By B(X), we also denote the set of all bounded linear operators on X into itself. If X is any Banach space and T ∈ B(X), then the adjoint T∗ of T is a bounded linear operator on the dual X∗ of X defined by (T∗ f )(x)= f (Tx) for all f ∈ X∗ and x ∈ X . LetX = {θ} be a nontrivial complex normed space and T : (T)→ X a linear operator defined on a subspace (T)⊆ X . We do not assume thatD(T) is dens...

0. Introduction. In this paper we consider factorizations of finite rank operators through finite-dimensional C∗-algebras. We are interested in factorization norms involving either the completely bounded norm ‖ ‖cb or Haagerup’s decomposable norm ‖ ‖dec (see [11]). Let us denote byMn the C∗-algebra of all n×n matrices with complex entries. Let A and B be two C∗-algebras, and let us consider a f...

(Here and everywhere else in the paper, the expectation E[·] is with respect to the uniform probability distribution on {−1, 1}.) The Parseval’s identity is the fact that ∑ S⊆[n] f̂(S) 2 = E[f(x)]. In particular, if f is boolean-valued then this implies that ∑ S⊆[n] f̂(S) 2 = 1. Given f : {−1, 1} → R and i ∈ [n], we define the discrete derivative ∂if : {−1, 1} → R by ∂if(x) = f(x1, x2, · · · , 1,...

For a unified approach to the study of the distributions of like objects on chessboards, the numbers defined by where A, denotes the partial Cwith respect to u) difference operator, are examined. This approach facilitates the treatment of further generalizations of such problems.

saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. because of heterogeneous nature of cell populations, the cell population balance equation (pbe) can be used to capture the dynamic behavior of such cultures. in this work, an unstructured-segregated model is used for d...

Abstract—Closed die forging is a very complex process, and measurement of actual forces for real material is difficult and time consuming. Hence, the modelling technique has taken the advantage of carrying out the experimentation with the proper model material which needs lesser forces and relatively low temperature. The results of experiments on the model material then may be correlated with t...

In this paper we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods in complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficien...