Mass separator for radioactive isotopes

A new isotope separator has been designed, constructed, and put into routine operation for separation of ¹³³Xe providing a major advancement and significant cost reduction in preparation of this radioactive isotope. The design features and advantages are discussed that expedite high purity separation of relatively small quantities of this isotope. These advantages could be easily used to expedite separation of other shorter-lived radioactive isotopes.     

Some results on linear nabla Riemann-Liouville fractional difference equations

In this paper, we establish some criteria for boundedness, stability properties, and separation of solutions of autonomous nonlinear nabla Riemann-Liouville scalar fractional difference equations. To derive these results, we prove the variation of constants formula for nabla Riemann-Liouville fractional difference equations.     

Experimental and Theoretical Evidence of Spin-Orbit Heavy Atom on the Light Atom 1H NMR Chemical Shifts Induced through H⋅⋅⋅I− Hydrogen Bond

Spin-orbit (SO) heavy-atom on the light-atom (SO-HALA) effect is the largest relativistic effect caused by a heavy atom on its light-atom neighbors, leading, for example, to unexpected NMR chemical shifts of ¹H, ¹³C, and ¹⁵N nuclei. In this study, a combined experimental and theoretical evidence for the SO-HALA effect transmitted through hydrogen bond is presented. Solid-state NMR data for a series of 4-dimethylaminopyridine salts containing I⁻, Br⁻ and Cl⁻ counter ions were obtained experimentally and by theoretical calculations. A comparison of the experimental chemical shifts with those calculated by a standard DFT methodology without the SO contribution to the chemical shifts revealed a remarkable error of the calculated proton chemical shift of a hydrogen atom that is in close contact with the iodide anion. The addition of the relativistic SO correction in the calculations significantly improves overall agreement with the experiment and confirms the propagation of the SO-HALA effect through hydrogen bonds.     

Electrophilicity Scale of Activated Amides: 17O NMR and 15N NMR Chemical Shifts of Acyclic Twisted Amides in N−C(O) Cross-Coupling

The structure and properties of amides are of tremendous interest in organic synthesis and biochemistry. Traditional amides are planar and the carbonyl group non-electrophilic due to n_N→π*_C=O conjugation. In this study, we report electrophilicity scale by exploiting ¹⁷O NMR and ¹⁵N NMR chemical shifts of acyclic twisted and destabilized acyclic amides that have recently received major attention as precursors in N-C(O) cross-coupling by selective oxidative addition as well as precursors in electrophilic activation of N-C(O) bonds. Most crucially, we demonstrate that acyclic twisted amides feature electrophilicity of the carbonyl group that ranges between that of acid anhydrides and acid chlorides. Furthermore, a wide range of electrophilic amides is possible with gradually varying carbonyl electrophilicity by steric and electronic tuning of amide bond properties. Overall, the study quantifies for the first time that steric and electronic destabilization of the amide bond in common acyclic amides renders the amide bond as electrophilic as acid anhydrides and chlorides. These findings should have major implications on the fundamental properties of amide bonds.     

ОПРЕДЕЛЕНИЕ ВРЕМЕНИ ЖИЗНИ μ-МЕЗОНОВ ПО АНОМАЛЬНОМУ ПОГЛ0Щ ЕНИЮ МЕТОДОМ ЯДЕРНЫХ ЭМУЛЬСИЙ

- ;- . ( ) . , - .     

Real

The famous problem involves applying two maps: and to positive integers. If is even, one applies , if it is odd, one applies . The conjecture states that each trajectory of the system arrives to the periodic orbit . In this paper, instead of choosing each time which map to apply, we allow ourselves more freedom and apply both and independently of . That is, we consider the action of the free semigroup with generators and on the space of positive real numbers. We prove that this action is minimal (each trajectory is dense) and that the periodic points are dense. Moreover, we give a full characterization of the group of transformations of the real line generated by and .

     

Rotating an interval and a circle

We compare periodic orbits of circle rotations with their counterparts for interval maps. We prove that they are conjugate via a map of modality larger by at most 2 than the modality of the interval map. The proof is based on observation of trips of inhabitants of the Green Islands in the Black Sea.

     

The precision of DCE-MRI using the tissue homogeneity model with continuous formulation of the perfusion parameters

The present trend in dynamic contrast-enhanced MRI is to increase the number of estimated perfusion parameters using complex pharmacokinetic models. However, less attention is given to the precision analysis of the parameter estimates. In this paper, the distributed capillary adiabatic tissue homogeneity pharmacokinetic model is extended by the bolus arrival time formulated as a free continuous parameter. With the continuous formulation of all perfusion parameters, it is possible to use standard gradient-based optimization algorithms in the approximation of the tissue concentration time sequences. This new six-parameter model is investigated by comparing Monte-Carlo simulations with theoretically derived covariance matrices. The covariance-matrix approach is extended from the usual analysis of the primary perfusion parameters of the pharmacokinetic model to the analysis of the perfusion parameters derived from the primary ones. The results indicate that the precision of the estimated perfusion parameters can be described by the covariance matrix for signal-to-noise ratio higher than ~ 20 dB. The application of the new analysis model on a real DCE-MRI data set is also presented.     

FINITE ELEMENT APPROXIMATION OF A NONLINEAR STEADY-STATE HEAT CONDUCTION PROBLEM

1. Introduction Anciellt Chinese mathematicians have done many fund~al discoveries, even thoughmad of them are now usually called by western names, e.g., the Pascal triangle, the HornerIcheme, the Gaussian elimination, see [231. In the modern era3 Chinese mathematiciare have.jalso got many priorities. For instance, the fast Proof Of convergence of the finite element methodfor a linear elliptic boundary vajue problem was done in the pioneering work [61 by K. Feng in1965 (for the English tra…