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141.
142.
We prove the Cramér theorem forK-invariant Gaussian measures on irreducible symmetric spacesX=G/K withG semisimple noncompact. To do this we use a kind of Abel transform ofK-invariant measures onX.This research is supported by KBN Grant. 相似文献
143.
Alexander Koldobsky 《Journal of Theoretical Probability》1994,7(1):135-145
Let μ be a measure in a Banach spaceE, f be an even function onR. We consider the potentialg(a)=f E f(‖x?a‖)dμ(x). The question is as follows: For whichf does the potentialg determine μ uniquely? In this article we give answers in the cases whereE=l ∞ n and wheref(t)=|t| p andE is a finite dimensional Banach space with symmetric analytic norm. Calculating the Fourier transform of the functionf(‖x‖ ∞) we give a new proof of the J. Misiewicz's result that the functionf(‖x‖ ∞) is positive definite only iff is a constant function. 相似文献
144.
Holger Dette 《Transactions of the American Mathematical Society》1996,348(2):691-711
A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.
145.
Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.
146.
The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC
behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals. 相似文献
147.
We propose a new approach for high-throughput continuous titration based on a flow ratiometry. The method was applied to potentiometric titrations of acids and bases. A base solution, the flow rate FB of which was varied in response to controller output voltage Vc, was merged with an acid solution under constant total (acid + base) flow rate. Downstream, the pH of the mixed solution was measured with a flow-through glass electrode. Initially, Vc, and thus FB was increased linearly. At the instant the equivalence point (EP) was sensed, the ramp direction of Vc was reversed from upward to downward. The direction was reversed to upward when EP was sensed again. Such the feedback-based operation gives a triangular waveform of Vc, because there is a delay corresponding mainly to the transit time of merged solutions to reach the sensor. The value of Vc that gives EP composition, VE, was estimated by averaging the most recent maximum and minimum values of Vc. Next, fixed triangular waves of Vc was used to control FB. The amplitude and the scan rate of the waves were fixed narrower and faster, respectively, than those in the feedback-based operation in order to improve the throughput rate. The EP can be located as long as the scan range covers VE. These automated processes limited the titration to just the narrow range around EP, and thus realized extremely high throughput rate of maximally 17.6 titrations per minute (=3.4 s per titration) at R.S.D. = 0.35%. 相似文献
148.
Glycosylations are notoriously difficult reactions that require extensive optimization regarding the type of anomeric leaving group, solvent, reaction temperature, and reaction time. Described is the use of a silicon‐based microreactor to screen reaction conditions and to scale‐up synthetic procedures. For the first time, glycosyl phosphates were employed in a microreactor. The optimized reaction conditions were successfully transferred to a batch process. 相似文献
149.
The decomposition of N2O in a 13.56-MHz parallel-plate system was studied usingin situ Fourier transform infrared (FTIR) spectroscopy. Areas of two infrared absorption bands of N2O recorded at 8 cm–1 resolution were used to estimate relative gas-phase dissociation as a function of rf power and flow rate at 500 mT. Flow rate was found to strongly affect band areas over the range of powers investigated (10–90 W). The effect of rf power on band areas diminished above 40 W, probably due to poor plasma confinement. Distortion of the band shapes by the plasma permitted rotational temperatures to be estimated. Rotational temperature increased essentially linearly with power at constant flow rate, reaching 450 K at 80 W, but was independent of flow rate at constant power. Rotational temperatures were also found to depend on the temperature of the electrodes, which were heated by plasma exposure. No infrared-active product species were observed even under batch conditions where all N2O was irreversibly dissociated. This lack of detectable products and a 50% pressure rise observed in a batch study suggest that N2 and O2 are the primary stable discharge products. 相似文献
150.
Moreno-Cid A Yebra MC Cancela S Cespón RM 《Analytical and bioanalytical chemistry》2003,377(4):730-734
Iron was extracted on-line from solid meat samples by a simple and rapid continuous ultrasound-assisted extraction system (CUES). The CUES is connected to a flow injection manifold, which allows the on-line flame atomic absorption spectrometric determination of iron. A Plakett–Burman design was used for the optimisation of the CUES. The method achieved a total sampling frequency of 11 samples per hour with a relative standard deviation for the complete procedure of 0.4%. The detection limit was 0.6 g g–1 (dry mass) for a sample amount of 30 mg. Accurate results were obtained by measuring the certified reference materials BCR-186 (pig kidney) and BCR-184 (bovine muscle). The analytical procedure was applied to different real meat samples with satisfactory results. 相似文献