In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log2n) time. Our data structure needs O(nlogn) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other. 相似文献
A new kinetic approach to flowing chemical system is introduced, based on the elimination of reaction extents attached to linearly dependent reactions. The method is applied to analyze the propagation of acoustic waves in a reacting chemical mixture.
A high-precision exact-matching quadruple isotope dilution method (ID4MS) was employed for the quantitation of nitrate in an air-dried spinach powder Certified Reference Material (CRM). The analyte was extracted in hot water following addition of 15NO\({}_{3}^{-}\) internal standard. The blend was then treated with sulfamic acid to remove nitrite and with triethyloxonium tetrafluoroborate to promote aqueous conversion of nitrate into volatile EtONO2. The derivative was analyzed by headspace GC–MS with 3-min elution time. The method performance was validated with a series of tests which demonstrated adequate selectivity and ruggedness. This method supported the development of novel SPIN-1 CRM giving a modest contribution to its uncertainty (uchar = 0.85%). With respect to previous attempts, the SPIN-1 was proven stable, homogeneous (uhom = 0.44%), and suitable for spinach monitoring under EU regulations. On dried basis, the nitrate content of SPIN-1 was found to be 22.53 ± 0.43 mg/g (Uc = 1.9%, k = 2). The material was also used in an inter-laboratory study where four laboratories employed a total of ten measurement methods.
Reactions of (norbornadiene)Cr(CO)4 or cis-(piperidine)2Mo(CO)4 with R2Sb-SbR2, and cyclo-(R′Sb)n (R′ = Et, n-Pr; n = 4, 5) give the complexes cyclo-[M(CO)4(R2Sb-SbR′- SbR′-SbR2)] (1: M = Cr, R = Me, R′= Et; 2: M = Mo, R = Et, R′ = Et; 3: M = Mo, R = Et, R′ = n-Pr). Not accessible to established characterization methods, the oily, extremely reactive unpurified mixture of 3 with scrambled ligands was characterized by mass spectrometry using liquid injection field desorption ionization (LIFDI). 相似文献
Aromatic hydrocarbons with fused benzene rings and regular triangular shapes, called n-triangulenes according to the number of rings on one edge, form groundstates with n-1 unpaired spins because of topological reasons. Here, we focus on methodological aspects emerging from the density functional theory (DFT) treatments of dimer models of the n = 2 triangulene (called also phenalenyl), observing that it poses interesting new problems to the issue of long-range corrections. Namely, the interaction comprises simultaneous spincoupling and van der Waals effects, i.e., a technical conjuncture not considered explicitly in the benchmarks calibrating long-range corrections for the DFT account of supramolecular systems. The academic side of considering dimer models for calculations and related analysis is well mirrored in experimental aspects, and synthetic literature revealed many compounds consisting of stacked phenalenyl cores, with intriguing properties, assignable to their long-range spin coupling. Thus, one may speculate that a thorough study assessing the performance of state-of-the-art DFT procedures has relevance for potential applications in spintronics based on organic compounds. 相似文献
Zeolites are widely used in many commercial processes, mostly as catalysts or adsorbents. Understanding their intimate structure at the nanoscale is the key to control their properties and design the best materials for their ever increasing uses. Herein, we report a new and controllable fluoride treatment for the non‐discriminate extraction of zeolite framework cations. This sheds new light on the sub‐structure of commercially relevant zeolite crystals: they are segmented along defect zones exposing numerous nanometer‐sized crystalline domains, separated by low‐angle boundaries, in what were apparent single‐crystals. The concentration, morphology, and distribution of such domains analyzed by electron tomography indicate that this is a common phenomenon in zeolites, independent of their structure and chemical composition. This is a milestone to better understand their growth mechanism and rationally design superior catalysts and adsorbents. 相似文献