Acoustic field in a closed layered shell with resonant systems

The acoustic field inside a shell excited by a spatially inhomogeneous harmonic pressure field is studied. The shell is assumed to have a finite length, a set of orthogonal stiffening ribs, two ends bounding the acoustic volume, and a sound-insulating structure, which includes layers of sound-insulating material, resonant elements, and an interior panel. The shell is considered to be orthotropic with boundary conditions corresponding to a free support. For the acoustic field in the closed volume, analytical expressions are derived with allowance for the elastoacoustic interaction of the shell with the sound-insulating layers and with the medium both inside the shell (with arbitrary impedance values at the ends) and outside it. These expressions are used to investigate the effect of different types of resonant systems on the sound field inside the shell.     

A biogenetically patterned enantiospecific synthesis of allopupukeanones

The first enantiospecific synthesis of allopupukeanones has been accomplished starting from 6-methylcarvone. A biogenetically patterned rearrangement of a pupukeanane to allopupukeanane was employed as the key step.     

An efficient synthesis of isothiazolidines via sulfonium ylides formed by the reaction of thietanes and nitrene

An efficient synthesis of isothiazolidines in good yields is described.     

Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system

For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented.     

The influence of pulse duration on the stress levels in ablation of ceramics: A finite element study

We present a finite element model to investigate the dynamic thermal and mechanical response of ceramic materials to pulsed infrared radiation. The model was applied to the specific problem of determining the influence of the pulse duration on the stress levels reached in human dental enamel irradiated by a CO₂ laser at 10.6 μm with pulse durations between 0.1 and 100 μs and sub-ablative fluence. Our results indicate that short pulses with durations much larger than the characteristic acoustic relaxation time of the material can still cause high stress transients at the irradiated site, and indicate that pulse durations of the order of 10 μs may be more adequate both for enamel surface modification and for ablation than pulse durations up to 1 μs. The model presented here can easily be modified to investigate the dynamic response of ceramic materials to mid-infrared radiation and help determine optimal pulse durations for specific procedures.     

Simple, expedient methods for the determination of water and electrolyte contents of cellulose solvent systems

The concentrations of water, W, and electrolytes present in solutions of LiCl in N,N-dimethylacetamide, LiCl/DMAc, and of tetrabutylammonium fluoride. x-hydrate in DMSO, TBAF.xW/DMSO can be accurately and expediently determined by three independent methods, UV–vis, FTIR and EMF measurement. The first relies on the use of solvatochromic probes whose spectra are sensitive to solution composition. It is applicable to W/LiCl/DMAc solutions but not to TBAF.xW/DMSO, because the charge-transfer complex bands of the probes are suppressed by strong interactions with the latter electrolyte. Integration of ν_OH band of water may be employed in order to determine [W], hence [electrolyte] by weight difference. EMF measurement uses ion-selective electrodes in order to determine [electrolyte], hence [W] by weight difference. Results of the latter method were in excellent agreement with those of FTIR. The reason for the failure of Karl Fischer titration is addressed, and the relevance of the results obtained to functionalization of cellulose under homogenous solution conditions is briefly commented on.     

A thermodynamic description of the distribution of water in H2O-tributyl phosphate and H2O-tributyl phosphate-solvent systems

Various methods for describing the distribution of water in the H₂O-tributyl phosphate (TBP) system were considered. An equation for describing the deviations from the Henry law was proposed. A three-parameter equation for calculating the distribution of water in H₂O-TBP-solvent systems was derived. It is based on the additive solubility model and allows for the dependence of the activity coefficients on the TBP concentration. Based on the published data, the parameters of the equation for a number of systems were calculated.     

Two modifications of the least cost per period heuristic for dynamic lot-sizing

This paper proposes two constructive heuristics for the well-known single-level uncapacitated dynamic lot-sizing problem. The proposed heuristics, called net least period cost (nLPC) and nLPC(i), are developed by modifying the average period cost concept from Silver and Meal's heuristic, commonly known as least period cost (LPC). An improved tie-breaking stopping rule and a locally optimal decision rule are proposed in the second heuristic to enhance performance. We test the effectiveness of the proposed heuristics by using 20 benchmarking test problems frequently used in the literature. Furthermore, we perform a large-scale simulation study involving three factors, 50 experimental conditions, and 100?000 randomly generated problems to evaluate the proposed heuristics against LPC and six other well-known constructive heuristics in the literature. The simulation results show that both nLPC and nLPC(i) produce average holding and setup costs lower than or equal to those of LPC in every one of the 50 experimental conditions. The proposed heuristics also outperform each of the six other heuristics evaluated in all experimental conditions, without an increase in computational requirements. Lastly, considering that both nLPC and nLPC(i) are fairly simple for practitioners to understand and that lot-sizing heuristics have been commonly used in practice, there should be a very good chance for practical applications of the proposed heuristics.     

Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.