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

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Synthesis and antimycobacterial activity of purine conjugates with (S)-lysine and (S)-ornithine

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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.