A bstract Track functions describe the collective effect of fragmentation quarks and gluons into charged hadrons, making them a key ingredient for jet substructure measurements at hadron colliders, where track-based offer superior angular resolution. The first moment track function, describing average energy deposited in particles, is simple well-studied object. However, higher-point correlatio...

Sequential Monte Carlo and quantum mechanical calculations of the electronic polarization of the ground and first vertical excited states of 1H-benzotriazole in water are made. Using statistically uncorrelated configurations and CASSCF ab initio calculations the increase in the ground and excited state dipole moments of 1Hbenzotriazole from gas phase to aqueous environment are obtained as 2.89 ...

Contents 1. Introduction. 2. The distribution function of a random variable. 3. Classification of random variables. 4. Some special discrete probability distributions. 5. Some special continuous probability distributions. 6. Location characteristics of a real-valued random variable. 7. Dispersion characteristics of a real-valued random variable. 8. Joint distribution functions. 9. Independence ...

This note analyzes the distributional properties of Pareto Type III random variables. The orignal two parameters distribution proposed by Pareto is expanded in a three parameters version and both its density and characteristic function are derived. The analytic expression of the inverse distribution function is also obtained, together with a simple series expansion of its moments of any order. ...

Abstract We obtain a combinatorial formula for the positive integer moments of partition function $$C\beta E_{N}$$ C β E N field, or equivalently characteristic polynomial ensemble. then use this to establish larg...

In this paper , a steganalysis scheme based on multiple features formed by statistical moments of wavelet characteristic functions is proposed. Our theoretical analysis has pointed out that the defined n-th statistical moment of a wavelet characteristic function is related to the n-th derivative of the corresponding wavelet histogram, and hence is sensitive to data embedding. The selection of t...

in this paper, a new and ecient approach is applied for numerical approximationof the linear dierential equations with variable coecients based on operational matriceswith respect to hermite polynomials. explicit formulae which express the hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of theoriginal expansion coecients of the function itse...

Abstract We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal polynomials; b) constructed from Cauchy transforms of the same orthogonal polynomials and finally c) those constructed from both orthogonal polynomials and the...