Positive solutions for three-point nonlinear fractional boundary value problems.
Positive trigonometric sums and applications.
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.
Positivity and contractivity in the dynamics of clusters’ splitting with derivative of fractional order
Classical models of clusters’ fission have failed to fully explain strange phenomenons like the phenomenon of shattering (Ziff et al., 1987) and the sudden appearance of infinitely many particles in some systems with initial finite particles number. Furthermore, the bounded perturbation theorem presented in (Pazy, 1983) is not in general true in solution operators theory for models of fractional order γ (with 0 < γ ≤ 1). In this article, we introduce and study a model that can be understood as...
Positivity and stabilization of fractional 2D linear systems described by the Roesser model
A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation...
Possibly every real function is continuous on a non-meagre set.
Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
The purpose of the paper is to extend results of the potential theory of the classical Schrödinger operator to the α-stable case. To obtain this we analyze a weak version of the Schrödinger operator based on the fractional Laplacian and we prove the Conditional Gauge Theorem.
Power-monotone sequences and Fourier series with positive coefficients.
Power-monotone sequences and Fourier series with positive coefficients.
Poznámka k článku V. Petrůva
Poznámka k jednomu problému K. Kartáka
Poznámka k první větě o střední hodnotě integrálního počtu
Poznámka k větě o substituci pro Riemannův integrál
Poznámka k větě o substituci pro Riemannův integrál
Poznámka ke Gauss-Ostrogradského formuli
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
Prevalence of backward stochastic differential equations with unique solution.
Prevalence of "nowhere analyticity"
This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study to Gevrey classes of functions.
Prevalence of some known typical properties.