Towards a characterization of generalized twisted field planes

In this work we study semifield planes of orderq ⁿ(q=p ^r ,p prime) with a collineation whose order is ap-primitive divisor ofq ⁿ–1.Research supported in part by NSF Grant No. DMS-9107372Research supported in part by NSF grants RII-9014056, component IV of the EPSCoR of Puerto Rico grant and ARO grant for Cornell MSI.     

The Cosmological Constant in the Framework of Gravito-Magnetodynamic Waves in Weak Gravitational Fields

Using the linearization of Einstein's equations for weak gravitational fields, a specific model of gravito-magnetofluid is elaborated. The study of wave formation and propagation in such a medium is necessarily connected to the existence of the cosmological constant.     

R-Matrices for Leibniz Algebras

Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties.     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.     

Synthesis and characterization of mid‐ and end‐chain functional telechelics by controlled polymerization methods and coupling processes

Well‐defined polystyrene‐ (PSt) or poly(ε‐caprolactone) (PCL)‐based polymers containing mid‐ or end‐chain 2,5 or 3,5‐ dibromobenzene moieties were prepared by controlled polymerization methods, such as atom transfer radical polymerization (ATRP) or ring opening polymerization (ROP). 1,4‐Dibromo‐2‐(bromomethyl)benzene, 1,3‐dibromo‐5‐(bromomethyl)benzene, and 1,4‐dibromo‐2,5‐di(bromomethyl)benzene were used as initiators in ATRP of styrene (St) in conjunction with CuBr/2,2′‐bipyridine as catalyst. 2,5‐Dibromo‐1,4‐(dihydroxymethyl)benzene initiated the ROP of ε‐caprolactone (CL) in the presence of stannous octoate (Sn(Oct)₂) catalyst. The reaction of these polymers with amino‐ or aldehyde‐functionalized monoboronic acids, in Suzuki‐type couplings, afforded the corresponding telechelics. Further functionalization with oxidable groups such as 2‐pyrrolyl or 1‐naphthyl was attained by condensation reactions of the amino or aldehyde groups with low molecular weight aldehydes or amines, respectively, with the formation of azomethine linkages. Preliminary attempts for the synthesis of fully conjugated poly(Schiff base) with polymeric segments as substituents, by oxidative polymerization of the macromonomers, are presented. All the starting, intermediate, or final polymers were structurally analyzed by spectral methods (¹H NMR, ¹³C NMR, and IR). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 727–743, 2006     

Structural impacts on thallus and algal cell components of two lichen species in response to low-level air pollution in pacific northwest forests.

Lichens have long been regarded as bioindicators of air pollution, and structural studies typically have indicated negative impacts in highly polluted areas. In this research, Parmelia sulcata and Platismatia glauca were collected from one clean and two polluted sites in the Pacific Northwest forests of the United States to investigate the anatomical and ultrastructural responses of relatively resistant lichens to moderate air pollution. Light microscopy of polluted materials revealed only slight increases in the algal cell proportions of the thallus, and a decrease in the fungal cells of the medulla. Using transmission electron microscopy, increased lipid droplets in the cytoplasm and an increase in the cell wall thickness of the photobionts were found in the polluted lichens. These results were compared with physiological data in which the net carbon uptake did not show any significant differences; however, the total chlorophyll content was heightened in the polluted samples. The increased total chlorophyll content and the absence of any changes in the algal cell proportions of the polluted samples suggest that the photobionts possessed a higher chlorophyll content per unit volume of the photobiont at polluted sites. The results also indicate that lichens have altered their storage allocation in different cellular compartments. This may be a result of symbiotic readjustment(s) between the photobiont and the mycobiont. In comparison with the physiological results from these two species, these changes do not represent damaging effects by low-level air pollution.     

Z/E-photoisomerizations of olefins with 4npi- or (4n + 2)pi-electron substituents: zigzag variations in olefin properties along the T(1) state energy surfaces

[Figure: see text]. A quantum chemical study has been performed to assess changes in aromaticity along the T1 state Z/E-isomerization pathways of annulenyl-substituted olefins. It is argued that the point on the T1 energy surface with highest substituent aromaticity corresponds to the minimum. According to Baird (J. Am. Chem. Soc. 1972, 94, 4941), aromaticity and antiaromaticity are interchanged when going from S0 to T1. Thus, olefins with S0 aromatic substituents (set A olefins) will be partially antiaromatic in T1 and vice versa for olefins with S0 antiaromatic substituents (set B olefins). Twist of the C=C bond to a structure with a perpendicular orientation of the 2p(C) orbitals (3p*) in T1 should lead to regaining substituent aromaticity in set A and loss of aromaticity in set B olefins. This hypothesis is verified through quantum chemical calculations of T1 energies, geometries (bond lengths and harmonic oscillator measure of aromaticity), spin densities, and nucleus independent chemical shifts whose differences along the T1 PES display zigzag dependencies on the number of -electrons in the annulenyl substituent of the olefin. Aromaticity changes are reflected in the profiles of the T1 potential energy surfaces (T1 PESs) for Z/E-isomerizations because olefins in set A have minima at 3p* whereas those in set B have maxima at such structures. The proper combination (fusion) of the substituents of set A and B olefins could allow for design of novel optical switch compounds that isomerize adiabatically with high isomerization quantum yields.     

Elementary operators with H∞-symbols

Let T be a c.n.u. contraction on a Hilbert spaceH and let u-(u₁,...,u_n) be an n-tuple of H(T). We calculate various joint spectra of u(T) and apply the results to study the spectral and index theories of elementary operators associated with n-tuples of the above type.Both authors have been partially supported by NSF grants.     

Parameterization of peptide 13C carbonyl chemical shielding anisotropy in molecular dynamics simulations.

NMR chemical shielding anisotropy (CSA) relaxation is an important tool in the study of dynamical processes in proteins and nucleic acids in solution. Herein, we investigate how dynamical variations in local geometry affect the chemical shielding anisotropy relaxation of the carbonyl carbon nucleus, using the following protocol: 1) Using density functional theory, the carbonyl (13)C' CSA is computed for 103 conformations of the model peptide group N-methylacetamide (NMA). 2) The variations in computed (13)C' CSA parameters are fitted against quadratic hypersurfaces containing cross terms between the variables. 3) The predictive quality of the CSA hypersurfaces is validated by comparing the predicted and de novo calculated (13)C' CSAs for 20 molecular dynamics snapshots. 4) The CSA fluctuations and their autocorrelation and cross correlation functions due to bond-length and bond-angle distortions are predicted for a chemistry Harvard molecular mechanics (CHARMM) molecular dynamics trajectory of Ca(2+)-saturated calmodulin and GB3 from the hypersurfaces, as well as for a molecular dynamics (MD) simulation of an NMA trimer using a quantum mechanically correct forcefield. We find that the fluctuations can be represented by a 0.93 scaling factor of the CSA tensor for both R(1) and R(2) relaxations for residues in helix, coil, and sheet alike. This result is important, as it establishes that (13)C' relaxation is a valid tool for measurement of interesting dynamical events in proteins.