Results 261 to 270 of about 61,672 (299)

Simple Variational Bound to the Entropy

Physical Review, 1964
The following variational principle is obtained for the entropy $S(E)$ of a system with energy $E:S(E)\ensuremath{\geqq}\ensuremath{-}k \mathrm{ln}(\mathrm{Trace}{U}^{2})$ for all non-negative Hermitian density matrices $U$ with Trace $U=1$, Trace $HU=E$; $H$ is the Hamiltonian and $k$ is Boltzmann's constant.
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Functionals of Bounded Frechet Variation

Canadian Journal of Mathematics, 1949
In a series of papers which will follow this paper the authors will present a theory of functionals which are bilinear over a product A × B of two normed vector spaces A and B. This theory will include a representation theory, a variational theory, and a spectral theory.
Morse, Marston, Transue, William
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A generalization of bounded variation

Acta Mathematica Hungarica, 1990
The notion of bounded \(p\)-variation was introduced by \textit{N. Wiener} in 1924 [see Mass. J. Math. 3, 72--94 (1924; JFM 50.0203.01)]. \textit{D. Waterman} [Stud. Math. 44, 107--117 (1972; Zbl 0207.06901)] and \textit{Z. A. Chanturiya} [Dokl. Akad. Nauk SSSR 214, 63--66 (1974; Zbl 0295.26008)] have made important contributions concerning the concept
Kita, H., Yoneda, K.
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Omniscience Principles and Functions of Bounded Variation

MLQ, 2002
Omniscience principles are general statements that can be proved classically but not constructively. They are used to show that other, more subject-specific statements that imply some omniscience principle do not have a constructive proof. The strongest omniscience principle is the law of excluded middle itself.
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Variational bounds to the overlap

Chemical Physics Letters, 1975
Abstract Starting from a closed expression for the overlap, variational upper and lower bounds to the overlap are derived by means of operator inequalities.
Thomas Hoffmann-Ostenhof, Maria Hoffmann-Ostenhof   +1 more
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ON FUNCTIONS OF BOUNDED $ p$-VARIATION

Mathematics of the USSR-Izvestiya, 1968
In this article we obtain an asymptotic formula for the approximations to functions in the class (, ) by Fourier sums in the metric of (). We find sufficient conditions and also criteria for the continuity of the derivative of a function in the class . We also give some results on the Fourier coefficients of functions in the above class.
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A generalization of bounded variation

Acta Mathematica Hungarica, 2002
The author proves some properties of the class \(\text{B}\Lambda(p(n)\uparrow \infty,\varphi)\). In particular he shows that if \(f\in \text{BV}(p(n)\uparrow\infty,\varphi)\), then \(f\in \text{B}\Lambda(p(n)\uparrow \infty,\varphi)\). The author establishes the exact order of the Fourier coefficients of functions in \(\text{B}\Lambda (p(n)\uparrow ...
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Functions of Bounded Variation

2015
We know that if f is integrable, then the lower and upper sums of every partition F approximate its integral from below and above, and so the difference between either sum and the integral is at most \(S_{F} - s_{F} =\varOmega _{F}\), the oscillatory sum corresponding to F.
Miklós Laczkovich, Vera T. Sós
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Bounded Variation in Binary Sequences

2022
Christoph Buchheim, Maja Hügging
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Bivariate functions of bounded variation: Fractal dimension and fractional integral

Indagationes Mathematicae, 2020
, P Viswanathan
exaly