Rational conformal correlation functions of gauge-invariant local fields in four dimensions

Global conformal invariance in Minkowski space and the Wightman axioms imply strong locality (Huygens principle) and rationality of correlation functions, thus providing an extension of the concept of a vertex algebra to higher (even) dimensions D. We (p)review current work on a model of a Hermitian scalar field L of scale dimension 4 (D = 4) which can be interpreted as the Lagrangian of a gauge field theory that generates the algebra of gauge-invariant local observables in a conformally invariant renormalization group fixed point.     

Are current-induced forces conservative?

The expression for the force on an ion in the presence of current can be derived from first principles without any assumption about its conservative character. However, energy functionals have been constructed that indicate that this force can be written as the derivative of a potential. On the other hand, there exist specific arguments that strongly suggest the contrary. We propose physical mechanisms that invalidate such arguments and demonstrate their existence with first-principles calculations. While our results do not constitute a formal resolution to the fundamental question of whether current-induced forces are conservative, they represent a substantial step forward in this direction.     

A functional model for polynomially posinormal operators

In this paper we introduce a class of operators naturally extending the classes of hyponormal and posinormal operators. For this class we construct a generating family of eigendistributions, unitary invariants and a functional model.     

Current-induced embrittlement of atomic wires

Recent experiments suggest that gold single-atom contacts and atomic chains break at applied voltages of 1 to 2 V. In order to understand why current flow affects these defect-free conductors, we have calculated the current-induced forces on atoms in a Au chain between two Au electrodes. These forces are not by themselves sufficient to rupture the chain. However, the current reduces the work to break the chain, which results in a dramatic increase in the probability of thermally activated spontaneous fracture of the chain. This current-induced embrittlement poses a fundamental limit to the current-carrying capacity of atomic wires.     

Two-dimensional conformal quantum field theory

On leave of absence from the Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria.     

Influence of pH of the BSA solutions on velocity of the rising bubbles and stability of the thin liquid films and foams

Influence of pH of the BSA solutions on velocity of the rising bubbles, stability of foams, and properties of single foam and wetting films was studied. It was found that the solution pH affected significantly the BSA surface activity and properties of the protein adsorption layer under dynamic and static conditions. At pH close to the isoelectric point (pH_IEP=4.8) the BSA showed the highest surface activity. The equilibrium microscopic foam films of thicknesses of 64–80 nm, depending on the BSA concentration, were obtained at pH=5.8. Under dynamic conditions the bubble rising velocity was reduced in a highest degree and the foam formed were most stable at the solutions pH-5.8 and 4.8. Lowering the bubble velocity shows that the BSA adsorption layer was formed, which retarded fluidity of the bubble surface. When the solution pH was significantly lower (pH=3.9) or much higher (pH=10) than the pH_IEP then the BSA practically had no influence on the bubble velocity and the foam stability was drastically reduced. Moreover, the pH variations affected also the time of the three-phase contact (TPC) formation on mica surface covered by the BSA adsorption layers. These pH dependent changes in the BSA surface activity indicate that the BSA linear conformers, existing at pH far away from the pH_IEP, have much higher affinity to aqueous phase resulting from higher net electrical charge present over the extended BSA molecule conformers.     

Detection of multivariate outliers in business survey data with incomplete information

Many different methods for statistical data editing can be found in the literature but only few of them are based on robust estimates (for example such as BACON-EEM, epidemic algorithms (EA) and transformed rank correlation (TRC) methods of Béguin and Hulliger). However, we can show that outlier detection is only reasonable if robust methods are applied, because the classical estimates are themselves influenced by the outliers. Nevertheless, data editing is essential to check the multivariate data for possible data problems and it is not deterministic like the traditional micro editing where all records are extensively edited manually using certain rules/constraints. The presence of missing values is more a rule than an exception in business surveys and poses additional severe challenges to the outlier detection. First we review the available multivariate outlier detection methods which can cope with incomplete data. In a simulation study, where a subset of the Austrian Structural Business Statistics is simulated, we compare several approaches. Robust methods based on the Minimum Covariance Determinant (MCD) estimator, S-estimators and OGK-estimator as well as BACON-BEM provide the best results in finding the outliers and in providing a low false discovery rate. Many of the discussed methods are implemented in the R package ${\tt{rrcovNA}}$ which is available from the Comprehensive R Archive Network (CRAN) at http://www.CRAN.R-project.org under the GNU General Public License.     

γ-Active Constraints in Convex Semi-Infinite Programming

In this article, we extend the definition of γ-active constraints for linear semi-infinite programming to a definition applicable to convex semi-infinite programming, by two approaches. The first approach entails the use of the subdifferentials of the convex constraints at a point, while the second approach is based on the linearization of the convex inequality system by means of the convex conjugates of the defining functions. By both these methods, we manage to extend the results on γ-active constraints from the linear case to the convex case.     

Motzkin predecomposable sets

We introduce and study the family of sets in a finite dimensional Euclidean space which can be written as the Minkowski sum of a compact and convex set and a convex cone (not necessarily closed). We establish several properties of the class of such sets, called Motzkin predecomposable, some of which hold also for the class of Motzkin decomposable sets (i.e., those for which the convex cone in the decomposition is requested to be closed), while others are specific of the new family.     

Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy

A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton–Jacobi–Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton–Jacobi–Bellman equation.