New Extensions of Popoviciu’s Inequality

Popoviciu’s inequality is extended to the framework of h-convexity and also to convexity with respect to a pair of quasi-arithmetic means. Several applications are included.

     

On the q-ampleness of the tensor product of two line bundles

Multiple zeta values (MZVs) are generalizations of Riemann zeta values at positive integers to multiple variable setting. These values can be further generalized to level N multiple polylog values by evaluating multiple polylogs at Nth roots of unity. In this paper, we consider another level N generalization by restricting the indices in the iterated sums defining MZVs to congruence classes modulo N, which we call the MZVs at level N. The goals of this paper are twofold. First, we shall lay down the theoretical foundations of these values such as their regularizations and double shuffle relations. Second, we will generalize the bracket functions related to multiple divisor sums defined by Bachmann and Kühn to arbitrary level N and study their relations to MZVs at level N. The brackets are all q-series and similar to MZVs, they have both weight and depth filtrations. But unlike that of MZVs, the product of brackets usually has mixed weights; however, after projecting to the highest weight we can obtain an algebra homomorphism from brackets to MZVs. Moreover, the image of the derivation \({\mathfrak{D}=q\frac{d}{dq}}\) on brackets vanishes on the MZV side, which gives rise to many nontrivial \({\mathbb{Q}}\)-linear relations.     

Dependency of particle sizes and colloidal stability of polyelectrolyte complex dispersions on polyanion structure and preparation mode investigated by dynamic light scattering and atomic force microscopy

Polyelectrolyte complex (PEC) dispersions were prepared by controlled mixing of three random copolymers of sodium 2-acrylamido-2-methylpropanesulfonate (AMPS) with either t-butyl acrylamide (TBA) [P(AMPS54-co-TBA46) and P(AMPS37-co-TBA63)] or methyl methacrylate (MM) [P(AMPS52-co-MM48)] with an ionene-type polycation, containing 95 mol % N,N-dimethyl-2-hydroxypropyleneammonium chloride repeat units (PCA5), with their structural characteristics being deeply investigated by dynamic light scattering (DLS) and atomic force microscopy (AFM). Shape, size, and polydispersity of the PEC dispersions were directly observed by AFM as a function of polyanion structure, the ratio between charges, n-/n+, and the titrant addition rate (TAR). The particle sizes increased and the colloidal stability decreased with the increase of the nonionic comonomer content and with the decrease of TAR. It was demonstrated that the medium particle sizes of the complex nanoparticles adsorbed on silicon wafers measured by AFM, in the dry state, were close but always lower than those measured by DLS, both before and after the complex stoichiometry.     

Skeletal diversity through radical cyclization of tetrahydropyridine scaffolds

Suitably functionalized tetrahydropyridines (methyl pipecolates) have been used as conformationally biased templates for radical cyclizations to access benzoisoquinuclidines and linearly fused indenopiperidines. Variation of skeletal types is determined by location of a radical-initiating element.     

Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category

If H is a Hopf algebra with bijective antipode and α, β ∈ Aut _Hopf (H), we introduce a category , generalizing both Yetter-Drinfeld modules and anti-Yetter-Drinfeld modules. We construct a braided T-category having all the categories as components, which, if H is finite dimensional, coincides with the representations of a certain quasitriangular T-coalgebra DT(H) that we construct. We also prove that if (α, β) admits a so-called pair in involution, then is isomorphic to the category of usual Yetter-Drinfeld modules . Research partially supported by the programme CERES of the Romanian Ministry of Education and Research, contract no. 4-147/2004.     

Asymptotic behaviour of families of real curves

We consider the family of fibres of a polynomial function f on a smooth noncompact algebraic real surface and we characterise the regular fibres of f which are atypical due to their asymptotic behaviour at infinity. We compare to the similar problem in the complex case. Received: 5 May 1998 / Revised version: 20 March 1999     

Total Aseptization of Boar Semen,to Increase the Biosecurity of Reproduction in Swine

The aim of the study was to establish the complete microbiological profile of boar semen (Sus scrofa domesticus) and to choose the most effective antiseptic measures in order to control and optimize AI reproduction in pig farms. One hundred and one semen samples were collected and analyzed from several pig farms. The microbiological profile of ejaculates was determined by evaluating the degree of contamination of fresh semen and after dilution with specific extenders. The bacterial and fungal load of fresh boar semen recorded an average value of 82.41/0.149 × 10³ CFU/mL, while after diluting the ejaculates the contamination value was 0.354/0.140 × 10³ CFU/mL. Twenty-four germs (15 bacterial and 9 fungal species) were isolated, the most common being Candida parapsilosis/sake (92%) and Escherichia coli (81.2%). Modification of the sperm collection protocol (HPBC) reduced contamination in raw sperm by 49.85% in bacteria (significant (p < 0.00001) and by 9.67% in fungi (non-significant (p < 0.111491). The load in bacteria and filamentous fungi can be controllable, but not in levuras fungi. Some fluconazole-added extenders (12.5 mg%), ensure fungal aseptization, and even an increase in sperm progressivity (8.39%) for at least a 12 h shelf life after dilution. Validation of sperm aseptization was done by maintaining sow fecundity unchanged after AI (insignificant p > 0.05).     

Synthesis and Biological Evaluation of New N-Acyl-α-amino Ketones and 1,3-Oxazoles Derivatives

In order to develop novel bioactive substances with potent activities, some new valine-derived compounds incorporating a 4-(phenylsulfonyl)phenyl fragment, namely, acyclic precursors from N-acyl-α-amino acids and N-acyl-α-amino ketones classes, and heterocycles from the large family of 1,3-oxazole-based compounds, were synthesized. The structures of the new compounds were established using elemental analysis and spectral (UV-Vis, FT-IR, MS, NMR) data, and their purity was checked by reversed-phase HPLC. The newly synthesized compounds were evaluated for their antimicrobial and antibiofilm activities, for toxicity on D. magna, and by in silico studies regarding their potential mechanism of action and toxicity. The 2-aza-3-isopropyl-1-[4-(phenylsulfonyl)phenyl]-1,4-butanedione 4b bearing a p-tolyl group in 4-position exhibited the best antibacterial activity against the planktonic growth of both Gram-positive and Gram-negative strains, while the N-acyl-α-amino acid 2 and 1,3-oxazol-5(4H)-one 3 inhibited the Enterococcus faecium biofilms. Despite not all newly synthesized compounds showing significant biological activity, the general scaffold allows several future optimizations for obtaining better novel antimicrobial agents by the introduction of various substituents on the phenyl moiety at position 5 of the 1,3-oxazole nucleus.     

The effect of PVC on thermal and catalytic degradation of polyethylene, polypropylene and polystyrene by a continuous flow reactor

A continuous flow reactor was operated at atmospheric pressure and feed rate of 0–1.5 kg h⁻¹ for degradation of PE, PP and PS in presence of 1–2 wt% PVC. The degradation temperatures were between 360 and 440 °C depending on the feeding material. The influence of PVC, temperature and silica-alumina catalysts on degradation behavior and on the properties of the products was studied and discussed. Different effects were observed for binary PE/PVC, PP/PVC, PS/PVC and complex PE/PP/PS/PVC mixtures due to specific interactions between PVC and each hydrocarbon polyolefin. Silica-alumina catalysts decreased the Cl concentration in oils but it seems to generate high amounts of Cl-containing organic compounds in gases.