Hydromagnetic rotating flow of third grade fluid

This work investigates the flow of a third grade fluid in a rotating frame of reference. The fluid is incompressible and magnetohydrodynamic （MHD）. The flow is bounded between two porous plates, the lower of which is shrinking linearly. Mathematical modelling of the considered flow leads to a nonlinear problem. The solution of this nonlinear problem is computed by the homotopy analysis method （HAM）. Graphs are presented to demonstrate the effect of several emerging parameters, which clearly describe the flow characteristics.     

Conservation laws via the partial Lagrangian and group invariant solutions for radial and two-dimensional free jets

The conservation laws for Prandtl’s boundary layer equations for an incompressible fluid governing the flow in radial and two-dimensional jets are investigated. For both radial and two-dimensional jets the partial Lagrangian method is used to derive conservation laws for the system of two differential equations for the velocity components. The Lie point symmetries are calculated for both cases and a symmetry is associated with the conserved vector that is used to establish the conserved quantity for the jet. This associated symmetry is then used to derive the group invariant solution for the system governing the flow in the free jet.     

Nonseparable UHF algebras I: Dixmier's problem

There are three natural ways to define UHF (uniformly hyperfinite) C^∗-algebras, and all three definitions are equivalent for separable algebras. In 1967 Dixmier asked whether the three definitions remain equivalent for not necessarily separable algebras. We give a complete answer to this question. More precisely, we show that in small cardinality two definitions remain equivalent, and give counterexamples in other cases. Our results do not use any additional set-theoretic axioms beyond the usual axioms, namely ZFC.     

Iterative learning control for MIMO nonlinear systems with arbitrary relative degree and no states measurement

This article presents a state observer based iterative learning control to solve the trajectory tracking problem of a class of time‐varying Multi‐Input‐Multi‐Output nonlinear systems with arbitrary relative degree. For this purpose, an asymptotically stable observer is derived for the system under consideration. There after, this observer is integrated with the iterative learning controller by replacing the state in the control law with its estimation yielded by the state observer. Hence, the stability of the whole control (nonlinear system plus controller plus observer) is guaranteed. Simulation result on nonlinear system shows that the trajectory tracking error decreases through the iterations. © 2013 Wiley Periodicals, Inc. Complexity 19: 37–45, 2013     

Network flow-based approaches for integrated aircraft fleeting and routing

Given a schedule of flights to be flown, the aircraft fleeting and routing problem (AFRP) consists of determining a minimum-cost route assignment for each aircraft so as to cover each flight by exactly one aircraft while satisfying maintenance requirements and other activity constraints. We investigate network flow-based heuristic approaches for this problem. Computational experiments conducted on real-data given by TunisAir show that the proposed heuristic consistently yields very near-optimal solutions while requiring modest CPU effort.     

Von Neumann's Problem and Large Cardinals

It is a well-known problem of Von Neumann to discover whetherthe countable chain condition and weak distributivity of a completeBoolean algebra imply that it carries a strictly positive probabilitymeasure. It was shown recently by Balcar, Jech and Pazák,and by Velikovi, that it is consistent with ZFC, modulo theconsistency of a supercompact cardinal, that every ccc weaklydistributive complete Boolean algebra carries a contiuous strictlypositive submeasure – that is, it is a Maharam algebra.We use some ideas of Gitik and Shelah and implications fromthe inner model theory to show that some large cardinal assumptionsare necessary for this result. 2000 Mathematics Subject Classification03E55, 28A60 (primary), 03E75 (secondary).     

Four and more

We isolate several large classes of definable proper forcings and show how they include many partial orderings used in practice.     

Evaluation of the tool life and fracture toughness of cutting tools boronized by the paste boriding process

The present study evaluates the tool life and the fracture toughness of AISI M2 steel cutting tools boronized by the paste boriding process. The treatment was done in selective form on the tool tips of the steels. The temperatures were set at 1173 and 1273 K with 4 h of exposure time and modifying the boron carbide paste thicknesses in 3 and 4 mm. Microindentation fracture toughness method was used on the borided tool at the temperature of 1273 K and a 4 mm paste thickness, with a 100 g load at different distances from the surface. Also, the borided cutting tools were worn by the turning process that implied the machining of AISI 1018 steel increasing the nominal cutting speed, of 55 m/min, in 10 and 25% and maintaining the feed and the depth cut constants. The tool life was evaluated by the Taylor's equation that shows the dependence of the experimental parameters of the boriding process.     

Generalized p(x)-elliptic system with nonlinear physical data

This paper considers the following Dirichlet problem of the form \[-\text{div}\,\big(\Phi(Du-\Theta(u)\big)=v(x)+f(x,u)+\text{div}\,\big(g(x,u)\big),\] which corresponds to a diffusion problem with a source $v$ in moving and dissolving substance, the motion is described by $g$ and the dissolution by $f$. By the theory of Young measure we will prove the existence result in variable exponent Sobolev spaces $W^{1,p(x)}_0(\Omega;\R^m)$.