An order bounded disjointness preserving operator T on an Archimedean vector lattice is algebraic if and only if the restriction of Tn! to the vector sublattice generated by the range of Tm is strongly diagonal, where n is the degree of the minimal polynomial of T and m is its ‘valuation’.

Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) 6= 2 then L is generated over K by an element whose minimal polynomial is of the form t + at + bt + ct+ d for some a, b, c, d ∈ K. We show that this theorem fails in

This lecture introduces the Jordan canonical form of a matrix — we prove that every square matrix is equivalent to a (essentially) unique Jordan matrix and we give a method to derive the latter. We also introduce the notion of minimal polynomial and we point out how to obtain it from the Jordan canonical form. Finally, we make an encounter with companion matrices. 1 Jordan form and an applicati...

in this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where a~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisti...

in this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. numerical examples are presented to illustrate the proposed method.

a common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the weierstrass canonical form. the weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. the present ...

In previous works, we have shown our discovery of C60@SWNT and first described the general mechanism of filling, which involves the vapor phase transport of C60 molecules to openings in the SWNTs' walls. Here, we discuss the high-yield synthesis of C60@SWNT by refinements to our method. Yields are measured by a calibrated weight uptake technique, a methodology that is not subject to many of the...