A multilateral Bailey lemma and multiple Andrews–Gordon identities

A multilateral Bailey lemma is proved, and multiple analogues of the Rogers–Ramanujan identities and Euler’s pentagonal theorem are constructed as applications. The extreme cases of the Andrews–Gordon identities are also generalized using the multilateral Bailey lemma where their final form are written in terms of determinants of theta functions.     

Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data

Journal of Optimization Theory and Applications - In this paper, we study robust necessary optimality conditions for a nondifferentiable complex fractional programming with uncertain data. A robust...     

Zero-one integer programs with few constraints —Efficient branch and bound algorithms

The 0–1 integer programming problem and its special case, the 0–1 knapsack problem are frequently encountered in modeling various design and decision making processes. This paper is a follow-up paper to [4] and deals with the development of an effective solution procedure for 0–1 integer programs with few constraints. Detailed computational experiments are carried out and different separation, branching and bounding rules are compared using an experimental branch and bound code. An efficient branch and bound procedure is developed, tested and compared with previously developed optimal algorithms. It is suggested that this procedure may also be used as a heuristic method for large problems by early termination of the tree search. This scheme is tested and found to be very effective.     

A convenient synthesis of amino-substituted 1,3,5-oxadiazinium salts

Diacyl chlorides react with dialkylcyanamide in the presence of a Lewis acid to give amino-substituted bis-1,3,5-oxadiazinium salts in excellent yields. A mechanism leads to the formation of the product has been postulated. All new compounds have been characterized by ¹H-nmr, ¹³C-nmr, ir-spectroscopy and elemental analysis.     

An analysis of the reflective component of small-angle X-ray scattering patterns from crazed polystyrene

An investigation of the reflective component of small-angle x-ray scattering patterns of polystyrene crazes is performed. It is shown that the strong streak parallel to the tensile axis consists predominantly of reflected radiation, while the remaining pattern is composed entirely of diffracted radiation. X-ray reflection off unparallel regions of crazes is discussed and the nature of the reflection is also considered in terms of collimation quality. An analysis methodology based on craze tip angular distribution is proposed.     

On-line small-angle and wide-angle x-ray scattering studies on melt-spinning poly(vinylidene fluoride) tape using synchrotron radiation

On-line small-angle and wide-angle x-ray scattering experiments were performed during the melt spinning of polyvinylidene fluoride using the DESY synchrotron light source. In these studies, the melt-spinning apparatus consisting of a screw extruder, a metering pump, and a take-up motor system were assembled on two separate stepper-motor-driven platforms. To investigate the structure development during crystallization, the tape location at the desired distance from the die could be positioned at the beam level with synchronous vertical movement of extruder and take-up platforms. Small-angle and wide-angle x-ray patterns were taken simultaneously with a two-dimensional wire detector and one-dimensional wire detector. In a separate study, two-dimensional WAXS data were also taken under identical processing conditions to observe the off-equator diffraction behavior during the crystallization. The data obtained for a variety of take-up speeds generally indicate that SAXS d-spacings first appear large in the early stages of crystallization and gradually decrease along the spin-line (as the crystallization progresses). As the take-up speed increases, the crystallization onset position moves away from the die and d-spacings observed at the onset increase. In addition, the shape of the discrete scattering pattern starts as a meridional streak and converts to a teardrop shape with the tip of the pattern pointing toward the beam stop at the early stages of crystallization for high take-up speeds. This does not occur at low take-up speeds and is attributed to the differences in crystallization behavior which is spherulitic or sheaflike to row nucleated crystallites. Our studies also showed that SAXS patterns appear earlier than the wide-angle crystalline diffraction peaks indicating the SAXS technique to be more sensitive to the structural changes at these stages. An idealized model is developed to explain the observed patterns at high take-up speeds. This consists of two regimes. In regime 1, the periodic fluctuations due to the alternating crystalline and amorphous regions form along the regions where eventually the “shish” structures develop. In the second stage, a volume filling crystallization takes place between the existing crystallites along the shish structure and simultaneously radial overgrowth of crystallites (i.e., the “kebabs”) takes place. This causes the observed reduction in the average d-spacing. © 1993 John Wiley & Sons, Inc.