Jet physics in ALICE

The strong suppression of high-p_T hadrons observed in heavy ion collisions at RHIC indicates the interaction of high energy partons with a dense colored medium prior to hadronization. We review the main results from the high-p_T hadron analysis at RHIC and what they tell us about the medium. We then concentrate on the new possibilities that the wider kinematic range at the LHC will offer and how they will help us to better characterize the medium produced in these collisions.     

A manifestation of magnetism of bismuth in iron garnet films

Bismuth iron garnet films prepared through electron-beam and laser-induced evaporation on (001)-oriented substrates of scandium gallium gadolinium garnet are investigated using ferromagnetic resonance. It is assumed that the additional minima observed in the angular dependence of the resonance field can be associated with the magnetic moment of bismuth ions.     

A numerical study of time-dependent schr?dinger equation for multiphoton vibrational interaction of NO molecule, modelled as Morse oscillator, with intense far-infrared femtosecond lasers

For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four different intensities,I = 1 × 10⁸, 1 × 10¹³, 5 × 10¹⁶, and 5 × 10¹⁸ W cm⁻² respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent elevation to the vibrational continuum, have been obtained and analysed. Dedicated to Professor C N R Rao on his 70th birthday An erratum to this article is available at .     

Two observations about free graded hopf algebras

This paper records two results about graded Hopf algebras that do not appear to be stated explicitly in the literature. Let B be a graded set, graded by the positive integers. Let V be the graded vector space with basis B over a field K of characteristic zero and V^'=K⊕V, where K is in grading zero. Let L ne the free graded Lie algebra on B over K and let T be the free graded tensor algebra on B. The first result is the "graded Witt formula" giving the dimension of the subspace of L in each grading. The second result is the observation that any graded coassociative, co-commutative comultiplication Δ:V^'→V^'⊗V^', with co-unit the projection V¹→K. extends to a graded Hopf algebra structure on T that is in fact isomorphic to the natural graded Hopf algebra structure on T. In the ungraded case the statement analogous to the second result is false.     

Stability of solutions to the Cauchy problem for a plane hyperbolic system with time-periodic coefficients

Considering a plane hyperbolic system with time-periodic coefficients, we construct a version of the direct Lyapunov method with the condition on the derivative of the Lyapunov functional along the trajectories of the system which is weakened by use of periodicity of the coefficients. We exhibit an illustrative example.     

Partition of Euclidean space into polyhedra induced by a small deformation of the densest lattice sphere packing

The number of combinatorially nonequivalent Dirichlet-Voronoi diagrams constructed for the centers of balls in the packing obtained from the densest lattice packing of equal spheres by a small displacement of the spheres is estimated. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 79–84, 2005.     

Convergence of optimal controls in some optimization problems

We consider the behavior of bundles of optimal controls when the initial state of the system goes to some given vector. We investigate three types of optimization problems: problems with fixed process length and a free right endpoint; problems with fixed process length and a fixed right endpoint; time-optimal problems. The article is a review of recent results obtained by the author. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 301–314, 2004.     

Colorings of spaces,and random graphs

This work deals with some problems on the embeddings of finite geometric graphs into the random ones. In particular, we study here applications of the random graph theory to the Nelson-Erdös-Hadwiger problem on coloring spaces.     

Necessary first-order conditions for optimal crossing of a given region

We consider a nonlinear optimal control problem with an integral functional in which the integrand is the characteristic function of a closed set in the phase space. An approximation method is applied to prove the necessary conditions of optimality in the form of a Pontryagin maximum principle without any prior assumptions on the behavior of the optimal trajectory. Similarly to phase-constrained problems, we derive conditions of nondegeneracy and pointwise nontriviality of the maximum principle. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 179–204, 2004.