Related papers: Reflection Identities of Harmonic Sums and pole de…
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…
We extend our previous work devoted to the computation of the next-to-next-to-leading order spin-orbit correction (corresponding to 3.5PN order) in the equations of motion of spinning compact binaries, by: (i) Deriving the corresponding…
We summarize our recent result for a splitting function for small x evolution which includes resummed small x logarithms deduced from the leading order BFKL equation with the inclusion of running coupling effects. We compare this improved…
We rigorously establish some exact properties of reflection symmetric spin systems with antiferromagnetic crossing bonds: At least one ground state has total spin zero and a positive semidefinite coefficient matrix. The crossing bonds obey…
From new integral representations of the $n$-th derivative of Bessel functions with respect to the order, we derive some reflection formulas for the first and second order derivative of $J_{\nu }\left( t\right) $ and $% Y_{\nu }\left(…
Bulgarian Solitaire is an interesting self-map on the set of integer partitions of a fixed number $n$. As a finite dynamical system, its long-term behavior is well-understood, having recurrent orbits parametrized by necklaces of beads with…
Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes…
To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a…
We give a criterion for a finitely generated odd-angled Coxeter group to have a proper finite index subgroup generated by reflections. The answer is given in terms of the least prime divisors of the exponents of the Coxeter relations.
The NLL corrections to the BFKL kernel are known to be very large, to the extent that even for small values of alpha_s, they lead to physical cross sections which are not positive definite. It is shown in the context of a toy model, that…
The small-$x_B$ deep inelastic scattering in the saturation region is governed by the non-linear evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the BK equation for the evolution of color dipoles.…
We consider spectral decomposition of the harmonic oscillator in $\mathbb R^n$ in terms of two different orthonormal bases in $L^2(\mathbb R^n)$ consisting of its eigenfunctions. Then, using purely functional analysis tools we provide…
We review the result for the BFKL Pomeron intercept at N=4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion $j_0=2-2\lambda^{-1/2}-\lambda^{-1} + 1/4 \, \lambda^{-3/2} + 2(3\zeta_3+1) \, \lambda^{-2}…
We perform the isospin decomposition of proton and neutron SLAC data in the region $0.01 \leq x \leq 0.1$. The isovector part is well described by a power behaviour $x^{\alpha}$, where $\alpha$ leads to the validity of Bjorken sum rule and…
The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of…
A four-term recurrence relation for squared spherical Bessel functions is shown to yield closed-form expressions for several types of finite weighted sums of these functions. The resulting sum rules, which may contain an arbitrarily large…
In this paper, we explore identities that allow for representation of positive integers raised to positive integral powers as sums of nested sums of smaller positive integral powers. We begin by establishing the base identity involving…
We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index…
We propose a phenomenological study of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach applied to the data on the proton structure function $F_2$ measured at HERA in the small-$x_{Bj}$ region ($x_{Bj}<0.01$) and $Q^2$ in the range 5 to…
An analytical approximation for the eigenvalues of $\mathcal{PT}$ symmetric Hamiltonian $\mathsf{H} = -d^{2}/dx^{2} - (\mathrm{i}x)^{\epsilon+2}$, $\epsilon > -1$ is developed via simple basis sets of harmonic-oscillator wave functions with…