In this paper, a new notion of frames is introduced: -operator frame as generalization of -frames in Hilbert C-modules introduced by A. Alijani and M. A. Dehghan [2] and we establish some results.

In this paper, we defi ne the notion of C-a ne maps in the unital -rings and we investigate the C -extreme points of the graph and epigraph of such maps. We show that for a C -convex map f defi ned on a unital -ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C -face of the epigraph of f. Moreover, we prove some results about the C  -faces of C -convex sets in -rings.

In this paper, we  nd explicit solution to the operator equation TXS 􀀀 SX T = A in the general setting of the adjointable operators between Hilbert C-modules, when T; S have closed ranges and S is a self adjoint operator.

Let A be an algebra. A linear mapping  : A! A is called a derivation if  (ab) =  (a)b + a (b) for each a; b 2 A. Given two derivations  and  0 on a C-algebra A, we prove that there exists a derivation
on A such that   0 =
2 if and only if either  0 = 0 or  = s 0 for some s 2 C.

We introduce variational inequality problems on Hilbert C-modules and we prove several existence results for variational inequalities de ned on closed convex sets. Then relation between variational inequalities, C-valued metric projection and  xed point theory on Hilbert C-modules is studied.

Let ,be a linear ,-endomorphism on a C ,-algebra A so that , (A) acts on a Hilbert space H which including K(H) and let f, tgt2R be a ,-C ,-dynamical system on A with the generator , : In this paper, we demonstrate some conditions under which f, tgt2R is implemented by a C0-groups of unitaries on H. In particular, we prove that for a rank-one projection p 2 A,which is invariant under , t,there is a C0-group futgt2R of unitaries in B(H) such that , t(a) = ut, (a)u ,t: Furthermore, introducing the concepts of ,-inner endomorphism and ,-bijective map, we prove that each ,-bijective linear endomorphism on A is a ,-inner endomorphism, where ,ia idempotent. Finally, as an application, we characterize each so-called ,-C ,-dynamical system on the concrete C ,-algebra A: = B(H) ,B(H),where H is a separable Hilbert space and ,is the linear ,-endomorphism , (S,T) = (0,T) on A:

The reconfigurable vibrating screen (RVS)machine is an innovative beneficiation machine designedfor screening different mineral particles of varying sizesand volumes required by the customers’ through the geometrictransformation of its screen structure. The successfulRVS machine upkeep requires its continuous, availability, reliability and maintainability. The RVSmachine downtime, which could erupt from its breakdownand repair, must also be reduced to the barest minimum. This means, there is a need to design and develop amaintenance system model that could be used to effectivelymaintain the RVS machine when utilized in surface andunderground mines. In view of this, this paper aims todevelop a maintenance system model that could be used toeffectively maintain the RVS machine when used in surfaceand underground mines. The maintenance systemmodel unfolds the predictive (i. e. diagnosis and prognosis)algorithms, the e-maintenance strategic tools as well as thedynamic maintenance strategic algorithms required toeffectively maintain the RVS machine. Four different casestudies were presented in this paper to illustrate theapplicability of this maintenance system model in maintainingand managing the RVS machine when utilized inthe mining industries.