use the equation: . ... The second column contains B-V. See Target Count Rates . ... If one knows the spectral index (which is zero for a source with a flat continuum), V + AB can also be calculated as the monochromatic Oke system magnitude at the corrected mean wavelength of the filter: . ...

spaceweb@oulu.fi - last update: 28 May 1995, 0800 UT . Advanced plasma theories are extremely important when one tries to explain, for example, the various waves and instabilities found in the plasma environment. ... In the kinetic theory it is necessary to know only the distribution function for the system of particles. ... The dependence of the distribution function on the independent variables r , v , and t is governed by an equation known as the Boltzmann equation . ... Hot plasma theory . ...

The 6th INTEGRAL Workshop . The Obscured Universe . ... The main goal of this workshop is to consider (via invited and contributed talks and posters) the scientific problems in the field of high energy astrophysics which are possible to solve using the International Gamma-Ray Astrophysics Laboratory INTEGRAL as well as to present and discuss the scientific results already obtained by this observatory and its coordinated observations with on-ground telescopes and other spacecrafts. ...

Next: Initial conditions Up: Old neutron star distribution Previous: Introduction . The problem to be solved is to find stationary space distribution of stars which have had certain initial space and velocity distributions and move in a given potential. ... In principle, the most straightforward way to obtain the solution is to integrate directly the equations of motion for a sufficiently large number of stars with different initial conditions. ... Then space density is given by . ...

... Development of Ideas of Structure and Evolution of Stars. Integral Features of Stars, Which Determine Their Structure, Direction and Rate of Evolutuion. ... Connection between Potential and Thermal Energy of Star. ... Structure of a Main Sequence Star. Features of Massive Stars Evolution on the Main Sequence. Internal Structure of the Sun. ... White Dwarfs, Their Features. ... Evolution from the Main Sequence of Massive Stars. ... Evolution of Small Mass Stars till White Dwarfs Sequence. ...

... 8, ``Celestial Mechanics'', 2002 Rotation theory of celestial bodies: dynamical relations of the pole motion and nutation Yu. ... Problem By construction Earth rotation theory the studies of the precession--nutation motion and pole motion are considered usually separately. ... The angle Q between the polar axis of inertia and axis of rotation is small (of order 10 \Gamma6 ). ... The perturbation theory of the Earth rotation has been constructed in the elastic Andoyer and angle--action variables. ...

SUBROUTINE TAP_SAHA ( ZELEM, TEMP, NEL, ION_MIN, ION_MAX, U, CHI, IONFRN, STATUS ) . ... Provides ionisation potential for a given ion. ... Purpose: Calculate relative abundances of ions of species K. Language: Fortan 90 Invocation: CALL TAP_SAHA ( zelem, temp, nel, ion_min, ion_max, u, chi, : ion_frn, status ) Description: Calculate relative ionisation fractions of ions j = 1,.... for atomic species (Z), given temperature and electron density, using the Saha ionisation equation. ... ION_MAX. ...

... Assured of a reliable method of solving the normal equations, we now consider the equations of condition. The observed magnitude m of a star at M air masses with true instrumental magnitude is modelled as ([ 10 ], [ 28 ]) . ... The effective extinction coefficient depends on the effective spectral gradient [ 29 ] of the star, for which we use some color index, affected by half the atmospheric reddening ([ 26 ], [ 10 ]): . ... Thus, for the B band of UBV, we use the (U-V) color. ...

... DEPENDENCE OF ORDINARY WAVE ANOMALOUS ABSORPTION ON THE SOUNDING PROBLEM PARAMETERS . ... Transformation of electromagnetic wave into plasma waves plays an important role in different processes taking place in ionospheric plasma. ... According to modern point of view transformation of ordinary wave into plasma waves plays an important role in small-scale random irregularities generation when ionospheric plasma is heated by power radio wave [1,2]. ... Anomalous attenuation. ...

... Astro Space Center, Profsojuznaya 84/32, GSP-7, 117997, Moscow, Russia . ... The algorithm allows to work easily with the first and the second derivatives of a visibility function phases and amplitudes. This approach is important for high orbiting Space VLBI data processing. ... where is a measurements of the visibility function and is an approximating function. ... If is a 2-D complex function (a model), the bi-orthogonal approximation is known in VLBI as a self-calibration algorithm. ...

... A Bayesian value for may be found simply by treating it as another parameter in our hypothesis space. ... where in the last factor we can drop the conditioning on since it is alone that induces the data . ... Evaluating the appropriate Gaussian integral gives . ... Nevertheless, for realistically large data sets, the distribution is so strongly peaked that it overwhelms any reasonable prior on , and so we assign the Bayesian value of the regularisation constant to be that which maximises . ...

... Formulas are very similar to equations. Consider for now only equations with one unknown variable , denoted by some letter, which can be x but can also be different. An equation is an equality between two mathematical expressions containing the unknown number (maybe in several places), as well as other numbers which are known. ... For instance--if you multiply two sides of a formula by the same number, the result is still a valid formula, even if what you multiply contains unknown numbers. ...

... Thanks to special permission from Cambridge University Press, we are able to bring you the complete Numerical Recipes in Fortran 77 book On-Line! ... 1.0 Introduction 1 . ... 2.4 Tridiagonal and Band Diagonal Systems of Equations 42 . ... 3.2 Rational Function Interpolation and Extrapolation 104 . ... 7.2 Transformation Method: Exponential and Normal Deviates 277 . ... 9.6 Newton-Raphson Method for Nonlinear Systems of Equations 372 . ... 12.3 FFT of Real Functions, Sine and Cosine Transforms 504 . ...

... Please let me know if you find any errors. \begin{equation} \mathrm{lb}(x) \equiv \log_{\rm 2}(x) \end{equation} . ... begin{equation} \log_{a}(1) = 0 \end{equation} . ... begin{equation} \log_{a}(x) = \frac{\log_{b}(x)}{\log_{b}(a)} \end{equation} . ... begin{equation} \sin(\alpha) \equiv \frac{\mathrm{opp}}{\mathrm{hyp}} \end{equation} . ... begin{equation} \sin(\alpha) = \frac{1}{2 \mathrm{i}} \left( \mathrm{e}^{\mathrm{i} \alpha} - \mathrm{e}^{-\mathrm{i} \alpha} \right) \end{equation} . ...

... Archives . ... If you do not mind the time predictor, it is hard to believe that this is a light curve, time dependent data. ... It?s hard to say this data set is designed for time series analysis apart from the complication in statistical inference due to measurement errors. How to design the statistical study with measurement errors, huge gaps in time, and unequal time intervals is complex and unexplored. ... The following is R output without measurement errors. ... Chandra Blog . ...

... This program was created for correlating chosen regions in the series of fts images. ... Chosen regions' . ... In this section the program counts the integral for each region of the grid for each image. ... As a matter of fact, the integral is total brightness of the region and it is counted by 'int_tabulated' IDL function. ... In addition, the program will show the count of the regions which correlate with the corresponding region (the brighter region means the bigger count) and its contour. ...

SAS home . SAS Watchout items . ... This thread contains a step-by-step recipe to extract a light curve of a point-like source for all the X-ray cameras, subtracting the background and correcting for exposure loses. ... The SAS task barycen performs this correction. ... If the following files are available: a) RGS event list; b) RGS source list, a call to the task performing light curve extraction, correction and background subtraction rgslccorr allows a user to create the light curve. ...