Tractability frontiers in probabilistic team semantics and existential second-order logic over the reals

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic inclusion logic. We furthermore relate these formalisms to linear programming, and doing so obtain PTIME data complexity for the logics. Moreover, on finite structures, we show that the full existential second-order logic with additive real arithmetic can only express NP properties. Lastly, we present a sound and complete axiomatization for probabilistic inclusion logic at the atomic level.     

Left invariant special Kähler structures

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.     

Synthesis and structural characterization of novel bridged platinum(II) biscarbene complexes

Novel bridged platinum(II) biscarbene complexes are reported: 1,1′-dimethyl-3,3′-methylene-4-diimidazolin-2,2′-diylidene platinum(II) (3) and 1,1′-dimethyl-3,3′-ethylene-4-diimidazolin-2,2′-diylidene platinum(II) complexes 4 are directly accessible in high yields starting from platinum halides. The one-pot synthesis obviates the need for multi-step reactions via metal precursors or free carbenes. An X-ray crystal structure of 1,1′-dimethyl-3,3′-methylene-4-diimidazolin-2,2′-diylidene platinum(II) dibromide (3b) confirmed the structural similarity to the known corresponding palladium complexes. Since free 1,1′-di-R-3,3′-methylene-4-diimidazolin-2,2′-diylidenes are only available in low yields this synthetic route provides an easy access to the corresponding carbene complexes.     

Analysis of grid file algorithms

Grid file algorithms were suggested in [12] to provide multi-key access to records in a dynamically growing file. We specify here two algorithms and derive the average sizes of the corresponding directories. We provide an asymptotic analysis. The growth of the indexes appears to be non-linear for uniform distributions:O(v ^c ) orO(v ), wherec=1+b^–1, =1+(s-1)/(sb+1),s is the number of attributes being used,v the file size, andb the page capacity of the system. Finally we give corresponding results for biased distributions and compare transient phases.     

Synthesis, spectroscopic characterization and reactivities of linear and butterfly chromium/selenium complexes containing substituted cyclopentadienyl ligands: crystal structures of [{η-MeC5H4Cr(CO)2}2Se] and [{η-EtO2CC5H4Cr(CO)2}2Se2]

The Cr-Cr singly-bonded dimers [{η⁵-RC₅H₄Cr(CO)₃}₂] (1, R=Me; 2, R=CO₂Et) reacted with an equivalent of elemental selenium in THF at room temperature to give the linear Cr₂Se complexes [{η⁵-RC₅H₄Cr(CO)₂}₂Se] (3, R=Me; 4, R=CO₂Et), whereas the linear Cr₂Se complex (5, R=MeCO) reacted with excess NaBH₄, Ph₃PCHPh or 2,4-dinitrophenylhydrazine under respective conditions to afford the linear Cr₂Se derivatives [{η⁵-RC₅H₄Cr(CO)₂}₂Se] (6, R=MeCH(OH); 7, R=PhCHCMe; 8, R=2,4-(NO₂)₂C₆H₃NHNCMe). Similarly, while the butterfly Cr₂Se₂ complexes [{η⁵-RC₅H₄Cr(CO)₂}₂Se₂] (9, R=Me; 10, R=CO₂Et) could be produced either by reaction of dimers 1 and 2 with an excess amount of elemental selenium, or by reaction of the linear complexes 3 and 4 with an equivalent of elemental selenium, the butterfly Cr₂Se₂ derivatives [{η⁵-RC₅H₄Cr(CO)₂}₂Se₂] (12, R=MeCH(OH); 13, R=PhCHCMe; 14, R=2,4-(NO₂)₂C₆H₃NHNCMe) were yielded by reaction of the butterfly Cr₂Se₂ complex (11, R=MeCO) with an excess quantity of NaBH₄, Ph₃PCHPh and 2,4-dinitrophenylhyazine. Both the linear complexes 3, 4, 6-8 and the butterfly complexes 9, 10, 12-14 are new, which have been fully characterized by elemental analysis, spectroscopy and X-ray crystallography.     

The static dielectric constant of solutions of water inn-alcohols at 15, 25, 35, and 45°C

Dielectric constants (measured at 1 MHz) are reported for solutions of water (concentration range 0 to 0.2 mole fraction) in 1-propanol at 25°C, and in 1-butanol, 1-pentanol, and 1-hexanol at 15, 25, 35, and 45°C. These results, together with literature values for solutions of water in methanol, ethanol, 1-heptanol, and 1-octanol, show that water interacts with alcohols in at least two ways: (1) it can participate in the formation of dynamic hydrogen-bonded chains, thereby raising the polarizability; (2) it can form relatively stable structures such as H₂O(ROH)₄ which have zero net dipole moment and consequently diminish volume polarizability. For C _n H _2n+1 OH alcohols,n≥4, most of the initially added water forms complexes: consequently, addition of water to these alcohols lowers the dielectric constant.     

Visual observation of contact-induced intercrystalline migration of aromatic species adsorbed in zeolites by fluorescence microscopy.

Intercrystalline migration and a migration-assisted chemical reaction of adsorbed aromatic species between zeolite particles in physical contact were visualized by fluorescence microscopy coupled with a particle manipulation technique. The luminescence color characteristics of particular zeolite particles originating from the specific photochemistry of adsorbed species was exploited to follow the migration of the molecules. Two examples are shown that are relevant to the visualization of the time-dependent migration process: A one guest-two sets of zeolite crystals system: chrysene (Chry)-loaded zeolite Na+ -X (the sodium form of zeolite X) crystals were placed in contact with unloaded Tl+ -X (thallium-exchanged X) crystals and allowed to stand at room temperature. Initially, the blue fluorescence of Chry was detected only from the Na+ -X particles, but later, the development of green phosphorescence emission was discernible from the Tl+ -X which suggests that Chry migrated from the Na+ -X to the Tl+ -X crystals. A two guest-species systems: Electron-donating Chry-loaded Na+ -X crystals were placed in contact with electron-accepting 1,2,4,5-tetracyanobenzene (TCNB)-loaded Na+ -X or Na+ -Y crystals. With time, the former system (Chry/Na+ -X and TCNB/Na+ -X) gave rise to the emission of Chry-TCNB charge-transfer complexes resulting mainly from the migration of Chry while the latter system (Chry/Na+ -X and TCNB/Na+ -Y) afforded the same emission resulting largely from the migration of TCNB. The present investigation reveals that there is a certain direction for guest migration depending on the zeolite host and the nature of host-guest or guest-guest interaction.     

Modular design of icosahedral metal clusters

The concept of crystalline module, that is, an unambiguously isolated, repeated quasi-molecular element, is introduced. This concept is more general than the concept of crystal lattice. The generalized modular approach allows extension of the methods and principles of crystallography to quasi-crystals, clusters, amorphous solids, and periodic biological structures. Principles of construction of aperiodic, nonequilibrium regular modular structures are formulated. Limitations on the size of icosahedral clusters are due to the presence of spherical shells with non-Euclidean tetrahedral tiling in their structure. A parametric relationship between the structures of icosahedral fullerenes and metal clusters of the Chini series was found.     

Contribution to the techniques of enumeration ofKekulé structures

Four auxiliary classes of benzenoids are introduced, and formulas are given for their number ofKekulé structures (K). An enumeration method forK of different important classes of benzenoids is illustrated by examples. The utilization of essentially disconnected benzenoids is a special feature of the method.

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Ein Beitrag zur Methodik der Bestimmung möglicherKekulé-Strukturen

Zusammenfassung Es werden Hilfsklassen von benzenoiden Aromaten eingeführt und Formeln zur zahlenmäßigen Auswertung möglicherKekulé-Strukturen angegeben (K). Die Auswertungsmethode fürK wird an verschiedenen wichtigen Klassen benzenoider Verbindungen exemplarisch gezeigt. Die Verwendbarkeit essentiell abgekoppelter aromatischer Bauelemente ist eine spezielle Eigenschaft dieser Methode.

     

Hydrate inclusion compounds

There are three general classes of hydrate inclusion compounds: the gas hydrates, the per-alkyl onium salt hydrates, and the alkylamine hydrates. The first are clathrates, the second are ionic inclusion compounds, the third are semi-clathrates. Crystallization occurs because the H₂O molecules, like SiO₂, can form three-dimensional four-connected nets. With water alone, these are the ices. In the inclusion hydrates, nets with larger voids are stabilized by including other guest molecules. Anions and hydrogen-bonding functional groups can replace water molecules in these nets, in which case the guest species are cations or hydrophobic moieties of organic molecules. The guest must satisfy two criteria. One is dimensional, to ensure a comfortable fit within the voids. The other is functional. The guest molecules cannot have either a single strong hydrogen-bonding group, such as an amide or a carboxylate, or a number of moderately strong hydrogen-bonding groups, as in a polyol or a carbohydrate.The common topological feature of these nets is the pentagonal dodecahedra: i.e., 5¹²-hedron. These are combined with 5¹²6²-hedra, 5¹²6³-hedra, 5¹²6⁴-hedra and combinations of these polyhedra, to from five known nets. Two of these are the well-known 12 and 17 Å cubic gas hydrate structures,Pm3n, Fd3m; one is tetragonal,P4 ₂/mnm, and two are hexagonal,P6 ₃/mmc andP6/mmm. The clathrate hydrates provide examples of the two cubic and the tetragonal structures. The alkyl onium salt hydrates have distorted versions of thePm3n cubic, the tetragonal, and one of the hexagonal structures. The alkylamine hydrate structures hitherto determined provide examples of distorted versions of the two hexagonal structures.There are also three hydrate inclusion structures, represented by single examples, which do not involve the 5¹²-hedra. These are 4(CH₃)₃CHNH₂·39H₂O which is a clathrate; HPF₆·6H₂O and (CH₃)₄NOH·5H₂O which are ionic-water inclusion hydrates. In the monoclinic 6(CH₃CH₂CH₂NH₂)·105H₂O and the orthorhombic 3(CH₂CH₂)₂NH·26H₂O, the water structure is more complex. The idealization of these nets in terms of the close-packing of semi-regular polyhedra becomes difficult and artificial. There is an approach towards the complexity of the water salt structures found in the crystals of proteins.