S U M M A R Y We present an alternative to the classical mode coupling method scheme often used in global seismology to compute synthetic seismograms in laterally heterogeneous earth model and Frechet derivatives for tomographic inverse problem with the normal modes first-order Born approximation. We start from the first-order Born solution in the frequency domain and we use a numerical scheme ...

A long-standing problem that arises when constructing the mathematical apparatus of quantum mechanics is need to work with unbounded operators. Since space nuclear operators preconjugate for algebra all bounded operators, we can consider states a system as and observables. In this case, taking trace product operator (a state) observable) gives average value observable in fixed state. The existe...

Abstract The method proposed is intended to solve implicit conservative operator difference schemes for a grid initial-boundary value problems on simplex system of equations gas dynamics in the mixed Euler-Lagrangian variables. To find solution such scheme at time step, it represented as single equation nonlinear function two arguments from space – direct product spaces gas-dynamic quantities. ...

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...