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## Orbit Decidability, Applications and Variations

### Extended Abstracts Fall 2012 (2014-01-01): 1 , January 01, 2014

## Small Nonnegative Solutions of Additive Equations

### Diophantine Equations and Inequalities in Algebraic Number Fields (1991-01-01): 111-126 , January 01, 1991

Let α_{1}…,α_{2s} be 2*s* nonzero elements of *P.* Consider the additive equation of the type
9.1
$$
{\alpha _1}\lambda _1^k + \cdots + {\alpha _s}\lambda _s^k - {\alpha _{s + 1}}\lambda _{s + 1}^k - \cdots - {\alpha _{2s}}\lambda _{2s}^k = 0.
$$

## Block SSOR preconditionings for high order 3d fe systems

### BIT (1989-12-01) 29: 805-823 , December 01, 1989

For solving 3D high order hierarchical FE systems the block SSOR preconditioned CG algorithms based on new stripwise block two-color orderings of degrees of freedom and providing for efficient concurrent/vector implementation are suggested. As demonstrated by numerical results for the 3D Navier equations approximated using hierarchical order*p*, 2 ≤*p* ≤ 5, FE's the convergence rate of such BSSOR-CG algorithms is only slightly dependent on*p* and mesh nonunformity.

## Mondphasen, Osterrechnung und ewiger Kalender

### Monatshefte für Mathematik und Physik (1917-12-01) 28: A14 , December 01, 1917

## Biharmonic Maps

### Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields (2013-01-01): 243-304 , January 01, 2013

The last five decades have witnessed many developments in the theory of harmonic maps. To become acquainted to some of these, the reader is referred to two reports and a survey paper by Eells and Lemaire [119, 122, 124] about the developments of harmonic maps up to 1988 for details. Several books on harmonic maps [203, 205, 206, 389, 425] are also available. In this chapter, we follow the notions and notations of harmonic maps between Riemannian manifolds by Eells- Sampson [129] in the introduction.We discuss the crucial topics in harmonic maps including fundamentals, regularity, maps of surfaces, maps of KRahler manifolds, maps into groups and Grassmannians, harmonic maps, loop groups, and integrable systems, harmonicmorphisms, maps of singular spaces, and transversally harmonic maps. Since the theory of harmonic maps has been developed over half a century, it is impossible to provide full details. However, we try to present the most important components of the topics.

## Large Deviations for Multivalued Stochastic Differential Equations

### Journal of Theoretical Probability (2010-12-01) 23: 1142-1156 , December 01, 2010

We prove a large deviation principle of Freidlin–Wentzell type for multivalued stochastic differential equations with monotone drifts that in particular contain a class of SDEs with reflection in a convex domain.

## Singular Integrals on Product Homogeneous Groups

### Integral Equations and Operator Theory (2013-05-01) 76: 55-79 , May 01, 2013

We consider singular integral operators with rough kernels on the product space of homogeneous groups. We prove *L*^{p} boundedness of them for
$${p \in (1,\infty)}$$
under a sharp integrability condition of the kernels.

## Aussagen- und Schaltungsalgebra

### Algebra für Informatiker (1985-01-01): 207-246 , January 01, 1985

### Zusammenfassung

Dieselben algebraischen Strukturen liefern die mathematische Beschreibung sowohl für die Kombination von Aussagen,als auch von Schaltungen. Darauf beruht die Möglichkeit, Aussagen durch Schaltungen darzustellen und somit das gesamte Computerwesen.

## Über die Integration der Whittakerschen Differentialgleichung in geschlossener Form

### Monatshefte für Mathematik und Physik (1937-12-01) 46: 1-9 , December 01, 1937

## Nonself-similar flow with a shock wave reflected from the center of symmetry and new self-similar solutions with two reflected shocks

### Computational Mathematics and Mathematical Physics (2013-03-01) 53: 350-368 , March 01, 2013

In some problems concerning cylindrically and spherically symmetric unsteady ideal (inviscid and nonheat-conducting) gas flows at the axis and center of symmetry (hereafter, at the center of symmetry), the gas density vanishes and the speed of sound becomes infinite starting at some time. This situation occurs in the problem of a shock wave reflecting from the center of symmetry. For an ideal gas with constant heat capacities and their ratio γ (adiabatic exponent), the solution of this problem near the reflection point is self-similar with a self-similarity exponent determined in the course of the solution construction. Assuming that γ on the reflected shock wave decreases, if this decrease exceeds a threshold value, the flow changes substantially. Assuming that the type of the solution remains unchanged for such γ, self-similarity is preserved if a piston starts expanding from the center of symmetry at the reflection time preceded by a finite-intensity reflected shock wave propagating at the speed of sound. To answer some questions arising in this formulation, specifically, to find the solution in the absence of the piston, the evolution of a close-to-self-similar solution calculated by the method of characteristics is traced. The required modification of the method of characteristics and the results obtained with it are described. The numerical results reveal a number of unexpected features. As a result, new self-similar solutions are constructed in which two (rather than one) shock waves reflect from the center of symmetry in the absence of the piston.