RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Anomalies in the Absorption and Reflection of a High-Power Ultrashort Laser Pulse by a Plasma with a Solid-State Density

The patterns of absorption and reflection of an ultrashort laser pulse by a plasma with a solid-state density, which are realized in the mode of the normal skin effect, are studied. It is shown that a decrease in low-power pulse duration shorter than the period corresponding to the fundamental frequency of radiation leads to an increase in the absorption coefficient. If the pulse power is so high as to provide electron heating during a time shorter than the reciprocal fundamental frequency, nonlinear suppression of absorption takes place and the spectrum of the reflected radiation contains odd harmonics of the fundamental frequency.     

紫外可调谐辐射的波长自动跟踪研究

脉冲染料激光器的可见光波段辐射通过共线倍频和非共线混频实现紫外波段的连续可调谐输出.本文报道了一种闭环跟踪方法;在调谐起始波长处,将取样光束在垂直相位匹配方向分割成等光强的两部分,然后在波长调谐时比较和平衡这两部分光强.对该方法在理论上作了分析并在实验中得到成功的验证.获得的自动跟踪效率大于90%.     

单个波长到多个波长的变换实验

报道一种波长变换的新方法.采用此方法不需要任何泵浦光便能够直接将信号光变换成在特定谱宽内的任意多个任意波长的变换光,这对于将来的波分复用光网络提供了较大的方便.此波长变换的原理是利用色散位移光纤的非线性效应产生超连续光谱(SC)信号,由于这种SC信号携带有变换光信号,对这种连续谱进行滤波便能够得到所需要的任意频率的变换信号.此变换方式具有变换频带宽,偏振不敏感的优点。     

双波长分光光度法同时测定岩石矿物中的微量金和钯

本文提出以硫代米蚩酮为显色剂，用双波长分光光度法同时测定岩石矿物中的微量金和钯的方法，消除了测定金钯的相互干扰，该方法简便，快速，选择性好，用于矿石样品中金和钯的测定，结果满意。     

A neuro-fuzzy system for X-ray spectra interpretation

A decision scheme for the interpretation of spectra from wavelength dispersive X-ray fluorescence spectrometry is described that encompasses elements from three areas of artificial intelligence: fuzzy logic, rule based expert systems and neural net technology.After transforming the recorded spectra to line spectra by appropriate background correction a reasoning scheme is applied that takes into account not only the observed spectra, but also the recording conditions and prior spectroscopic information regarding the relative emission probabilities and the usefulness of the different lines for the purpose of element identification. The latter is done on the basis of a previously described scheme to compute conditional a posteriori Bayes probabilities for a mean matrix. These different pieces of information are then assembled into a battery of fuzzy rules. The importance of the rules as well as the importance of the X-ray lines is determined in a training process, similar to the one in a feedforward back-propagation network.To further stabilize the results this network is pruned in a second training cycle. This, however, had little effect on the quality of interpretation.The advantages of this approach to the interpretation of X-ray spectra over older ones are numerous: the system adapts itself to better interpret spectra that are of greater importance to a laboratory as these are better represented in the training set; the fuzzy logic is capable of working with incomplete and uncertain knowledge, and the neural network results based on these fuzzy rules is readily interpretable by the X-ray spectroscopist as every rule can be expressed also in natural language as in any classical rule based system.On leave from Silesian University, Katowice, Poland     

Solid Phase Extraction and Simultaneous Spectrophotometric Determination of Trace Amounts of Copper and Iron Using Mixture of Ligands

 A novel sensitive and simple method for rapid and selective extraction, preconcentration and determination of iron (as its bathophenanthroline complex) and copper (as its neocuproine complex) using octadecyl silica cartridges and dual wavelength spectrophotometry is presented. The dual wavelength method (533 nm for the iron-bathophenanthroline and 454 nm for the copper-neocuproine as the analytical wavelength) is used to eliminate spectral interferences. Extraction efficiency and the influence of flow rates of sample solution and eluent, pH, amount of neocuproine, bathophenanthroline and hydroxylamine hydrochloride, type and least amount of eluent for elution of iron and copper complexes from cartridge, break-through volume and limit of detection are evaluated. The effects of various cationic and anionic interferences on percent recovery of iron and copper are also studied. Extraction efficiencies >95% are obtained by elution of cartridges with minimal amount of organic solvent. Iron and copper were determined in the range of 3–100 ng mL⁻¹. The limits of detection are 0.98 and 1.13 ng mL⁻¹ for iron and copper, respectively. The proposed method is applied successfully to the determination of both analytes in river, tap and well water samples. Author for correspondence. E-mail: yyamini@modares.ac.ir Received September 18, 2002; accepted December 12, 2002 Published online May 5, 2003     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.