127,978 research outputs found
Complex fuzzy linear systems
In paper the complex fuzzy linear equation nbspnbspin which nbspis a crisp complex matrix and nbspis an arbitrary complex fuzzy numbers vector, is investigated. The complex fuzzy linear system is converted to a equivalent high order fuzzy linear system . Numerical procedure for calculating the complex fuzzy solution is designed and thenbsp sufficient condition for the existence of strong complex fuzzy solution is derived. A example is given to illustrate the proposed method.nbs
Linear systems with adiabatic fluctuations
We consider a dynamical system subjected to weak but adiabatically slow
fluctuations of external origin. Based on the ``adiabatic following''
approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the
strength of fluctuations and 1/|\mu| refers to the time scale of evolution of
the unperturbed system to obtain a linear differential equation for the average
solution. The theory is applied to the problems of a damped harmonic oscillator
and diffusion in a turbulent fluid. The result is the realization of
`renormalized' diffusion constant or damping constant for the respective
problems. The applicability of the method has been critically analyzed.Comment: Plain Latex, no figure, 21 page
Linear systems on irregular varieties
Let be a normal complex projective variety, a subvariety,
a morphism to an abelian variety such that
injects into and let be a line bundle on
.
Denote by the connected \'etale cover induced by the -th
multiplication map of , by the preimage of
and by the pull-back of to . For general, we study the restricted linear system : if for some this gives a generically finite map
, we show that f is independent of or
sufficiently large and divisible, and is induced by the {\em eventual map}
such that factorizes through .
The generic value of is
called the {\em (restricted) continuous rank.} We prove that if is the pull
back of an ample divisor of , then extends to
a continuous function of , which is differentiable except
possibly at countably many points; when we compute the left derivative
explicitly.
In the case when and are smooth, combining the above results we prove
Clifford-Severi type inequalities, i.e., geographical bounds of the form
where .Comment: Revised version, 37 pages. The final section has been remove
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