Free expansions of the intersection of manifolds of universal algebras

The theory of free expansions in the intersection of a finite number of manifolds of universal algebras satisfying a given set of conditions (for example, in the manifold of all groups) is extended to the case of the intersection of any set of manifolds of universal algebras.Translated from Matematicheskie Zametki, Vol. 7, No. 5, pp. 551–562, May, 1970.     

Subalgebras of free products of algebras of the variety\mathfrak{u}_{m,n}

The variety \(\mathfrak{u}_{m,n} \) is defined by the system of n-ary operations ω_i,..., ω_m, the system of m-ary operations ?_i,..., ?_n, 1≤ m ≤ n, and the system of identities $$\begin{gathered} x_1 ...x_n \omega _1 ...x_1 ...x_n \omega _m \varphi _i = x_i (i = 1,...,n), \hfill \\ x_1 ...x_m \varphi _1 ...x_1 ...x_m \varphi _n \omega _j = x_j (i = 1,...,m), \hfill \\ \end{gathered} $$ It is proved in this paper that the subalgebra U of the free product \(\Pi _{i \in I}^* A_i \) of the algebras A_i (i ε I) can be expanded as the free product of nonempty intersections U ∩ A_i (i ε I) and a free algebra.     

Dielectric relaxation phenomena of rigid polar liquid molecules under giga hertz electric field

The dielectric relaxation phenomena of rigid polar liquid molecules chloral and ethyltrichloroacetate (j) in benzene, n-hexane and n-heptane (i) under 4.2, 9.8 and 24.6 GHz electric fields at 30°C are studied to show the possible existence of double relaxation times τ ₂ and τ ₁ for rotations of the whole and the flexible parts of molecules. The probability of showing double relaxation is more in aliphatic solvents indicating their nonrigidity. The symmetric and asymmetric distribution parameters γ and δ are obtained from X _ij ^′ /X _0ij and X _ij ^″ /X _0ij and w _j →0 where X _ij ^′ and X _ij ^″ are real and imaginary parts of the complex orientational susceptibility X _i ^* and X _0ij is the low frequency susceptibility which is real. X _ij ’s are involved with the measured dielectric relative permittivities ε _ij ^′ , ε _in ^″ , ε _0ij and ε _∞ij of solutions. The theoretical weighted contributions c ₁ and c ₂ towards dielectric dispersions by Fröhlich’s method are compared with the experimental ones obtained from the graphical variation of X _ij ^′ /X _0ij and X _ij ^″ /X _0ij with weight fractions w _j ’s at w _j → 0. The measured dipole moments μ ₂ and μ ₁ of the whole and the flexible part of a polar molecule in terms of the linear coefficients β’s of X _ij ^′ ’s with w _j ’s and the estimated τ ₂ and τ ₁ reveal their associations with aliphatic solvents. The theoretical dipole moments μ _theo’s from the available bond angles and bond moments of the substituent polar groups of the molecules with the estimated μ’s suggest the mesomeric, inductive and electromeric effects in them under GHz electric field.     

New modifications in 15 UD pelletron at nuclear science centre

The 15 UD pelletron at NSC has been operational and performed well during the last 11 years. There have been major modifications performed for upgradation of pelletron system over this period. Major upgradations which have been implemented are new resistor network system for voltage gradient, doublet to singlet unit conversion for accelerator units, turbopump based gas stripper system etc. In addition accelerator mass spectroscopy program has also been started. A new multi-cathode source, Wien filter etc. have been procured and will be added soon in the system. An overview of the most significant upgradations undertaken and other activities for the system are being reported in the present paper.     

Thermochemical parameters of CHFO and CF2O

Thermochemical properties of CHFO and CF 2O and their derivatives were calculated by using coupled-cluster theory (U)CCSD(T) calculations with the aug-cc-pV nZ ( n = D, T, Q, 5) basis sets extrapolated to the complete basis set limit with additional corrections. The predicted properties include the following. Enthalpies of formation (298 K, kcal/mol): Delta H f (CF 2O) = -144.7, Delta H f(CHFO) = -91.1, Delta H f (CFO (*)) = -41.6. Bond dissociation energy (0 K, kcal/mol): BDE(CFO-F) = 120.7, BDE(CHO-F) = 119.1, BDE(CFO-H) = 100.2. Ionization potential (eV): IP 1(CF 2O) = 13.04, IP 2(CF 2O) = 14.09, IP 1(CHFO) = 12.41, IP 2(CHFO) = 13.99, IP 1(CFO (*)) = 9.34. Proton affinity (298 K, kcal/mol), PA O(CF 2O) = 148.8, PA O(CHFO) = 156.7, PA F(CHFO) = 154.5 kcal/mol. Electron affinity: EA(CFO (*)) = 2.38 eV. Triplet-singlet separation gap (eV): Delta E T1-S0(CF 2O) = 4.47, Delta E T1-S0(CHFO) = 4.36. Triplet-triplet transition energy (eV): Delta E T2-T1(CF 2O) = 0.44. The new calculated values contribute to solving some persistent discrepancies in the literature. The effects of F-atoms on thermochemical parameters are not linearly additive, and the changes are largely dominated by the first F-substitution. On the basis of the calculated proton affinities of CF 2O and CF 3OH, the nucleophilicities of the oxygen atoms are, within computational errors, the same in both compounds.     

Coupled-cluster study of the electronic structure and energetics of tetrasulfur, S4

Ab initio electronic structure calculations are reported for S4. Geometric and energetic parameters are calculated using the singles and doubles coupled-cluster method, including a perturbutional correction for connected triple excitation, CCSD(T), together with systematic sequences of correlation consistent basis sets extrapolated to the complete basis set limit. The geometry for the ground state singlet C2v structure of S4 is in good agreement with the microwave structure determined for S4. There is a low-lying D2h transition state at 1.6 kcal/mol which interchanges the long S-S bond. S4 has a low-lying triplet state (3B 1u) in D2h symmetry which is 10.8 kcal/mol above the C2v singlet ground state. The S-S bond dissociation energy for S4 into two S2(3Sigma*g) molecules is predicted to be 22.8 kcal mol(-1). The S-S bond energy to form S3+S(3P) is predicted to be 64 kcal/mol.     

Ethylene production by the oxidative condensation of methane in the presence of MnMW/SiO<Subscript>2</Subscript> catalysts (M = Na,K, and Rb)

The samples of MnMW/SiO₂ (M = Na, K, and Rb) were synthesized using various synthesis methods under varied heat treatment conditions and their physicochemical properties and activity in the reaction of the oxidative condensation of methane (OCM) were studied for the development of an effective catalyst for the resource-saving process of natural gas conversion into ethylene. It was found that the preparation method exerts an effect on the textural characteristics of the samples and the reducing properties of the cations of manganese and tungsten. It was determined that the composition of a W-containing phase depends on the alkali metal, and a ratio between the polymorphous modifications of SiO₂ is controlled by the method of synthesis and the conditions of catalyst heat treatment. It was established that the yield of C₂ hydrocarbons in the OCM reaction increased with the use of incipient wetness impregnation instead of the method of mixing with a suspension for catalyst preparation and with an increase in the catalyst heat treatment temperature from 700 to 1000°C. The optimum composition of the catalyst and the condition of its synthesis were found: 2Mn_0.8Na₃W/SiO₂ obtained by the impregnation method and calcined at 1000°C ensured the yield of target products of ~20% with a CH₄ conversion of ~35% at a reaction temperature of 850°C.     

Provably secure dynamic identity-based three-factor password authentication scheme using extended chaotic maps

With the aim of guaranteeing secure communication through public networks, three-factor password authentication (TF-PWA) scheme plays a key role in many internet applications. Since in TF-PWA scheme, the communicating entities can mutually authenticate each other and generate a shared session key, which will be used for secure exchange of messages in succeeding communication among them. As a result, the TF-PWA schemes gain enormous consideration in recent years. More recently, due to light-weight features of the extended chaotic map, it is also extensively applied in designing of public key encryption, key agreement, image encryption, S-box, hash function, digital signature, password authentication, etc. The aim of this paper was to design a dynamic identity-based three-factor password authentication scheme using extended chaotic map (ECM-TF-PWA) in the random oracle model. The proposed scheme is provably secure based on the intractability assumption of chaotic map-based Diffie–Hellman problem. The informal security analysis gives the evidence that our scheme protects all attacks and provides functionality attributes that are needed in a three-factor authentication system. Besides, the performance discussion shows that our scheme performs better than others in respect of computation and communication cost.