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Monotonicity of certain functionals under rearrangement

Adriano Garsia, Eugène Rodemich (1974)

Annales de l'institut Fourier

We show here that a wide class of integral inequalities concerning functions on [ 0 , 1 ] can be obtained by purely combinatorial methods. More precisely, we obtain modulus of continuity or other high order norm estimates for functions satisfying conditions of the type ∫ 0 1 ∫ 0 1 Ψ f ( x ) - f ( y ) p ( x - y ) d x d y < ∞ where Ψ ( u ) and p ( u ) are monotone increasing functions of | u | .Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...

More on the Continuity of Real Functions

Keiko Narita, Artur Kornilowicz, Yasunari Shidama (2011)

Formalized Mathematics

In this article we demonstrate basic properties of the continuous functions from R to Rn which correspond to state space equations in control engineering.

Morse-Sard theorem for delta-convex curves

D. Pavlica (2008)

Mathematica Bohemica

Let f : I → X be a delta-convex mapping, where I ⊂ ℝ is an open interval and X a Banach space. Let C f be the set of critical points of f . We prove that f ( C f ) has zero 1 / 2 -dimensional Hausdorff measure.

Multiplicity and uniqueness for a class of discrete fractional boundary value problems

Lv Zhanmei, Gong Yanping, Chen Yi (2014)

Applications of Mathematics

The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green's function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012).

Multipliers of spaces of derivatives

Jan Mařík, Clifford E. Weil (2004)

Mathematica Bohemica

For subspaces, X and Y , of the space, D , of all derivatives M ( X , Y ) denotes the set of all g ∈ D such that f g ∈ Y for all f ∈ X . Subspaces of D are defined depending on a parameter p ∈ [ 0 , ∞ ] . In Section 6, M ( X , D ) is determined for each of these subspaces and in Section 7, M ( X , Y ) is found for X and Y any of these subspaces. In Section 3, M ( X , D ) is determined for other spaces of functions on [ 0 , 1 ] related to continuity and higher order differentiation.

Multiplying balls in the space of continuous functions on [0,1]

Marek Balcerzak, Artur Wachowicz, Władysław Wilczyński (2005)

Studia Mathematica

Let C denote the Banach space of real-valued continuous functions on [0,1]. Let Φ: C × C → C. If Φ ∈ +, min, max then Φ is an open mapping but the multiplication Φ = · is not open. For an open ball B(f,r) in C let B²(f,r) = B(f,r)·B(f,r). Then f² ∈ Int B²(f,r) for all r > 0 if and only if either f ≥ 0 on [0,1] or f ≤ 0 on [0,1]. Another result states that Int(B₁·B₂) ≠ ∅ for any two balls B₁ and B₂ in C. We also prove that if Φ ∈ +,·,min,max, then the set Φ - 1 ( E ) is residual whenever E is residual in...

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