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1.
A divisor d ∈ ?+ of n ∈ ?+ is said to be a unitary divisor of n if (d, n/d) = 1. In this article we examine the greatest common unitary divisor (GCUD) reciprocal least common unitary multiple (LCUM) matrices. At first we concentrate on the difficulty of the non-existence of the LCUM and we present three different ways to overcome this difficulty. After that we calculate the determinant of the three GCUD reciprocal LCUM matrices with respect to certain types of functions arising from the LCUM problematics. We also analyse these classes of functions, which may be referred to as unitary analogs of the class of semimultiplicative functions, and find their connections to rational arithmetical functions. Our study shows that it does make a difference how to extend the concept of LCUM.  相似文献   
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Considering lower closed sets as closed sets on a preposet (P, ≤), we obtain an Alexandroff topology on P. Then order preserving functions are continuous functions. In this article we investigate order preserving properties (and thus continuity properties) of integer-valued arithmetical functions under the usual divisibility relation of integers and power GCD matrices under the divisibility relation of integer matrices.  相似文献   
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Multivariate data analysis methods (4-way Candecomp-PARAFAC model solved with Multilinear Engine (ME-1)) were used to interpret the data of over two decades to study the changes in the water of Lake Saimaa in Finland. Earlier studies have shown that it is difficult to extract the natural background from the other sources of variation. By using the multilinear model three interpretable factors representing natural and anthropogenic processes could be extracted. The natural long-term variation, seasonal fluctuation and dilution of discharges in the recipient area could be extracted into their own factors, which could be easily visualized. The variation could be also presented with estimated variation in the water quality parameters caused by each of these natural or anthropogenic processes. Received: 27 September 2000 / Revised: 11 January 2001 / Accepted: 14 January 2001  相似文献   
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A mass spectrometric identification and differentiation of pyrimidin-4(3H)- and -4(1H)-ones was carried out. N-Substitution at position 1 or 3 made the distinction of the two sets of compounds very easy because of their characteristic fragmentation pathways. Most interesting were the spectra of the N-unsubstituted derivatives, which illustrated a predominance of the two possible NH tautomers in relation to the 4-hydroxy structure.  相似文献   
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A simple and general standard-addition method for a single-component determination is presented. The method uses two independent variables for the calculation of the analyte concentration (the amount of sample taken and the amount of analyte added) and one dependent variable, the response. The sensitivity and the response of the blank can also be estimated from the model by changing the amount of the sample and the amount of the analyte addition. In the simples case, a linear equation is assumed to exist between the variables. Geometrically, the model can be expressed by the response plane in the variable-space. The method has all the advantages of the ordinary standard-addition method but also includes automatic blank elimination and versatile matrix-interference control. Two examples of the use of the method are based on graphite-furnace atomic absorption spectrometry of chromium and lead. Standard statistical packages are applied.  相似文献   
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Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.  相似文献   
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Ammonia, isobutane and methane chemical ionization mass spectra have been measured for some substituted cis-1,3-cyclopentane dicarboxylic acids and their derivatives. The relative proton affinities of the different functional groups determine the protonation site in the molecule and thereby greatly affect the fragmentation. Intramolecular catalysis clearly facilitates the elimination of water in cases where functional groups can interact with each other.  相似文献   
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