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The inclusion relation between Sobolev and modulation spaces
inclusion relation Sobolev modulation spaces
2010/11/30
The inclusion relations between the Lp-Sobolev spaces and the modulation spaces is determined explicitly. As an application,mapping properties of unimodular Fourier multiplier ei|D|
between Lp-Sobol...
Fluctuations arise universally in Nature as a re ection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, uctuations encode fundamental aspects of the ph...
Betti numbers of edge ideals of uniform hypergraphs
Betti number hypergraph Hilbert function Stanley-Reisner ring
2010/11/29
We describe the Betti numbers of the edge ideals I(G) of uniform hypergraphs G such that I(G) has linear graded free resolution.
Twisted acyclicity of a circle and link signatures
Twisted acyclicity of a circle link signatures
2010/11/30
Homology of the circle with non-trivial local coefficients is trivial.From this well-known fact we deduce geometric corollaries concerning links of codimension two. In particular, the Murasugi-Tristra...
Extending PT symmetry from Heisenberg algebra to E2 algebra
Extending PT symmetry Heisenberg algebra E2 algebra
2010/12/15
The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u; J] = iv, [v; J] = iu, [u; v] = 0. We can construct the Hamiltonian H = J2 +gu, where g is a real p...
One considers the monistic conception of a geometry, where there is only one fundamental quantity (world function). All other geometrical quantities a derivative quantities (functions of the world fun...
In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold (M, h , i). We then draw some geometric conclusions with the aid of the maximum principle.
Supplemental material to the article "Partitions of the triangles of the cross polytope into surfaces''
cross polytope simplicial complexes triangulated surfaces difference cycle
2010/12/6
We present a constructive proof, that there exists a decomposition of the 2-skeleton of the
k-dimensional cross polytope k into closed surfaces of genus ¤ 1, each with a transitive
automorphism gro...
Thermodynamic Geometry and Hawking Radiation
Quantum Gravity Hawking Radiation Horizon Perturbations Vaidya Geometry
2010/12/15
This work explores the role of thermodynamic fluctuations in the two parameter Hawking adiating
black hole configurations. The system is characterized by an ensemble of arbitrary mass and radiation f...
Geometric continuity and compatibility conditions for 4-patch surfaces
4-patch surface tangent plane continuity curvature continuity compatibility conditions
2010/11/29
When considering regularity of surfaces, it is its geometry that is of interest. Thus, the concept of geometric regularity or geometric continuity of a specific order is a relevant concept. In this pa...
Cyclic polygons in classical geometry
cyclic polygon Euclidean geometry hyperbolic geometry spherical geometry
2010/12/7
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
The Fundamental Lemma is a somewhat obscure combinatorial identity introduced by Robert P. Langlands [L79] as an ingredient in the theory of auto-morphic representations.
Dense graphs with a large triangle cover have a large triangle packing
Dense graphs with large triangle cover large triangle packing
2010/11/29
It is well known that a graph with m edges can be made triangle-free by removing (slightly less
than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make
triangle-f...
A result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry ne...
Multiplying Pessimistic Estimators:Deterministic Approximation of Max TSP and Maximum Triangle Packing
derandomization approximation algorithms pessimistic estimators maximum traveling salesman problem
2012/12/3
We give a generalization of the method of pessimistic estimators, in which we compose estimators by multiplying them. We give conditions on the pessimistic estimators of two expectations, under which ...