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In this paper, we prove three types of rigidity results related to CAT(-1) spaces, namely the rigidity of the isometric actions on CAT(-1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles.
      
This is done by reducing the problem to the case of bipartite quivers of a special form and using a function DP on three matrices, which is a mixture of the determinant and two pfaffians.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
This wavelet basis is obtained from three wavelet generators by scaling, translation and rotation, and the wavelets are supported either by one corner triangle or a pair of adjacent triangles in the triangulation of level k - 1.
      
Every frame is a sum of three (but not two) orthonormal bases-and other frame representations
      
We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H.
      
In this article we develop analytical and computational tools arising from harmonic analysis on the motion group of three-dimensional Euclidean space.
      
To this end, we review the theory of unitary representations of the motion group of three dimensional Euclidean space.
      
In particular, we are able to treat the Pinsky phenomenon for eigenfunction expansions of piecewise smooth functions with jump across the boundary of a ball on such manifolds, in dimension three.
      
In this article, we study three interconnected inverse problems in shift invariant
      
Our main results relate the convergence of the chromatic expansions to the asymptotic behavior of the coefficients appearing in the three term recurrence satisfied by the corresponding family of orthogonal polynomials PMn(ω).
      
The model with three common biophoric sites such as center of triazole ring for A, center of phenyl ring for B, and charge heteroatom for C.
      
This progress is situated at three different levels.
      
The CoMFA analysis was performed by calculating steric and electrostatic interaction energies around a three dimensional grid.
      
For the GRA model, thirteen molecules were used as training set and three as test set to evaluate the external predictability of the equations generated using GFA [r2 = 0.650 and r2pred = 0.807].
      
Two new C19 quassinoids 1 and 2 were isolated from the stem bark of Ailanthus excelsa along with three known quassinoids excelsin, glaucarubin and polyandrol.
      
1) for R isomers with correlation coefficient r =0.9, chance= 0.05 and match= 0.47 has four biophoric sites and three secondary sites while the best model for S isomers (model no.
      
2) with correlation coefficient r =0.86, chance =0.01 and match = 0.45 has three biophoric sites and two secondary sites.
      
Three chemical entities were synthesized as analogs of fenbufen as well as open ring analog of suldinac and celecoxib.
      
 

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