An existence result for linear partial differential equations with coefficients in an algebra of generalized functions

We prove the existence of solutions for essentially all linear partial differential equations with -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy's equation has solutions whenever its right-hand side is a classical -function.

     

Chapter 15 DEA/AR analysis of the 1988–1989 performance of the Nanjing textiles corporation

This article employs new data envelopment analysis/assurance region (DEA/AR) methods to evaluate the efficiency of the 35 textile factories of the Nanjing Textiles Corporation (NTC), Nanjing, China. The returns to scale (RTS) of these factories were studied without assuming that the optimal DEA solutions were unique. All DMUs are identified with pointsE (Extreme Efficient),E (Efficient but not an extreme point) andF (Frontier but not efficient). We then further identify the nonfrontier DMUs with pointsNE, NE andNF according to whether they are projected onto a point inE, E, orF en route to evaluating their performances. All of the inefficient factories were in classNF and had unique optimal primal-dual solution pairs. Consequently, the solution pairs satisfy the strong complementary slackness condition (SCSC). Application of cone-ratio (CR) ARs reduced significantly the number of factories in classE, and showed that some AR-efficient factories were more flexible in adopting the mixture of central planning and market economies that China currently is trying to use. Also, linked-cone (LC) ARs were applied to measure maximum and minimum profit ratios. The SCSC multiplier space approach was utilized to analyze the sensitivity of the efficiency results to potential errors in the data with and without ARs. The results in this article suggest that collective units had a better performance than state-owned units in the two consecutive years analyzed.This paper was written while the author was at the School of Economics and Management, Southeast University, Nanjing 210018, P.R. China.     

Pathwise rate- stability for input-output processes

An input-output processZ = {Z(t), t 0} is said to be-rate stable ifZ(t) = o((t)) for some non-negative function(t). We prove that the processZ is -rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions for-rate-stability can be verified from input data. For example, using input information, we establish-rate stability of the workload for multiserver queues, an ATM multiplexer, and-rate stability of queue-length processes for infinite server queues.     

Prox-regular functions in variational analysis

The class of prox-regular functions covers all l.s.c., proper, convex functions, lower- functions and strongly amenable functions, hence a large core of functions of interest in variational analysis and optimization. The subgradient mappings associated with prox-regular functions have unusually rich properties, which are brought to light here through the study of the associated Moreau envelope functions and proximal mappings. Connections are made between second-order epi-derivatives of the functions and proto-derivatives of their subdifferentials. Conditions are identified under which the Moreau envelope functions are convex or strongly convex, even if the given functions are not.

     

Flow injection analysis of potassium using an all-solid-state potassium-selective electrode as a detector

The concentration of potassium was determined by a combination of flow injection analysis (FIA) with an all-solid-state potassium sensor detection. The all-solid-state potassium-selective electrode possessing long-term potential stability was fabricated by coating an electroactive polypyrrole/poly(4-styrenesulfonate) film electrode with a plasticized poly(vinyl chloride) membrane containing valinomycin. The simple FIA system developed in this laboratory demonstrated sensitivity identical to that in the batch system and achieved considerably rapid assay (150 samples h⁻¹). Analyses of soy sauce and control serum samples by this FIA system yielded results in good agreement with those obtained by conventional measurements.     

Interactions between naproxen and maltoheptaose,the non-cyclic analog ofβ-cyclodextrin

The crystallinity of naproxen in solid combinations with amorphous maltoheptaose, the non-cyclic analog of -cyclodextrin, was assessed using differential scanning calorimetry supported by X-ray powder diffractometry. Cogrinding induced a decrease in drug crystalinity to an extent which depended on the grinding time, and was most pronounced for the combination of equimolecular composition. Thermal analysis showed that the mechanism behind the conversion of crystalline naproxen into the amorphous state by cogrinding with maltoheptaose differed from that with randomly substituted, amorphous -cyclodextrins. Interactions of naproxen with maltoheptaose in aqueous solution were studied by means of fluorescence spectroscopy, phase-solubility analysis, and computeraided molecular modelling. Maltoheptaose can wrap up naproxen, taking on a cyclic conformation and forming a pseudo inclusion complex (apparent binding constant K_{1: 1} = 1.0 × 10³ (–20%) L mol^–1 at 25 °C) which is about as stable as the true inclusion complex with -cyclodextrin in the lowest temperature range (0-100 K). A better complexing ability for naproxen in terms of binding constant values, however, was displayed by both native and derivatized -cyclodextrins, the hosts with covalently-bound cyclic structures.     

High-temperature TG/DSC/QMS applications in environmental protection

The decomposition reactions of polystyrene, phenolic resin and a protective undercoating material for automobiles which contains PVC were tested using a new type of thermal analysis — mass spectrometry coupling system for measurements to 1500C or 2000C, which is based on the principle of a two-step skimmer orifice system. The results will be presented, with particular emphasis on the detection sensitivity of the new system for the products of decomposition.The capability of this coupling system to detect even heavy metals such as lead and silver in the waste gases from decomposition or after evaporation at high temperatures will also be demonstrated.     

Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .     

Structures of boron chelates of mono- and diacylketene aminals

The molecular and crystal structures of diphenylboron chelates of acetylketeneN-benzoylaminal and 2-(N-benzoyl)diaminomethylene-4-dimethylaminomethylenecyclohexane-1,3-dione and the structure of the difluoroboron complex of diacetylketeneN-benzoylaminal were established. It was found that the aminovinylcarbonyl fragment of the ligand is involved in the formation of a boron-containing ring. A delocalized -electron system over the NCCCO fragment of the chelate ring is characteristic of the molecules studied both in crystals and solutions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2541–2546, October, 1996.     

On the generation of test patterns for multiple faults

This article presents a new method to generate test patterns for multiple stuck-at faults in combinational circuits. We assume the presence of all multiple faults of all multiplicities and we do not resort to their explicit enumeration: the target fault is a single component of possibly several multiple faults. New line and gate models are introduced to handle multiple fault effect propagation through the circuits. The method tries to generate test conditions that propagate the effect of the target fault to primary outputs. When these conditions are fulfilled, the input vector is a test for the target fault and it is guaranteed that all multiple faults of all multiplicities containing the target fault as component are also detected. The method uses similar techniques to those in FAN and SOCRATES algorithms to guide the search part of the algorithm, and includes several new heuristics to enhance the performance and fault detection capability. Experiments performed on the ISCAS'85 benchmark circuits show that test sets for multiple faults can be generated with high fault coverage and a reasonable increase in cost over test generation for single stuck-at faults.