Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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Relative kinetic stability towards redox decomposition of cerium(IV) complexes with some organic compounds

Monatshefte für Chemie - Chemical Monthly - A comparative analysis is performed on the stability constants $${\upbeta }_{1yn}$$ and intramolecular redox decomposition rate constants $$k_{n\; =...     

Spin and quark states in the probability representation of quantum mechanics

A short review of the general principles of constructing tomograms of spin and quark states is presented.     

Astrogeometry: Toward mathematical foundations

Inimage processing (e.g., inastronomy), the desired black-and-white image is, from the mathematical viewpoint, aset. Hence, to process images, we need to process sets. To define a generic set, we need infinitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to finite-parameter families of sets that will be used to approximate the desired sets. The wrong choice of a family can lead to longer computations and worse approximation. Hence, it is desirable to find the family that it isthe best in some reasonable sense. In this paper, we show how the problems of choosing the optimal family of sets can be formalized and solved. As a result of the described general methodology, forastronomical images, we get exactly the geometric shapes that have been empirically used by astronomers and astrophysicists; thus, we have atheoretical explanation for these shapes.     

Prediction problem in quantum mechanics is intractable (NP-Hard)

It is proved that both the prediction problem and the problem of reconstructing the state from the observations in quantum mechanics are NP-hard.     

Trends in sorption preconcentration combined with noble metal determination.

Nowadays much attention is being paid to the determination of trace amounts of noble metals in geological, industrial, biological and environmental samples. The most promising techniques, such as inductively coupled plasma atomic emission spectrometry (ICP-AES), inductively coupled plasma mass spectrometry (ICP-MS) and electrothermal atomic absorption spectrometry (ETAAS) are characterized by high sensitivity. However, the accurate determination of trace noble metals has been limited by numerous interferences generated from the presence of matrix elements. To decrease, or eliminate, these interferences, the sorption preconcentration of noble metals is often used prior to their instrumental detection. A great number of hyphenated methods of noble metal determination using sorption preconcentration have been developed. This review describes the basic types of available sorbents, preconcentration procedures and preparations of the sorbent to the subsequent determination of noble metals. The specific features of instrumental techniques and examples of ETAAS, FAAS, ICP-AES, ICP-MS determinations after the sorption preconcentration of noble metals are considered. The references cited here were selected mostly from the period 1996 - 2006.     

A two-dimensional Minkowski ?(x) function

A function from a triangle to itself is defined that has both interesting number theoretic and analytic properties. This function is shown to be a natural generalization of the classical Minkowski ?(x) function. It is shown there exists a natural class of pairs of cubic irrational numbers in the same cubic number field that are mapped to pairs of rational numbers, in analog to ?(x) mapping quadratic irrationals on the unit interval to rational numbers on the unit interval. It is also shown that this new function satisfies an analog to the fact that ?(x), while increasing and continuous, has derivative zero almost everywhere.