this study aims at presenting a numerical model for predicting grout flow and penetration length into the jointed rock mass using universal distinct element code (udec). the numerical model is validated using practical data and analytical method for grouting process. input data for the modeling, including geomechanical parameters along with grout properties, were obtained from a case study. the...

Denote the joint numerical radius of an m-tuple of bounded operators A = (A1, . . . , Am) by w(A). We give a complete description of maps f satisfying w(A − B) = w(f(A) − f(B)) for any two m-tuples of operators A = (A1, . . . , Am) and B = (B1, . . . , Bm). We also characterize linear isometries for the joint numerical radius, and maps preserving the joint numerical range of A. AMS Classificati...

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.

We define the (convex) joint numerical range for an infinite family of compact operators in a Hilbert space H. use this set to determine whether self-adjoint operator A with ±‖A‖ its spectrum is minimal respect diagonals fixed basis E H norm, that ‖A‖≤‖A+D‖, all diagonal D. also describe moment mS=conv{|v|2:v∈S and ‖v‖=1} subspace S⊂H terms ranges obtain equivalences between intersection moment...

In this paper, the notion of rank-k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for ϵ > 0; the notion of Birkhoff-James approximate orthogonality sets for ϵ-higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed denitions yield a natural genera...

This study aims at presenting a numerical model for predicting grout flow and penetration length into the jointed rock mass using Universal Distinct Element Code (UDEC). The numerical model is validated using practical data and analytical method for grouting process. Input data for the modeling, including geomechanical parameters along with grout properties, were obtained from a case study. The...

‎let $v$ be an $n$-dimensional complex inner product space‎. ‎suppose‎ ‎$h$ is a subgroup of the symmetric group of degree $m$‎, ‎and‎ ‎$chi‎ :‎hrightarrow mathbb{c} $ is an irreducible character (not‎ ‎necessarily linear)‎. ‎denote by $v_{chi}(h)$ the symmetry class‎ ‎of tensors associated with $h$ and $chi$‎. ‎let $k(t)in‎ (v_{chi}(h))$ be the operator induced by $tin‎ ‎text{end}(v)$‎. ‎the...