Quantum Invariants

In earlier work, we derived an expression for a partition function ?^(λ), and gave a set of analytic hypotheses under which ?^(λ) does not depend on a parameter λ. The proof that ?^(λ) is invariant involved entire cyclic cohomology and K-theory. Here we give a direct proof that . The considerations apply to non-commutative geometry, to super-symmetric quantum theory, to string theory, and to generalizations of these theories to underlying quantum spaces. Received: 12 January 1998 / Accepted: 1 May 1999     

Density and Approximation Properties of Markov Systems

Borwein, Bojanov, Erdélyi, and others, have studieddensity and approximation properties of those Markov systems of differentiablefunctions on a closed interval [a,b], having the property thatthe system of derivatives is a Markov system on the open interval (a,b).In this paper we show that several of these results are valid for anyMarkov system of continuous functions on a closed interval.     

Catalytic properties of polymer-colloid complexes based on polyethyleneimines and mono- and diquaternized 1,4-diazabicyclo[2.2.2]octane derivatives in the hydrolysis of phosphorus acids esters

Russian Chemical Bulletin - It is established by spectrophotometry that polyethyleneimines, mono- (MQD) and diquaternized (DQD) hexadecyl derivatives of 1,4-diazabicyclo[2.2.2]octane, and mixed...     

Reactions of methyl esters of adamantane acids with acetonitrile

Russian Chemical Bulletin - Methyl adamantane-1-carboxylate and methyl (1-adamantyl)acetate react with acetonitrile in the presence of sodium hydride to give 3-(1-adamantyl)-3-oxopropanenitrile and...     

Versatile Sugar Derivatives for the Synthesis of Potential Degradable Hydrophilic‐Hydrophobic Polyurethanes and Polyureas

Biodegradable polymers obtained from renewable natural sources are currently receiving increasing attention because they are an alternative to the traditional petroleum‐based plastics. In the present communication we describe the synthesis of the diol monomers 2,3,4‐tri‐O‐benzyl‐L‐arabinitol (ABnOH) and 2,3,4‐tri‐O‐benzylxylitol (XBnOH), and the diamino monomers 1,5‐diamino‐1,5‐dideoxy‐2,3,4‐tri‐O‐benzyl‐L‐arabinitol (ABnNH ₂ ) and 1,5‐diamino‐1,5‐dideoxy‐2,3,4‐tri‐O‐benzylxylitol (XBnNH ₂ ), which can be used in the preparation of new potentially biodegradable sugar‐based polymers. As an example, we describe the synthesis and characterization of a polyurethane [PU‐(ABnOH‐HMDI)] and a polyurea [PUR‐(ABnNH₂‐HMDI)] by poly addition reaction of ABnOH and ABnNH ₂ with 1,6‐hexamethylene diisocyanate.      

Estimating fish orientation from broadband, limited-angle, multiview, acoustic reflections

This article demonstrates that multiview, broadband (635-935 kHz), nearly monostatic, acoustic reflections recorded from lateral views of juvenile fish can be used to infer animal orientation. Calibrated acoustic data were recorded from live fish in a laboratory, while orientation was measured simultaneously via optical images. Using eight animals, two-dimensional data sets of target strength as a function of frequency and orientation were obtained. Fish length, lateral thickness, and dorsoventral thickness ranged from 24 to 48 mm, 3 to 7 mm and 10 to 20 mm, respectively. Preliminary estimates of orientation were computed from the direction of the gradient of the local autocorrelation function in the target strength image. These local estimates were then median-filtered over the full system bandwidth (but still limited-angle) to improve accuracy. Angular estimates were then corrected for systematic bias via a simple, one-dimensional model that approximated the animals' reflection by that of a bar target. Taken over all orientations, the average absolute error in orientation estimation is 5.6° to 17°, dependent on the data set. Results indicate, for most sets of views, reasonable estimates of lateral orientation can be obtained from broadband, multiview data over a set of limited angular reflections.     

Complex Reconfiguration of DNA Nanostructures

Nucleic acids have been used to create diverse synthetic structural and dynamic systems. Toehold‐mediated strand displacement has enabled the construction of sophisticated circuits, motors, and molecular computers. Yet it remains challenging to demonstrate complex structural reconfiguration in which a structure changes from a starting shape to another arbitrarily prescribed shape. To address this challenge, we have developed a general structural‐reconfiguration method that utilizes the modularly interconnected architecture of single‐stranded DNA tile and brick structures. The removal of one component strand reveals a newly exposed toehold on a neighboring strand, thus enabling us to remove regions of connected component strands without the need to modify the strands with predesigned external toeholds. By using this method, we reconfigured a two‐dimensional rectangular DNA canvas into diverse prescribed shapes. We also used this method to reconfigure a three‐dimensional DNA cuboid.     

Editorial

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