On the Mechanism of Self-Oscillations of a Supersonic Radial Jet Exhausting into an Ambient Space

2016 ◽  
Keyword(s):  
Ambient Space

SMOLYANOV–WEIZSÄCKER SURFACE MEASURES GENERATED BY DIFFUSIONS ON THE SET OF TRAJECTORIES IN RIEMANNIAN MANIFOLDS

2008 ◽  
Vol 11 (01) ◽  
pp. 21-31 ◽  
Author(s):  
ILYA V. TELYATNIKOV
Keyword(s):  
Brownian Motion ◽  
Euclidean Space ◽  
Diffusion Process ◽  
Riemannian Manifolds ◽  
Marginal Distribution ◽  
Diffusion Processes ◽  
Ambient Space ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Limit Surface

We consider surface measures on the set of trajectories in a smooth compact Riemannian submanifold of Euclidean space generated by diffusion processes in the ambient space. A construction of surface measures on the path space of a smooth compact Riemannian submanifold of Euclidean space was introduced by Smolyanov and Weizsäcker for the case of the standard Brownian motion. The result presented in this paper extends the result of Smolyanov and Weizsäcker to the case when we consider measures generated by diffusion processes in the ambient space with nonidentical correlation operators. For every partition of the time interval, we consider the marginal distribution of the diffusion process in the ambient space under the condition that it visits the manifold at all times of the partition, when the mesh of the partition tends to zero. We prove the existence of some limit surface measures and the equivalence of the above measures to the distribution of some diffusion process on the manifold.

scholarly journals Different structures on subspaces of OsckM

2013 ◽  
Vol 40 (1) ◽  
pp. 27-48
Author(s):  
Irena Comic ◽  
Radu Miron
Keyword(s):  
Vector Fields ◽  
Ambient Space

The geometry of OsckM spaces was introduced by R. Miron and Gh. Atanasiu in [6] and [7]. The theory of these spaces was developed by R. Miron and his cooperators from Romania, Japan and other countries in several books and many papers. Only some of them are mentioned in references. Here we recall the construction of adapted bases in T(OsckM) and T*(OsckM), which are comprehensive with the J structure. The theory of two complementary family of subspaces is presented as it was done in [2] and [4]. The operators J,?J, ?,??, p, p* are introduced in the ambient space and subspaces. Some new relations between them are established. The action of these operators on Liouville vector fields are examined.

Morse quasiflats I

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Jingyin Huang ◽  
Bruce Kleiner ◽  
Stephan Stadler
Keyword(s):  
Arbitrary Dimension ◽  
Ambient Space

Abstract This is the first in a series of papers concerned with Morse quasiflats, which are a generalization of Morse quasigeodesics to arbitrary dimension. In this paper we introduce a number of alternative definitions, and under appropriate assumptions on the ambient space we show that they are equivalent and quasi-isometry invariant; we also give a variety of examples. The second paper proves that Morse quasiflats are asymptotically conical and have canonically defined Tits boundaries; it also gives some first applications.

scholarly journals Multiprojective spaces and the arithmetically Cohen–Macaulay property

2018 ◽  
Vol 166 (3) ◽  
pp. 583-597 ◽  
Author(s):  
GIUSEPPE FAVACCHIO ◽  
JUAN MIGLIORE
Keyword(s):  
Ambient Space ◽  
Inclusion Property ◽  
New Construction ◽  
Multiprojective Spaces

AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.

scholarly journals Every timelike geodesic in Anti-de Sitter spacetime is a circle of the same radius

2016 ◽  
Vol 25 (01) ◽  
pp. 1650007 ◽  
Author(s):  
Leszek M. Sokołowski ◽  
Zdzisław A. Golda
Keyword(s):  
Flat Space ◽  
De Sitter Space ◽  
Ambient Space ◽  
Alternative Proof ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Timelike Geodesic ◽  
Sitter Spacetime

In this paper, we refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti-de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by [Formula: see text], lying on a Euclidean two-plane. Then, we outline an alternative proof for [Formula: see text]. We also make a comment on the shape of timelike geodesics in de Sitter space.

scholarly journals An integral formula for compact hypersurfaces in space forms and its applications

2003 ◽  
Vol 74 (2) ◽  
pp. 239-248 ◽  
Author(s):  
Luis J. Alías
Keyword(s):  
Scalar Curvature ◽  
Integral Formula ◽  
Flat Space ◽  
Gauss Map ◽  
Ambient Space ◽  
Geodesic Ball ◽  
Space Forms ◽  
Geodesic Spheres

AbstractIn this paper we establish an integral formula for compact hypersurfaces in non-flat space forms, and apply it to derive some interesting applications. In particular, we obtain a characterization of geodesic spheres in terms of a relationship between the scalar curvature of the hypersurface and the size of its Gauss map image. We also derive an inequality involving the average scalar curvature of the hypersurface and the radius of a geodesic ball in the ambient space containing the hypersurface, characterizing the geodesic spheres as those for which equality holds.

On the mechanism of self-oscillations of a supersonic radial jet exhausting into an ambient space

2016 ◽  
Vol 57 (2) ◽  
pp. 237-246 ◽  
Author(s):  
S. P. Kiselev ◽  
V. P. Kiselev ◽  
V. N. Zaikovskii
Keyword(s):  
Ambient Space

scholarly journals Non-abelian analogs of lattice rounding

2015 ◽  
Vol 7 (2) ◽  
Author(s):  
Evgeni Begelfor ◽  
Stephen D. Miller ◽  
Ramarathnam Venkatesan
Keyword(s):  
Euclidean Space ◽  
Word Problem ◽  
Discrete Group ◽  
Point Of View ◽  
Ambient Space ◽  
Basis Set ◽  
Theoretical Justification ◽  
Matrix Groups ◽  
Nearest Point ◽  
Random Products

AbstractLattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of non-abelian analogs of lattice rounding involving matrix groups. In one direction, we consider an algorithm for solving a normed word problem when the inputs are random products over a basis set, and give theoretical justification for its success. In another direction, we prove a general inapproximability result which essentially rules out

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