Fundamental solution of the operator for n>3
Zofia Szmydt, Bogdan Ziemian (1979)
Annales Polonici Mathematici
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Zofia Szmydt, Bogdan Ziemian (1979)
Annales Polonici Mathematici
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James H. Schmerl (2003)
Fundamenta Mathematicae
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The plane can be covered by n + 2 clouds iff .
Xiliang Bao, Francis Bonahon (2002)
Bulletin de la Société Mathématique de France
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A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic -space which, in the projective model for , is just the intersection of with a projective polyhedron whose vertices are all outside and whose edges all meet . We classify hyperideal polyhedra, up to isometries of , in terms of their combinatorial type and of their dihedral angles.
Adrian Karpowicz (2010)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We consider the following Darboux problem for the functional differential equation a.e. in [0,a]×[0,b], u(x,y) = ψ(x,y) on [-a₀,a]×[-b₀,b]where the function is defined by for (s,t) ∈ [-a₀,0]×[-b₀,0]. We prove a theorem on existence of the Carathéodory solutions of the above problem.
Mordechay B. Levin (2013)
Colloquium Mathematicae
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We prove the central limit theorem for the multisequence where , are reals, are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in . The main tool is the S-unit theorem.
Wojciech Bielas, Andrzej Kucharski, Szymon Plewik (2021)
Mathematica Bohemica
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We prove that the Niemytzki plane is -metrizable and we try to explain the differences between the concepts of a stratifiable space and a -metrizable space. Also, we give a characterisation of -metrizable spaces which is modelled on the version described by Chigogidze.
Frank J. Hall, Miroslav Rozložník (2016)
Czechoslovak Mathematical Journal
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A real matrix is a G-matrix if is nonsingular and there exist nonsingular diagonal matrices and such that , where denotes the transpose of the inverse of . Denote by a diagonal (signature) matrix, each of whose diagonal entries is or . A nonsingular real matrix is called -orthogonal if . Many connections are established between these matrices. In particular, a matrix is a G-matrix if and only if is diagonally (with positive diagonals) equivalent to a column permutation...
Junehyuk Jung (2014)
Journal of the European Mathematical Society
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Let be a hyperbolic surface and let be a Laplacian eigenfunction having eigenvalue with . Let be the set of nodal lines of . For a fixed analytic curve of finite length, we study the number of intersections between and in terms of . When is compact and a geodesic circle, or when has finite volume and is a closed horocycle, we prove that is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between and is . This bound is...
Christopher J. Leininger, Saul Schleimer (2014)
Journal of the European Mathematical Society
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We prove, for any , that there is a closed connected orientable surface so that the hyperbolic space almost-isometrically embeds into the Teichmüller space of , with quasi-convex image lying in the thick part. As a consequence, quasi-isometrically embeds in the curve complex of .
Mohammad Soleymani (2024)
Czechoslovak Mathematical Journal
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Let , be matrices. The concept of matrix majorization means the th column of is majorized by the th column of and this is done for all by a doubly stochastic matrix . We define rc-majorization that extended matrix majorization to columns and rows of matrices. Also, the linear preservers of rc-majorization will be characterized.
Mokhtar Kirane, Salim Messaoudi (2002)
Annales Polonici Mathematici
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We consider the systems of hyperbolic equations ⎧, t > 0, , (S1) ⎨ ⎩, t > 0, ⎧, t > 0, , (S2) ⎨ ⎩, t > 0, , (S3) ⎧, t > 0, , ⎨ ⎩, t > 0, , in with u(0,x) = u₀(x), v(0,x) = v₀(x), uₜ(0,x) = u₁(x), vₜ(0,x) = v₁(x). We show that, in each case, there exists a bound B on N such that for 1 ≤ N ≤ B solutions to the systems blow up in finite time.
Daniel Uzcátegui Contreras, Dardo Goyeneche, Ondřej Turek, Zuzana Václavíková (2021)
Communications in Mathematics
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It is known that a real symmetric circulant matrix with diagonal entries , off-diagonal entries and orthogonal rows exists only of order (and trivially of order ) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries and any complex entries of absolute value off the diagonal. As a particular case, we consider...
Jay Jorgenson, Jürg Kramer (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces , nowadays called Faltings’s delta function and here denoted by . For a given compact Riemann surface of genus , the invariant is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space of genus curves determined by to its boundary . In this paper we begin by revisiting a formula derived...
Sheng-Liang Yang, Yan-Xue Xu, Tian-Xiao He (2017)
Czechoslovak Mathematical Journal
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For integers , Brietzke (2008) defined the -central coefficients of an infinite lower triangular matrix as , with , and the -central coefficient triangle of as It is known that the -central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array with and , we obtain the generating function of its -central coefficients and give an explicit representation for the -central Riordan array in terms of the Riordan array ....
Ionut Chifan, Thomas Sinclair (2013)
Annales scientifiques de l'École Normale Supérieure
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Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in , , are virtually -superrigid.
Martine Babillot, Marc Peigné (2006)
Bulletin de la Société Mathématique de France
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We consider a large class of non compact hyperbolic manifolds with cusps and we prove that the winding process generated by a closed -form supported on a neighborhood of a cusp , satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp and the Poincaré exponent of . No assumption on the value of is required and this theorem generalises previous results due to Y. Guivarc’h, Y. Le Jan, J. Franchi and N. Enriquez. ...
Jan Brandts, Abdullah Cihangir (2019)
Applications of Mathematics
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A -simplex is the convex hull of affinely independent vertices of the unit -cube . It is nonobtuse if none of its dihedral angles is obtuse, and acute if additionally none of them is right. Acute -simplices in can be represented by -matrices of size whose Gramians have an inverse that is strictly diagonally dominant, with negative off-diagonal entries. In this paper, we will prove that the positive part of the transposed inverse of is doubly stochastic and has the...
Yuri Kifer (2014)
Annales de l'I.H.P. Probabilités et statistiques
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We consider “nonconventional” averaging setup in the form , where , is either a stochastic process or a dynamical system with sufficiently fast mixing while , and , grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.
Gabriel Vigny (2014)
Annales de l’institut Fourier
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Let be a dominant rational map of such that there exists with for all . Under mild hypotheses, we show that, for outside a pluripolar set of , the map admits a hyperbolic measure of maximal entropy with explicit bounds on the Lyapunov exponents. In particular, the result is true for polynomial maps hence for the homogeneous extension of to . This provides many examples where non uniform hyperbolic dynamics is established. One of the key tools is to approximate...