18,785 research outputs found
Information technology of developing test kits based on software requirements
The article presents an advanced information technology of developing test kits based on software requirements using regulated cascading decision charts, providing the increase of coverage completeness by the projected test kits of software requirements and the accuracy of the tests themselves. The article presents an advanced information technology of developing test kits based on software requirements using regulated cascading decision charts, providing the increase of coverage completeness by the projected test kits of software requirements and the accuracy of the tests themselves
Small-threshold behaviour of two-loop self-energy diagrams: two-particle thresholds
The behaviour of two-loop two-point diagrams at non-zero thresholds
corresponding to two-particle cuts is analyzed. The masses involved in a cut
and the external momentum are assumed to be small as compared to some of the
other masses of the diagram. By employing general formulae of asymptotic
expansions of Feynman diagrams in momenta and masses, we construct an algorithm
to derive analytic approximations to the diagrams. In such a way, we calculate
several first coefficients of the expansion. Since no conditions on relative
values of the small masses and the external momentum are imposed, the threshold
irregularities are described analytically. Numerical examples, using diagrams
occurring in the Standard Model, illustrate the convergence of the expansion
below the first large threshold.Comment: 28 pages (including 23 pages of text in latex and 5 pages with 6
figures in a separate postcript file
Free field representation for the O(3) nonlinear sigma model and bootstrap fusion
The possibility of the application of the free field representation developed
by Lukyanov for massive integrable models is investigated in the context of the
O(3) sigma model. We use the bootstrap fusion procedure to construct a free
field representation for the O(3) Zamolodchikov- Faddeev algebra and to write
down a representation for the solutions of the form-factor equations which is
similar to the ones obtained previously for the sine-Gordon and SU(2) Thirring
models. We discuss also the possibility of developing further this
representation for the O(3) model and comment on the extension to other
integrable field theories.Comment: 14 pages, latex, revtex v3.0 macro package, no figures Accepted for
publication in Phys. Rev.
Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory
We continue the investigation of massive integrable models by means of the
bootstrap fusion procedure, started in our previous work on O(3) nonlinear
sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear
sigma model we prove a similar relation between sine-Gordon theory and a
one-parameter deformation of the O(3) sigma model, the sausage model. This
allows us to write down a free field representation for the
Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral
representation for the generating functions of form-factors in this theory. We
also clear up the origin of the singularities in the bootstrap construction and
the reason for the problem with the kinematical poles.Comment: 16 pages, revtex; references added, some typos corrected. Accepted
for publication in Physical Review
Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams
It is shown how strictly four-dimensional integration by parts combined with
differential renormalization and its infrared analogue can be applied for
calculation of Feynman diagrams.Comment: 6 pages, late
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
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