Synthesis of N,N'-Diacyl-1,2-di-(4-pyridyl)ethylenedianiines

Reaction of N-(4-pyridylmethyl)benzamide N-oxides with acetic anhydride yielded dimerization compounds. This dimerization occurs at the atom attached to the pyridine ring. These compounds so obtained were evaluated for analgesic and antiinflammatory activity.     

On the Hilbert Evolution Algebras of a Graph

Evolution algebras are a special class of nonassociative algebras exhibiting connections with various fields of mathematics. Hilbert evolution algebras generalize the concept in the framework of Hilbert spaces. This allows us to deal with a wide class of infinite-dimensional spaces. We study Hilbert evolution algebras associated to a graph. Inspired by the definitions of evolution algebras we define the Hilbert evolution algebra that is associated to a given graph and the Hilbert evolution algebra that is associated to the symmetric random walk on a graph. For a given graph, we provide the conditions for these structures to be or not to be isomorphic. Our definitions and results extend to the graphs with infinitely many vertices. We also develop a similar theory for the evolution algebras associated to finite graphs.

     

Bernstein-Type Inequalities for Rational Functions with Prescribed Poles

We establish Bernstein-type inequalities for rational functionswith prescribed poles in the Chebyshev norm on the unit circlein the complex plane. Generalizations of polynomial inequalitiesof Erds-Lax and Turán are also obtained for such rational functions with restricted zeros.     

Electrostatic lattice coefficients and binding energy of orthorhombic La2-x Sr x CuO4

Three valency models for orthorhombic La_2-x Sr _x CuO₄ were investigated for increasing Sr concentrationsx (0x0.21): 1. Cu²⁺Cu³⁺, 2. apex O^2–O^– and 3. in-plane O^2–O^–. All calculations were done by using structural parameters valid for the temperature range from 10 to 22 K. We thereby calculated the electrostatic interaction energy which, next to ionization potentials and electron affinities, comprises a major of the binding energyE _B of crystals. Second-order effects were accounted for by calculating the strength of ionic dipole moments induced by crystal electric fields at relevant lattice sites. Their largest strengths are comparable to the dipole moment of the water molecule. Three out of five dipoles in La_2-x Sr _x CuO₄ vanish during the transition from the orthorhombic to the tetragonal phase. The binding energy differences between the different models suggest that the system is in a state of model 1. However, the differences are very small, being in the order of 0.3 to 0.76 eV atx=0.13.     

The Green relations approach to congruences on completely regular semigroups

On the congruence lattice (2(5) of a completely regular semigroup S the following mappings are considered _p: P and _p: VP, whereP is any of the Green relationsH, L, R orD. The equivalence relationsP andP ^V induced by these maps represent the main object of study in the paper. The former is a complete -congruence whereas the latter is a complete congruence onC(S). In particularH ,H ^V,L ^V,R ^V coincide with the kernel, trace, left trace and right trace relations onC(S), respectively. All essential properties known for the latter relations carry over to the new relationsP andP ^V. In addition, some interesting interplays of these provide for more richness in the theory of congruences on completely regular than is the case for the kernel-trace approach to congruences on regular semigroups.     

Homogenization of the heat equation for a domain with a network of pipes with a well-mixed fluid

We consider the linear heat equation in a domain occupied by a solid material with a network of pipes in which a well-mixed fluid is circulating. The temperature of the fluid in the pipe is uniform and its time variation is determined by the thermal flux on the wall of the pipe, plus a given internal source; continuity of the temperature across the pipe is also assumed. We suppose that we deal with a periodic geometry, with cells of size with inclusions of size r_g; we study in detail in the case r, referring to a previous paper for the case r In the limit »0 we get a homogenized equation. The limit depends strongly on the ratio between the time variation of the temperature in the inclusions and the thermal flux through the interface. The homogenized equation has a new specific heat, which depends on the porosity and the constant of proportionality between the time variation of temperature and the flux on the boundary of the pipe. We also have a new thermal conductivity depending on the microstructure, and volume sources appear. The main tool is the energy method and we generalize the classical results for the more standard boundary conditions for parabolic equations. Finally, we consider the network of pipes forming a random ball structure. We prove convergence for this case. The homogenized equation is of the same form as in the periodic case but auxiliary problems are stochastic.     

Some Normal Cryptogroups as Semigroups of Isomorphisms

Given a Clifford semigroup G, we construct special G-operands L and R which we term conformai. Certain suboperands of L and R we call threads and fix some special G-isomorphisms, which we term coherent, of threads in R onto threads in L. On the set of all coherent G-isomorphisms of threads in L onto threads in R we define a sandwich-type multiplication. When we restrict our threads to be cyclic suboperands of L and R, this construction produces a normal cryptogroup which we represent as $ S=[Y;S_{\alpha},\chi_{{\alpha},{\beta}}] $ -Without any restriction on the threads this produces a semigroup isomorphic with a remarkable ideal of the translational hull of S. Conversely, given a strong semilattice of completely simple semigroups, satisfying certain conditions, we can represent it isomorphically as indicated above.