On (q 2 + q + 2, q + 2)-arcs in the Projective Plane PG(2, q)

A (k,n)-arc in PG(2,q) is usually defined to be a set of k points in the plane such that some line meets in n points but such that no line meets in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow to be a multiset, that is, permit to contain multiple points. The case k=q ²+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q ²+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q ²+q+2 and minimum distance q ². Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q ²+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem.     

A family of decamethylmetallocene charge-transfer salt magnets using methyl tricyanoethylenecarboxylate (MTCE) as the electron acceptor

Methyl tricyanoethylenecarboxylate, MTCE, has been used as a one-electron acceptor building block for the synthesis of isomorphous decamethylmetallocene charge-transfer salt magnets of the formula [MCp*2][MTCE], M = Cr, Mn, and Fe. Functionally and electrochemically, MTCE is a hybrid between tetracyanoethylene (TCNE) and dimethyl dicyanofumarate (DMeDCF), two acceptors that have previously been found to support ferromagnetism. The X-ray crystal structure of the chromium analogue, [CrCp*2][MTCE], shows it to exist in the expected mixed stack structure in the orthorhombic space group Pnma with a = 14.739(3) A, b = 10.7869(19) A, and c = 15.771(3) A and Z = 4. As anticipated, all three family members exhibit dominant ferromagnetic coupling, which is presumed to reflect intrastack interactions. However, the bulk magnetic properties mostly differ from simple interpolations or extrapolations of the properties of their TCNE and DMeDCF analogues. Density functional theory calculations have been used to shed some light on this observation.     

Periodic systems of molecules as elements of Shchukarev's "supermatrix", i.e. the chemical element periodic system

Generations of Soviet scientists contributed invaluable insights into molecular classification. Unfortunately, this research is little appreciated in much of the world. Among these workers S. A. Shchukarev was of great importance. His and his followers' legacy includes a host of graphical displays showing enthalpies of formation of gaseous molecules from free atoms DeltaH(a) and standard enthalpies of formation of substances plotted on the atomic number of the central elements, on their oxidation states, their internuclear separations, and other variables for a wide range of molecules. These graphs serve as databases, from which data can be extracted, to moderate precision, visually. We discuss graphs for one very limited set, or "pleiade" (gas-phase oxides of nitrogen), and for three much broader sets, or subsystems (gas-phase fluorides of all main subgroup atoms and oxides of transition-metal atoms in gas-phase and in STP conditions). When dissolved in water, molecules lose their identities but periodicity is echoed in the acids and aquocations that are formed. We show, as an example in tabular form, that redox potentials of high-oxygen acids containing S, Se, and Te change concomitantly with DeltaH(a ) and DeltaH(f) of their hexafluorides. We present graphical evidence that three properties for cations of groups 1-3 (in the short version of the periodic chart) behave similarly and share the periodicity of the elements. One of the properties is related to the ionization potential, which is shown in a tabular example to vary concomitantly with energy of hydration. It was the ultimate goal of S. A. Shchukarev that the transformation of any one graphical database into any other, having different molecules under different conditions, would be made mathematically.     

Synthetic deuterated erythrite--a vibrational spectroscopic study

A comparison of deuterated and non-deuterated erythrite has been made using a combination of infrared and Raman spectroscopy. Infrared spectrum shows bands at 3442, 3358, 3194 and 3039 cm(-1). The band at 3442 cm(-1) is attributed to weakly hydrogen bonded water and the band at 3039 cm(-1) to strongly hydrogen bonded water. Deuteration results in the observation of OD bands at 2563, 2407 and 2279 cm(-1). The ratio of these bands change with deuteration. Deuteration shows that the strongly hydrogen bonded water is replaced in preference to the weakly hydrogen bonded water. Three HOH bending modes are observed at 1686, 1633, 1572 and DOD bending modes at 1236, 1203 and 1176 cm(-1). Deuteration causes the loss of intensity of the bands at 841, 710 and 561 cm(-1) and new bands are observed at 692, 648 and 617 cm(-1). These three bands are attributed to the water librational modes. Deuteration results in an additional Raman band at 809 cm(-1) with increasing intensity with extent of deuteration. Deuteration results in the shift of Raman bands to lower wavenumbers.     

The temporal representation of speech in a nonlinear model of the guinea pig cochlea

The temporal representation of speechlike stimuli in the auditory-nerve output of a guinea pig cochlea model is described. The model consists of a bank of dual resonance nonlinear filters that simulate the vibratory response of the basilar membrane followed by a model of the inner hair cell/auditory nerve complex. The model is evaluated by comparing its output with published physiological auditory nerve data in response to single and double vowels. The evaluation includes analyses of individual fibers, as well as ensemble responses over a wide range of best frequencies. In all cases the model response closely follows the patterns in the physiological data, particularly the tendency for the temporal firing pattern of each fiber to represent the frequency of a nearby formant of the speech sound. In the model this behavior is largely a consequence of filter shapes; nonlinear filtering has only a small contribution at low frequencies. The guinea pig cochlear model produces a useful simulation of the measured physiological response to simple speech sounds and is therefore suitable for use in more advanced applications including attempts to generalize these principles to the response of human auditory system, both normal and impaired.     

Radiative corrections and quantum gates in molecular systems

We propose a method for quantum information processing using molecules coupled to an external laser field. This utilizes molecular interactions, control of the external field, and an effective energy shift of the doubly excited state of two coupled molecules. Such a level shift has been seen in the two-photon resonance experiments recently reported by Hettich et al. Here we show that this can be explained in terms of the QED Lamb shift. We quantify the performance of the proposed quantum logic gates in the presence of dissipative mechanisms. The unitary transformations required for performing one- and two-qubit operations can be implemented with present day molecular technology. The proposed techniques can also be applied to coupled quantum dot and biomolecular systems.     

version of Hardy's theorem on semisimple Lie groups

We prove an analogue of the version of Hardy's theorem on semisimple Lie groups. The theorem says that on a semisimple Lie group, a function and its Fourier transform cannot decay very rapidly on an average.

     

Magnetic,spectroscopic and biological properties of copper(II) complexes of the tridentate ligand, α-N-methyl-S-methyl-β-N-(2-pyridyl)methylenedithiocarbazate(NNS) and the X-ray crystal structure of the [Cu(NNS)I2] complex

Copper(II) complexes of general formula, Cu(NNS)X ₂ · nH₂O (NNS = the 2-formylpyridine Schiff base of N-methyl-S-methyldithiocarbazate; X = Cl^–, Br^–, I^–, NCS^–; n = 0, 2) have been synthesized and characterized by elemental analysis and by magnetic and spectroscopic techniques. Based on magnetic and spectroscopic data, a monomeric five-coordinate square-pyramidal structure is assigned to these complexes. The crystal and molecular structure of [Cu(NNS)I₂] has been determined by X-ray diffraction. The complex has a monomeric square-pyramidal structure with the ligand coordinated to the copper(II) ion via the pyridine nitrogen atom, the azomethine nitrogen atom and the thione sulfur atom. The fourth and fifth coordination sites are occupied by the iodide ligands. Antimicrobial tests indicate that Schiff base is inactive against the bacteria, Bacillus subtilis (mutant defective DNA repair), Pseudomonas aeruginosa, methicillin resistant Staphylococcus aureus and Bacillus subtilis (wild type) and weakly active against the fungi, Candida albicans, Candida lypolytica, Saccharomyces cereviseae and Aspergillus ochraceous but its copper(II) complexes, Cu(NNS)X ₂ are strongly active against these organisms. A cytotoxicity study of the compounds against leukemic and cervical cancer cells showed that the Schiff base is inactive, but the complexes, [Cu(NNS)I₂] and [Cu(NNS)(NCS)₂] · 2H₂O exhibit significant activity against cervical cancer cells with CD₅₀ values of 4.8 and 4.2 g, respectively.