On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Have Pentaquark States Been seen?

The status of the search for pentaquark baryons is reviewed in light of new results from the first two dedicated experiments from CLAS at Jefferson Lab and of new analyses from several laboratories on the $Theta^+(1540)$. Evidence for and against two heavier pentaquark states is also discussed.Comment: Added some references, corrected typo

Holographic Non-equilibrium Heating

We study the holographic entanglement entropy evolution after a global sharp quench of thermal state. After the quench, the system comes to equilibrium and the temperature increases from $T_i$ to $T_f$. Holographic dual of this process is provided by an injection of a thin shell of matter in the black hole background. The quantitative characteristics of the evolution depend substantially on the size of the initial black hole. We show that characteristic regimes during non-equilibrium heating do not depend on the initial temperature and are the same as in thermalization. Namely these regimes are pre-local-equilibration quadratic growth, linear growth and saturation regimes of the time evolution of the holographic entanglement entropy. We study the initial temperature dependence of quantitative characteristics of these regimes and find that the critical exponents do not depend on the temperature, meanwhile the prefactors are the functions on the temperature.Comment: v1:12 pages, 9 figures; v2:The title and abstract are slightly changed, the discussion is enlarged, the pictures are changed to make presentation more clear and refs. added , 22 pages, 4 figures; v3: typos correcte

Holographic local quench and effective complexity

We study the evolution of holographic complexity of pure and mixed states in $1+1$-dimensional conformal field theory following a local quench using both the "complexity equals volume" (CV) and the "complexity equals action" (CA) conjectures. We compare the complexity evolution to the evolution of entanglement entropy and entanglement density, discuss the Lloyd computational bound and demonstrate its saturation in certain regimes. We argue that the conjectured holographic complexities exhibit some non-trivial features indicating that they capture important properties of what is expected to be effective (or physical) complexity.Comment: 33 pages, 19 figures; v2: typos corrected; 35 pages, references added, new appendix. Version to match published in JHE

Thermalization of holographic Wilson loops in spacetimes with spatial anisotropy

In this paper, we study behaviour of Wilson loops in the boost-invariant nonequilibrium anisotropic quark-gluon plasma produced in heavy-ion collisions within the holographic approach. We describe the thermalization studying the evolution of the Vaidya metric in the boost-invariant and spatially anisotropic background. To probe the system during this process we calculate rectangular Wilson loops oriented in different spatial directions. We find that anisotropic effects are more visible for the Wilson loops lying in the transversal plane unlike the Wilson loops with partially longitudinal orientation. In particular, we observe that the Wilson loops can thermalizes first unlike to the order of the isotropic model. We see that Wilson loops on transversal contours have the shortest thermalization time. We also calculate the string tension and the pseudopotential at different temperatures for the static quark-gluon plasma. We show that the pseudopotential related to the configuration on the transversal plane has the screened Cornell form. We also show that the jet-quenching parameter related with the average of the light-like Wilson loop exhibits the dependence on orientations.Comment: 39 pages, 12 figures; v3: typos corrected, to appear in Nucl. Phys.

Spectral multiplicity for powers of weakly mixing automorphisms

We study the behavior of maximal multiplicities $mm (R^n)$ for the powers of a weakly mixing automorphism $R$. For some special infinite set $A$ we show the existence of a weakly mixing rank-one automorphism $R$ such that $mm (R^n)=n$ and $mm(R^{n+1}) =1$ for all $n\in A$. Moreover, the cardinality $cardm(R^n)$ of the set of spectral multiplicities for $R^n$ is not bounded. We have $cardm(R^{n+1})=1$ and $cardm(R^n)=2^{m(n)}$, $m(n)\to\infty$, $n\in A$. We also construct another weakly mixing automorphism $R$ with the following properties: $mm(R^{n}) =n$ for $n=1,2,3,..., 2009, 2010$ but $mm(T^{2011}) =1$, all powers $(R^{n})$ have homogeneous spectrum, and the set of limit points of the sequence $\{\frac{mm (R^n)}{n} : n\in \N \}$ is infinite

Spin and orbital angular momentum of the proton

Since the announcement of the proton spin crisis by the European Muon Collaboration there has been considerable progress in unravelling the distribution of spin and orbital angular momentum within the proton. We review the current status of the problem, showing that not only have strong upper limits have been placed on the amount of polarized glue in the proton but that the experimental determination of the spin content has become much more precise. It is now clear that the origin of the discrepancy between experiment and the naive expectation of the fraction of spin carried by the quarks and anti-quarks in the proton lies in the non-perturbative structure of the proton. We explain how the features expected in a modern, relativistic and chirally symmetric description of nucleon structure naturally explain the current data. The consequences of this explanation for the presence of orbital angular momentum on quarks and gluons is reviewed and comparison made with recent results from lattice QCD and experimental data.Comment: Lectures at Aligarh University (4th DAE-BRNS Workshop on Hadron Physics, Feb 18-21, 200

Nucleon Resonances and Quark Structure

A pedagogical review of the past 50 years of study of resonances, leading to our understanding of the quark content of baryons and mesons. The level of this review is intended for undergraduates or first-year graduate students. Topics covered include: the quark structure of the proton as revealed through deep inelastic scattering; structure functions and what they reveal about proton structure; and prospects for further studies with new and upgraded facilities, particularly a proposed electron-ion collider.Comment: 21 pages, 15 figure

Improved approximation algorithm for k-level UFL with penalties, a simplistic view on randomizing the scaling parameter

The state of the art in approximation algorithms for facility location problems are complicated combinations of various techniques. In particular, the currently best 1.488-approximation algorithm for the uncapacitated facility location (UFL) problem by Shi Li is presented as a result of a non-trivial randomization of a certain scaling parameter in the LP-rounding algorithm by Chudak and Shmoys combined with a primal-dual algorithm of Jain et al. In this paper we first give a simple interpretation of this randomization process in terms of solving an aux- iliary (factor revealing) LP. Then, armed with this simple view point, Abstract. we exercise the randomization on a more complicated algorithm for the k-level version of the problem with penalties in which the planner has the option to pay a penalty instead of connecting chosen clients, which results in an improved approximation algorithm