Von Neumann's Problem and Large Cardinals

It is a well-known problem of Von Neumann to discover whetherthe countable chain condition and weak distributivity of a completeBoolean algebra imply that it carries a strictly positive probabilitymeasure. It was shown recently by Balcar, Jech and Pazák,and by Velikovi, that it is consistent with ZFC, modulo theconsistency of a supercompact cardinal, that every ccc weaklydistributive complete Boolean algebra carries a contiuous strictlypositive submeasure – that is, it is a Maharam algebra.We use some ideas of Gitik and Shelah and implications fromthe inner model theory to show that some large cardinal assumptionsare necessary for this result. 2000 Mathematics Subject Classification03E55, 28A60 (primary), 03E75 (secondary).     

Libera and Hilbert matrix operator on logarithmically weighted Bergman,Bloch and Hardy-Bloch spaces

We show that if α > 1, then the logarithmically weighted Bergman space \(A_{{{\log }^\alpha }}^2\) is mapped by the Libera operator L into the space \(A_{{{\log }^{\alpha - 1}}}^2\), while if α > 2 and 0 < ε ≤ α?2, then the Hilbert matrix operator H maps \(A_{{{\log }^\alpha }}^2\) into \(A_{{{\log }^{\alpha - 2 - \varepsilon }}}^2\).We show that the Libera operator L maps the logarithmically weighted Bloch space \({B_{{{\log }^\alpha }}}\), α ∈ R, into itself, while H maps \({B_{{{\log }^\alpha }}}\) into \({B_{{{\log }^{\alpha + 1}}}}\).In Pavlovi?’s paper (2016) it is shown that L maps the logarithmically weighted Hardy-Bloch space \(B_{{{\log }^\alpha }}^1\), α > 0, into \(B_{{{\log }^{\alpha - 1}}}^1\). We show that this result is sharp. We also show that H maps \(B_{{{\log }^\alpha }}^1\), α > 0, into \(B_{{{\log }^{\alpha - 1}}}^1\) and that this result is sharp also.     

Nonstandard models and analytic equivalence relations

We improve a result of Hjorth concerning the nature of thin analytic equivalence relations. The key lemma uses a weakly compact cardinal to construct certain nonstandard models, which Hjorth obtained using 's.

     

Optimality conditions for discrete optimal control problems with equality and inequality type of constraints

We consider nonlinear discrete optimal control problems with variable endpoints and with equality and inequality type of constraints on control. We derive new nontrivial first and second-order necessary optimality conditions.      

First and second order necessary optimality conditions for a discrete-time optimal control problem with a vector-valued objective function

The paper deals with a nonlinear discrete-time optimal control problem with a vector-valued objective function of terminal type. For the admissible controls of the problem under consideration which satisfy the additional regularity condition of the Lyusternik type we prove the first and second necessary optimality conditions extending such the classical optimality conditions as the Euler condition and the negativity of second variation of the objective function.     

Parallel acquisition of two-dimensional NMR spectra of several nuclear species

We show that two or more two-dimensional NMR correlation spectra can be recorded in a single shot, using a multicoil radio-frequency probe and receiver system designed for simultaneous parallel acquisition of signals from different nuclear species such as 1H, 13C, and 15N. Dubbed PANSY (parallel acquisition NMR spectroscopy), this new technique shows promise for recording several multidimensional NMR spectra of different nuclear species in a very short time.     

Application for optical thermometers calibration based on virtual instruments

In this paper we present a new developed application for calibration of optical thermometers which is implemented in the Serbian Metrology Institute. The method for calibration of optical thermometer–pyrometer is based on measuring blackbody temperature via thermocouple standards and measuring voltage on pyrometer in temperature range from 550 to 1650 °C. The objective is to precisely determinate calibration curve of pyrometer—transfer function. The metrology traceability was realized through thermocouples standard which has traceability to the international standard. A developed application has a role to control and supervise calibration process. Based on virtual instruments (VI), application offers monitoring measurement parameters in real time on three charts. The main advantage of the developed VI application is reduction of measurement uncertainty of type A by increased accuracy with multi—temperature measurement up to 3 thermocouples on temperature equilibrium in the measurement system and automatic data processing by converting voltage to temperature, calculating the mean value and standard deviation of the mean value. Advantage is also reflected in permanent data logging while application is running and low cost and user friendly interface One of the goals is to improve quality of metrological services through this application and support the establishment of a traceability chain to SI.