Approximation by Genuine qq-Bernstein-Durrmeyer Polynomials in Compact Disks in the case q>1q > 1

This paper deals with approximating properties of the newly defined $q$-generalization of the genuine Bernstein-Durrmeyer polynomials in the case $q>1$, whcih are no longer positive linear operators on $C[0,1]$. Quantitative estimates of the convergence, the Voronovskaja type theorem and saturation of convergence for complex genuine $q$-Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. In particular, it is proved that for functions analytic in \left\{ z\in\mathbb{C}:\left\vert z\right\vert q, the rate of approximation by the genuine $q$-Bernstein-Durrmeyer polynomials ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical genuine Bernstein-Durrmeyer polynomials. We give explicit formulas of Voronovskaja type for the genuine $q$-Bernstein-Durrmeyer for $q>1$

Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata

Cellular automata are widely used to model natural or artificial systems. Classically they are run with perfect synchrony, i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. For some particular rules, varying the synchrony rate continuously produces a qualitative change in the behaviour of the cellular automaton. We investigate the nature of this change of behaviour using Monte-Carlo simulations. We show that this phenomenon is a second-order phase transition, which we characterise more specifically as belonging to the directed percolation or to the parity conservation universality classes studied in statistical physics

Approximation by q-Szasz operators

his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the $q$-Sz\'{a}sz operators ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Sz\'{a}sz--Mirakjan operators

The Stock of Intangible Capital in Canada: Evidence from the Aggregate Value of Securities

This paper measures the size of the stock of intangible capital in Canada using newly released data on the market value of all securities in the economy. The approach taken relies on a quantitative application of the q-theory of investment to generate the quantity of capital owned by firms. I find that the intangible capital stock accounted for approximately 30% of overall capital since 1994. Of this, the R&D reported by national accounts makes up only 23%. These results imply that official Canadian statistics failed to account for 26% of the value of the capital stock in their 2005 quarterly data collection. In addition, I find that the magnitude of the intangible capital stock is comparable to that reported using a cost approach, confirming the size of the findings and ascertaining the need to include intangibles in empirical models and in investment data.q-Theory, Unrecorded Capital, Intangible Capital

What are Some of the Best Ways to Assess and Measure Operational Team Performance in a Lean Innovation Environment?

[Excerpt] Lean innovation is a concept that has been gaining attention in the recent years. It began as a concept for start-ups; entrepreneurs with creative ideas wanting to provide the most value to their stakeholders using the least resources, but has quickly grown popular in large companies as well. As companies strive to differentiate their offerings in the rapidly globalizing world amid tough competition and depleting resources, lean innovation could provide a logical solution to many related problems. With principles like value for customer, experimentation with ‘pivoting’, speed, teamwork, and efficiency, lean innovation is being applied in many companies. The question that arises, then, is how to successfully evaluate the teams performing in a lean innovation environment, given the different dynamics like higher failure rate and higher costs involved with the innovation process, that did not exist in traditional organizational setups. Since lean innovation is a relatively new concept, there is little research available with respect to teams in a lean environment specifically. However, there are ways to evaluate teams, taking into consideration the principles highlighted above. The following sections shall focus on highlighting some of the best practices of assessing teams that are applicable to an environment which has one or more of the aforementioned dynamics

What is the Impact of Eliminating Performance Ratings?

[Excerpt] Ratingless performance management became trendy in recent years when companies found that traditional performance ratings cost huge amounts of money and time without significant positive impact on performance. However, simply eliminating performance ratings cannot achieve desirable results. In this paper, we summarize the research surrounding ratingless performance management and present some alternatives to the traditional methods