Direct and Inverse Problems for the Heat Equation with a Dynamic type Boundary Condition

This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon the data of the classical solution are shown by using the generalized Fourier method. This paper also investigates the inverse problem of finding a time-dependent coefficient of the heat equation from the data of integral overdetermination condition

Neutrino Electromagnetic Form Factors Effect on the Neutrino Cross Section in Dense Matter

The sensitivity of the differential cross section of the interaction between neutrino-electron with dense matter to the possibly nonzero neutrino electromagnetic properties has been investigated. Here, the relativistic mean field model inspired by effective field theory has been used to describe non strange dense matter, both with and without the neutrino trapping. We have found that the cross section becomes more sensitive to the constituent distribution of the matter, once electromagnetic properties of the neutrino are taken into account. The effects of electromagnetic properties of neutrino on the cross section become more significant for the neutrino magnetic moment mu_nu > 10^{-10} mu_B and for the neutrino charge radius R > 10^{-5} MeV^{-1}.Comment: 24 pages, 10 figures, submitted to Physical Review

On algebraic models of relativistic scattering

In this paper we develop an algebraic technique for building relativistic models in the framework of direct-interaction theories. The interacting mass operator M in the Bakamjian-Thomas construction is related to a quadratic Casimir operator C of a non-compact group G. As a consequence, the S matrix can be gained from an intertwining relation between Weyl-equivalent representations of G. The method is illustrated by explicit application to a model with SO(3,1) dynamical symmetry.Comment: 10 pages, to appear in J. Phys. A : Math. Theo

Mean-field driven first-order phase transitions in systems with long-range interactions

We consider a class of spin systems on $\Z^d$ with vector valued spins (\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions $d\ge3$, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions $d=1,2$ for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique ``state,'' then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.Comment: 57 pages; uses a (modified) jstatphys class fil

The recognition and valuation of an asset’s productivity in business accounting and reporting

In this article we have considered the problems of classification and recognition of a specific type of asset, namely cattle embryos, as well as analyzed the characteristic features of this type of asset. We also substantiated its recognition as a biological asset in accordance with IFRS 41 "Agriculture". The possibility of applying the approach to embryos’ valuation by means on fair value has been proved based on the convergence of selection calculations’ methods and the income discounting method. The calculations have shown that the evaluation of the embryos depends on conditions and patterns of their usage. The results of the study will allow more reasonably forming professional judgment in the primary recognition of the biological asset and its valuation at the reporting dates in the financial statements.peer-reviewe

Relativistic theory of inverse beta-decay of polarized neutron in strong magnetic field

The relativistic theory of the inverse beta-decay of polarized neutron, $\nu _{e} + n \to p + e ^{-}$, in strong magnetic field is developed. For the proton wave function we use the exact solution of the Dirac equation in the magnetic filed that enables us to account exactly for effects of the proton momentum quantization in the magnetic field and also for the proton recoil motion. The effect of nucleons anomalous magnetic moments in strong magnetic fields is also discussed. We examine the cross section for different energies and directions of propagation of the initial neutrino accounting for neutrons polarization. It is shown that in the super-strong magnetic field the totally polarized neutron matter is transparent for neutrinos propagating antiparallel to the direction of polarization. The developed relativistic approach can be used for calculations of cross sections of the other URCA processes in strong magnetic fields.Comment: 41 pages in LaTex including 11 figures in PostScript, discussion on nucleons AMM interaction with magnetic field is adde

Some problems of spectral theory of fourth-order differential operators with regular boundary conditions

In this paper, we consider the problem yıv + q (x) y = λy, 0 < x < 1, y (1) − (−1) σ y (0) + αy (0) + γ y (0) = 0, y (1) − (−1) σ y (0) + βy (0) = 0, y (1) − (−1) σ y (0) = 0, y (1) − (−1) σ y (0) = 0 where λ is a spectral parameter; q (x) ∈ L1 (0, 1) is a complex-valued function; α, β, γ are arbitrary complex constants and σ = 0, 1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established and it is proved that all the eigenvalues, except for a finite number, are simple in the case αβ = 0. It is shown that the system of root functions of this spectral problem forms a basis in the space L p (0, 1), 1 < p < ∞, when αβ = 0; moreover, this basis is unconditional for p = 2

Spectral properties of some regular boundary value problems for fourth order differential operators

In this paper we consider the problem y ıv + p2(x)y 00 + p1(x)y 0 + p0(x)y = λy, 0 < x < 1, y (s) (1) − (−1)σy (s) (0) +Xs−1 l=0 αs,ly (l) (0) = 0, s = 1, 2, 3, y(1) − (−1)σy(0) = 0, where λ is a spectral parameter; pj(x) ∈ L1(0, 1), j = 0, 1, 2, are complex-valued functions; αs,l, s = 1, 2, 3, l = 0, s − 1, are arbitrary complex constants; and σ = 0, 1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established in the case α3,2 + α1,0 =6 α2,1. It is proved that the system of root functions of this spectral problem forms a basis in the space Lp(0, 1), 1 < p < ∞, when α3,2 +α1,0 6= α2,1, pj(x) ∈ W j 1 (0, 1), j = 1, 2, and p0(x) ∈ L1(0, 1); moreover, this basis is unconditional for p = 2

On Basicity In Lp (0, 1) (1 < p < ∞) Of The System Of Eigenfunctions Of One Boundary Value Problem. I

The basis properties of the spectral problem is investigated for differential operator of the second order with the spectral parameter in both boundary conditions. In this part of the paper the oscillation properties of eigenfunctions are established and the asymptotic formulae are derived for eigen values and eigenfunctions