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91.
Let be a nonnegative real matrix which is expanding, i.e. with all eigenvalues , and suppose that is an integer. Let consist of exactly nonnegative vectors in . We classify all pairs such that every in the orthant has at least one radix expansion in base using digits in . The matrix must be a diagonal matrix times a permutation matrix. In addition must be similar to an integer matrix, but need not be an integer matrix. In all cases the digit set can be diagonally scaled to lie in . The proofs generalize a method of Odlyzko, previously used to classify the one--dimensional case.
92.
Eric Bach Richard Lukes Jeffrey Shallit H. C. Williams. 《Mathematics of Computation》1996,65(216):1737-1747
Let be a positive integer. We say looks like a power of 2 modulo a prime if there exists an integer such that . First, we provide a simple proof of the fact that a positive integer which looks like a power of modulo all but finitely many primes is in fact a power of . Next, we define an -pseudopower of the base to be a positive integer that is not a power of , but looks like a power of modulo all primes . Let denote the least such . We give an unconditional upper bound on , a conditional result (on ERH) that gives a lower bound, and a heuristic argument suggesting that is about for a certain constant . We compare our heuristic model with numerical data obtained by a sieve. Some results for bases other than are also given.
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Jeffrey Bub 《Foundations of Physics Letters》1993,6(1):21-35
Elby (1993) has raised certain problems that appear to be devastating for modal interpretations of quantum mechanics, but do not arise for Bohm's pilot wave theory. Here I show that the features Elby identifies as objectionable in my version of the modal interpretation have their counterpart in Bohm's theory. To the extent that Bohm's theory works as a no collapse solution to the measurement problem - and I think it does - so does my modal interpretation. 相似文献
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The time-resolved ESR signal of a triplet radical pair was detected upon excitation of a solid mixture of acridine and acridan at room temperature. The ZFS parameters of the triplet radical pair were determined to be D=−0.0100 cm−1 and E=0.00053 cm−1. The structure of the radical pair is discussed on the basis of the data. 相似文献
100.
Ketan Patel Dr. Michael J. Dunn Siegfried Günther Wilhelm Postel Angelika Görg 《Electrophoresis》1988,9(9):547-554
Horizontal two-dimensional polyacrylamide gel electrophoresis with immobilised pH gradients in the first dimension has been applied to the analysis of human skin fibroblast and muscle myoblast total cell proteins. Excellent two-dimensional separations of skin fibroblast proteins were obtained using pH 4-10 immobilised pH gradient gels with a long interelectrode distance (16 cm), but resolution was degraded, particularly of the more acidic proteins, by the use of shorter (10 cm) gels. Improved resolution of acidic and basic proteins was obtained using separate pH 4-7 and pH 7-10 immobilised pH gradient gels respectively in the first dimension. Two-dimensional protein maps of skin fibroblast proteins were visualised both by silver staining and by autoradiography of samples labelled synthetically with [35S]methionine. Horizontal two-dimensional electrophoresis, using pH 4-7 and pH 7-10 immobilised pH gradient gels in the first dimension, was applied to the analysis of protein samples from skin fibroblasts and muscle myoblasts dual-labelled synthetically with [35S]methionine and [75Se]selenomethionine in an attempt to identify sets of proteins specific to each cell type. In addition, two-dimensional maps or protein samples derived from normal individuals and patients with Duchenne muscular dystrophy were compared to search for protein changes associated with the disease state. Although sets of qualitative protein spot differences were observed by visual inspection of the two-dimensional gels, more rigorous qualitative and quantitative analysis of the patterns using a computerised analysis system will be required to obtain the maximum amount of information from these data. 相似文献