Compactness of the space of non-randomized policies in countable-state sequential decision processes

For sequential decision processes with countable state spaces, we prove compactness of the set of strategic measures corresponding to nonrandomized policies. For the Borel state case, this set may not be compact (Piunovskiy, Optimal control of random sequences in problems with constraints. Kluwer, Boston, p. 170, 1997) in spite of compactness of the set of strategic measures corresponding to all policies (Schäl, On dynamic programming: compactness of the space of policies. Stoch Processes Appl 3(4):345–364, 1975b; Balder, On compactness of the space of policies in stochastic dynamic programming. Stoch Processes Appl 32(1):141–150, 1989). We use the compactness result from this paper to show the existence of optimal policies for countable-state constrained optimization of expected discounted and nonpositive rewards, when the optimality is considered within the class of nonrandomized policies. This paper also studies the convergence of a value-iteration algorithm for such constrained problems.     

Automatic methods of the processing of data from track detectors on the basis of the PAVICOM facility

New automatic methods essentially simplify and increase the rate of the processing of data from track detectors. This provides a possibility of processing large data arrays and considerably improves their statistical significance. This fact predetermines the development of new experiments which plan to use large-volume targets, large-area emulsion, and solid-state track detectors [1]. In this regard, the problem of training qualified physicists who are capable of operating modern automatic equipment is very important. Annually, about ten Moscow students master the new methods, working at the Lebedev Physical Institute at the PAVICOM facility [2–4]. Most students specializing in high-energy physics are only given an idea of archaic manual methods of the processing of data from track detectors. In 2005, on the basis of the PAVICOM facility and the physicstraining course of Moscow State University, a new training work was prepared. This work is devoted to the determination of the energy of neutrons passing through a nuclear emulsion. It provides the possibility of acquiring basic practical skills of the processing of data from track detectors using automatic equipment and can be included in the educational process of students of any physical faculty. Those who have mastered the methods of automatic data processing in a simple and pictorial example of track detectors will be able to apply their knowledge in various fields of science and technique. Formulation of training works for pregraduate and graduate students is a new additional aspect of application of the PAVICOM facility described earlier in [4].     

Comparison of shelf-life appraisal techniques for the estimation of the limiting date of stability for agrifood reference materials

Reference materials play a major role for the verification of the quality control of biological and chemical analysis. Due to the poor availability of certified reference materials, external reference materials (ERM) are intensively developing in complement and as a consequence of proficiency testing schemes (PTS). However, the use of any reference material must be time-limited, whereas the assigned reference value may change with time and it is under the responsibility of the material producer to indicate the date until this can be used for calibration purpose with some guarantee. This article compares different methods used to determine the limiting date of stability (LDS) in food and food-related reference materials, using some specific analytes (moisture, protein and oil contents) as stability-monitoring analytes. LDS is defined as the moment when the assigned values of one or several analytes can no longer be guaranteed by the producer. For most of the ERMs used as examples (i.e., rapeseed, bread wheat, durum wheat) the calculated periods of stability were longer than the present storage times used in BIPEA. However, for sunflower, the rapid degradation of the monitoring analytes indicates a shorter time than forecast.     

Zinc chloride-catalyzed chloromethylation of resins for solid phase peptide synthesis

Zinc chloride has been found to catalyze chloromethylation of resins for solid phase peptide synthesis, producing low levels of chloromethylation more accurately and under more convenient conditions than does SnCl₄. The preparation of a stable solution of the ZnCl₄ catalyst in THF is described, and data are presented detailing the effects of varying temperature, time, and the concentrations of catalyst and chloromethyl methyl ether on the chloromethylation reaction.     

Small polaron dynamics: A self-consistent nonlinear spin-field model

The motion of an electron strongly and locally coupled to the lattice deformation is considered as a dynamical system. Our study is based on a model where the electron remains to two adjacent diatomic molecules vibrating around positions which evolve in time as the charge distribution of the electron gradually shifts from one of the molecules to the other one. This model is cast into an intuitively more accesible model of spin $\text{1}\text{2}$ in an external field plus a reaction field. Within a semiclassical approach this is a Hamiltonian system expressed with two sets of action-angle variables. We show how the regular trajectories (describing the cooperative mechanism between the charge transfer and rearrangement of the molecular positions) in this phase space gradually disappear and global stochasticity sets in as either the ratio of the electron hopping rate over the electron-lattice coupling constant or the total energy is varied.     

The radiation gauge static potential for non-abelian gauge fields

The static potential between a fermion and an anti-fermion in a group singlet state is calculated, through two loops, in the radiation gauge first order formalism. The results of this calculation imply that the Coulomb propagator is not sufficient to determine the static potential: a new function of the coupling constant α_s(?t) is also required.     

Relativistic theory of parity violation in many-electron atoms

We present a theoretical framework for the calculation of parity-mixing effects of the weak interaction in many-electron atoms which is based on first principles. The starting point is an external-field no-pair Hamiltonian H₊ which allows for a consistent treatment of effects coming from virtual electron-positron pairs and can be used as a basis for a systematic program of calculations. We show that the matrix element $\text{M}$ for parity-violating E1 transitions, given by quantum electrodynamics, gets an appreciable contribution $\text{M}$^pair from states involving an extra electron-positron pair. However on eliminating the velocity operator α in favor of the length operator iωr, we find cancellations which result in an accurate formula for $\text{M}$ involving only the positive-energy N-electron eigenstates of H₊ as intermediate states and the length form, iωr · ?, of the dipole operator. We discuss the implications of our results for calculations of amplitudes for parity-violating radiative E1 transitions in many-electron atoms. Our analysis includes a study of the effects coming from the weak electron-electron interaction as well as those arising from the weak electron-nucleus interaction.     

Lifetime measurement in the β system (c1Φ-a1Δ) of TiO

The radiative lifetime of the v′ = 0 level of the c¹Φ state of TiO has been measured from observations on fluorescent decay of a single rotational level, following excitation by laser radiation. The value is τ₀ = 17.5 ± 1.0 nsec. From this is derived a transition probability of 5.71 × 10⁷ sec^?1 and an emission f value of 0.270. Transition probabilities for the other bands in the β system have been calculated.