Multiple H-Rearrangements in 10-Benzylthio-dithranol Radical Cations

10-Alkylthio- and 10-arylthio-derivatives of dithranol (anthralin; 1,8-dihydroxy-9-anthrone) are of interest in search for new anti-psoriatic agents2 , 3 ). By working out ms procedures for unequivocal identification of trace amounts of these compounds4 ) it was established that in case of 10-phenylthio-dithranol putative by-products, especially one giving rise to ions at m/z = 226 (dithranol), are artefacts of thermal reaction in the mass spectrometer1). In the EI-MS of those 10-substituted dithranols containing a S-CH2R chain, however, these ions (m/z = 226) arise from M + * as well. Scope and mechanism of their formation was examined by analyzing compound 1 and its D-labelled derivatives 2 and 3

On Weingarten transformations of hyperbolic nets

Weingarten transformations which, by definition, preserve the asymptotic lines on smooth surfaces have been studied extensively in classical differential geometry and also play an important role in connection with the modern geometric theory of integrable systems. Their natural discrete analogues have been investigated in great detail in the area of (integrable) discrete differential geometry and can be traced back at least to the early 1950s. Here, we propose a canonical analogue of (discrete) Weingarten transformations for hyperbolic nets, that is, C^1-surfaces which constitute hybrids of smooth and discrete surfaces "parametrized" in terms of asymptotic coordinates. We prove the existence of Weingarten pairs and analyse their geometric and algebraic properties.Comment: 41 pages, 30 figure

Thinplate Splines on the Sphere

In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a widely used tool in myriad applications. The analogues for ${\mathbb S}^{d-1}$ are the thin plate splines for the sphere. The topic was first discussed by Wahba in the early 1980's, for the ${\mathbb S}^2$ case. Wahba presented the associated semi-reproducing kernels as infinite series. These semi-reproducing kernels play a central role in expressions for the solution of the associated spline interpolation and smoothing problems. The main aims of the current paper are to give a recurrence for the semi-reproducing kernels, and also to use the recurrence to obtain explicit closed form expressions for many of these kernels. The closed form expressions will in many cases be significantly faster to evaluate than the series expansions. This will enhance the practicality of using these thinplate splines for the sphere in computations

The Impacts of Spatially Variable Demand Patterns on Water Distribution System Design and Operation

Open Access articleResilient water distribution systems (WDSs) need to minimize the level of service failure in terms of magnitude and duration over its design life when subject to exceptional conditions. This requires WDS design to consider scenarios as close as possible to real conditions of the WDS to avoid any unexpected level of service failure in future operation (e.g., insufficient pressure, much higher operational cost, water quality issues, etc.). Thus, this research aims at exploring the impacts of design flow scenarios (i.e., spatial-variant demand patterns) on water distribution system design and operation. WDSs are traditionally designed by using a uniform demand pattern for the whole system. Nevertheless, in reality, the patterns are highly related to the number of consumers, service areas, and the duration of peak flows. Thus, water distribution systems are comprised of distribution blocks (communities) organized in a hierarchical structure. As each community may be significantly different from the others in scale and water use, the WDSs have spatially variable demand patterns. Hence, there might be considerable variability of real flow patterns for different parts of the system. Consequently, the system operation might not reach the expected performance determined during the design stage, since all corresponding facilities are commonly tailor-made to serve the design flow scenario instead of the real situation. To quantify the impacts, WDSs’ performances under both uniform and spatial distributed patterns are compared based on case studies. The corresponding impacts on system performances are then quantified based on three major metrics; i.e., capital cost, energy cost, and water quality. This study exemplifies that designing a WDS using spatial distributed demand patterns might result in decreased life-cycle cost (i.e., lower capital cost and nearly the same pump operating cost) and longer water ages. The outcomes of this study provide valuable information regarding design and operation of water supply infrastructures; e.g., assisting the optimal design

LOT: Logic Optimization with Testability - new transformations for logic synthesis

A new approach to optimize multilevel logic circuits is introduced. Given a multilevel circuit, the synthesis method optimizes its area while simultaneously enhancing its random pattern testability. The method is based on structural transformations at the gate level. New transformations involving EX-OR gates as well as Reed–Muller expansions have been introduced in the synthesis of multilevel circuits. This method is augmented with transformations that specifically enhance random-pattern testability while reducing the area. Testability enhancement is an integral part of our synthesis methodology. Experimental results show that the proposed methodology not only can achieve lower area than other similar tools, but that it achieves better testability compared to available testability enhancement tools such as tstfx. Specifically for ISCAS-85 benchmark circuits, it was observed that EX-OR gate-based transformations successfully contributed toward generating smaller circuits compared to other state-of-the-art logic optimization tools