Evaluation of Casimir Energies Through Spectral Functions

We consider applications of elliptic differential operators and their associated spectral functions in quantum field theory problems. The role of zeta functions and traces of heat kernels in the regularization of Casimir energies is emphasized, and the renormalization procedure is discussed with simple examples.     

Models of linear logic

We engage a study of nonmodal linear logic which takes times ⊗ and the linear conditional ⊸ to be the basic connectives instead of times and linear negation ()^⊥ as in Girard's approach. This difference enables us to obtain a very large subsystem of linear logic (called positive linear logic) without an involutionary negation (if the law of double negation is removed from linear logic in Girard's formulation, the resulting subsystem is extremely limited). Our approach enables us to obtain several natural models for various subsystems of linear logic, including a generic model for the so-called minimal linear logic. In particular, it is seen that these models arise spontaneously in the transition from set theory to multiset theory. We also construct a model of full (nonmodal) linear logic that is generic relative to any model of positive linear logic. However, the problem of constructing a generic model for positive linear logic remains open. Bibliography: 2 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 220, 1995, pp. 23–35. Original     

Traveling-wave solutions and their application to inverse problems of sorption dynamics

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 67–74, 1994.     

Modified General Relativity and Cosmology

Aspects of the modified general relativity theory of Rastall, Al-Rawaf and Taha are discussed in both the radiation- and matter-dominated flat cosmological models. A nucleosynthesis constraint on the theory's free parameter is obtained and the implication for the age of the Universe is discussed. The consistency of the modified matter-dominated model with the neoclassical cosmological tests is demonstrated.     

Mössbauer studies on some new magnetic oxides

Three new magnetic oxides have been synthesised, viz., Li₂Fe₃VO₈, YFe₃TiO₈ and CaFe₃VO₈. XRD studies show that the first compound has a cubic symmetry of spinel type while the latter two show orthorhombic symmetry. All the three compounds are magnetic at room temperature, however, the first compound shows a large magnetic moment as compared to the other two. Their Mössbauer spectra at room temperature show distinct hyperfine split spectral lines. The present preliminary investigation indicates that the long range order is ferrimagnetic in Li₂Fe₃VO₈ and CaFe₃VO₈ while in YFe₃TiO₈ it is more likely to be canted antiferromagnetic.     

Dynamics of a polymer chain in an array of obstacles

On the basis of the model “polymer chain in an array of obstacles” the influence of the topology effects on the dynamics of concentrated polymer systems is investigated theoretically. The 1/z-expansion (where z is the coordinational number of the lattice of obstacles) is proposed for this problem. By means of this expansion the diffusion coefficient of a linear unclosed polymer chain is calculated. The equilibrium properties of linear closed chain (i.e. ring) unentangled with either of the edges of the lattice are investigated in detail. In particular, it is shown that the diffusion coefficient D of the center of mass of closed chain consisting of N links is proportional to N^−5/2.     

19F NMR chemical shifts and C−F bonds in graphite fluorides

Institute for Inorganic Chemistry, Siberian Branch, USSR Academy of Sciences. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 4, pp. 170–172, July–August, 1989.