The Cauchy problem for the higher order equations in the mKdV hierarchy is investigated with data in the spaces b H s (R) defined by the norm ‖v0‖ b Hr s (R) := ‖〈ξ〉 b v0‖Lr′ ξ , 〈ξ〉 = (1 + ξ) 1 2 , 1 r + 1 r = 1. Local well-posedness for the jth equation is shown in the parameter range 2 ≥ r > 1, s ≥ 2j−1 2r . The proof uses an appropriate variant of the Fourier restriction norm method. A coun...

Fractional-order differential equations are powerful tools for the representation of dynamic systems that exhibit long-term memory effects. The verified simulation such system models with help interval allows computation guaranteed enclosures domains reachable pseudo states over a certain finite time horizon. In previous work author, an iteration scheme—derived on basis Picard iteration—was pub...

In this paper, the optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (BSDEs, for short) where the generators, the terminal values, and the barriers are all switched with positive costs. The value process is characterized by a system of multi-dimensional reflected BSDEs with oblique reflection, whose existence and uniqueness is by no m...

Let G be a non-trivial, loopless graph and for each non-trivial subgraph H of G, let g(H) = |E(H)| |V(H)|−ω(H) . The graph G is 1-balanced if γ(G), the maximum among g(H), taken over all nontrivial subgraphs H of G, is attained when H = G. This quantity γ(G) is called the fractional arboricity of the graph G. The value γ(G) appears in a paper by Picard and Queyranne and has been studied extensi...

Applications of a novel time-integration technique to the non-linear and linear dynamics mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations taken as starting guess for Iteration necessary symbolic operations need be performed only before time-stepping procedure starts. In previous investigation, we demonstrated computational ...

in this paper the 3d inversion of gravity data using two different regularization methods, namely tikhonov regularization and truncated singular value decomposition (tsvd), is considered. the earth under the survey area is modeled using a large number of rectangular prisms, in which the size of the prisms are kept fixed during the inversion and the values of densities of the prisms are the mode...