Functions related to convexity and smoothness of normed spaces

We introduce a few functions related to convexity and smoothness of normed spaces. Those functions turn out to be moduli of convexity or smoothness or play an intermediate role. We calculate the exact formulas for introduced functions in some classical Banach spaces. An application to geometry of normed spaces is also indicated.     

Spin-glass behaviour in the coordination polymer [Co(C3H3N2)2]n

The magnetic behaviour of the coordination polymer [Co(C(3)H(3)N(2))(2)](n) has been investigated by magnetization and specific heat measurements. Low-field magnetic susceptibility shows the presence of two maxima at approximately 8 and 4 K (T(f)), which reflect short-range low-dimensional antiferromagnetic behaviour and the existence of a spin-glass-like state, respectively. The latter state was observed by magnetic irreversibility in both the zero-field cooled and field-cooled data, and was also confirmed by specific heat measurements. The magnetic specific heat (C(mag)) shows a lack of any long-range ordered peaks. Instead, a broad maximum near T(f) was observed in the C(mag)(T)/T-curve. Below T(f), the C(mag)(T) data follow the relation: C(mag)(T)/T = gamma + AT. We suggest that the competition of the antiferromagnetic (AF) intra-chain and the ferromagnetic (F) inter-chain interactions in a low-dimensional arrangement of magnetic Co(2+) ions can produce the spin-glass behaviour in the sample. The susceptibility data was analyzed in terms of a spin S = 3/2 Heisenberg linear-chain model with a small exchange energy and is consistent with the presence of both F and AF interactions. The splitting of the crystal field energy levels of the Co(2+) ions causes a Schottky-type specific heat anomaly of around 60 K.     

Classification of genomic data: some aspects of feature selection

Feature selection, while working with genomic data sets, is of particular interest, not only for classification (diagnostics) improvement, but also for the data interpretability. Application of the multivariate feature selection approaches allows an efficient reduction of data dimensionality, but as demonstrated in our study, sets of the selected variables depend on the objective function of the classifier. It is possible to select different subset of genes for classification due to the correlation of genes but their interpretation ought to be cautiously made.     

New look inside human breast ducts with Raman imaging. Raman candidates as diagnostic markers for breast cancer prognosis: Mammaglobin,palmitic acid and sphingomyelin

Looking inside the human body fascinated mankind for thousands of years. Current diagnostic and therapy methods are often limited by inadequate sensitivity, specificity and spatial resolution. Raman imaging may bring revolution in monitoring of disease and treatment. The main advantage of Raman imaging is that it gives spatial information about various chemical constituents in defined cellular organelles in contrast to conventional methods (liquid chromatography/mass spectrometry, NMR, HPLC) that rely on bulk or fractionated analyses of extracted components. We demonstrated how Raman imaging can drive the progress on breast cancer just unimaginable a few years ago. We looked inside human breast ducts answering fundamental questions about location and distribution of various biochemical components inside the lumen, epithelial cells of the duct and the stroma around the duct during cancer development. We have identified Raman candidates as diagnostic markers for breast cancer prognosis: carotenoids, mammaglobin, palmitic acid and sphingomyelin as key molecular targets in ductal breast cancer in situ, and propose the molecular mechanisms linking oncogenes with lipid programming.     

Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics

The paper presents a method for transforming a given sound and complete n-sequent proof system into an equivalent sound and complete system of ordinary sequents. The method is applicable to a large, central class of (generalized) finite-valued logics with the language satisfying a certain minimal expressiveness condition. The expressiveness condition decrees that the truth-value of any formula φ must be identifiable by determining whether certain formulas uniformly constructed from φ have designated values or not. The transformation preserves the general structure of proofs in the original calculus in a way ensuring preservation of the weak cut elimination theorem under the transformation. The described transformation metod is illustrated on several concrete examples of many-valued logics, including a new application to information sources logics.     

Kinetic study of free‐radical polymerization photoinitiated by cyanine‐borate salts. II.

A series of cyanine butyltriphenylborate salts were prepared and tested as initiators of free‐radical polymerization photoinitiated via a photoinduced electron‐transfer process. For the majority of the tested series, the highest rate of photoinitiated free‐radical polymerization was observed when sec‐butyl radicals were formed. Essentially, there was no influence of the quantum yield of the free‐radical formation on the rate of the free‐radical polymerization initiated by the cyanine‐borate salts. The experimental data revealed that the relationship between the rate of polymerization and the free energy change for the electron transfer displayed typical Marcus region kinetic behavior. The photoreduction of the cyanine butyltriphenylborate salts produced colorless products. The efficiency of the bleached‐dye formation had no effect on the overall efficiency of photoinitiated polymerization. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2365–2374, 2000     

Studies on the mechanism of decomposition of 1-methyl-1-(1-naphthyl)ethyl hydroperoxides to 2-(1-naphthyloxy)propenes

Abstract  

Thermal decomposition of 1-methyl-1-(4-methyl-1-naphthyl)ethyl hydroperoxide under gas chromatography-mass spectroscopy (GC–MS) conditions gives 2-((4-methyl-1-naphthyl)oxy)propene as the main product (50.5%), without any detectable traces of the isomeric 2-((5-methyl-1-naphthyl)oxy)propene. This finding excludes the rearrangement pathway of 1-methyl-1-(1-naphthyl)ethyl hydroperoxides to the corresponding 2-(1-naphthyloxy)propenes, which involves formation of a naphthofuran derivative as an intermediate and transfer of the isopropenyloxy group to the 8 position. This result, as well as our previous density functional theory (DFT) calculations, points to the rearrangement pathway involving an oxirane-type intermediate as the most plausible pathway to 2-(1-naphthyloxy)propenes. This rearrangement is responsible for the unusual inhibition effects of 1-methyl-1-(1-naphthyl)ethyl hydroperoxide on the liquid-phase oxidation of isopropylarenes with oxygen.     

Thermodynamic and transport properties of (1,2-ethanediol + 1-nonanol) at temperatures from (298.15 to 313.15) K

Densities and kinematic viscosities have been measured for (1,2-ethanediol + 1-nonanol) over the temperature range from (298.15 to 313.15) K. The speeds of sound in those mixtures within the temperature range from (293.15 to 313.15) K have been measured as well. Using the measurement results, the molar volumes, isentropic compressibility coefficients, molar isentropic compressibilities, and the corresponding excess and deviation values (excess molar volumes, excess isentropic compressibility coefficients, excess molar isentropic compressibilities, differently defined deviations of the speed of sound, and dynamic viscosity deviations) were calculated. The excess Gibbs free energies estimated by the use of the UNIQUAC model are also reported. The excess molar volumes and Gibbs free energies are positive, whereas the compressibility excesses are s-shaped. The excess and deviation values are expressed by Redlich–Kister polynomials and discussed in terms of variations of the structure of the system caused by the participation of two different alcohol molecules in the dynamic intermolecular association process through hydrogen bonding. The effect of temperature is discussed. The predictive abilities of the McAllister equation for viscosities of the mixtures under test have also been examined.     

Riboflavin as a source of autofluorescence in Eisenia fetida coelomocytes

Immunocompetent cells of earthworms (coelomocytes) contain adherent amoebocytes and large eleocytes (chloragocytes); the latter are filled with numerous granules. We have previously shown that eleocytes of several (but not all) earthworm species exhibit strong autofluorescence detectable by fluorescent microscopy and flow cytometry. In the present article, the molecular origin of eleocytes autofluorescence was elucidated in coelomocytes expelled via dorsal pores in the integument of Eisenia fetida subjected to electric shock (1 min at 4.5 V). Spectrofluorometry (excitation and emission spectra and fluorescence lifetime), together with HPLC analysis of coelomocyte suspensions and supernatants, indicated that riboflavin but not FMN (flavin mononucleotide) or FAD (flavin-adenine dinucleotide) is the main fluorophore responsible for eleocyte fluorescence in this species. Additionally, lipofuscins are suspected to participate in this phenomenon.     

The Effect of Hemp Cake (Cannabis sativa L.) on the Characteristics of Meatballs Stored in Refrigerated Conditions

Hemp cake, a by-product of cold pressing oil from hemp seeds, is a nutritious ingredient that could be used for the production of new or reformulated meat products. The aim of this study was to determine the influence of inclusion of 0.9%, 2.6%, 4.2%, and 7.4% (w/w) hemp cake (Cannabis sativa L.) on the physicochemical and textural properties, oxidation, and sensory acceptance of cooked and vacuum-packed meatballs during refrigerated storage. The addition of 7.4% hemp cake enhanced the amount of dry matter and reduced the content of water. Lightness (L*) and redness (a*) values reduced significantly with higher levels of hemp supplementation. Regardless of the amount of hemp additive, pH, color parameters did not differ significantly during the 12 days of storage. Hemp cake significantly decreased protein and lipid oxidation: the inhibitory effect of adding 7.4% hemp cake on protein carbonyl group formation and TBARS values reached 11.16% and 36.5%, respectively, after 10 days of storage. Sensory analysis revealed that meatballs prepared with 0.9% and 2.6% hemp cake gained higher overall scores. The results indicate that hemp cake, a material considered mainly as waste, may be destined for food purposes and be an alternative ingredient for the production of sustainable meat products.