The reaction of 2-(1-hydroxyimino-2-oxo-2-phenylethyl)-6-R-pyrimidin-4(3H)-ones with an excess of p-toluenesulfochloride proceeds in two stages involving consecutive oxidation of the oxygen atom of the hydroxyimino group and the oxygen atom of the amide fragment of the pyrimidine ring. The reaction of the resulting ditosylates with ethylenediamine proceeds via replacement of the sulfonyl group in the 2-position of the pyrimidine ring. The examples of 2-[1-benzoyl-2-(2-furyl)vinyl]-6-methylpyrimidin-4(3H)-one, 2-[2-(4-nitrophenyl)vinyl]-6-methylpyrimidine-4(3H)-one, and 6-methyl-2-(2-oxo-2-phenylethylthio)pyrimidin-4(3H)-one were used to consider the relationship between the structure of the substrate and the direction of the tosylation reaction.

Reactions of 1,4-benzoquinone with 2-(2-oxo-2-arylethylidene)-2,3-dihydro-1H-pyrimidine-4-ones in glacial acetic acid proceed selectively to give 2-[1-(2,5-dihydrophenyl)-2-oxo-2-arylethylidene]-2,3-dihydropyrimidine-4(1H)-ones.

It was established that unsubstituted amides of imidazole-4,5-dicarboxylic acid are characterized by large (up to 15000 cm–1) Stokes shifts. It was found that the structural factors determining the character of transitions of the molecules of esters and hydrazides in the initial and excited states are similar. The effect of the lipophilicity of the compounds on the Stokes shifts and fluorescence quantum yields is discussed.

Reaction of potassium thiocyanate with 2-[2-oxo-1-(1-tosyloxyimino)-2-phenylethyl]pyrimidin-4-(3H)-one derivatives led to the formation of a new fused heterocyclic system with a common nitrogen atom, substituted 7H-[1,2,5]thiadiazolo[2,3-a]pyrimidin-7-one.

The reaction of 6-methyl-2-(2-oxo-2-phenylethylidene)-2,3-dihydropyrimidine-4(1H)-one with arylhydrazines leads in high yields to the corresponding hydrazones, in which the ethylidene fragment of the starting compound is transformed to the ethylene fragment. By oxidation of the hydrazones with hydrogen peroxide or selenium dioxide the corresponding 6-methyl-2-[2-phenyl-2-(arylhydrazono)acetyl]-3H-pyrimidine-4-ones were synthesized.

Derivatives of 2‐methylidene‐1,3‐dihydropyrimidin‐4‐ones 2a, 2b, 2c, 2d, 2e, 2f, 2g were synthesized by interaction of 6‐methyl‐2‐thiouracil and 6‐phenyl‐2‐thiouracil 1a, 1b with some activated halogenides: diethyl bromomalonate, ethyl 2‐chloro‐3‐oxobutanoate, ethyl 2‐bromocyanoacetate, 2‐bromo‐5,5‐dimethylcyclohexan‐1,3‐dione, and bromomalononitrile. The boiling of 1a with ethyl 2‐bromocyanoacetate in mixture of ethanol and EtONa results in intramolecular cyclization and formation of thiazolo[3,2‐a]pyrimidin‐5‐one 3. Interaction of 1a with 3‐chloropentane‐2,4‐dione and 2‐bromo‐1,3‐diphenylpropane‐1,3‐dione yielded corresponding S‐substituted thiopyrimidines 4a,4b. In general, the products of 1b S‐alkylation are less prone to sulfur extrusion. Reaction of 1b with diethyl bromomalonate in the absence of EtONa stops at the S‐alkylation step, while in the presence of EtONa in ethanol or PPh3 in dioxane 2‐(ethoxycarbonylmethyl)thio‐6‐phenyl‐1,3‐dihydropyrimidin‐4(1H)‐one 6 is formed exclusively. Molecular structure and crystal structure of 2‐(1,1‐diethoxycarbonylmethyliden)‐6‐methyl‐1,3‐dihydropyrimidin‐4(1H)‐one 2a are discussed.

2-(2-Oxo-2-arylethylidene)-2,3-dihydropyrimidine-4(1H)-ones react with aromatic and heteroaromatic aldehydes to form the unsaturated ketones, whereas in the case of 3- and 4-benzaldehydes the corresponding trans-2-styrylpyrimidine-4(3H)-ones were obtained. A possible mechanism of hydrolytic cleavage of the product of condensation of 2-(2-oxo-2-phenylethylidene)-2,3-dihydropyrimidine-4(1H)-one with paraformaldehyde under acid catalysis and mechanochemical activation has been discussed.

The reaction of 6-methyl-2-(2-oxo-2-phenylethylidene)-2,3-dihydropyrimidin-4(1 H )-one and of its nitrosation product with hydroxylamine stops at the stage of forming the corresponding oximes. The reaction of 6-methyl-2-(2-oxo-2-phenylethylidene)-2,3-dihydropyrimidin-4(1 H )-one with hydrazine yields a mixture of 3-amino-5-phenylpyrazole and 3-methyl-2-pyrazolin-5-one in 71 and 62% yields, respectively. The ketoxime is used in the synthesis of a series of imidazole N (3)-oxides substituted at the 1, 4, and 5 positions of the imidazole ring.

The synthesis of 2-(2-amino-4-arylthiazol-5-yl)pyrimidin-4(3H)-ones from the available 2-(2-oxo-2-arylethylidene)-2,3-dihydropyrimidin-4(1H)-ones was developed.

A possibility to obtain pyrimidines, containing oxoalkyl moiety in 2 position of the ring from the available 6-methyl-2-thiouracil was shown.

Dibenzimidazo crown ethers were synthesized by alkylation of α,ω-bis(benzimidazol-2-yl)alkanes and 1,2-bis(benzimidazol-2-ylsulfanyl)ethane with tri- and tetraethylene glycol bis(4-toluenesulfonates). The structure of 6,7,9,10,12,13,21,22-octahydro[1,14,6,9,4,11]dioxadithiadiazacyclohexadecino[4,5- a :11,10- a ′]dibenzimidazole was studied by X-ray analysis.

5,10-Dioxo-5H,10H-diimidazo[1,5-a;1',5'-d]pyrazine-5,10-dicarboxylic acid dichloride in Friedel-Crafts reaction conditions formed with benzene the corresponding 1,6-dibenzoyl derivative 2, which reacted with alcohols and amines to give the keto esters and keto amides of 4(5)-benzoylimidazol-5(4)-carboxylic acids. The reaction of compound 2 with hydrazine gave substituted imidazo[4,5-f]pyridazine, and with o-phenylenediamine gave a derivative of imidazo[4,5-f]-1,4-benzodiazocine - a new heterocyclic system.

[1,2,3]Triazolo[4,5-d]pyrimidine 3-oxides were synthesized by replacement of the amino group in 6-aminouracil by hydroxyamino, coupling of the resulting 6-hydroxyaminopyrimidine with benzenediazonium salts, and oxidation of 6-hydroxyamino-5-phenylazouracils with a solution of K-3[Fe(CN)(6)] in water.

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Calculation is carried out of estimation errors using discrete Fourier transform of the amplitude and frequency of a monoharmonic signal. Analytic expressions are presented of upper estimates of the maximum errors which depend on the observation interval and signal sampling frequency. The effect of signal smoothing by the Kaiser window on the errors is studied.

The influence of discretization methods to properties of digital models of a continuous system is studied. The object of the study consists in an oscillation system of the second order, which is discretizated by using formulas of numerical integration, the state space equation, and the method of invariance of the impulse characteristic. An equivalent proper frequency and equivalent damping coefficient are introduced in order to estimate characteristics of free oscillations of the discrete system of the second order.

A general method has been developed for the preparation of 14-remembered cyclic lactams, lactones, and thiolactones from heteroaromatic amino acids.