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Proceedings of the London Mathematical Society, 1933
Die Anzahl der linear-unabhängigen Seminvarianten (oder Kovarianten) vom Grade \(\delta\) und Gewichten \(\alpha,\beta,\gamma\) einer ternären Form \(a_x^n\) ist gleich dem Koeffizienten von \(y^\beta z^\gamma\) in der erzeugenden Funktion \[ (1 - y) (1 - z) (1 - \frac{z}{y}) \sum_{r+s=0}^n y^{r\delta} z^{s\delta} \mathop{{\prod}'}_{\rho+\sigma=0}^n ...
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Die Anzahl der linear-unabhängigen Seminvarianten (oder Kovarianten) vom Grade \(\delta\) und Gewichten \(\alpha,\beta,\gamma\) einer ternären Form \(a_x^n\) ist gleich dem Koeffizienten von \(y^\beta z^\gamma\) in der erzeugenden Funktion \[ (1 - y) (1 - z) (1 - \frac{z}{y}) \sum_{r+s=0}^n y^{r\delta} z^{s\delta} \mathop{{\prod}'}_{\rho+\sigma=0}^n ...
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Generalized Lipschitz Functions
Computational Methods and Function Theory, 2006Lipschitz classes with variable exponents \(\text{Lip}_{\alpha(t)}\) are introduced. The exponents \({\alpha(t)}\) (called test functions) are supposed to be real-valued continuous functions defined in the right neighbourhood of zero satisfying the following conditions: \[ 1)\;{\alpha(t) = \alpha + o(1)},\;\alpha\in {\mathbb R};\quad 2) \;\int_{0}^{t} \
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Portfolio Generating Functions
SSRN Electronic Journal, 1998A general method is presented for constructing dynamic equity portfolios through the use of mathematical generating functions. The return on these functionally generated portfolios is related to the return on the market portfolio by a stochastic differential equation.
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Harmonic generalized functions in generalized function algebras
Monatshefte für Mathematik, 2009The analysis of properties of harmonic generalized functions within the framework of Colombeau theory is carried out. The authors present generalizations of the maximum principle and Liouville's theorem for harmonic generalized functions. The Dirichlet problem is solved by an application of the Poisson formula in the framework of generalized functions.
Pilipović, Stevan +1 more
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Generating Functions for Hermite Functions
Canadian Journal of Mathematics, 1959Hermite's function Hn(x) is denned for all complex values of x and n bywhere F (α; γ; x) is Kummer's function with the customary indices omitted. It satisfies the differential equation1.1of whichis a second solution. Every solution of (1.1) is an entire function.
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Generating Functions for Ultraspherical Functions
Canadian Journal of Mathematics, 1968The ultraspherical function1.1for |1 — x| < 2 is a solution of the differential equation1.2This equation has two independent solutions; of the two, only Pn(λ)(x) is analytic at x = 1, aside for some special values of λ, which we shall not consider.
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Composition and functions of bacterial membrane vesicles
Nature Reviews Microbiology, 2023Masanori Toyofuku +2 more
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Gene regulation by long non-coding RNAs and its biological functions
Nature Reviews Molecular Cell Biology, 2020Luisa Statello +2 more
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The expanding regulatory mechanisms and cellular functions of circular RNAs
Nature Reviews Molecular Cell Biology, 2020Ling-Ling Chen
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The regulation and functions of DNA and RNA G-quadruplexes
Nature Reviews Molecular Cell Biology, 2020Jochen Spiegel +2 more
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