On Some Multidimensional Hilbert-Type Inequalities in the Discrete Case

Motivated by the results of Huang, we deduce a pair of discrete multidimensional Hilbert-type inequalities involving a homogeneous kernel of negative degree. We also establish conditions under which the constant factors involved in the established inequalities are the best possible. Finally, we consider some particular settings with homogeneous kernels and weight functions. In this way, we obtain generalizations of some results known from the literature.З метою узагальнення результат Хуанга отримано дві дискретні багатовимiрнi нєрівності гільбертового типу з однорідним ядром від'ємного степеня. Також встановлено умови, за яких сталі множники, що входять до отриманих нерівностей, є найкращими з можливих. Розглянуто деякі конкретні випадки однорідних ядер та вагових функцій. Це дає змогу узагальнити деякі відомі результати

Lipid composition of liver in rats fed diets supplemented with egg yolks of modified composition

The aim of this study was to examine the effects of diets supplemented with egg yolks of modified composition on the fatty-acid composition and lipid content in rat’s liver. During four weeks of the experiment 64 Wistar rats were divided into four groups of 16 individuals each (eight individuals of both sexes) and fed a commercial feed mixture for rats (group C) or diet containing 70% commercial mixture for rats and 30% freshly cooked egg yolks from laying hens fed diets with 3% fish oil (group F), 3% palm olein (group P) or 3% lard (group L). Dietary supplementation with egg yolks significantly increased the hepatic cholesterol pool in rats, regardless of the type of fat in the diet of laying hens from which the eggs originated. The content of α-linolenic acid in the liver of male rats in group P was 4-6 times higher compared to males in the other groups. Liver lipids and their fatty-acid composition differ by both, sex and dietary modified egg yolk composition in rats

Perforacija nazofarinksa zbog tupe traume vrata uzrokovane padom uslijed epileptičkog napadaja

Perforacija ždrijela uzrokovana tupom traumom vrata je rijetkost. Prikazujemo slučaj perforacije nazofarinksa uslijed tupe traume vrata kod 29-godišnje bolesnice. Bolesnica se javila s tegobama pojačane osjetljivosti, bolnosti i disfagije u području prednje strane vrata, koje su nastale nakon pada uslijed epileptičkog napadaja. Klinički pregled glave i vrata, te fiberendoskopski pregled ždrijela i grkljana nisu ukazivali ni na kakvu ozljedu. Po učinjenom MSCT-a verificiran je parafaringealni emfizem nastao radi perforacije nazofarinksa. Bolesnica je uspješno liječena antibioticima širokoga spektra, analgeticima i jednodnevnom restrikcijom peroralnog unosa hrane i tekućine, te je oporavak bio uspješan. Pristup bolesniku s tupom traumom vrata trebao bi uključivati adekvatnu slikovnu dijagnostiku (radiografski nalaz ili nalaz CT-a). Način liječenja ovisi o mjestu i veličini perforacije ždrijela, te je individualan za svakog bolesnika

Some sharp inequalities for integral operators with homogeneous kernel

One goal of this paper is to show that a big number of inequalities for functions in L-p(R+), p >= 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0 < p < 1. Some useful new variants of these results are pointed out and a number of known and new Hardy-Hilbert type inequalities are derived. Moreover, a new Polya-Knopp (geometric mean) inequality is derived and applied. The constants in all inequalities in this paper are sharp