‎let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $a$ be an $n-$square quaternion matrix‎. ‎in this paper‎, ‎some results on the $k-$numerical range of $a$ are investigated‎. ‎moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $a$ are introduced‎, ‎and some of their algebraic properties are studied‎.

because of high strength to weight ratio, 6061 aluminum has many applications in different industries like automotive and aerospace industries and can help to reduction of fuel consumption. forming limit diagram (fld) is a useful method for sheet metal formability identification. whereas calculation of forming limit diagram by experimental tests is expensive and time consumption, in the present...

efficiency of numerical methods is an important problem in dynamic nonlinear analyses. it is possible to use of numerical methods such as beta-newmark in order to investigate the structural response behavior of the dynamic systems under random sea wave loads but because of necessity to analysis the offshore systems for extensive time to fatigue study it is important to use of simple stable meth...

Direct Numerical Simulations (DNS) of the distribution function of conformation of small axisymmetric particles is considered from a numerical point of view. The mathematical modelling of microstructured uid has to take into account (i) the e ect of the surrounding uid onto the microstructure and (ii) the e ect of the microstructures on the uid. We consider (i) the simulation of the conformatio...