Chapter

Appendix

January 2000
Advances in Imaging and Electron Physics 154:225-272

DOI:10.1007/978-1-4615-4247-6_6

In book: Interstellar Propagation of Electromagnetic Signals (pp.225-272)

Authors:

National Academy of Sciences of Ukraine

The direct numerical evaluation of Eq.(2.4-45) by computer runs into difficulties. To recognize the reason we list in Tables 6.1-1 typical values of λ1, λ2, λp1, and λp2. The magnitude of λl and λ2 lies between 1 and 2.51 x 10-3 for p ≥ 0.05 but the magnitude of c pλp1 for ŋ in the range from 1 to 100 and c p = 1.98 x 10-12 is in the order of 10-14 to 10-19 and c pλp2 is even smaller except when p is very close to 0.5. The computer must produce small differences of numbers of the order of 1020, which requires too much precision. Our way around this difficulty uses a series expansion in powers of c p.

ResearchGate has not been able to resolve any citations for this publication.

ResearchGate has not been able to resolve any references for this publication.

Article

Log canonical thresholds of smooth Fano threefolds

October 2008 · Russian Mathematical Surveys

The complex singularity exponent is a local invariant of a holomorphic function determined by the integrability of fractional powers of the function. The log canonical thresholds of effective -divisors on normal algebraic varieties are algebraic counterparts of complex singularity exponents. For a Fano variety, these invariants have global analogues. In the former case, it is the so-called ... [Show full abstract] -invariant of Tian; in the latter case, it is the global log canonical threshold of the Fano variety, which is the infimum of log canonical thresholds of all effective -divisors numerically equivalent to the anticanonical divisor. An appendix to this paper contains a proof that the global log canonical threshold of a smooth Fano variety coincides with its -invariant of Tian. The purpose of the paper is to compute the global log canonical thresholds of smooth Fano threefolds (altogether, there are 105 deformation families of such threefolds). The global log canonical thresholds are computed for every smooth threefold in 64 deformation families, and the global log canonical thresholds are computed for a general threefold in 20 deformation families. Some bounds for the global log canonical thresholds are computed for 14 deformation families. Appendix A is due to J.-P. Demailly.

Article

Cyclic affine difference sets of order 8 modulo 16

January 1996

The prime power conjecture asserts that the order of an affine difference set is an integral power of a prime number. K. T. Arasu and D. Jungnickel [J. Comb. Theory, Ser. A 52, No. 2, 188-196 (1989; Zbl 0695.05011)] showed that if the order of an abelian affine difference set is even, then the order is either two or four or is divisible by eight. Recently, T. D. VanAken [J. Stat. Plann. Inference ... [Show full abstract] 62, No. 1, 125-133 (1997; Zbl 0878.05013)] extended this direction of research by studying cyclic affine difference sets whose orders are congruent to eight modulo sixteen. This paper applies several known numerical constraints in this case and using an extensive computer search shows that no cyclic affine difference sets of order less than one-million and congruent to eight modulo sixteen exists (except for the known case of order eight).

Article

A direct numerical procedure for the Cauchy problem for the heat equation

October 1976 · Journal of Mathematical Analysis and Applications

For the Cauchy problem, ut = uxx, 0 < x < 1, 0 < t ⩽ T, u(0, t) = f(t), 0 < t ⩽ T, ux(0, t) = g(t), 0 < t ⩽ T, a direct numerical procedure involving the elementary solution of υt = υxx, 0 < x, 0 < t ⩽ T, υx(0, t) = g(t), 0 < t ⩽ T, υ(x, 0) = 0, 0 < x and a Taylor's series computed from f(t) − υ(0, t) is studied. Continuous dependence better than any power of logarithmic is obtained. Some ... [Show full abstract] numerical results are presented.

Article

Full-text available

A Fixed Point Method for Convex Systems

October 2012 · Applied Mathematics

We present a new fixed point technique to solve a system of convex equations in several variables. Our approach is based on two powerful algorithmic ideas: operator-splitting and steepest descent direction. The quadratic convergence of the proposed approach is established under some reasonable conditions. Preliminary numerical results are also reported.

Article

TRANSFOCAL APLANATIC SYSTEMS OF TWO MIRRORS.

June 1975

G.M. Popov

Transfocal aplanatic systems of two aspherical mirrors are examined. Exact formulas are derived for the meridional planes of the mirror surfaces, and their representation in the form of power series is given. Numerous system variations are shown in tables, and the residual aberrations of some of them are calculated on a computer. The systems can be used in instruments designed for the visible, ... [Show full abstract] ultraviolet and infrared spectral regions.

Article

Interaction between a sheet source and a moving compressible plasma

June 1990 · Journal of Applied Physics

Kimio Nakagawa

The problem of radiation from a sheet current source in a moving compressible plasma is treated. In order to know the interaction between the sheet source and the moving plasma, first the sign of the radial component of the propagation constant is determined accurately on the basis of the radiation condition. Then the radiation power is investigated numerically for various sets of the direction ... [Show full abstract] of the source and that of the moving plasma. In particular, it is found that the source is given an energy by the surrounding plasma medium under certain conditions.

Article

Remarks on Hamiltonian properties of powers of digraphs

June 1994 · Discrete Applied Mathematics

Günter Schaar

In the last thirty years many authors were engaged in considering the Hamiltonian behaviour of powers of undirected graphs. Started by Sekanina (1960), the investigations in this field have resulted in a lot of interesting and partly very profound propositions; for instance, the famous theorem of Fleischner (1974) on squares of blocks. The surprising thing is that in the case of directed graphs, ... [Show full abstract] however, no result of this kind has been published. In this note it is attempted to illustrate the reasons responsible for that different situation and to make a small first step in considering Hamiltonian properties of powers of digraphs.

Article

Über ein Charakteristiken-Differenzenverfahren zur Berechnung laminarer Grenzschichten

March 1958 · Zeitschrift für angewandte Mathematik und Physik

The difference method ofLuckert-Hartree-Iglisch for the continuation of a boundary layer with a given pressure distribution is applied to an example to study various aspects of the method such as its adaptibility to automatic computers and the possibility of reducing the numerical work by suitable transformation of the variables. The method shows the step-wise dependence of the solution on the ... [Show full abstract] prescribed pressure distribution more directly than, e.g., power series expansions of the Blasius-Howarth type.

Article

Efficient Exact Algorithms through Enumerating Maximal Independent Sets and Other Techniques

October 2007 · Theory of Computing Systems

We give substantially improved exact exponential-time algorithms for a number of NP-hard problems. These algorithms are obtained using a variety of techniques. These techniques include: obtaining exact algorithms by enumerating maximal independent sets in a graph, obtaining exact algorithms from parameterized algorithms and a variant of the usual branch-and-bound technique which we call the ... [Show full abstract] "colored" branch-and-bound technique. These techniques are simple in that they avoid detailed case analyses and yield algorithms that can be easily implemented. We show the power of these techniques by applying them to several NP-hard problems and obtaining new improved upper bounds on the running time. The specific problems that we tackle are: (1) the Odd Cycle Transversal problem in general undirected graphs, (2) the Feedback Vertex Set problem in directed graphs of maximum degree 4, (3) Feedback Arc Set problem in tournaments, (4) the 4-Hitting Set problem and (5) the Minimum Maximal Matching and the Edge Dominating Set problems. The algorithms that we present for these problems are the best known and are a substantial improvement over previous best results. For example, for the Minimum Maximal Matching we give an O*(1.4425n) algorithm improving the previous best result of O*(1.4422m) [35]. For the Odd Cycle Transversal problem, we give an O*(1.62n) algorithm which improves the previous time bound of O*(1.7724n) [3].

Conference Paper

Full-text available

A 3-D Adaptive Loading Algorithm for Direct Detection Optical OFDM System

May 2016

We propose an adaptive loading algorithm to flexibly tailor each OFDM subcarrier in three dimensions including modulation formats, power and FEC codes. With look-up table operation introduced, the iterations are notably reduced without performance sacrifice.

Article

Full-text available

Neutrino processes with power law dispersion relations

December 2011 · Physical Review D

We compute various processes involving neutrinos in the initial and/or final state and we assume that neutrinos have energy momentum relation with a general power law

E^2 =p^2+ \xi_n p^n

correction due to Lorentz invariance violation. We find that for

n>2

the bounds on

\xi_n

from direct time of flight measurement are much more stringent than from constraining the neutrino Cerenkov decay ... [Show full abstract] process.

Article

Full-text available

Studying the infrared behaviour of gluon and ghost propagators using large asymmetric lattices

December 2006

We report on the infrared limit of the quenched lattice Landau gauge gluon propagator computed from large asymmetric lattices. In particular, the compatibility of the pure power law infrared solution

(q^2)^{2\kappa}

of the Dyson-Schwinger equations is investigated and the exponent

\kappa

is measured. Some results for the ghost propagator and for the running coupling constant will also be ... [Show full abstract] shown.

Last Updated: 21 Nov 2024