An interesting triangle

A peculiar triangle and its properties, which can become the basis for a number of challenging constructions, are discussed.     

Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Il'iushin

Received April 9, 2001 / Published online August 16, 2001     

Generalized strain and stress tensors associated by duality

Received April 23, 2001 / Published online August 16, 2001     

Some Information Theoretic Ideas Useful in Statistical Inference

In this paper we discuss four information theoretic ideas and present their implications to statistical inference: (1) Fisher information and divergence generating functions, (2) information optimum unbiased estimators, (3) information content of various statistics, (4) characterizations based on Fisher information. This paper was written while the first author was visiting the University of Cyprus, Department of Mathematics and Statistics.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.     

Curcumin as the OO bidentate ligand in "2 + 1" complexes with the [M(CO)3]+ (M = Re, 99mTc) tricarbonyl core for radiodiagnostic applications

The synthesis and characterization of "2 + 1" complexes of the [M(CO)(3)](+) (M = Re, (99m)Tc) core with the β-diketones acetylacetone (complexes 2, 8) and curcumin (complexes 5, 10 and 6, 11) as bidentate OO ligands, and imidazole or isocyanocyclohexane as monodentate ligands is reported. The complexes were synthesized by reacting the [NEt(4)](2)[Re(CO)(3)Br(3)] precursor with the β-diketone to generate the intermediate aqua complex fac-Re(CO)(3)(OO)(H(2)O) that was isolated and characterized, followed by replacement of the labile water by the monodentate ligand. All complexes were characterized by mass spectrometry, NMR and IR spectroscopies, and elemental analysis. In the case of complex 2, bearing imidazole as the monodentate ligand, X-ray analysis was possible. The chemistry was successfully transferred at (99m)Tc tracer level. The curcumin complexes 5 and 6, as well as their intermediate aqua complex 4, that bear potential for radiopharmaceutical applications due to the wide spectrum of pharmacological activity of curcumin, were successfully tested for selective staining of β-amyloid plaques of Alzheimer's disease. The fact that the complexes maintain the affinity of the mother compound curcumin for β-amyloid plaques prompts for further exploration of their chemistry and biological properties as radioimaging probes.     

Higgs production cross-section in a Standard Model with four generations at the LHC

We present theoretical predictions for the Higgs boson production cross-section via gluon fusion at the LHC in a Standard Model with four generations. We include QCD corrections through NLO retaining the full dependence on the quark masses, and the NNLO corrections in the heavy quark effective theory approximation. We also include electroweak corrections through three loops. Electroweak and bottom-quark contributions are suppressed in comparison to the Standard Model with three generations.     

Honey Phenolic Compound Profiling and Authenticity Assessment Using HRMS Targeted and Untargeted Metabolomics

Honey consumption is attributed to potentially advantageous effects on human health due to its antioxidant capacity as well as anti-inflammatory and antimicrobial activity, which are mainly related to phenolic compound content. Phenolic compounds are secondary metabolites of plants, and their content in honey is primarily affected by the botanical and geographical origin. In this study, a high-resolution mass spectrometry (HRMS) method was applied to determine the phenolic profile of various honey matrices and investigate authenticity markers. A fruitful sample set was collected, including honey from 10 different botanical sources (n = 51) originating from Greece and Poland. Generic liquid–liquid extraction using ethyl acetate as the extractant was used to apply targeted and non-targeted workflows simultaneously. The method was fully validated according to the Eurachem guidelines, and it demonstrated high accuracy, precision, and sensitivity resulting in the detection of 11 target analytes in the samples. Suspect screening identified 16 bioactive compounds in at least one sample, with abscisic acid isomers being the most abundant in arbutus honey. Importantly, 10 markers related to honey geographical origin were revealed through non-targeted screening and the application of advanced chemometric tools. In conclusion, authenticity markers and discrimination patterns were emerged using targeted and non-targeted workflows, indicating the impact of this study on food authenticity and metabolomic fields.     

On the isometries of ideal polyhedra

Résumé  On montre que siX est un polyèdre idéal complet fini satisfaisant la condition CAT(−1) locale, alors toute isométrie deX homotope à l’identité est l’identité, pourvu queπ ₁(X) ne soit pas élémentaire. On montre aussi que le groupe des isométies deX est fini.      

A Generalization of the Poincaré--Bendixson Theorem for Compact 3-manifolds

It is shown that compressible cylindrical ends in compact foliated 3-manifolds spiral onto toral leaves.Mathematics Subject Classification (2000).57R30, 57M99.