Parametric and Non-Parametric Minima.
Parametric extension of the Poincaré theorem
Parametric monotone generalized equations in reflexive Banach spaces.
Partial Differentiation, Differentiation and Continuity on n -Dimensional Real Normed Linear Spaces
In this article, we aim to prove the characterization of differentiation by means of partial differentiation for vector-valued functions on n-dimensional real normed linear spaces (refer to [15] and [16]).
Partial Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces
In this article, we define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).
Partial regularity of minimizers of quasiconvex integrals
Perron type integration on -dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence
Perron-type integration on -dimensional intervals and its properties
Pettis integration
Pfeffer integrability does not imply -integrability
Plongements lipschitziens dans
Polynomial approximation and twenty years later.
Polynomials and degrees of maps in real normed algebras
Let be the algebra of quaternions or octonions . In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial has a root in . As a consequence, the Jacobian determinant is always non-negative in . Moreover, using the idea of the topological degree we show that a regular polynomial over has also a root in . Finally, utilizing multiplication () in , we prove various results on the topological degree of products...
Positively homogeneous functions and the Łojasiewicz gradient inequality
It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.
Preparation theorems for matrix valued functions
We generalize the Malgrange preparation theorem to matrix valued functions satisfying the condition that vanishes to finite order at . Then we can factor near (0,0), where is inversible and is polynomial function of depending on . The preparation is (essentially) unique, up to functions vanishing to infinite order at , if we impose some additional conditions on . We also have a generalization of the division theorem, and analytic versions generalizing the Weierstrass preparation...
Preparation theorems for systems
Příklad k jednomu obrácení Greenovy věty
Products and projective limits of function spaces
We introduce a notion of a product and projective limit of function spaces. We show that the Choquet boundary of the product space is the product of Choquet boundaries. Next we show that the product of simplicial spaces is simplicial. We also show that the maximal measures on the product space are exactly those with maximal projections. We show similar characterizations of the Choquet boundary and the space of maximal measures for the projective limit of function spaces under some additional assumptions...
Projectively Solid Sets and an N-dimensional Piccard's Theorem
We discuss functions f : X × Y → Z such that sets of the form f (A × B) have non-empty interiors provided that A and B are non-empty sets of second category and have the Baire property.
Properties of -smooth mappings with one-dimensional gradient range.