Cardinality of retracts of monounary algebras

For an uncountable monounary algebra (A, f) with cardinality κ it is proved that (A, f) has exactly 2_κ retracts. The case when (A, f) is countable is also dealt with. This work was suported by the the Slovak VEGA Grant No. 1/3003/06. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-20-004104.     

Pseudo‐merohedrally twinned tetra­kis­(1H‐imidazole‐κN3)bis­(N‐nitro­cyanamidato‐κN)copper(II)

Crystals of the title complex, [Cu(CN₃O₂)₂(C₃H₄N₂)₄], the structure of which has been determined by single‐crystal X‐ray diffraction at 304 K, appear to be pseudo‐merohedrally twinned. Transformation to a monoclinic C‐centred cell was necessary in order to derive the twin law. Twin refinement in a triclinic unit cell significantly reduced the R value. The asymmetric unit of the triclinic cell consists of one mol­ecule in a general position and two half entities with the Cu atom on a centre of inversion. The coordination of the Cu atom is quasi‐octa­hedral, with four imidazole N‐atom donors in the equatorial plane and two cyano N atoms from the N‐nitro­cyanamidate anion in axial positions. Owing to symmetry in the centrosymmetric mol­ecules, the trans imidazole ligands are parallel, while those in the non‐centrosymmetric mol­ecule make angles of 22.8 (2) and 77.9 (2)°.     

Tail Behavior and Breakdown Properties of Equivariant Estimators of Location

For translation and scale equivariant estimators of location, inequalities connecting tail behavior and the finite-sample breakdown point are proved, analogous to those established by He et al. (1990, Econometrika, 58, 1195–1214) for monotone and translation equivariant estimators. Some other inequalities are given as well, enabling to establish refined bounds and in some cases exact values for the tail behavior under heavy- and light-tailed distributions. The inequalities cover translation and scale equivariant estimators in great generality, and they involve new breakdown-related quantities, whose relations to the breakdown point are discussed. The worth of tail-behavior considerations in robustness theory is demonstrated on examples, showing the impact of the basic two techniques in robust estimation: trimming and averaging. The mathematical language employs notions from regular variation theory.     

Packing of Incongruent Circles on the Sphere

 In this paper we provide an upper bound to the density of a packing of circles on the sphere, with radii selected from a given finite set. This bound is precise, e.g. for the system of incircles of Archimedean tilings (4, 4, n) with n ? 6. A generalisation to the weighted density of packing is applied to problems of solidity of a packing of circles. The simple concept of solidity was introduced by L. Fejes Toóth [6]. In particular, it is proved that the incircles of the faces of the Archimedean tilings (4,6,6), (4,6,8) and (4, 6, 10) form solid packings.     

Calculation of the critical currents of Bi(2223)/Ag tapes and coils with reduced anisotropy in Ic(B) characteristic — effect of different proportional representations of the filaments oriented parallel and perpendicularly to the tape surface

A mathematical model was developed to allow for the prediction of critical currents in Bi(2223)/Ag-sheathed tapes that consist of two groups of filaments, having crystalline texture (c-axis) predominantly in two directions orthogonal to each other and to the length of the conductor (filaments oriented parallel and perpendicular to the tape surface). Using the theory presented, it is possible to estimate the upper limit of critical currents in the tapes prepared with a two-axial rolling technique. Magnetic field and angular dependencies of critical currents were obtained at 77 K measuring tapes with various proportional representations of filaments oriented in both preferred directions, i.e., the parallel and perpendicular directions. The results of calculation indicate that the anisotropy in the I_c(B) characteristic should be reduced considerably using the two-axial rolling. Unfortunately, the effect of anisotropy reduction is accompanied by simultaneous decrease in the current-carrying capacity of the tapes. The data obtained for short tape samples were utilised to estimate the critical currents of the individual turns of a small cylindrical magnet, assembled of eight pancake coils. It is shown that only a slight increase in the critical current of the magnet can be expected if the winding should be made of the tape with reduced anisotropy in the I_c(B) characteristic. The factors that limit the increase of the magnet critical current are discussed in detail.     

The Progress of Ageing of Lignin-containing Paper Induced by Light and its Relation to Chemiluminescence – Temperature Runs

Lignin-containing papers from different sources and of different age were irradiated by the visible light and the progress of the degradation reaction was followed by non-isothermal chemiluminescence method. Kinetic data obtained for papers degraded in oxygen were compared with double fold endurance test and carbonyl groups concentration. The effect of lignin on degradation of cellulose after deacidification treatment of the paper by methoxymagnesium methylcarbonate (MMMC) was ascertained and a mechanism of co-oxidation of lignin and cellulose in originally alkaline conditions was outlined.     

Experimental and theoretical studies of the C2F4 + O reaction: nonadiabatic reaction mechanism

In this work, the C(2)F(4)(X(1)A(g)) + O((3)P) reaction was investigated experimentally using molecular beam-threshold ionization mass spectrometry (MB-TIMS). The major primary products were observed to be CF(2)O (+ CF(2)) and CF(3) (+ CFO), with measured approximate yields of % versus %, respectively, neglecting minor products. Furthermore, the lowest-lying triplet and singlet potential energy surfaces for this reaction were constructed theoretically using B3LYP, G2M(UCC, MP2), CBS-QB3, and G3 methods in combination with various basis sets such as 6-31G(d), 6-311+G(3df), and cc-pVDZ. The primary product distribution for the multiwell multichannel reaction was then determined by RRKM statistical rate theory and weak-collision master equation analysis. It was found that the observed production of CF(3) (+ CFO) can only occur on the singlet surface, in parallel with formation of ca. 5 times more CF(2)O(X) + CF(2)(X(1)A(1)). This requires fast intersystem crossing (ISC) from the triplet to the singlet surface at a rate of ca. 4 x 10(12) s(-1). The theoretical calculations combined with the experimental results thus indicate that the yield of triplet CF(2)(?(3)B(1)) + CF(2)O formed on the triplet surface prior to ISC is < or =35%, whereas singlet CF(2)(X(1)A(1)) + CF(2)O is produced with yield > or =60%, after ISC. In addition, the thermal rate coefficients k(O + C(2)F(4)) in the T = 150-1500 K range were computed using multistate transition state theory and can be expressed as k(T) = 1.67 x 10(-16) x T(1.48) cm(3) molecule(-1) s(-1); they are in agreement with the available experimental results in the T = 298-500 K range.     

Analysis of NMR J couplings in partially protected galactopyranosides

[carbohydrate structure: see text] Hydrogen bond mediated NMR J couplings offer additional structural information. The interpretation of these usually small (h)J couplings are, however, not necessarily straightforward. In the present case of a carbohydrate system, a four-bond classical W coupling, (4)J(HO4,H5), is more reasonable on the basis of, in particular, density functional theory calculations of spin-spin coupling constants at the UB3LYP/6-311G** level of theory.     

Formation of the 1∶2∶3 structure in Y-Ba-Cu(Fe)-O system studied by Mössbauer spectroscopy

Annealing time and temperature dependence of Y, Ba, Cu, Fe nitrade mixture towards new phases creation was revealed by Mössbauer spectroscopy. The observed changes can be assigned to chemical decomposition of corresponding nitrades and creation of intermedial and final Y₁Baz(Cuo.o3Feo. o3)3Ox phase.