The invertibility of the operator d/dt + A(t) in the space of bounded functions

We give various conditions for the unique invertibility of the operator d/dt + A(t) in the space of functions bounded on the whole line. The methods we use essentially rely on the almost-periodicity of the operator-function A(t).Translated from Matematicheskie Zametki, Vol. 19, No. 1, pp. 99–104, January, 1976.     

Pseudotoric structures on toric symplectic manifolds

We prove the existence of a rank-one pseudotoric structure on an arbitrary smooth toric symplectic manifold. As a consequence, we propose a method for constructing Chekanov-type nonstandard Lagrangian tori on arbitrary toric manifolds.     

Thermodynamic Properties and Thermal Expansion of Tm<Subscript>2</Subscript>O<Subscript>3</Subscript> · 2ZrO<Subscript>2</Subscript> Solid Solution

The isobaric heat capacity of Tm₂O₃ · 2ZrO₂ solid solution was measured by adiabatic calorimetry and differential scanning calorimetry (DSC), and smoothed values of the enthalpy changes, entropy, and reduced Gibbs free energy in the temperature range 8–1200 K were calculated. Thermal expansion was studied by X-ray diffraction in the temperature range 298–1173 K.     

Low-Temperature Heat Capacities of Terbium Molybdate Phosphates M 2 I Tb(MoO4)(PO4) (MI = Na or K)

The heat capacities of Na₂Tb(MoO₄)(PO₄) and K₂Tb(MoO₄)(PO₄) were measured by adiabatic calorimetry at low temperatures (6.34–333.74 and 7.20–341.17 K, respectively). Smoothed thermal-capacities values were used to calculate the entropy, enthalpy increments, and reduced Gibbs energy. The respective values at 298.15 K are as follows: for Na₂Tb(MoO₄)(PO₄), C _p ⁰ (298.15 K) = 240.1 ± 0.2 J/(K mol), ⁰ (298.15 K) = 307.4 ± 0.4 J/(K mol), H ⁰(298.15 K) ? H ⁰(0) = 44.95 ± 0.03 kJ/mol, and Φ⁰(298.15 K) = 156.6 ± 0.5 J/(K mol); and for K₂Tb(MoO₄)(PO₄): C _p ⁰ (298.15 K) = 245.1 ± 0.1 J/(K mol), S ⁰(298.15 K) = 322.9 ± 0.1 J/(K mol), H ⁰(298.15 K) ? H ⁰(0) = 46.58 ± 0.02 kJ/mol, and Φ⁰(298.15 K) = 166.6 ± 0.2 J/(K mol). The noncooperative magnetic component of the heat capacity was estimated.     

New functionalization opportunities for <Emphasis Type="Italic">peri</Emphasis>-hydroxynaphthoyl and <Emphasis Type="Italic">peri</Emphasis>-fused heterocyclic compounds

A capability was studied of hydrogenated α-pyrone heterocycle in 7-methoxy-4-(4-methoxy-phenyl)-3,4-dihydro-2H-benzo[h]chromen-2-one to undergo aminolysis under the treatment with hydrazine hydrate, primary and secondary aliphatic and aromatic amines. A new approach was developed to the preparation of perihydroxyketone of naphthalene series containing a specific functional substituent in the ortho-position with respect to hydroxy group. The effect was revealed of an acetyl group in the position 9 of 7-methoxy-4-(4-methoxyphenyl)-3,4-dihydro-2H-benzo[h]chromen-2-one on the reaction of this compound with aliphatic amines and hydrazine hydrate. 9-Methoxy-1-(4-methoxyphenyl)-6-methyl-3H-benzo[de]pyrido[3,2,1-if]cinnolin-3-one [9-methyl-6-methoxy-3-(4-methoxyphenyl)-10,10a-diazapyren-1-one] was obtained, a new bis-peri-fused heteroaromatic system.