Computing a Counting Polynomial of an Infinite Family of Linear Polycene Parallelogram Benzenoid Graph P(a,b)

Omega polynomial was defined by M.V. Diudea in 2006 as  where the number of edges co-distant with e is denoted by n(e). One can obtain Theta Θ, Sadhana Sd and Pi Π polynomials by replacing xn(e) with n(e)xn(e), x|E|-n(e) and n(e)x|E|-n(e) in Omega polynomial, respectively. Then Theta Θ, Sadhana Sd and Pi Π indices will be the first derivative of Θ(x), Sd(x) and Π(x) evaluated at x=1. In this paper, Pi Π(G,x) polynomial and Pi Π(G) index of an infinite family of linear polycene parallelogram benzenoid graph P(a,b) are computed for the first time

Geometrical Theory of Analytic Functions

The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria

Measurement of differential cross sections for single diffractive dissociation in sqrt(s) = 8 TeV pp collisions using the ATLAS ALFA spectrometer

none13siA dedicated sample of Large Hadron Collider proton-proton collision data at centre-of-mass energy sqrt(s) = 8 TeV is used to study inclusive single diffractive dissociation, pp → X p. The intact final-state proton is reconstructed in the ATLAS ALFA forward spectrometer, while charged particles from the dissociated system X are measured in the central detector components. The fiducial range of the measurement is −4.0 < log10ξ < −1.6 and 0.016 < |t| < 0.43 GeV2, where ξ is the proton fractional energy loss and t is the squared four-momentum transfer. The total cross section integrated across the fiducial range is 1.59 ± 0.13 mb. Cross sections are also measured differentially as functions of ξ, t, and ∆η, a variable that characterises the rapidity gap separating the proton and the system X. The data are consistent with an exponential t dependence, dσ/dt ∝ eBt with slope parameter B = 7.65 ± 0.34 GeV−2. Interpreted in the framework of triple Regge phenomenology, the ξ dependence leads to a pomeron intercept of α(0) = 1.07 ± 0.09.openG Aad, K Bachas, G Chiodini, E Gorini, F Gravili, L Longo, A Mirto, M Primavera, M Reale, E Schioppa, S Spagnolo, A Ventura, and ATLAS CollaborationAad, G; Bachas, K; Chiodini, G; Gorini, E; Gravili, F; Longo, L; Mirto, A; Primavera, M; Reale, M; Schioppa, E; Spagnolo, S; Ventura, A; ATLAS Collaboration, An

Measurement of differential cross sections for single diffractive dissociation in √s = 8 TeV pp collisions using the ATLAS ALFA spectrometer

A dedicated sample of Large Hadron Collider proton-proton collision data at centre-of-mass energy √ s = 8 TeV is used to study inclusive single diffractive dissociation, pp → Xp. The intact final-state proton is reconstructed in the ATLAS ALFA forward spectrometer, while charged particles from the dissociated system X are measured in the central detector components. The fiducial range of the measurement is −4.0 &lt; log10 ξ &lt; −1.6 and 0.016 &lt; |t| &lt; 0.43 GeV2 , where ξ is the proton fractional energy loss and t is the squared four-momentum transfer. The total cross section integrated across the fiducial range is 1.59 ± 0.13 mb. Cross sections are also measured differentially as functions of ξ, t, and ∆η, a variable that characterises the rapidity gap separating the proton and the system X. The data are consistent with an exponential t dependence, dσ/dt ∝ e Bt with slope parameter B = 7.65 ± 0.34 GeV−2 . Interpreted in the framework of triple Regge phenomenology, the ξ dependence leads to a pomeron intercept of α(0) = 1.07 ± 0.09