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## 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
$$
{\alpha _1}\lambda _1^k + \cdots + {\alpha _s}\lambda _s^k - {\alpha _{s + 1}}\lambda _{s + 1}^k - \cdots - {\alpha _{2s}}\lambda _{2s}^k = 0.
$$

## Mondphasen, Osterrechnung und ewiger Kalender

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

## Strict measure rigidity for unipotent subgroups of solvable groups

### Inventiones mathematicae (1990-12-01) 101: 449-482 , December 01, 1990

## 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.

## 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.

## Geometrical problem solving — the state of the art c. 1635

### Redefining Geometrical Exactness (2001-01-01): 211-221 , January 01, 2001

The present chapter concludes my discussion of the early modern tradition of geometrical problem solving before Descartes. Problem solving constituted the primary context of Descartes’ geometrical studies to which Part II is devoted. His contributions, however, changed the theory and practice of geometrical problem solving in so fundamental a manner that they eclipsed many of the techniques, concepts, and concerns of the earlier tradition. It is therefore appropriate to conclude Part I by a sketch of the state of the art of geometrical problem solving around 1635, that is, just before Descartes published his innovations (and also before Fermat’s new techniques began to circulate among cognoscenti).

## An application of number theory to ergodic theory and the construction of uniquely ergodic models

### Israel Journal of Mathematics (1979-09-01) 33: 231-240 , September 01, 1979

Using a combinatorial result of N. Hindman one can extend Jewett’s method for proving that a weakly mixing measure preserving transformation has a uniquely ergodic model to the general ergodic case. We sketch a proof of this reviewing the main steps in Jewett’s argument.