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1.
One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups. 相似文献
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Karmarkar S Koberda M Momani J Kotecki D Garber R 《Journal of chromatography. A》2004,1039(1-2):147-153
In this paper we describe the development and validation of a solid-phase extraction procedure, followed by ion-exclusion chromatographic determination of citrate and acetate in medical fluids. The medical fluids contained trace levels of non-polar compounds, which were not of interest for the purposes of assay requirements, but due to their strong affinity towards the ion-exclusion chromatography column necessitated a 180-min long runtime to elute. The developed SPE procedure, based on trapping the hydrophobic compounds, on a reversed-phase material, while allowing analytes of interest elute off unretained, shortened the runtime to 35 min. The procedure is simple since it has only two steps, conditioning of the SPE cartridge with acetonitrile and treating the sample. The SPE procedure followed by ion-exclusion chromatographic determination was successfully validated per the International Conference on Harmonization (ICH) guidelines in terms of specificity, accuracy as recovery versus untreated sample, precision, range, linearity of response, ruggedness, stability of treated samples, and robustness. The validation data showed that the method is specific, accurate, precise, rugged, and robust. The validated method has been routinely used in the manufacturing environment. 相似文献
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Journal of Algebraic Combinatorics - The well-known Worpitzky identity $$\begin{aligned} (x+1)^n = \sum \limits _{k=0}^{n-1} A_{n,k} {{x+n-k} \atopwithdelims (){n}} \end{aligned}$$ provides a... 相似文献
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Treatment of the tert-butyldimethylsilyl ethers 1a-f with Jones reagent gave the carboxylic acids 2a-f in excellent yield in the absence of potassium fluoride. 相似文献
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Karmarkar S Garber R Genchanok Y George S Yang X Hammond R 《Journal of chromatographic science》2011,49(6):439-446
In this paper, an application of Quality by Design (QbD) concepts to the development of a stability indicating HPLC method for a complex pain management drug product containing drug substance, two preservatives, and their degradants is described. The QbD approach consisted of (i) developing a full understanding of the intended purpose, (ii) developing predictive solutions, (iii) designing a meaningful system suitability solution that helps to identify failure modes, and (iv) following design of experiments (DOE) approach. The starting method lacked any resolution among drug degradant and preservative oxidative degradant peaks, and peaks for preservative and another drug degradant. The method optimization was accomplished using Fusion AE? software (S-Matrix Corporation, Eureka, CA) that follows a DOE approach. Column temperature (50 ± 5°C), mobile phase buffer pH (2.9 ± 0.2), initial % acetonitrile (ACN, 2 ± 1%), and initial hold time (2.5, 5, or 10 min) of the HPLC method were simultaneously studied to optimize separation of the unresolved peaks. The optimized HPLC conditions (column temperature of 50°C, buffer pH of 3.1, 3% initial ACN with 2.5 min initial hold) resulted in fully resolved peaks in the two critical pairs. The QbD based method development helped in generating a design space and operating space with knowledge of all method performance characteristics and limitations and successful method robustness within the operating space. 相似文献
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In order to resolve several discrepancies in spin assignments to levels in 125Sb, directional correlations and polarization-directional correlations have been measured for several γ-γ cascades in 125Sb populated from the decay of 125Sn. Earlier results obtained from using NaI and Ge(Li) and NaI detectors were difficult to interpret due to the complex structure of the decay scheme. To improve the experimental situation, we have used two coaxial Ge(Li) detectors for the angular correlation measurements and a coaxial Ge(Li)-planar Ge(Li) combination for the polarization-directional correlations. Combination of the results of these measurements give unique spin assignments of ?, ?, +, + and + to the 1982 keV, 1890 keV, 1420 keV, 1089 keV and 1067 keV levels, respectively. The determined E2/M1 mixing ratios are : δ(470) = 0.010±0.027, δ(1067) = ?0.86±0.18, and δ(916) = ?0.02±0.01. 相似文献
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Van Veldhuizen JJ Gillingham DG Garber SB Kataoka O Hoveyda AH 《Journal of the American Chemical Society》2003,125(41):12502-12508
Design, synthesis, characterization, and catalytic activity of six enantiomerically pure Ru-based metathesis catalysts are disclosed (3a-3f). The new chiral catalysts were prepared through steric and electronic alterations of the parent catalyst system (3). The present studies indicate that the effect of structural modifications of chiral complex 3 does not always correspond to those of the related achiral complexes. The present findings illustrate that modified Ru complexes (3e and 3f) deliver reactivity levels that are more than 2 orders of magnitude higher than 3. Reactivity and physical data are provided that shed light on the origin of activity differences. Some members of the new generation of chiral Ru catalysts promote asymmetric ring-opening (AROM) and ring-closing (ARCM) metatheses that cannot be effected by the first generation chiral catalyst (3). 相似文献