On Polynomial Approximation of Entire Functions with Index-Pair (p, q)

In this paper we have studied interpolation errors for functions in C(E), the normed algebra of analytic functions on a compact set E. The lower (p, q)-order and generalized lower (p, q)-type have been characterized in terms of these approximation errors. Finally, we have derived necessary conditions for f $\in C(E)$ to be extended to an entire function of perfectly regular (p, q)-growth with respect to a proximate order

Conservation and Diversity of Seed Associated Endophytes in Zea across Boundaries of Evolution, Ethnography and Ecology

Endophytes are non-pathogenic microbes living inside plants. We asked whether endophytic species were conserved in the agriculturally important plant genus Zea as it became domesticated from its wild ancestors (teosinte) to modern maize (corn) and moved from Mexico to Canada. Kernels from populations of four different teosintes and 10 different maize varieties were screened for endophytic bacteria by culturing, cloning and DNA fingerprinting using terminal restriction fragment length polymorphism (TRFLP) of 16S rDNA. Principle component analysis of TRFLP data showed that seed endophyte community composition varied in relation to plant host phylogeny. However, there was a core microbiota of endophytes that was conserved in Zea seeds across boundaries of evolution, ethnography and ecology. The majority of seed endophytes in the wild ancestor persist today in domesticated maize, though ancient selection against the hard fruitcase surrounding seeds may have altered the abundance of endophytes. Four TRFLP signals including two predicted to represent Clostridium and Paenibacillus species were conserved across all Zea genotypes, while culturing showed that Enterobacter, Methylobacteria, Pantoea and Pseudomonas species were widespread, with γ-proteobacteria being the prevalent class. Twenty-six different genera were cultured, and these were evaluated for their ability to stimulate plant growth, grow on nitrogen-free media, solubilize phosphate, sequester iron, secrete RNAse, antagonize pathogens, catabolize the precursor of ethylene, produce auxin and acetoin/butanediol. Of these traits, phosphate solubilization and production of acetoin/butanediol were the most commonly observed. An isolate from the giant Mexican landrace Mixteco, with 100% identity to Burkholderia phytofirmans, significantly promoted shoot potato biomass. GFP tagging and maize stem injection confirmed that several seed endophytes could spread systemically through the plant. One seed isolate, Enterobacter asburiae, was able to exit the root and colonize the rhizosphere. Conservation and diversity in Zea-microbe relationships are discussed in the context of ecology, crop domestication, selection and migration

The generalized type of entire functions with index-pair (p, q)

The article contains no abstrac

On the approximation of entire functions over Carathéodory domains

summary:Let $D$ be a Carathéodory domain. For $1\leq p\leq \infty$, let $L^p(D)$ be the class of all functions $f$ holomorphic in $D$ such that $\|f\|_{D,p}=[\frac{1}{A}\int\int_{D}^{}|f(z)|^p\,dx\,dy]^{1/p}<\infty$, where $A$ is the area of $D$. For $f\in L^p(D)$, set $$E_n^p(f)=\inf _{t\in \pi _n} \|f-t\|_{D,p}\,;$$ $\pi _n$ consists of all polynomials of degree at most $n$. In this paper we study the growth of an entire function in terms of approximation error in $L^p$-norm on $D$

Location error resilient geographical routing for vehicular ad-hoc networks

The efficiency and scalability of geographical routing depend on the accuracy of location information of vehicles. Each vehicle determines its location using global positioning system (GPS) or other positioning systems. Related literature in geographical routing implicitly assumes accurate location information. However, this assumption is unrealistic considering the accuracy limitation of GPS and obstruction of signals by road side environments. The inaccurate location information results in performance degradation of geographical routing protocols in vehicular environments. In this context, this study proposes a location error resilient geographical routing (LER-GR) protocol. Rayleigh distribution-based error calculation technique is utilised for assessing error in the location of neighbouring vehicles. Kalman filter-based location prediction and correction technique is developed to predict the location of the neighbouring vehicles. The next forwarding vehicle is selected based on the least error in location information. Simulations are carried out to evaluate the performance of LER-GR in realistic environments, considering junction-based as well as real map-based road networks. The comparative performance evaluation attests the location error resilient capability of LER-GR in a vehicular environment