Time-limited and band-limited environment: Signals and systems

Of concern is an environment made up of signals and systems tightly confined both in time and frequency. Such an environment is often encountered in transmission line circuits, radar, sonar, and optical circuits, and when the principal signals are well-defined sharp pulses. It will be seen that once this environment is achieved, the signals and systems possess some attractive properties. A conventional system may preserve the symmetry of a propagating signal or change its symmetry from even to odd or from odd to even. Another system may be used to predict the arrival of an incoming pulse with a high degree of accuracy. Electrical networks may also be associated with these properties. Approximation problems, existence theorems, and realization schemes will be addressed and developed.     

Impulse stress wave propagation in elongated bodies: Apparent deviations from circuit realizability principles

Of concern is the undistorted propagation of pulse stress waves in long thin bodies. The primary signals are arbitrarily sharp pulses projected along thex-axis. It will be seen that these pulses travel close to the speed of sound in unbounded media. Secondary pulses follow representing interactive disturbances traveling along they-axis. But the process brings out certain anomalies in circuit realizability requirements. These issues, transmission parameters, and coupling between the various signals are studied in detail. The results are supported by experiments.Work supported by TecSonics Inc., Twinsburg Ohio.     

Spectroscopic investigation of adsorbed 7-(4-ethyl-1-methyloctyl)-8-quinolinol (kelex 100) and of its gallium(III) complex: Comparison with the behaviours observed in solvent extraction systems

The adsorption of a long hydrocarbon chain oxine derivative, 7-(4-ethyl-1-methyloctyl)-8-quinolinol, on the macromolecular Amberlite XAD-7 support is shown by FT-IR spectroscopy to be the result of only weak extractant-support interactions. It is also shown that the chelation ability of the extractant towards gallium(III) does not suffer from the presence of the solid support. Finally the stereochemistry (fac or mer configuration) of the tris-7-(4-ethyl-1 -methyloctyl)-8-quinolinato gallium(III) complex formed either in solution in an organic diluent or on the support is discussed on the basis of ¹H and ¹³C NMR and FIR data.     

Some rheological properties of highly crosslinked polysiloxanes

Seven crosslinked polydimethylsiloxanes were prepared from carboxyl-terminated siloxane oligomers of different average lengths and a trifunctional imine. The 10-sec torsion modulus was measured as a function of temperature, and compression-deflection data were obtained on swollen specimens. Polymer-solvent interaction parameters were calculated from equilibrium swelling ratios and modulus data. The plots of modulus versus temperature show two distinct transitions for all the crosslinked polymers. The low-temperature transition corresponds to the siloxane chains, whereas the high-temperature transition should be attributed to the portion of the network chain derived from the crosslinking agent and the organic part of the oligosiloxane. On shortening the siloxane blocks, both transitions shift to successively higher temperatures and higher modulus levels. However, the siloxane transition temperature shows only a limited rise even when the average block length becomes quite small. The low siloxane polymers seem to exhibit two swelling maxima, each corresponding to one of the constituents. The studied materials from nonrandom copolymeric structures typical of block polymers. Such microphase systems can probably be expected in crosslinked polymers whenever the crosslinking agent participates significantly in the network chains and its compatibility with the flexible chains species is poor.     

The reactions of ureas with glyoxylic acid and methyl glyoxylate

The reactions of urea, methylurea and dimethylureas with glyoxylic acid and its methyl ester to give α-substituted hydantoic acid derivatives (4, 5, 6, 7) and substituted allantoic acid derivatives (8) is discussed. The cyclization of the hydantoates and allantoates to 5-substituted hydantoins (11, 12) is also described.     

Advertising Budgeting,Wearout and Copy Replacement

In this paper we offer a formulation for the "Copy Life Cycle" phenomenon. In particular, we introduce simultaneously three decision variables, the optimal advertising expenditures during a given planning horizon, the optimal times for copy replacements and the optimal investments in the new copies. The analysis and the solution of the problem is carried out by a mixed optimization technique based on dynamic programming and optimal control theory.