Displaying similar documents to “Transitivity and partial order”

On systems of linear algebraic equations in the Colombeau algebra

Jan Ligęza, Milan Tvrdý (1999)

Mathematica Bohemica

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From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra ¯ of generalized real numbers. It is worth mentioning that the algebra ¯ is not a field.

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

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Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator ( y ) 1 w ( t ) ( r ( t ) y ) , t [ a , ) are established. These conditions are based on a recently proved relationship between spectral properties of and oscillation of a certain associated second order differential equation.

Linear integral equations in the space of regulated functions

Milan Tvrdý (1998)

Mathematica Bohemica

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n this paper we investigate systems of linear integral equations in the space 𝔾 L n of n -vector valued functions which are regulated on the closed interval [ 0 , 1 ] (i.e. such that can have only discontinuities of the first kind in [ 0 , 1 ] ) and left-continuous in the corresponding open interval ( 0 , 1 ) . In particular, we are interested in systems of the form x(t) - A(t)x(0) - 01B(t,s)[d x(s)] = f(t), where f 𝔾 L n , the columns of the n × n -matrix valued function A belong to 𝔾 L n , the entries of B ( t , . ) have a bounded variation...