The concave-convex procedure (CCCP) is a majorization-minimization algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms like sparse support vector machines (SVMs), transductive SVMs, sparse principal component analysis, etc. Though widely used in many applications, the con...

We consider the M(t)/M(t)/S queue with catastrophes. The bounds of the rate of convergence to the limit regime and the estimates of the limit probabilities are obtained. We also study the bounds for the mean of the queue and consider an example.

converge a.e. for all f in L log log(L) but fail to have a finite limit for an f ∈ L. In fact, we show that for each Orlicz space properly contained in L, 1 ≤ q < ∞, there is a sequence along which the ergodic averages converge for functions in the Orlicz space, but diverge for all f ∈ L . This extends the work of K. Reinhold, who, building on the work of A. Bellow, constructed a sequence for w...

We consider Mt/Mt/S-type queueing model with group services. Bounds on the rate of convergence for the queue-length process are obtained. Ordinary Mt/Mt/S queue and Mt/Mt/S type queueing model with group services are studied as examples.

The concept of -convergence was introduced in [P. Schaefer, Proc. Amer. Math. Soc. 36(1972)104-110] by using invariant mean.In this paper we apply this method to prove some Korovkin type approximation theorems. [Mustafa Obaid. Some approximation theorems via -convergence. Life Sci J 2012;9(4):1527-1530] (ISSN:10978135). http://www.lifesciencesite.com. 231

A solid understanding of convergence behaviour is essential to the design and analysis of iterative methods. In this paper we explore the convergence of inexact iterative methods in general, and inexact Newton methods in particular. A direct relationship between the convergence of inexact Newton methods and the forcing terms is presented in both theory and numerical experiments.

See, for example, Billingsley (Prob. & Measure) for a proof. Donsker’s theorem deals with the convergence, in distribution, of the empirical process. In what follows I will assume the basic concepts of convergence in distribution for stochastic processes assuming values in a metric space. Billingsley’s book on weak convergence (especially the 2nd edition) is an excellent reference (in particula...

We prove that the Morava-K-theory-based Eilenberg-Moore spectral sequence has good convergence properties whenever the base space is a p-local finite Postnikov system with vanishing (n + 1)st homotopy group.

A lattice theory of scalar bosons in the fundamental representation of the gauge group SU(Nc) and of the global symmetry group SU(Nf) is shown to induce a standard gauge theory only at large Nf . The system is in a deconfined phase at strong scalar self-coupling and any finite Nf . The requirement of convergence of the effective gauge action imposes a lower limit on the scalar mass.

Intuitionistic set theory without choice axioms does not prove that every Cauchy sequence of rationals has a modulus of convergence, or that the set of Cauchy sequences of rationals is Cauchy complete. Several other related non-provability results are also shown.