Refine
Has Fulltext
- yes (24)
Year of publication
- 2006 (24) (remove)
Document Type
- Preprint (24) (remove)
Language
- English (24)
Keywords
We consider a system of infinitely many hard balls in R<sup>d undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with a local time term. We prove that the set of all equilibrium measures, solution of a detailed balance equation, coincides with the set of canonical Gibbs measures associated to the hard core potential added to the smooth interaction potential.
In the present work, phenomena in the ionosphere are studied, which are connected with earthquakes (16 events) having a depth of less than 50 km and a magnitude M larger than 4. Analysed are night-time Es-spread effects using data of the vertical sounding station Petropavlovsk- Kanchatsky (φ=53.0°, λ=158.7°) from May 2004 until August 2004 registered every 15 minutes. It is found that the maximum distance of the earthquake from the sounding station, where pre-seismic phenomena are yet observable, depends on the magnitude of the earthquake. Further it is shown that 1-2 days before the earthquakes, in the premidnight hours, the appearance of Es-spread increases. The reliability of this increase amounts to 0.95.
The statistical analysis of the variations of the dayly-mean frequency of the maximum ionospheric electron density foF2 is performed in connection with the occurrence of (more than 60) earthquakes with magnitudes M > 6.0, depths h < 80 km and distances from the vertical sounding station R < 1000 km. For the study, data of the Tokyo sounding station are used, which were registered every hour in the years 1957-1990. It is shown that, on the average, foF2 decreases before the earthquakes. One day before the shock the decrease amounts to about 5 %. The statistical reliability of this phenomenon is obtained to be better than 0.95. Further, the variations of the occurrence probability of the turbulization of the F-layer (F spread) are investigated for (more than 260) earthquakes with M > 5.5, h < 80 km, R < 1000 km. For the analysis, data of the Japanese station Akita from 1969-1990 are used, which were obtained every hour. It is found that before the earthquakes the occurrence probability of F spread decreases. In the week before the event, the decrease has values of more than 10 %. The statistical reliability of this phenomenon is also larger than 0.95. Examining the seismo-ionospheric effects, here periods of time with weak heliogeomagnetic disturbances are considered, the Wolf number is less than 100 and the index ∑ Kp is smaller than 30.
On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.
We develop an approach to the problem of optimal recovery of continuous linear functionals in Banach spaces through information on a finite number of given functionals. The results obtained are applied to the problem of the best analytic continuation from a finite set in the complex space Cn, n ≥ 1, for classes of entire functions of exponential type which belong to the space Lp, 1 < p < 1, on the real subspace of Cn. These latter are known as Wiener classes.
Contents: Part I: Symplectic Geometry Chapter 1: Symplectic Spaces and Lagrangian Planes Chapter 2: The Symplectic Group Chapter 3: Multi-Oriented Symplectic Geometry Chapter 4: Intersection Indices in Lag(n) and Sp(n) Part II: Heisenberg Group, Weyl Calculus, and Metaplectic Representation Chapter 5: Lagrangian Manifolds and Quantization Chapter 6: Heisenberg Group and Weyl Operators Chapter 7: The Metaplectic Group Part III: Quantum Mechanics in Phase Space Chapter 8: The Uncertainty Principle Chapter 9: The Density Operator Chapter 10: A Phase Space Weyl Calculus
We study the Cauchy problem for the oscillation equation of the couple-stress theory of elasticity in a bounded domain in R3. Both the displacement and stress are given on a part S of the boundary of the domain. This problem is densely solvable while data of compact support in the interior of S fail to belong to the range of the problem. Hence the problem is ill-posed which makes the standard calculi of Fourier integral operators inapplicable. If S is real analytic the Cauchy-Kovalevskaya theorem applies to guarantee the existence of a local solution. We invoke the special structure of the oscillation equation to derive explicit conditions of global solvability and an approximation solution.