How much is that DAWG in the window? a moving window algorithm for the directed acyclic word graph

There is a class of data compression techniques that involve replacing repeating strings by pointers to previous occurrences of those strings. In order to implement these techniques, it would be useful to have an index which can quickly locate repeats within a fixed window of the text seen so far. One such index is the directed acyclic word graph (DAWG). An algorithm is presented which constructs the DAWG for a fixed window of k letters moving from left to right along the input text. It is shown that this algorithm has worst case behavior proportional to nk, where n is the length of the input text and k is the size of the window. This bound is the best possible for a window moving through the DAWG and also for a window moving through the suffix tree, a functionally related structure. The average case for the algorithm is analyzed under the assumption that input strings are random texts constructed from a fixed alphabet where each letter has equal probability. The resulting upper bound is O(nlogk).     

Stereoselective syntheses of polyhydroxylated azepane derivatives from sugar-based epoxyamides. Part 1: synthesis from d-mannose

An approach to the synthesis of polyhydroxyazepane derivatives from sugar-based epoxyamides or epoxyalcohols, in which the total regioselective epoxide opening by nitrogen nucleophiles is the key step, is described. Thus, novel polyhydroxyazepane carboxamides and aminomethyl polyhydroxyazepanes, with potential pharmacological interest, are synthesized from diacetone d-mannose. Configurational assignments of the obtained products were determined.     

Kinetics of the reactions of OH radicals with 2‐methoxy‐6‐(trifluoromethyl)pyridine,diethylamine, and 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol at 298 ± 2 K

Rate constants for the reactions of 2‐methoxy‐6‐(trifluoromethyl)pyridine, diethylamine, and 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol with OH radicals have been measured at 298 ± 2 K using a relative rate method. The measured rate constants (cm³ molecule^?1 s^?1) are (1.54 ± 0.21) × 10^?12 for 2‐methoxy‐6‐(trifluoromethyl)pyridine, (1.19 ± 0.25) × 10^?10 for diethylamine, and (1.76 ± 0.38) × 10^?12 for 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol, where the indicated errors are the estimated overall uncertainties including those in the rate constants for the reference compounds. No reaction of 2‐methoxy‐6‐(trifluoromethyl)pyridine with gaseous nitric acid was observed, and an upper limit to the rate constant for the reaction of 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol with O₃ of <7 × 10^{? 20} cm³ molecule^?1 s^?1 was determined. Using a 12‐h average daytime OH radical concentration of 2 × 10⁶ molecule cm^?3, the lifetimes of the volatile organic compounds studied here with respect to reaction with OH radicals are 7.5 days for 2‐methoxy‐6‐(trifluoromethyl)pyridine, 1.2 h for diethylamine, and 6.6 days for 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol. Likely reaction mechanisms are discussed. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 631–638, 2011     

Nitration of 2-substituted pyrimidine-4,6-diones,structure and reactivity of 5,5-gem-dinitropyrimidine-4,6-diones

Nitration of some 2-substituted pyrimidine-4,6-diones in sulfuric acid was studied, which afforded previously unknown 5,5-gem-dinitropyrimidine-4,6-diones in high yields. The gem-dinitro products were easily attacked by nucleophiles with concomitant formation of gem-dinitroacetyl derivatives, which in turn could be further hydrolyzed to salts of dinitromethane and triureas.     

Orbital angular momentum exchange in the interaction of twisted light with molecules

In the interaction of molecules with light endowed with orbital angular momentum, an exchange of orbital angular momentum in an electric dipole transition occurs only between the light and the center of mass motion; i.e., internal "electronic-type" motion does not participate in any exchange of orbital angular momentum in a dipole transition. A quadrupole transition is the lowest electric multipolar process in which an exchange of orbital angular momentum can occur between the light, the internal motion, and the center of mass motion. This rules out experiments seeking to observe exchange of orbital angular momentum between light beams and the internal motion in electric dipole transitions.