Graphs with Special Arcs and Cryptography

A combinatorial method of encryption with a similarity to the classical scheme of linear coding has been suggested by the author. The general idea is to treat vertices of a graph as messages and arcs of a certain length as encryption tools. We will study the quality of such an encryption in the case of graphs of high girth by comparing the probability to guess the message, (vertex) at random with the probability of breaking the key, i.e. guessing the encoding arc. In fact, the quality is good for graphs which are close to the Erdös bound, defined by the Even Cycle Theorem.In the case of parallelotopic graphs, there is a uniform way to match arcs with strings in a certain alphabet. Among parallelotopic graphs we distinguish linguistic graphs of affine type whose vertices (messages) and arcs (encoding tools) both could be naturally identified with vectors over the GF(q), and neighbors of the vertex defined by a system of linear equations. We will discuss families of linguistic and parallelotopic graphs of increasing girth as the source for assymmetric cryptographic functions and related open key algorithms.Several constructions of families of linguistic graphs of high girth with good quality, complexity and expansion coefficients will be considered. Some of those constructions have been obtained via group-theoretical and geometrical techniques.     

A catalyst-free one-step synthesis of N-pyrimidinyl amidines from endocyclic enamines and 4-azidopyrimidines

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Synthesis of mesoionic[1,2,3]triazolo[5,1-d][1,2,5]triazepines

Intramolecular cyclization of 1-amino-3-phenacyl-4-carbohydrazido-1,2,3-triazolium-5-olates has been shown to take place via selective interaction of the carbonyl group with the terminal amino function of the hydrazido group to form a 1,2,5-triazepine ring. Minor products, resulting from the interaction of the α-nitrogen atom of the hydrazido group with the carbonyl function, having a N-amino-pyridazine structure were also detected and isolated. A general method for the synthesis of novel mesoionic 2-amino-7-aryl-4-oxo-2,4,5,8-tetrahydro[1,2,3]triazolo[5,1-d][1,2,5]triazepin-9-ium-3-olates was developed.     

Electronic spectroscopy and ionization potential of UO2 in the gas phase

The electronic spectroscopy of UO(2) has been examined using multiphoton ionization with mass-selected detection of the UO(2) (+) ions. Supersonic jet cooling was used to reduce the spectral congestion. Twenty-two vibronic bands of neutral UO(2) were observed in the range from 17,400 to 32,000 cm(-1). These bands originated from the U(5fphi(u)7ssigma(g))O(2) X (3)Phi(2u) and (3)Phi(3u) states. The stronger band systems are attributed to metal-centered 7p<--7s transitions. Threshold ionization measurements were used to determine the ionization potentials of UO and UO(2). These were found to be higher than the values obtained previously from electron impact measurements but in agreement with the results of recent theoretical calculations.     

Accurate ionization potentials for UO and UO2: a rigorous test of relativistic quantum chemistry calculations

Accurate ionization potential (IP) measurements provide essential thermodynamic information and benchmark data that can be used to evaluate the validity of electronic structure models. Calculations of the first IP of UO2 using relativistic methods consistently predict values that are approximately 0.7 eV higher than the accepted experimental value. The present measurements validate the theoretical calculations and show that the previous determinations corresponded to the ionization of thermally excited molecules. Similarly, new measurements of the IP for UO show that the currently accepted value is too low by 0.4 eV.     

The regioselectivity of the formation of 2-pyrazolylthiazoles and their precursors from the reaction of 2-hydrazinothiazoles with 4,4,4-trifluoro-1-hetaryl-1,3-butanediones

Reaction of 2-hydrazinothiazoles 1 with 1-thienyl- and 1-furyl-1,3-butanediones 2a,b in methanol in the presence of hydrochloric acid mainly leads to a mixture of pyrazoles 3 and pyrazolines 4 or pyrazoles 3 and 5 in strong acidic conditions. Isomeric hydrazones 6 and pyrazolines 4 were formed and isolated in these reactions in the absence of hydrochloric acid. It has been shown that the regioselectivity in the reaction of diketones 2 with hydrazine 1 is governed by both the concentration of acid and the nature of substituents in the 1,3-diketones 2. Cyclization of hydrazones 6 is shown to occur under milder conditions than dehydration for pyrazolines 4. The new heterocyclic compounds were prepared and fully characterized by NMR spectra and by X-ray analysis for 3c.     

Synthesis of tetrazole containing 1,2,3-thiadiazole derivatives via U-4CR and their anti-TMV activity

A series of novel tetrazole containing 1,2,3-thiadiazole derivatives were designed and synthesized via Ugi reaction. Their structures were confirmed by melting points, IR, 1H NMR, and HRMS (ESI). Preliminary bioassay indicated that most target compounds exhibited very good direct anti-TMV activity at 100 μg/mL, which was equal to or higher than that of ribavirin. Among them, compounds 4b, 4c and 4i also showed equivalent protection effect to ribavirin in vivo at 100 μg/mL.