Abstract We are concerned with the defocusing modified Korteweg–de Vries equation equipped particular type of irregular initial conditions that given as linear combination Dirac delta function and Cauchy principal value. For value problem we prove existence smooth self-similar solution, whose profile is Ablowitz–Segur solution second Painleve equation. Our method to use approach based on Rieman...

We consider a mathematical model for the gas flow through one-way valve and focus on two issues. First, we propose way to eliminate chattering (the fast switch off of valve) by slightly modifying design valve. This mathematically amounts construction coupling Riemann solver with suitable stability property, namely, coherence. provide numerical comparison behavior valves. Second, analyze, both a...

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann model is proposed. It is showed that the accelerated expanding universe is guaranteed by a constrained RandersFinsler structure without invoking dark energy. The geodesic in Randers-Finsler space is studied. The additional term in the geodesic equation acts as repulsive forc...

Mathematisch-naturwissenschaftlichen Fakultät Doctor of Philosophy Twisted Second Moments and Explicit Formulae of the Riemann Zeta-Function by Nicolas Martinez Robles Verschiedene Aspekte, die analytische Zahlentheorie und die Riemann zeta-Funktion verbinden, werden erweitert. Dies beinhaltet: 1. explizite Formeln, die eine Verbindung zwischen der Möbiusfunktion und den nichttrivialen Nullstel...

In this present work, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the direct algebraic method are employed for constructing the exact complex solutions of non-linear time-fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. Reference to this paper should be made as follows: Taghiz...

1 Riemann integration 2 1.1 Partitions and Riemann sums . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 A criterion for integrability . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Upper and Lower Riemann Sums . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 The refinement of a partition . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 Properties of upper an...

This paper is concerned with the kinetics of propagating phase boundaries in a bar made of a special nonlinearly elastic material. First, it is shown that there is a kinetic law of the form f = 91 (.S ) relating the driving traction f at a phase boundary to the phase boundary velocity s that corresponds to a notion of maximum dissipation analogous to the concept of maximum plastic work. Second,...

In this paper, we study semi-discrete central-upwind difference schemes with a modified multidimensional limiting process (MLP) to solve two-dimensional hyperbolic systems of conservation laws. In general, high-order central difference schemes for conservation laws involve no Riemann solvers or characteristic decompositions but have a tendency to smear linear discontinuities. To overcome this d...