A link between combinatorial designs and three-weight linear codes

In this paper, we show that partial geometric designs can be constructed from certain three-weight linear codes, almost bent functions and ternary weakly regular bent functions. In particular, we show that existence of a family of partial geometric difference sets is equivalent to existence of a certain family of three-weight linear codes. We also provide a link between ternary weakly regular bent functions, three-weight linear codes and partial geometric difference sets.     

Statistical convergence of double-complex Picard integral operators

In this work, we study the statistical approximation properties of the double-complex Picard integral operators. We also show that our statistical approach is more applicable than the classical one.     

A principle of linear covariance for quantum mechanics and the electronic structure theory of molecules and other atom clusters

Quantum mechanical equations should look the same in any non-orthonormal or orthonormal basis frame when properly formulated so as to be fully covariant under the largest group indicated. Non-orthonormal frames are crucial especially for the quantum theory of chemistry. Various methods such as valence-bond, localized orbital, molecular orbital, etc. result from a single formulation using the principle of linear covariance which is stated, proved, and exemplified. Molecular quantities with the full inclusion of overlaps are derived with the same ease as without overlaps.     

Recognition-mediated assembly of nanoparticles into micellar structures with diblock copolymers

Polystyrene-based diblock copolymers, featuring diaminotriazine functionality on one of the blocks were used to assemble complementary uracil-functionalized nanoparticles into micellar aggregates. The size of these self-assembled aggregates was controlled by block length, as determined in solution (using dynamic light scattering), and in thin films (using transmission electron microscopy).     

Directed graphs of structurally stable potential energy surfaces representing a-priori reaction pathways

An intrinsic property of potential energy surfaces (PES) that holds within the adiabatic approximation is established: its structural stability.We derive the condition that ensures this property: There cannot be any integral curve of the gradient field of the PES that connects two classical transition state configurations without passing through another critical configuration in between.Under this situation, we can establish a one-to-one correspondence: a whole class of adiabatic PES defining one reaction mechanism is associated to a directed graph. Thus, the problem of finding a-priori pathways involving a given number m of chemical species narrows down to a classifying certain directed graphs with m sinks. The combinatorial method is derived in this paper.Detailed examples on a-priori pathways for degenerate thermal rearrangements and on 1-2 hydrocarbon shifts are worked out and found in agreement with experimental evidence.     

Non-unitary classification of molecular electronic structures and other atom clusters

Molecules or reacting assemblies of an isomeric set of atoms become related to each other regardless of any spatial symmetry by the principle of linear covariance and the valency dyad field introduced in two previous papers by the author. Crucial electronic indices characterize certain equivalence classes into which molecules get classified under transformations which are in general non-unitary.     

Semileptonic decays of d mesons in three-flavor lattice QCD

We present the first three-flavor lattice QCD calculations for D-->pilnu and D-->Klnu semileptonic decays. Simulations are carried out using ensembles of unquenched gauge fields generated by the MILC Collaboration. With an improved staggered action for light quarks, we are able to simulate at light quark masses down to 1/8 of the strange mass. Consequently, the systematic error from the chiral extrapolation is much smaller than in previous calculations with Wilson-type light quarks. Our results for the form factors at q(2)=0 are f(D-->pi)(+)(0)=0.64(3)(6) and f(D-->K)(+)(0)=0.73(3)(7), where the first error is statistical and the second is systematic, added in quadrature. Combining our results with experimental branching ratios, we obtain the Cabibbo-Kobayashi-Maskawa matrix elements |V(cd)|=0.239(10)(24)(20) and |V(cs)|=0.969(39)(94)(24), where the last errors are from experimental uncertainties.     

Structural covariance of graphs

Algebraic structures including multiple rank tensors, linear and non-linear operators are related to and represented with various types of graphs. Special emphasis is placed on linear operators e.g. on the Hibert space. A different graph represents the same operator depending on the basis frame used, in general non-orthonormal. All such graphs are shown to belong in one equivalence class and are termed structurally covariant. Crucial indices related to eigenvalues but invariant under any basis frame changes including non-orthonormal ones provide one way to characterize each class. A set of rules are given that allow one to find the graphs structurally covarinat with a given one and/or to deduce the class indices directly by simple pictorial manipulations on a graph. Applications in various fields including the quantum theory of molecules and reactions are indicated.     

New method for qualitative quantum chemical deductions on organic or inorganic molecules or clusters directly from structural formulas or ORTEP diagrams

A pictorial blackboard mnemonic type method presented allows the molecular orbital level patterns, the numbers of non-bonding, bonding, and anti-bonding orbitals to be figured out from the actual or tentative structural formulas (or ORTEP diagrams) of saturated or unsaturated molecules or intermediates regardless of symmetry. The simple pictorial rules are illustrated on: bicyclo[p.q.0] hydrocarbons, pyridine, alkyl groups, quaternium ions, some amines, ethers, water and alcohols, and on some fluorohydrocarbons. The readily obtained MO level patterns, e.g. during rearrangements, give a handle on the qualitative behaviour of various structures or species. The method applies also to metal atom and other clusters.List of abbreviations AO Atomic orbital - ECI Electron count index - H.F. Hartree-Fock - LPI Level pattern indices - MO Molecular orbital - SC Structurally covariant - SCF Self-consistent field - SEF Structural-electronic formula - SF Structural formula - VB Valence-bond - VIF Valency points interaction formula - VP Valency point - VL VP-VP' interaction line - VSEPR Valence shell electron pair repulsion