On some extremalities in the approximate integration

Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations we do not use any other assumptions apart from higher order convexity itself. The obtained inequalities refine the inequalities of Hadamard type. They are applied to give error bounds of quadrature operators under the assumptions weaker from the commonly used

On some inequality of Hermite-Hadamard type

It is well-known that the left term of the classical Hermite-Hadamard inequality is closer to the integral mean value than the right one. We show that in the multivariate case it is not true. Moreover, we introduce some related inequality comparing the methods of the approximate integration, which is optimal. We also present its counterpart of Fejer type.Comment: Submitted to Opuscula Mat

Hermite-Hadamard type inequalities for Wright-convex functions of several variables

We present Hermite--Hadamard type inequalities for Wright-convex, strongly convex and strongly Wright-convex functions of several variables defined on simplice

Low energy threshold corrections to neutrino masses and mixing angles

We compute the low energy threshold corrections to neutrino masses and mixing in the Standard Model (SM) and its minimal supersymmetric version, using the effective theory technique. We demonstrate that they stabilize the renormalization group (RG) running with respect to the choice of the scale to which the RG equation is integrated. This confirms the correctness of the recent re-derivation of the RGE for the SM in hep-ph/0108005. The explicit formulae for the low energy threshold corrections corrections can be applied to specific models of neutrino masses and mixing.Comment: 20 pages, 2 postscript figure

Integration of Poland into EU global industrial networks: the evidence and the main challenges

In this paper, we attempt to identify the achievements of one decade of transformation of the Polish economy in effecting the integration of its manufacturing sector with those of the broader European and global economy, using the automotive industry as an illustrative example. We begin with a broad picture of the current situation in Poland, looking particularly at the motivations of EU-based investors. We then discuss the automobile industry, again examining the motives of foreign investors and the effects of policy on their behavior. Next, we examine the chief public and private actors in the integration process, with a particular focus on their roles in trying to push Poland's integration in the direction of high value added and high innovation. Finally, we briefly discuss the impact of Poland's accession to the EU on industrial networking, and then summarize our conclusions and suggest a research framework for testing the hypothesis (formulated on the basis of our observations of the Polish case) that the market orientation of a given industry, measured by the ratio of the trade balance in that industry to its total domestic output, depends among other things on ownership structure, with the domestically-owned sector tending to use locally developed technologies and the foreign-owned sector tending to transfer in technology from abroad

Support-type properties of convex functions of higher order and Hadamard-type inequalities

It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree no greater than the order of convexity. In this paper the attaching method is developed. It is applied to obtain the general result Theorem 2, from which the mentioned above support theorem and some related properties of convex functions of higher (both odd and even) order are derived. They are applied to obtain some known and new Hadamard-type inequalities between the quadrature operators and the integral approximated by them. It is also shown that the error bounds of quadrature rules follow by inequalities of this kind.Comment: In the journal version of the paper an example given in Remark 4 was not correct. Here we give a proper on