Hierarchical models of unified theories

A modernized conception of hierarchical structure of reality is proposed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–6, December, 1980.     

Banach spaces of distributions having two module structures

After a discussion of a space of test functions and the corresponding space of distributions, a family of Banach spaces (B, ∥ ∥_B) in standard situation is described. These are spaces of distributions having a pointwise module structure and also a module structure with respect to convolution. The main results concern relations between the different spaces associated to B established by means of well-known methods from the theory of Banach modules, among them B₀ and $\text{B}\text{?}$, the closure of the test functions in B and the weak relative completion of B, respectively. The latter is shown to be always a dual Banach space. The main diagram, given in Theorem 4.7, gives full information concerning inclusions between these spaces, showing also a complete symmetry. A great number of corresponding formulas is established. How they can be applied is indicated by selected examples, in particular by certain Segal algebras and the A_p-algebras of Herz. Various further applications are to be given elsewhere.     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

Allocating Warehouse Stock in a Retail Chain

The context is that of a retail chain where stock is purchased into a central warehouse from which branch stocks are replenished. This paper considers possible methods of allocating limited warehouse stock to branches, and uses simulation to quantify the resulting benefits.     

Two-fluid and population balance models for subcooled boiling flow

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUSIG (MUltiple-SIze-Group) model implemented in the computer code CFX4.4 is further developed to accommodate the wall nucleation at the heated wall and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison using empirical relationships for the active nucelation site density and local bubble diameter is also investigated. Good agreement is achieved with the local radial void fraction, bubble Sauter diameter and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency through the consideration of additional momentum equations or developing an algebraic slip model to account for bubble separation.     

Study on the possibilities of controlling the laser output beam properties by an intracavity deformable mirror

The possibilities of controlling the laser beam properties by a deformable mirror introduced into the laser optical cavity were studied theoretically and experimentally. The experiments were performed under conditions of an industrial high power transverse flow cw CO₂ laser operating with a stable resonator of a folded configuration. A deformable bimorph mirror of a surface profile controlled by the voltage applied to the mirror electrodes is implemented to the laser system as a back cavity mirror or as a one of the inner folding mirrors. The near-and far-field characteristics of the laser beam versus the resonator configuration controlled by the changes of the focal length of the deformable mirror are discussed in the paper. The analysis reveals that the resonator with an inner deformable mirror is much more sensitive to the mirror curvature variations than the resonator in which the deformable mirror is used as a back cavity mirror. The presented results show that dynamic and controllable changes in the resonator properties result in the controlled modification and optimisation of the laser output power and spatial parameters of the laser radiation.