Tootfinder

This https://arxiv.org/abs/2311.04039 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Free Integral Calculus
We study the problem of conditional expectations in free random variables and provide closed formulas for the conditional expectation of resolvents of arbitrary non-commutative polynomials in free random variables onto the subalgebra of an arbitray subset of the variables. More precisely, given a linearization of the resolvent we compute a linearization of its conditional expectation. The coefficients of the expressions obtained in this process involve certain Boolean cumulant functionals which…

This https://arxiv.org/abs/2310.18408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Alternative effective mass functions in the modified Mukhanov-Sasaki equation of loop quantum cosmology
Modifications to the Mukhanov-Sasaki equation in loop quantum cosmology (LQC) have been phenomenologically explored using polymerization of the connection and related variables in the classical expressions in order to capture the quantum gravity effects in cosmological perturbations which replace the classical big bang by a big bounce. Examples of this strategy include the dressed metric and the hybrid approaches whose inter-relationship at an effective level was demonstrated by the authors rec…

Action-Angle Variables for Axisymmetric Potentials via Birkhoff Normalization
Sam Hadden
https://arxiv.org/abs/2404.16941 https://arx…

Action-Angle Variables for Axisymmetric Potentials via Birkhoff Normalization
We describe a method for calculating action-angle variables in axisymmetric galactic potentials using Birkhoff normalization, a technique from Hamiltonian perturbation theory. An advantageous feature of this method is that it yields explicit series expressions for both the forward and inverse transformations between the action-angle variables and position-velocity data. It also provides explicit expressions for the Hamiltonian and dynamical frequencies as functions of the action variables. We t…

This https://arxiv.org/abs/2403.17952 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums
In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new formulas of Mneimneh-type binomial sums involving generalized (alternating) harmonic numbers. Further, we establish a new identity relating the multiple zeta star values $ζ^\star(m+2,\{1\}_{r-1})$ and specific multiple polylogarithms by applying the Toeplitz prin…

This https://arxiv.org/abs/2310.13437 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Black hole thermodynamics in natural variables: Quadrophenia
It was recently observed in arXiv:2304.07320 for thermal Kerr-Newman black holes in 4d flat space that one can rewrite the conventional thermodynamics on the inner and outer horizons in terms of left- and right-moving variables with a remarkable simplification of the corresponding expressions. With the goal of illustrating the wide applicability of these newly proposed natural variables, we extend the original observation in four independent directions that can be further superimposed on each o…

Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution
Jean-Christophe Pain
https://arxiv.org/abs/2402.11298 https://

Clebsch-Gordan coefficients, hypergeometric functions and the binomial distribution
A particular case of degenerate Clebsch-Gordan coefficient can be expressed with three binomial coefficients. Such a formula, which may be obtained using the standard ladder operator procedure, can also be derived from the Racah-Shimpuku formula or from expressions of Clebsch-Gordan coefficients in terms of $_3F_2$ hypergeometric functions. The O'Hara interesting interpretation of this Clebsch-Gordan coefficient by binomial random variables can also be related to hypergeometric functions ($_2F_…

Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums
Ende Pan, Ce Xu
https://arxiv.org/abs/2403.17952 https://arxiv.org/pdf/240…

Mneimneh-type Binomial Sums of Multiple Harmonic-type Sums
In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new formulas of Mneimneh-type binomial sums involving generalized (alternating) harmonic numbers. Further, we establish a new identity relating the multiple zeta star values $ζ^\star(m+2,\{1\}_{r-1})$ and specific multiple polylogarithms by applying the Toeplitz prin…

FORM-based global reliability sensitivity analysis of systems with multiple failure modes
Iason Papaioannou, Daniel Straub
https://arxiv.org/abs/2403.12822

FORM-based global reliability sensitivity analysis of systems with multiple failure modes
Global variance-based reliability sensitivity indices arise from a variance decomposition of the indicator function describing the failure event. The first-order indices reflect the main effect of each variable on the variance of the failure event and can be used for variable prioritization; the total-effect indices represent the total effect of each variable, including its interaction with other variables, and can be used for variable fixing. This contribution derives expressions for the varia…