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On periodic pharmonic functions on Cayley tree.
, 803
"... Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index pharmonic function is a constant. For some normal subgroups of infinite index we describe a class of (nonconstant) periodic pharmonic functions. If p = 2, the ph ..."
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Cited by 2 (2 self)
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Abstract: We show that any periodic with respect to normal subgroups (of the group representation of the Cayley tree) of finite index pharmonic function is a constant. For some normal subgroups of infinite index we describe a class of (nonconstant) periodic pharmonic functions. If p = 2, the pharmonicity
Experimental verification of a negative index of refraction,”
 Science,
, 2001
"... Abstract: We studied a twodimensional squarelattice photonic crystal with allangle negative refraction at its first band. Using this photonic crystal, we designed and fabricated a flat lens functioning as a cylindrical lens by increasing the vertical dimension of the photonic crystal. Twodimensi ..."
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Cited by 377 (9 self)
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Abstract: We studied a twodimensional squarelattice photonic crystal with allangle negative refraction at its first band. Using this photonic crystal, we designed and fabricated a flat lens functioning as a cylindrical lens by increasing the vertical dimension of the photonic crystal
Oligomorphic permutation groups
 LONDON MATHEMATICAL SOCIETY STUDENT TEXTS
, 1999
"... A permutation group G (acting on a set Ω, usually infinite) is said to be oligomorphic if G has only finitely many orbits on Ω n (the set of ntuples of elements of Ω). Such groups have traditionally been linked with model theory and combinatorial enumeration; more recently their grouptheoretic pro ..."
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Cited by 320 (26 self)
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A permutation group G (acting on a set Ω, usually infinite) is said to be oligomorphic if G has only finitely many orbits on Ω n (the set of ntuples of elements of Ω). Such groups have traditionally been linked with model theory and combinatorial enumeration; more recently their group
GRAPHS OF BOUNDED DEGREE AND THE pHARMONIC BOUNDARY
, 806
"... Abstract. Let p be a real number greater than one and let G be a connected graph of bounded degree. In this paper we introduce the pharmonic boundary of G. We use this boundary to characterize the graphs G for which the constant functions are the only pharmonic functions on G. It is shown that any ..."
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Cited by 8 (3 self)
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that any continuous function on the pharmonic boundary of G can be extended to a function that is pharmonic on G. Some properties of this boundary that are preserved under roughisometries are also given. Now let Γ be a finitely generated group. As an application of our results we characterize
Numerical Methods for pHarmonic Flows and Applications to Image Processing
 SIAM J. NUMER. ANAL
, 2002
"... We propose in this paper an alternative approach for computing pharmonic maps and flows: instead of solving a constrained minimization problem on S N i, we solve an unconstrained minimization problem on the entire space of functions. This is possible, using the projection on the sphere of any arbi ..."
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Cited by 43 (6 self)
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We propose in this paper an alternative approach for computing pharmonic maps and flows: instead of solving a constrained minimization problem on S N i, we solve an unconstrained minimization problem on the entire space of functions. This is possible, using the projection on the sphere of any
Regularity of generalized sphere valued pharmonic
, 2003
"... Abstract. We prove (see Theorem 1.3 below) that a generalized harmonic map into a round sphere, i.e. a map u ∈ W 1,1loc (, Sn−1) which solves the system div (ui∇uj − uj∇ui) = 0, i, j = 1,..., n, is smooth as soon as ∇u  ∈ Lq for any q> 1, and the norm of u in BMO is sufficiently small. Here, ..."
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, ⊂ Rm is open, and m, n are arbitrary. This extends various earlier results of Almeida [1], Ge [15], and R. Moser [38]. A version of this result for generalized pharmonic maps into spheres is also proved. The proofs rely on the duality of Hardy space and BMO combined with Lp stability of the Hodge
Quantized Feedback Stabilization of Linear Systems
 IEEE Trans. Automat. Control
, 2000
"... This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that ..."
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Cited by 293 (27 self)
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functional that maps a realvalued function into a piecewise constant function taking on a finite...
Pigeon hole principle
 Journal of Formalized Mathematics
, 1990
"... Summary. We introduce the notion of a predicate that states that a function is onetoone at a given element of its domain (i.e. counterimage of image of the element is equal to its singleton). We also introduce some rather technical functors concerning finite sequences: the lowest index of the given ..."
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Cited by 261 (13 self)
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Summary. We introduce the notion of a predicate that states that a function is onetoone at a given element of its domain (i.e. counterimage of image of the element is equal to its singleton). We also introduce some rather technical functors concerning finite sequences: the lowest index
Nonlinear elliptic partial differential equations and pharmonic functions on graphs
, 2013
"... In this article we study the wellposedness (uniqueness and existence of solutions) of nonlinear elliptic Partial Differential Equations (PDEs) on a finite graph. These results are obtained using the discrete comparison principle and connectivity properties of the graph. This work is in the spirit ..."
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Cited by 1 (0 self)
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In this article we study the wellposedness (uniqueness and existence of solutions) of nonlinear elliptic Partial Differential Equations (PDEs) on a finite graph. These results are obtained using the discrete comparison principle and connectivity properties of the graph. This work is in the spirit
THE FIRST L pCOHOMOLOGY OF SOME FINITELY GENERATED GROUPS AND pHARMONIC FUNCTIONS
, 2005
"... Abstract. Let G be a finitely generated infinite group and let p> 1. In this paper we make a connection between the first L pcohomology space of G and pharmonic functions on G. We also describe the elements in the first L pcohomology space of groups with polynomial growth, and we give an inclu ..."
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Abstract. Let G be a finitely generated infinite group and let p> 1. In this paper we make a connection between the first L pcohomology space of G and pharmonic functions on G. We also describe the elements in the first L pcohomology space of groups with polynomial growth, and we give
Results 1  10
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1,642