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.     

Aqua­(phthalocyaninato)magnesium n‐propyl­amine disolvate

The crystals of the title compound, [Mg(C₃₂H₁₆N₈)(H₂O)]·2C₃H₉N, are built up from MgPc(H₂O) [Pc is phthalo­cyaninate(2−)] and n‐propyl­amine mol­ecules that inter­act via O—H⋯N hydrogen bonds. The MgPc(H₂O) mol­ecule is non‐planar. The central Mg atom is coordinated by the four equatorial isoindole N atoms of the Pc ring system and by the O atom of an axial water mol­ecule. The Mg atom is displaced by 0.509 (1) Å from the N₄ plane towards the water O atom. MgPc(H₂O)·2(n‐propyl­amine) mol­ecules related by the inversion centre are linked by N—H⋯O hydrogen bonds to form a dimeric aggregate.     

Pulverized coal plasma gasification

A number of experiments on the plasma-vapor gasification of brown coals of three types have been carried out using an experimental plant with an electric-arc reactor of the combined type. On the basis of the material and heat balances, process parameters have been obtained: the degree of carbon gasification (_c), the level of sulfur conversion into the gas phase (_s), the synthesis gas concentration (CO+Hz) in the gaseous products, and the specific power consumption for the gasification process. The degree of gasification was 90.5-95.0%, the concentration of the synthesis gas amounted to 84.7–85.7%, and the level of sulfur conversion into the gas phase was 94.3–96.7%. Numerical study of the process of plasma gasification of coals was carried out using a mathematical model of motion, heating, and gasification of polydisperse coal particles in an electric-arc reactor of the combined type with an internal heat source (arc). The initial conditions for a conjugate system of nonlinear differential equations of the gas dynamics and kinetics of a pulverized coal stream interacting with the electric arc and oxidizer (water vapor) agree with the initial conditions of the experiments. The computation results satisfactorily correlate with the experimental data. The mathematical model can be used for the determination of reagent residence time and geometrical dimensions of the plasma reactor for the gasification of coals.Nomenclature c _i volume concentration of components (kmol m^–3) - x longitudinal coordinate (m) - f _i source members, determined by variation of the ith component due to chemical reactions in unit volume in unit time (kmol m^–3s^–1) - velocity (m s^–1) - M _s ash mass in one particle (kg) - C _D particle drag coefficient - 3.14 - r _s particle radius (m) - d particle diameter (m) - density (kg m^–3) - C _p heat capacity of components (J mol^t– K^–1) - Q _j thermal effect of reaction (J kmol^–1) - E_j activation energy of reaction - N _l volume concentration of particles of thelth fraction (m^–3) - T temperature (K) - emissivity factor of coal particles - 5.67 × 10^–8, blackbody emissivity coefficient (W m^–2 K^–4) - P pressure (Pa) - S reactor cross section (m²) - D reactor diameter (m) - V reactor volume (m³) - L _R reactor length (m) - F _W friction force on the wall (N) - f _g friction coefficient - residence time (s) - Nu Nusselt number - Re Reynolds number - Pr Prandtl number - thermal conductivity of gas (J m^– s^–1 K^–1) - R 8.3 × 10³, universal gas constant (J kmol K^–1) - µ _i molecular mass of component (kg kmol^–1) - dynamic viscosity coefficient of gas (kg m^–1 s^–1) - thermal efficiency of plasma reactor - q_arc specific heat flow from arc (W m^–3) - P ₁ heat supplied in vapor at T = 405 K (W) - P ₂ heat loss to wall (W) - P ₃ heat loss in the gas and slag separator chamber (W) - P ₄ heat loss in the synthesis gas oxidation chamber (W) - P ₅ heat loss in the slag catcher (W) - P ₆ heat carried away in the off-gas (W) - P heat input of arc (W) - P _arc electric power of arc (W) - Q_sp specific power consumption (kw Hr kg^–1) - d _w specific heat flow to wall (W m^–2) - _c degree of carbon gasification (%) - _s level of sulfur conversion into gas phase (%)     

Thermal properties of rare earth dodecaborides

We have measured heat capacity and thermal expansion of rare earth dodecaborides REB₁₂ (RE=Y, Tb-Tm, Lu). YB₁₂ and LuB₁₂ are diamagnetics whereas the other dodecaborides are ordered antiferromagnetically. The amplitude of the heat capacity discontinuity at the Néel temperature and the shape of the heat capacity variation in the critical region for all these antiferromagnetics are characteristics for amplitude-modulated magnetic structures. In the ordered state TbB₁₂ reveals two first-order phase transitions, most likely due to magnetic structure changes. The heat capacity of ErB₁₂ just below the Néel point shows an anomaly of unclear origin. From the Schottky contribution to the heat capacity we have determined crystal field parameters. They are completely different than that is estimated from Point Charge Model.     

Aqua(phthalocyaninato‐κ4N)magnesium(II) 3‐chloropyridine disolvate

The structure of the title compound, [Mg(C₃₂H₁₆N₈)(H₂O)]·2C₅H₄ClN, comprises MgPcH₂O [Pc is phthalocyaninate(2−)] and 3‐chloropyridine solvent molecules interacting via O—H...N hydrogen bonds and π–π interactions. The central Mg atom is (4+1)‐coordinated by four equatorial isoindole N atoms of the macrocycle and by the O atom of an axial water molecule. The MgPcH₂O molecule is not planar, the Mg atom being displaced by 0.496 (2) Å from the isoindole N₄ plane towards the water O atom. MgPcH₂O molecules related by a twofold screw axis interact via O—H...N_azamethine hydrogen bonds, forming a polymeric chain along the b axis, while those related by inversion centres form π–π interacting dimers.     

Barker–Larman Problem for Convex Polygons in the Hyperbolic Plane

We solve an analogue of the Barker–Larman problem for convex polygons in the hyperbolic plane.     

Crotonic,cynnamic, and propiolic acids motifs in the synthesis of thiopyrano[2,3-d][1,3]thiazoles via hetero-Diels–Alder reaction and related tandem processes

Various novel thiopyrano[2,3-d][1,3]thiazol-2-one-6-carboxylic acids derivatives were synthesized in 54–86% yields via hetero-Diels–Alder reactions and related acylation-based tandem processes of 5-arylidene-4-thioxo-2-thiazolidinones with crotonic, propiolic, and cynnamic acids derivatives. Stereo- and regioselectivity of cycloaddition were investigated.     

Anomalous High Temperature Structural Behavior of Potential Multifunctional Material SmCo0.5Cr0.5O3

Crystal structure parameters of the mixed cobaltite–chromite SmCo_0.5Cr_0.5O₃ in the temperature range of 298–1173 K were derived from in situ high-resolution X-ray synchrotron powder diffraction data. Similar to the parent SmCoO₃ compound, SmCo_0.5Cr_0.5O₃ reveals anomalous thermal expansion reflected in abnormal temperature dependence of the unit cell dimensions and the selected interatomic distances and angles. These anomalies are associated with temperature induced changes of spin state of Co³⁺ ions and coupled insulator-metal transition. Observed decreasing behavior of the bandwidth W points on the increasing population of the exited spin states of Co³⁺ ions in SmCo_0.5Cr_0.5O₃ with increasing temperature. First principle calculations revealed antiferromagnetic ground state of SmCo_0.5Cr_0.5O₃ as the most stable.     

The formation of carbon nanotubes on copper electrodes under the arc discharge conditions

The results of experiments on the pyrolysis of hydrocarbon gases in electric arc discharge between copper electrodes and the results of computer simulation by the method of molecular orbitals have been presented. The complex of studies of the plasma-chemical method of carbon nanotubes formation from carbon vapor showed the feasibility of growing carbon nanotubes on copper nanoparticles, which can be promoters for the reaction of the formation of hexagonal structures similar to carbon nanotubes.