Germanomolybdic acid and its reaction with basic organic dyestuffs-I Spectrophotometric determination of ge(iv) with xanthene dyes

The interaction between germanomolybdic acid and four xanthene dyes (Rhodamine B, Rhodamine 6G, Rhodamine S and Pyronine G) is studied and the conditions for spectrophotometric determination of Ge(IV) with these reagents are established.     

A comparison of underwater hearing sensitivity in bottlenose dolphins (Tursiops truncatus) determined by electrophysiological and behavioral methods

Variable stimulus presentation methods are used in auditory evoked potential (AEP) estimates of cetacean hearing sensitivity, each of which might affect stimulus reception and hearing threshold estimates. This study quantifies differences in underwater hearing thresholds obtained by AEP and behavioral means. For AEP estimates, a transducer embedded in a suction cup (jawphone) was coupled to the dolphin's lower jaw for stimulus presentation. Underwater AEP thresholds were obtained for three dolphins in San Diego Bay and for one dolphin in a quiet pool. Thresholds were estimated from the envelope following response at carrier frequencies ranging from 10 to 150 kHz. One animal, with an atypical audiogram, demonstrated significantly greater hearing loss in the right ear than in the left. Across test conditions, the range and average difference between AEP and behavioral threshold estimates were consistent with published comparisons between underwater behavioral and in-air AEP thresholds. AEP thresholds for one animal obtained in-air and in a quiet pool demonstrated a range of differences of -10 to 9 dB (mean = 3 dB). Results suggest that for the frequencies tested, the presentation of sound stimuli through a jawphone, underwater and in-air, results in acceptable differences to AEP threshold estimates.     

Note on nonstability of the linear recurrence

We prove a non-stability result for linear recurrences with constant coefficients in Banach spaces. As a consequence we obtain a complete solution of the problem of the Hyers-Ulam stability for those congruences in the complex Banach space.     

Structure and growth kinetics of the oxidation process of Fe(001) whisker surfaces over a 10-decade pressure range

Fe(001) surfaces of whiskers of good crystalline quality were oxidized in a pressure range from 10^? 7 mbar to 1 bar at different temperatures. Epitaxial Fe₃O₄ and FeO thin films with negligible strain were grown depending on the oxidation temperatures. The kinetics of the oxide thickness growth was measured and compared with the predictions of the Fromhold–Cook theory for oxidation of metals. Some discrepancies were found and a possible explanation is presented.     

On the stability of the first-order linear recurrence in topological vector spaces

Suppose that X is a sequentially complete Hausdorff locally convex space over a scalar field K, V is a bounded subset of X, (a_n)_n≥0 is a sequence in K?{0} with the property lim inf_n→∞|a_n|>1, and (b_n)_n≥0 is a sequence in X. We show that for every sequence (x_n)_n≥0 in X satisfying

     

Enumerating Cube Tilings

Cube tilings formed by $n$ -dimensional $4\mathbb Z ^n$ -periodic hypercubes with side $2$ and integer coordinates are considered here. By representing the problem of finding such cube tilings within the framework of exact cover and using canonical augmentation, pairwise nonisomorphic 5-dimensional cube tilings are exhaustively enumerated in a constructive manner. There are 899,710,227 isomorphism classes of such tilings, and the total number of tilings is 638,560,878,292,512. It is further shown that starting from a 5-dimensional cube tiling and using a sequence of switching operations, it is possible to generate any other cube tiling.     

Semiclassical method for calculating the energetic values of helium, lithium and beryllium atoms

In previous papers we have presented a wave model for conservative bound systems resulted from the equivalency between the Schrödinger and wave equations. We proved that the normal curves of the characteristic surface of the wave equation, denoted by C curves, are solutions of the Hamilton-Jacobi equation, written for the same system, and correspond to the same constants of motion as those resulting from the Schrödinger equation. In this paper we present a method for computing the energetic values of conservative bound systems which is based on the properties of the C curves. The method is applied to the 1s ² state of helium, 1s ²2s and 1s ²2p states of lithium and 1s ²2s ² state of beryllium. Our theoretical values are compared with experimental data taken from well-known books. The relative error of our method is less than 5 x 10^?3.