Ana Vukelić

A profile of an endosymbiont-enriched fraction of the coral Stylophora pistillata reveals proteins relevant to microbial-host interactions

This study examines the response of Symbiodinium sp. endosymbionts from the coral Stylophora pistillata to moderate levels of thermal “bleaching” stress, with and without trace metal limitation. Using quantitative high throughput proteomics, we identified 8098 MS/MS events relating to individual peptides from the endosymbiont-enriched fraction, including 109 peptides meeting stringent criteria for quantification, of which only 26 showed significant change in our experimental treatments; 12 of 26 increased expression in response to thermal stress with little difference affected by iron limitation. Surprisingly, there were no significant increases in antioxidant or heat stress proteins; those induced to higher expression were generally involved in protein biosynthesis. An outstanding exception was a massive 114-fold increase of a viral replication protein indicating that thermal stress may substantially increase viral load and thereby contribute to the etiology of coral bleaching and disease. In the absence of a sequenced genome for Symbiodinium or other photosymbiotic dinoflagellate, this proteome reveals a plethora of proteins potentially involved in microbial-host interactions. This includes photosystem proteins, DNA repair enzymes, antioxidant enzymes, metabolic redox enzymes, heat shock proteins, globin hemoproteins, proteins of nitrogen metabolism, and a wide range of viral proteins associated with these endosymbiont-enriched samples. Also present were 21 unusual peptide/protein toxins thought to originate from either microbial consorts or from contamination by coral nematocysts. Of particular interest are the proteins of apoptosis, vesicular transport, and endo/exocytosis, which are discussed in context of the cellular processes of coral bleaching. Notably, the protein complement provides evidence that, rather than being expelled by the host, stressed endosymbionts may mediate their own departure.

Sharp integral inequalities based on general Euler two-point formulae

We consider a family of two-point quadrature formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or R-integrable functions, are proved.

On generalizations of Ostrowski inequality via Euler harmonic identities.

Some generalizations of Ostrowski inequality are given, by using some Euler identities involving harmonic sequences of polynomials.

Hadamard and Dragomir-Agarwal Inequalities, the Euler Formulae and Convex Functions

The Euler formula is used with functions possessing various convexity and concavity properties to derive inequalities pertinent to numerical integration.

The extension of Montgomery identity via Fink identity with applications

The new extension of the weighted Montgomery identity is given by using Fink identity and is used to obtain some Ostrowski-type inequalities and estimations of the difference of two integral means.

Euler’s method for weighted integral formulae

Abstract We consider the weighted quadrature formulae using some Euler type identities. The results are applied to obtain some error estimates for the Chebyshev–Gauss formulae of the first and the second kind.

Refinements of the majorization-type inequalities via green and fink identities and related results

Abstract In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

Integral Error Representation of Hermite Interpolating Polynomial and Related Inequalities for Quadrature Formulae

AbstractWe consider integral error representation related to the Hermite inter-polating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder’s inequality and some inequalities for the Cebysev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered.

Bounds for the Chebyshev functional and applications to the weighted integral formulae

The aim of this paper is to provide some error estimates for the general weighted n-point quadrature formulae by using some inequalities for the Chebyshev functional. The above results are applied to obtain some new bounds for the Gauss-Chebyshev formulae of the first and the second kind.

Generalisations of Steffensen's inequality via Fink identity and related results

Starting from the result given in [1] where the authors gave the extension of weighted Montgomery identity using Fink identity from [5], we give the generalizations of Steffensen inequality. Also, we investigate the exponential convexity of differences of the left-hand and right-hand side of these inequalities. Using these differences, we produce new exponentially convex functions. They are used in studying Stolarsky type means.