The gauge including magnetically induced current method

An overview of applications of the recently developed gauge including magnetically induced current method (GIMIC) is presented. The GIMIC method is used to obtain magnetically induced current densities in molecules. It provides detailed information about electron delocalization, aromatic character, and current pathways in molecules. The method has been employed in aromaticity studies on hydrocarbons, complex multi-ring organic nanorings, M?bius twisted molecules, inorganic and all-metal molecular rings and open-shell species. Recent studies on hydrogen-bonded molecules indicate that GIMIC can also be used to estimate hydrogen-bond strengths without fragmentation of the system. Preliminary results are presented on the applicability of GIMIC for investigating current transport in molecules attached to clusters simulating molecular conductivity measurements. Advantages and limitations of the GIMIC method are reviewed and discussed.     

Universal radius of injectivity for locally quasiconformal mappings

Ifn>2 and iff is a locally quasiconformal mapping from the ballB ⁿ= {x∈R ⁿ:⋎x⋎<1} intoR ⁿ ∪ {∞} thenf is injective inB ⁿ (r)={x∈R ⁿ:⋎x⋎ <r} wherer>0 depends only onn and the maximal dilatation off. Supported in part by the Samuel Neaman Fund, Special Year in Complex Analysis, Technion, I.I.T., Haifa, Israel, 1975/76.     

Some remarks on an existence problem for degenerate elliptic systems

The system which yields Beltrami's system if , is considered. Under a condition for the coefficients a non-existence theorem is proved.

     

Metrization of Weighted Graphs

We find a set of necessary and sufficient conditions under which the weight ${w: E \rightarrow \mathbb{R}^{+}}$ on the graph G = (V, E) can be extended to a pseudometric ${d : V \times V \rightarrow \mathbb{R}^{+}}$ . We describe the structure of graphs G for which the set ${\mathfrak{M}_{w}}$ of all such extensions contains a metric whenever w is strictly positive. Ordering ${\mathfrak{M}_{w}}$ by the pointwise order, we have found that the posets $({\mathfrak{M}_{w}, \leqslant)}$ contain the least elements ρ _0,w if and only if G is a complete k-partite graph with ${k \, \geqslant \, 2}$ . In this case the symmetric functions ${f : V \times V \rightarrow \mathbb{R}^{+}}$ , lying between ρ _0,w and the shortest-path pseudometric, belong to ${\mathfrak{M}_{w}}$ for every metrizable w if and only if the cardinality of all parts in the partition of V is at most two.     

Effect of Trichoderma reesei Proteinases on the Affinity of an Inorganic-Binding Peptide

An inorganic-binding peptide sequence with high affinity to silica-containing materials was fused to a glycoside hydrolase GH26 mannanase, ManA, from the extremely thermophilic bacterium Dictyoglomus thermophilum. The resulting recombinant enzyme produced in Escherichia coli, ManA-Linker, displayed high binding affinity towards synthetic zeolite while retaining its catalytic activity at 80 °C. ManA-Linker was able to bind to the zeolite at different pH levels, indicating a true pH-independent binding. However, complete degradation of the peptide linker was observed when the recombinant ManA-Linker was exposed to the supernatant from the filamentous fungus Trichoderma reesei. This degradation was caused by extracellular proteinases produced by T. reesei during its growth phase. Several derivatives of ManA-Linker were designed and expressed in E. coli. All the derivatives carrying a single sequence of the linker were still susceptible to T. reesei proteinase degradation. Complete substitution of the linker sequence by (GGGGS)₁₆ resulted in a proteinase-resistant ManA derivative, ManA-Linker-(GGGGS)₁₆, which was able to bind to zeolite in a pH-dependent manner.