The twistor structure of the biquaternionic projective point

Souček [1, 2] discovered an intriguing connection between the standard twistor correspondence and the biquaternionic projective line The biquaternionic projective point, also has twistor structure corresponding to the collection of α- or β-planes passing through the origin in spacetime. The duality between α- or β-planes is shown to correspond to the choice of left vs. right scalar action. Moreover, we find that is homeomorphic to the scheme      

New proof of the Calabi-Bernstein theorem

By means of a local integral formula on a maximal surface, which involves the hyperbolic angle between the unit normal vector field and a fixed timelike direction, we give a new proof of the parametric Calabi-Bernstein theorem. A suitable modification of the integral formula gives an independent proof to the non-parametric case of this result.     

Preparation,spectral and structural characterization of (2-benzoylpyridine N(4)-methyl-N(4)-phenylthiosemicarbazonato) chloropalladium(II)

The synthesis, as well as spectral and structural characterization, of (2-benzoylpyridine-N(4)-methyl-N(4)-phenylthiosemicarbazonato)chloropalladium(II), [Pd(Bz4MePh)Cl], is described. The unit cell contains two crystallographically independent molecules [Pd(1)(Bz4MePh)Cl], (1), and [Pd(2)(Bz4MePh)Cl], (2), stabilized by intra- and intermolecular hydrogen bonding. The distance between the Pd(1) and Pd(2) centres is 3.5038(11) Å. The spectroscopic techniques used in this study are the following: u.v.-visible, i.r. and ¹H n.m.r. The protonation constants, determined spectrophotometrically, of the uncoordinated HBz4MePh are pK_a1 = 10.82 ± 0.03 and pK_a2 = 4.09 ± 0.02.     

Studies of poly(vinylidene fluoride)/poly(vinyl pyrrolidone) blends. I. Thermal transitions by differential scanning calorimetry

Thermal measurements were carried out to investigate the macrostructure of as-cast poly(vinylidene fluoride) (PVDF)/poly(vinyl pyrrolidone) (PVP) blends. At high PVP content, above about 70 wt.%, the two components form a homogeneously mixed amorphous phase whose T_g varies with composition. Crystals are formed upon casting mixtures richer in PVDF; these systems exhibit complex thermal behavior that cannot be justified by a simple two-phase model. DSC measurements above room temperature on semicrystalline blends show, in addition to the melting of PVDF crystals at temperatures that decrease on increasing PVP content, a glass transition at about 80°C, independent of composition. Experimental results strongly support the hypothesis that an interphase, composed of essentially undiluted noncrystalline PVDF, is always associated with the lamellar crystals.     

A manganese(II) coordination polymer with a 3D porous structure: Synthesis,structure, and spectroscopic and magnetic behaviour

A manganese(II) complex with N,N′-bis(carboxymethyl)dithiooxamide (H₄GLYDTO), [Mn(H₂GLYDTO)(H₂O)₂]_n, has been synthesized and characterized by elemental analysis and thermogravimetric analysis, as well as by infrared, electronic and EPR spectroscopy and magnetic susceptibility measurements. The crystal and molecular structure of this complex was determined by single-crystal X-ray structure analysis. The compound shows a 3D porous framework with alternate left- and right-handed helical channels where the manganese(II) ions have an octahedral environment. Variable temperature magnetic measurements reveal the existence of very weak antiferromagnetic interactions through the syn-anti carboxylate bridge, with an exchange parameter of J/k = −0.12 K.     

Tin(IV) complexes with 2-pyridineformamide-derived thiosemicarbazones: Antimicrobial and potential antineoplasic activities

Reaction of tin tetrachloride with 2-pyridineformamide thiosemicarbazone (H2Am4DH) and its N(4)-methyl (H2Am4Me), N(4)-ethyl (H2Am4Et) and N(4)-phenyl (H2Am4Ph) derivatives gave [Sn(2Am4DH)Cl₃] (1), [Sn(2Am4Me)Cl₃] (2), [Sn(2Am4Et)Cl₃] (3) and [Sn(2Am4Ph)Cl₃] (4) as products, in which an anionic thiosemicarbazone coordinates to the metal centre along with three chloride ions. The crystal structures of 1 and 2 were determined. The thiosemicarbazones were moderately active against Candida albicans and Pseudomonas aeruginosa. Upon coordination to tin(IV) the antimicrobial activity of the thiosemicarbazones increases. The studied compounds proved to be toxic to Artemia salina, suggesting that they could present cytotoxic activity against solid tumors.     

An extension of Calabi's rigidity theorem to complex submanifolds of indefinite complex space forms

The rigidity for full holomorphic isometric immersions of an indefinite Kähler manifold into an indefinite complex space form is proved. All such immersions between indefinite complex projective (and hyperbolic) spaces are founded and examples of non-congruents holomorphic isometric immersions are exposed.     

Multi-Class Cost-Constrained Random Coding for Correlated Sources over the Multiple-Access Channel

This paper studies a generalized version of multi-class cost-constrained random-coding ensemble with multiple auxiliary costs for the transmission of N correlated sources over an N-user multiple-access channel. For each user, the set of messages is partitioned into classes and codebooks are generated according to a distribution depending on the class index of the source message and under the constraint that the codewords satisfy a set of cost functions. Proper choices of the cost functions recover different coding schemes including message-dependent and message-independent versions of independent and identically distributed, independent conditionally distributed, constant-composition and conditional constant composition ensembles. The transmissibility region of the scheme is related to the Cover-El Gamal-Salehi region. A related family of correlated-source Gallager source exponent functions is also studied. The achievable exponents are compared for correlated and independent sources, both numerically and analytically.