Model with uniquely deducible parameters for the combined analysis of two resonating vibrational states. Anharmonic resonances in molecules of asymmetric-gyroscope type

A model of an effective Hamiltonian with parameters that are uniquely deducible from the spectrum for the combined analysis of the rotational structure of two resonating vibrational states is proposed and validated. Anharmonic resonances in molecules of asymmetric-gyroscope type are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 108–112, February, 1982.     

Urea and urotropine conversion in the preparation of microspherical metal oxide particles by internal gelation

The results of studies on urea and urotropine product distribution in solutions formed in microspherical nuclear fuel preparation by internal gelation are presented. It is shown that urea, urotropine and formaldehyde, the urotropine hydrolysis product, undergo various conversions in solutions, resulting in methylolurea and urea-formaldehyde resins formation. Results on the influence of acidity on the process as a function of time are presented. The organic content in the resulting solutions and microspheres has been determined.     

Effect of methyltin trichloride on the activity of lactate dehydrogenase

The effect of MeSnCl₃, which is a highly toxic compound, on the activity of L-lactate:NAD oxidoreductase (lactate dehydrogenase) in the extract from the liver of Russian sturgeon (Asipenser gueldenstaedtiB.). Noncompetitive inhibition of the enzymatic reaction was discovered. This can be due to a change in the enzyme conformation caused by the action on the thiol groups, important for enzyme activity.     

High-order anharmonicity parameters in various representations of the diatomic potential function and exact relations between spectroscopic constants. application to the co molecule

Closed formulae for Born—Oppenheimer anharmonicity parameters a_n in terms of isotopically invariant constants U_mj are derived for Dunham, Simons—Parr—Finlan, Ogilvie—Tipping and Thakkar representations and are applied to the CO molecule. Models for a fit of vibration—rotation and pure rotational transitions based on the exact relations U_mj = f(U_k,o, U_k-1.1) and U_mj = α(U_k,1, U_k,2) are discussed.     

Single fault detection tests for circuits of functional elements

Circuits of functional elements in arbitrary complete finite bases are considered. The realizability of any Boolean function of n variables by an irredundant circuit admitting single fault detection tests having a length linear in n for constant faults is established.     

Optimal relationships between L^p-norms for the Hardy operator and its dual

We obtain sharp two-sided inequalities between $L^p$ -norms $(1<p<\infty )$ of functions $\textit{Hf}$ and $H^*f$ , where $H$ is the Hardy operator, $H^*$ is its dual, and $f$ is a nonnegative measurable function on $(0,\infty ).$ In an equivalent form, it gives sharp constants in the two-sided relationships between $L^p$ -norms of functions $H\varphi -\varphi $ and $\varphi $ , where $\varphi $ is a nonnegative nonincreasing function on $(0,+\infty )$ with $\varphi (+\infty )=0.$ In particular, it provides an alternative proof of a result obtained by Kruglyak and Setterqvist (Proc Am Math Soc 136:2005–2013, 2008) for $p=2k \,\,(k\in \mathbb N )$ and by Boza and Soria (J Funct Anal 260:1020–1028, 2011) for all $p\ge 2$ , and gives a sharp version of this result for $1<p<2$ .