Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production

We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The masters are evaluated by means of the differential equations method and expressed in terms of multiple polylogarithms and one- or two-fold integrals of polylogarithms and irrational functions, up to transcendentality four.Comment: 20 pages, ancillary file

Orthonormal rational functions on a semi-infinite interval

In this paper we propose a novel family of weighted orthonormal rational functions on a semi-infinite interval. We write a sequence of integer-coefficient polynomials in several forms and derive their corresponding differential equations. These equations do not form Sturm-Liouville problems. We overcome this disadvantage by multiplying some factors, resulting in a sequence of irrational functions. We deduce various generating functions of this sequence of irrational functions and find its associated Sturm-Liouville problems, which brings orthogonality. Then we study a Hilbert space of functions defined on a semi-infinite interval with its inner product induced by a weight function determined by the Sturm-Liouville problems mentioned above. We list two bases. One is the even subsequence of the irrational function sequence above and another one is the non-positive integer power functions. We raise one example of Fourier series expansion and one example of interpolation as applications.Comment: No comments up to no

On two generalisations of the final value theorem : scientific relevance, first applications, and physical foundations

The present work considers two published generalisations of the Laplace-transform final value theorem (FVT) and some recently appeared applications of one of these generalisations to the fields of physical stochastic processes and Internet queueing. Physical sense of the irrational time functions, involved in the other generalisation, is one of the points of concern. The work strongly extends the conceptual frame of the references and outlines some new research directions for applications of the generalised theorem

Personality and phobias in adolescence: age and gender in psychopathological expressions

Background: Although the understanding of adolescent phobias is important, this phenomenon has thus far not been adequately researched. This report, based on clinical experience, highlights prevalent phobic phenomena linked to personality characteristics. Methods: A sample of 241 adolescents from High School and the University of Messina, Italy was evaluated for phobic responses using the SAFA Scales. Personality types and aspects were assessed by the Myers-Briggs Type Indicator F Form. Results: The results were consistent with the reported literature and revealed that psychopathological phenomena such as anxiety, obsession, eating disorders and phobias decreased with aging; however, depression remained constant over time. Significant differences emerged regarding gender, with the presence of higher scores on all scales except obsession for the female group. Personality analysis revealed aspects linked to the relations between psychopathological variables, introversion/ extraversion (such as polar dimensions), and rational/ irrational functions. Conclusion: This research indicates that phobic phenomena may be underestimated in adolescents and links personality types and symptoms with phobic phenomena, indicating the potential need for interventions in adolescents

Generalized Calogero model in arbitrary dimensions

We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock space. There are towers of states, with equidistant energy spectra in each tower. We explicitely construct all polynomial eigenstates, namely the center-of-mass states and global dilatation modes, and find their corresponding eigenenergies. We also construct ladder operators for these global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behavior. The above results are universal for all systems with underlying conformal SU(1,1) symmetry.Comment: 14 pages, no figures, to be published in Phys.Lett.