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Pure States, Positive Matrix Polynomials and Sums of Hermitian Squares

Let M be an archimedean quadratic module of real t×t matrix polynomials in n variables, and let S ⊆ ℝn be the set of all points where each element of M is positive semidefinite. Our key finding is a ...
Nature

Trigonometric Sums And Summation Formulas

Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...
JSTOR Daily

Plana's Summation Formula for $\sum^\infty_{m=1,3,\ldots} m^{-2} \sin(m \alpha), m^{-3} \cos(m\alpha), m^{-2} A^m, m^{-3} A^m$

This is a preview. Log in through your library . Abstract The four series $$\sum^\infty_0 \sin(2k + 1)\alpha/(2k + 1)^2, \quad\sum^\infty_0 \cos(2k + 1)\alpha/(2k + 1 ...

Mathematical 'sum of zeros' trick exposes topological magnetization in quantum materials

A new study addresses a foundational problem in the theory of driven quantum matter by extending the Středa formula to ...