Minimal Symmetric Differences of Lines in Projective Planes

Let q be an odd prime power and let be the minimum size of the symmetric difference of r lines in the Desarguesian projective plane . We prove some results about the function , in particular showing that there exists a constant such that for .     

Study of gas generation in real L/ILW containers

To obtain reliable estimates of the quantities and rates of the gas production in L/ILW a series of measurements was carried in the last 7 years in Hungary. The typical gas production rates were 0.05–0.2 STP litre gas/day for CO₂ and CH₄ generation, and less for H₂. No explosive gas mixture was indicated in the L/ILW drums during the investigated storage period. Compositions of headspace gases in closed L/ILW vaults were in agreement with gas generation processes observed in L/ILW drums. The stable carbon isotope measurements show that the main source of the CO₂ gas is the degradation of organic matter and indicates microbial degradation processes as the main sources of CH₄. Typical tritium activity concentrations were <10 Bq/l gas in the drums and <1,000 Bq/l gas in the vaults. Typical ¹⁴C activity values of the headspace gases were <2.0 Bq/l gas in the drums and <1,000 Bq/l gas in the vaults.     

Hypergraph connectivity augmentation

Received May 1995 / Revised version received May 1996 Published online March 16, 1999     

Concentration-Dependent Interactions of Amphiphilic PiB Derivative Metal Complexes with Amyloid Peptides Aβ and Amylin**

Metal chelates targeted to amyloid peptides are widely explored as diagnostic tools or therapeutic agents. The attachment of a metal complex to amyloid recognition units typically leads to a decrease in peptide affinity. We show here that by separating a macrocyclic GdL chelate and a PiB targeting unit with a long hydrophobic C10 linker, it is possible to attain nanomolar affinities for both Aβ_1-40 (K_d=4.4 nm ) and amylin (K_d=4.5 nm ), implicated, respectively in Alzheimer's disease and diabetes. The Scatchard analysis of surface plasmon resonance data obtained for a series of amphiphilic, PiB derivative GdL complexes indicate that their Aβ_1-40 or amylin binding affinity varies with their concentration, thus micellar aggregation state. The GdL chelates also affect peptide aggregation kinetics, as probed by thioflavin-T fluorescence assays. A 2D NMR study allowed identifying that the hydrophilic region of Aβ_1-40 is involved in the interaction between the monomer peptide and the Gd³⁺ complex. Finally, ex vivo biodistribution experiments were conducted in healthy mice by using ¹¹¹In labeled analogues. Their pancreatic uptake, ∼3 %ID g⁻¹, is promising to envisage amylin imaging in diabetic animals.     

On the square root of a positive selfadjoint operator

We provide a short, elementary proof of the existence and uniqueness of the square root in the context of unbounded positive selfadjoint operators on real or complex Hilbert spaces.     

All regular Landsberg metrics are Berwald

This article negatively answers the long standing problem concerning the existence of non-Berwald Landsberg metrics.     

Singular Fibers in Elliptic Fibrations on the Rational Elliptic Surface

We determine the combinations of singular fibers a locally holomorphic elliptic fibration on the rational elliptic surface can admit. This problem has been answered for globally holomorphic elliptic fibrations by Persson and Miranda [12], [9]; we compare our methods and results to theirs. In particular, we find combinations of singular fibers which can be realized by locally holomorphic fibrations but not by globally holomorphic ones.     

On norm dependent positive definite functions

In the first part of the paper we prove a decomposition theorem for positive definite functions (Theorem 2.3) generalizing a result of de Leeuw and Glicksberg. Using this theorem, we then show (Theorem 3.1) that certain norm dependent positive definite functions are automatically continuous at every point different from zero.     

Continuous functions with impermeable graphs

We construct a Hölder continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We conclude that this function has impermeable graph—one of the key concepts introduced in this paper—and we present further examples of functions both with permeable and impermeable graphs. Moreover, we show that typical (in the sense of Baire category) continuous functions have permeable graphs. The first example function is subsequently used to construct an example of a continuous function on the plane which is intrinsically Lipschitz continuous on the complement of the graph of a Hölder continuous function with impermeable graph, but which is not Lipschitz continuous on the plane. As another main result, we construct a continuous function on the unit interval which coincides in a set of Hausdorff dimension 1 with every function of total variation smaller than 1 which passes through the origin.