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$L^p$ Matrix Coefficients for Nilpotent Lie Groups
Rocky Mountain Journal of Mathematics, 1996 Suppose that \(G\) is a connected nilpotent Lie group. For any irreducible unitary representation \(\pi\) of \(G\), denote by \(N_\pi\) its kernel. The main theorem of the paper under review is that there exists \(p\) in \([2,\infty)\), depending only on \(G\), such that the matrix coefficients \(g\mapsto\langle\pi(g)\xi,\eta\rangle\) lie in \(L^p(G/N_\
Corwin, Lawrence, Moore, Calvin C.
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P matrix properties, injectivity, and stability in chemical reaction systems [PDF]
, 2007 In this paper we examine matrices which arise naturally as Jacobians in chemical dynamics. We are particularly interested in when these Jacobians are P matrices (up to a sign change), ensuring certain bounds on their eigenvalues, precluding certain ...
Hadamard J. +3 more
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The almost semimonotone matrices
Special Matrices, 2019 A (strictly) semimonotone matrix A ∈ ℝn×n is such that for every nonzero vector x ∈ ℝn with nonnegative entries, there is an index k such that xk > 0 and (Ax)k is nonnegative (positive).
Wendler Megan
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Journal of Advanced Joining Processes, 2022 Due to their positive properties, AMC materials represent a current trend in industrial applications and thus a major research focus. But currently their difficult machinability limits a full establishment.
M. Winkler +4 more
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Spectra of matrices with P-matrix powers
Linear Algebra and its Applications, 1986 Let A be an \(n\times n\) matrix with all powers having all principal minors positive. It is not known if these conditions force the eigenvalues of A to be all positive. The authors prove that conclusion for \(n\leq 4\), and show in general that the eigenvalues of A with the same absolute value form the vertices of a regular polygon of odd order, with ...
Hershkowitz, Daniel, Johnson, Charles R.
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On the Burer-Monteiro method for general semidefinite programs
, 2020 Consider a semidefinite program (SDP) involving an $n\times n$ positive semidefinite matrix $X$. The Burer-Monteiro method uses the substitution $X=Y Y^T$ to obtain a nonconvex optimization problem in terms of an $n\times p$ matrix $Y$.
Cifuentes, Diego
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Multidimensional extension of the generalized Chowla-Selberg formula [PDF]
, 1997 After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous ...
Elizalde, E.
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On some properties of P-matrix sets
Linear Algebra and its Applications, 1999 AbstractA nonempty set %plane1D;49E; in ℝn×n is said to have the row-P-property if every row representative of %plane1D;49E; is a P-matrix. We show that this property is equivalent to saying that for every nonzero x in ℝn there is an index i with x1(Mx)1 > 0 for all M∈%plane1D;49E;.
Song, Yoon +2 more
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Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies [PDF]
, 1992 Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra.
A.B. Zamolodchikov +39 more
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Multistep Transformations of DNA Origami Domino Array via Mechanical Forces
Small Structures, 2023 Nanostructures that display controllable motions and functions are indispensable to build molecular nanomachines. Structural DNA nanotechnology, enabling precise design of complex static and dynamic structures, can be used to construct molecular ...
Yan Liu +8 more
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