Constructions of Small Complete Caps in Binary Projective Spaces

In the binary projective spaces PG(n,2) k-caps are called large if k > 2^n-1 and smallif k ≤ 2^n-1. In this paper we propose new constructions producing infinite families of small binary complete caps.AMS Classification: 51E21, 51E22, 94B05     

Computer search in projective planes for the sizes of complete arcs

The spectrum of possible sizes k of complete k-arcs in finite projective planes PG(2, q) is investigated by computer search. Backtracking algorithms that try to construct complete arcs joining the orbits of some subgroup of collineation group PΓ L (3, q) and randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete arc are given for q = 41, 43, 47, 49, 53, 59, 64, 71 ≤ q ≤ 809, q ≠ 529, 625, 729, and q = 821. New lower bounds on the second largest size of a complete arc are given for q = 31, 41, 43, 47, 53, 125. Also, many new sizes of complete arcs are obtained for 31 ≤ q ≤ 167.     

A family of semifields in odd characteristic

We study a large family of semifields in odd characteristic, which contains the commutative Budaghyan–Helleseth semifields as well as semifields which are not isotopic to commutative semifields. Using a large group of autotopisms we obtain a complete classification result in certain parametric subcases.     

Temperature-induced iron oxidation in bafertisite Ba2Fe${}_{4}^{2+}$Ti2(Si2O7)2O2(OH)2F2: X-ray diffraction and Mössbauer spectroscopy study

The high-temperature behavior of bafertisite was studied by combination of techniques in order to characterize the temperature-induced iron oxidation associated with deprotonation of an octahedral layer. The chemical formula of bafertisite from Darai-Pioz alkaline complex (Tajikistan) determined by electron-microprobe analyzes and Mössbauer spectroscopy is Ba _2.11(Fe\({}_{2.70}^{2+}\)Fe\({}_{0.17}^{3+}\)Mn _1.09Zr _0.04Na _0.03) (Ti _1.96Nb _0.07)(Si ₂ O ₇)₂ O ₂(OH _1.29 O _0.65 F _0.06)F ₂. In situ high-temperature powder X-ray diffraction revealed abrupt shift of reflections to the high-angle region and reduction of their intensity at T >?525 ^°C. The Mössbauer spectroscopy studies indicated that the crystal structure of bafertisite contains Fe in octahedral sites as predominantly ferric ions with Fe ³⁺/ ΣFe =?0.06, whereas bafertisite annealed at T =?600 ^°C has Fe in the same position with Fe ³⁺/ ΣFe up to 0.39. The differential scanning calorimetry and thermogravimetric analyzes reveal the occurrence of a broad exothermic effect at T ～ 537 ^°C associated with the mass loss corresponding to deprotonation. Since in the studied sample of bafertisite, Fe ²⁺ apfu strongly prevails over OH apfu, the stoichiometric (charged-balanced) high-temperature oxidized modification cannot be obtained. In the paper, the high-temperature behavior of bafertisite is discussed and compared to that of astrophyllite.     

Coni generalizzati e piani di Laguerre

LetE be an abstract infinite or finite set with |E|≥3 and letB be a non empty family of subsets ofE such that there exists at least a partitionF ofE withF?B. We callgeneralized cone some incidence structures (E,B,F) which comprehend ovoidal and Miquelian Laguerre planes, special Laguerre planes, Parabeln-Ebene and other interesting incidence structures. In this paper we investigate suchgeneralized cones and their automorphism groups and give some characterizations of ovoidal (Miquelian) Laguerre planes.     

Minimax estimates of a linear parameter function in a regression model under restrictions on the parameters and variance-covariance matrix

Minimax nonhomogeneous linear estimators of scalar linear parameter functions are studied in the paper under restrictions on the parameters and variance-covariance matrix. The variance-covariance matrix of the linear model under consideration is assumed to be unknown but from a specific set R of nonnegativedefinite matrices. It is shown under this assumption that, without any restriction on the parameters, minimax estimators correspond to the least-squares estimators of the parameter functions for the “worst” variance-covariance matrix. Then the minimax mean-square error of the estimator is derived using the Bayes approach, and finally the exact formulas are derived for the calculation of minimax estimators under elliptical restrictions on the parameter space and for two special classes of possible variance-covariance matrices R. For example, it is shown that a special choice of a constant q ₀ and a matrixW ₀ defining one of the above classes R leads to the well known Kuks—Olman admissible estimator (see [16]) with a known variance-covariance matrixW ₀. Bibliography:32 titles. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 79–92.     

Intracellular antimicrobial photodynamic therapy: a novel technique for efficient eradication of pathogenic bacteria

The increasing resistance of bacteria to antibiotics is a serious problem, caused in part by excessive and improper use of these drugs. One alternative to traditional antibiotic therapy is photodynamic antimicrobial chemotherapy (PACT) which is based on the use of a photosensitizer (PS), activated by illumination with visible light. The poor penetration of visible light through the skin limits the application of PACT to the treatment of skin infections or the use of invasive procedures. To overcome this problem we report the exploitation of light emitted as a result of the chemiluminescent reaction of luminol to excite the PS and we call this process chemiluminescent photodynamic antimicrobial therapy (CPAT). We studied the effect of free and liposome-encapsulated PS (methylene blue or toluidine blue) on bacteria under excitation by either white external light or chemiluminescence emitted by free or liposome-enclosed luminol. PACT showed slightly better performance that CPAT for free and encapsulated PS for both types of bacteria. CPAT resulted in a three log suppression of Staphylococcus aureus and two log suppression of Escherichia coli growth. The use of CPAT may prove to be a novel and more effective form of antimicrobial therapy, particularly for internal infections not easily accessible to traditional PACT.