Kemnitz’ conjecture revisited

AbstractA conjecture of Kemnitz remained open for some 20 years: each sequence of 4n-3 lattice points in the plane has a subsequence of length n whose centroid is a lattice point. It was solved independently by Reiher and di Fiore in the autumn of 2003. A refined and more general version of Kemnitz’ conjecture is proved in this note. The main result is about sequences of lengths between 3p-2 and 4p-3 in the additive group of integer pairs modulo p, for the essential case of an odd prime p. We derive structural information related to their zero sums, implying a variant of the original conjecture for each of the lengths mentioned. The approach is combinatorial

Privacy analysis of forward and backward untraceable RFID authentication schemes

In this paper, we analyze the rst known provably secure RFID authentication schemes that are designed to provide forward untraceability and backward untraceability: the L-K and S-M schemes. We show how to trace tags in the L-K scheme without needing to corrupt tags. We also show that if a standard cryptographic pseudorandom bit generator (PRBG) is used in the S-M scheme, then the scheme may fail to provide forward untraceability and backward untraceability. To achieve the desired untraceability features, we show that the S-M scheme can use a robust PRBG which provides forward security and backward security. We also note that the backward security is stronger than necessary for the backward untraceability of the S-M scheme

Mapping mechanism between density of states and ultraviolet-visible light absorption spectra

This paper constructs the mapping relation from density of states (DOS) to UV-vis spectra by using an ab initio perspective. Taking BiOIO3 semiconductor photocatalyst as an example, the experimental verification was also carried out. The optical response of the material considers the superposition benefits of all possible transitions. Directly using the difference between valence band maximum (VBM) and conduction band minimum (CBM) will lead to an underestimate of the energy band gap. This paper provides a new idea of linking the density functional theory (DFT) data with experiment phenomenon

Structurally Similar, Thermally Stable Copper(I), Silver(I), and Gold(I) Ethylene Complexes Supported by a Fluorinated Scorpionate

Treatment of Li­[PhBH₃] with excess 3-(C₂F₅)­PzH led to the B-phenylated tris­(pyrazolyl)­borate ligand as its lithium salt [PhB­(3-(C₂F₅)­Pz)₃]­Li. This ligand enabled the isolation of thermally stable group 11 metal ethylene adducts [PhB­(3-(C₂F₅)­Pz)₃]­M­(C₂H₄) (M = Au, Ag, Cu). They were characterized by spectroscopy and by X-ray crystallography. These ethylene adducts are structurally similar and feature three-coordinate trigonal-planar metal sites and a κ²-bonded tris­(pyrazolyl)­borate ligand. They are ideal for examining the trends involving ethylene complexes of the group 11 triad. The ethylene ¹³C NMR resonance of the [PhB­(3-(C₂F₅)­Pz)₃]­M­(C₂H₄) adducts in C₆D₁₂ appear at δ 58.9, 101.6, and 85.5 ppm, respectively, for M = Au, Ag, Cu. The M–C and M–N bond distances are largest in the silver complex and smallest in the copper complex

Structurally Similar, Thermally Stable Copper(I), Silver(I), and Gold(I) Ethylene Complexes Supported by a Fluorinated Scorpionate

Treatment of Li­[PhBH₃] with excess 3-(C₂F₅)­PzH led to the B-phenylated tris­(pyrazolyl)­borate ligand as its lithium salt [PhB­(3-(C₂F₅)­Pz)₃]­Li. This ligand enabled the isolation of thermally stable group 11 metal ethylene adducts [PhB­(3-(C₂F₅)­Pz)₃]­M­(C₂H₄) (M = Au, Ag, Cu). They were characterized by spectroscopy and by X-ray crystallography. These ethylene adducts are structurally similar and feature three-coordinate trigonal-planar metal sites and a κ²-bonded tris­(pyrazolyl)­borate ligand. They are ideal for examining the trends involving ethylene complexes of the group 11 triad. The ethylene ¹³C NMR resonance of the [PhB­(3-(C₂F₅)­Pz)₃]­M­(C₂H₄) adducts in C₆D₁₂ appear at δ 58.9, 101.6, and 85.5 ppm, respectively, for M = Au, Ag, Cu. The M–C and M–N bond distances are largest in the silver complex and smallest in the copper complex

Sequence alignment showing that the three key residues are highly conserved in the active site of the MYST HATs.

<p>The numbering is based on Tip60 alpha.</p

Gold(I) Chloride Coordinated 3-Hexyne

A linear gold(I) complex featuring a simple, unstrained alkyne has been synthesized using AuCl and 3-hexyne and characterized using X-ray crystallography. Density functional theory calculations show that σ donation from alkyne → Au dominates over the Au → alkyne π back-donation

Substrate-dependent activity curves for Tip60^ac (solid line) and Tip60^deac (dash line).

<p>(a): 500 µM H4-20 and varied concentration of [¹⁴C]-AcCoA ranging from 0 to 10 µM. Enzyme concentration was 0.005 µM. (b): 10 µM [¹⁴C]-AcCoA and varied concentration of H4-20 ranging from 0 to 1600 µM. Enzyme concentration was 0.01 µM.</p

Effects of C369 and E403 mutations on the autoacetylation of Tip60 protein.

<p>In each reaction, 5 µM Tip60 protein was incubated with 10 µM [¹⁴C]-AcCoA for 1 h. The reaction was quenched by protein loading dye. The mixtures were solved on 12% SDS-PAGE, dried in vacuum, visualized by phosphorimaging, and analyzed by QuantityOne software.</p

Effect of K327 mutation on HAT activity of Tip60.

<p>The HAT assays were performed at 30°C for 5 min and each reaction contained 10 µM [¹⁴C]-AcCoA, 200 µM H4-20, and 100 nM Tip60 protein.</p