A generalization of Ostrowski inequality on time scales for k points

In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.Comment: 10 page

Some Reverses of the Generalised Triangle Inequality in Complex Inner Product Spaces

Some reverses for the generalised triangle inequality in complex inner product spaces that improve the classical Diaz-Metcalf results and applications are given

A mean value theorem for systems of integrals

More than a century ago, G. Kowalewski stated that for each n continuous functions on a compact interval [a,b], there exists an n-point quadrature rule (with respect to Lebesgue measure on [a,b]), which is exact for given functions. Here we generalize this result to continuous functions with an arbitrary positive and finite measure on an arbitrary interval. The proof relies on a version of Caratheodory's convex hull theorem for a continuous curve, that we also prove in the paper. As applications, we give a representation of the covariance for two continuous functions of a random variable, and a most general version of Gruess' inequality.Comment: 7 page

Accentuate the negative

A survey of mean inequalities with real weights is given.Comment: 16 pages 3 figure

High frequency sampling of a continuous-time ARMA process

Continuous-time autoregressive moving average (CARMA) processes have recently been used widely in the modeling of non-uniformly spaced data and as a tool for dealing with high-frequency data of the form $Y_{n\Delta}, n=0,1,2,...$, where $\Delta$ is small and positive. Such data occur in many fields of application, particularly in finance and the study of turbulence. This paper is concerned with the characteristics of the process (Y_{n\Delta})_{n\in\bbz}, when $\Delta$ is small and the underlying continuous-time process (Y_t)_{t\in\bbr} is a specified CARMA process.Comment: 13 pages, submitte

On Landau\u27s theorems

In this paper we give some applications and special cases of a generalization of the Landau\u27s theorem for Frechet-differentiable functions

On Landau\u27s theorems

In this paper we give some applications and special cases of a generalization of the Landau\u27s theorem for Frechet-differentiable functions

Legislative framework regarding wastewater treatment in the Republic of Serbia and flow and transport modelling in the determination on effluent quality of wastewater treatment plant of Belgrade central sewerage system

The largest sewerage system in Belgrade is Belgrade Central Sewerage System, which covers the area of about 85% of the sewerage network, with about 1,250,000 inhabitants connected to the sewage infrastructure. The interaction of emission limit values, environmental quality standards, wastewater, effluent and recipient characteristic flows and qualities from the standpoint of environmental impact in the unfavorable environmental conditions was modelled to define the level of wastewater treatment at future Belgrade Central Sewerage System wastewater treatment plant

Teichm\"uller's problem in space

Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a spatial analogue of a classical result due to Teichm\"uller. Unlike Teichm\"uller's result, our bounds are explicit. Explicit bounds are based on two sharp well-known distortion results: the quasiconformal Schwarz lemma and the bound for linear dilatation. Moreover, Bernoulli type inequalities and asymptotically sharp bounds for special functions involving complete elliptic integrals are applied to simplify the computations. Finally, we discuss the behavior of the quasihyperbolic metric under quasiconformal maps and prove a sharp result for quasiconformal maps of R^n \ {0} onto itself.Comment: 25 pages, 2 figure

Uniqueness of nontrivially complete monotonicity for a class of functions involving polygamma functions

For $m,n\in\mathbb{N}$, let $f_{m,n}(x)=\bigr[\psi^{(m)}(x)\bigl]^2+\psi^{(n)}(x)$ on $(0,\infty)$. In the present paper, we prove using two methods that, among all $f_{m,n}(x)$ for $m,n\in\mathbb{N}$, only $f_{1,2}(x)$ is nontrivially completely monotonic on $(0,\infty)$. Accurately, the functions $f_{1,2}(x)$ and $f_{m,2n-1}(x)$ are completely monotonic on $(0,\infty)$, but the functions $f_{m,2n}(x)$ for $(m,n)\ne(1,1)$ are not monotonic and does not keep the same sign on $(0,\infty)$.Comment: 9 page