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Let B be a Borel subgroup of G; we write U for the unipotent radical of B and u for the Lie algebra of U.
      
Then we show how to use loop groups and hypercohomology to write explicit hamiltonians.
      
We write the discrete Fourier series as a quasi-interpolant and hence obtain convergence rates, in the aforementioned Sobolev spaces, for the discrete Fourier projection.
      
For any subset K of C and any integer m?1, write A(Dm, K)={f‖f: Dm→K is a continuous map, and f‖(Dm)° is analytit}.
      
For H∈A(Dm,C)(m?2), f∈A(D, D) and z∈D, write ΨH(f)(z)=H(z, f(z),...,fm-1(z)).
      
Using the concept of essential rank function and the Ehresmann partial order on the set of all simple matrices, we design an algorithm to write a determinantal variety as a union of its irreducible components.
      
By introducing specific degrees of reaction completion it becomes possible to write simplified conservation equations in a form simpler and more convenient for analysis and calculation.
      
The results obtained enabled us to write down the criteria for absolute and convective instability.
      
The observed effect is used to write a copy of the diffraction grating with a resolution of 1200 grooves/mm.
      
We write out sufficient conditions for uniform convergence and localization of spectral decompositions of functions from the Liouville class.
      
In particular, we write out the self-adjoint extension of the Laguerre operator whose eigenfunctions coincide with the Laguerre-Sonin polynomials and form an orthogonal basis in Π(α).
      
We prove the Weyl asymptotic formula for the number of eigenvalues of the Kohn-Laplace operator on a Heisenberg group and write out the leading term of asymptotics.
      
We write out the asymptotics as the number of electrons tends to infinity; this allows us to determine the temperature of the superconducting-to-normal state phase transition and the jump in the heat capacity.
      
We linearize the problem and, under the additional assumption that the distinguishing function is spherically symmetric, write the solution by using the formal power series method with recursion of the series coefficients.
      
For a function with real zeros, we write the growth regularity conditions (on the real axis and on the entire plane) in terms of lower bounds only for the absolute value of the derivative at the points λk.
      
A fundamental feature of this language is the ability to write such objects in the form of a sequence of symbols representing an image of the object and the ability to construct objects in the process of a program operation from subobject components.
      
Write/erase (W/E) cycles are simulated numerically.
      
It is found that the data reliability of the memory circuits considered is affected by the cross coupling of memory cells sharing a read/write line.
      
We write out the eikonal equations for Alfvèn and magnetoacoustic waves and derive the equations for the amplitudes of the zeroth approximation.
      
The algorithm was used to write a special complex of computer programs.
      
 

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