Linearly embeddable designs

We address the problem of determining when a plane algebraic cubic curve is complete as an (n, 3)-arc in \(\mathrm {PG}(2,q)\). Theoretical results are given for absolutely irreducible singular cubic curves, while computer based results are given for \(q\le 81\).     

Extremes of Gaussian processes with smooth random expectation and smooth random variance

Let ξ(t), t ∈ [0, T],T > 0, be a Gaussian stationary process with expectation 0 and variance 1, and let η(t) and μ(t) be other sufficiently smooth random processes independent of ξ(t). In this paper, we obtain an asymptotic exact result for P(sup _t∈[0,T](η(t)ξ(t) + μ(t)) > u) as u→∞.     

Diastereoselective hydrogenation of α,β-unsaturated but-2-enamides to access the chiral 3-(p-tolyl) butanoic acids

An alternative methodology for the synthesis of chiral 3-(p-tolyl) butanoic acids is presented. This was accomplished through the diastereoselective hydrogenation reaction of different chiral N-3-(p-tolyl) but-2-enamides, using Pd/C in EtOH, to produce the corresponding chiral N-3-(p-tolyl) butanamides with high chemical yields and moderate diastereomeric ratios. Removal of the chiral auxiliary from N-3-(p-tolyl) butanamides gave the respective enantiomerically pure acids.     

New acetylated flavone C-glycosides from Iris lactea

Chemical investigation of the aerial parts of Iris lactea afforded three new flavone C-glycosides including 4?-O-acetyl-embinin (1), 2?,4?-O-diacetyl-embinin (2) and 6″,4?-O-diacetyl-embinin (3) along with the known analogue embinin (4). Their structures were elucidated by 1D and 2D NMR spectroscopic analysis as well as by HRESIMS data. The sugars were characterized following acid hydrolysis of the respective glycosides and TLC analysis compared to known standards. Duplicated signals can be observed in the NMR spectra, indicating the presence of rotamers caused by rotational hindrance around the glycosyl-flavone CC linkage. All isolated compounds were tested for their antimicrobial and cytotoxic activities but found to be inactive.     

Unprecedented acid-catalyzed Wurtz-type coupling of meso-bromoindodicarbocyanine dyes

meso-Bromosubstituted indodicarbocyanine dyes produce dimeric molecules, together with the debrominated species, under acid catalysis. The relationship between the dimerization and hydrodebromination routes depends on the aryl substitution of the dyes. A possible reaction mechanism is also proposed.     

The rheology of hydrogels based on chitosan–gelatin (bio)polyelectrolyte complexes

Influence of the chitosan concentration in the low-concentrated acidic hydrogels formed by (bio)polyelectrolyte chitosan–gelatin complexes (at a constant gelatin concentration of 1%) was studied by shearing in steady flow and linear oscillations. These complexes, including native gelatin, demonstrate clearly expressed viscoelastic properties. Viscoelastic properties correlated well with the non-Newtonian behavior of hydrogels (according to the Cox–Merz rule). Increasing the chitosan concentration (from 0.1% to 0.6%) results in exponential growth of the apparent viscosity, yield stress, and storage modulus. However, a further increase in chitosan concentration to 0.8% leads to a reduction in these rheological parameters due to the electrostatic repulsion of similarly charged polyelectrolyte complexes under the high concentration of these complexes. The macro-rheological properties of chitosan–gelatin gels are mainly determined by the colloidal structure of sol-precursors in solutions. The yield stress dependence on the radius of the dispersed particles is of square type. Electron photomicrographs showed that the introduction of even small quantities of chitosan leads to radical changes in the supramolecular structure of the gelatin gel.     

Quasi-symmetric 2-(64,24,46) designs derived from AG(3,4)

This paper completes the enumeration of quasi-symmetric 2-$(64,24,46)$ designs supported by the dual code $C^{\perp }$ of the binary linear code $C$ spanned by the lines of $AG(3,4)$, initiated in Rodrigues and Tonchev (2015). It is shown that $C^{\perp }$ supports exactly 30,264 nonisomorphic quasi-symmetric 2-$(64,24,46)$ designs. The automorphism groups of the related strongly regular graphs are computed.     

Locally 2-fold symmetric manifolds are locally symmetric

A manifold is locally k-fold symmetric if for any point and any k-dimensional vector subspace tangent to this point, there exists a local isometry such that this point is a fixed point and the differential of the isometry restricted to that k-dimensional vector subspace is minus the identity. We show that for \(k \ge 2\), Riemannian, pseudoriemannian, and Finslerian locally k-fold symmetric manifolds are locally symmetric.     

Optimal signaling with cheap talk and money burning

We study Sender-optimal signaling equilibria with cheap talk and money-burning. Under general assumptions, the Sender never uses money-burning to reveal all states, but always wants to garble information for at least some states. With quadratic preferences and any log-concave density of the states, optimal communication is garbled for all states: money-burning, if used at all, is used to adjust pooling intervals. This is illustrated by studying in depth the well-known uniform-quadratic case. We also show how the presence of a cost of being “caught unprepared” that gives rise to a small change in a common assumption on the Receiver’s utility function makes full revelation through money-burning Sender-optimal.     

Improved lower bounds for the online bin stretching problem

We use game theory techniques to automatically compute improved lower bounds on the competitive ratio for the bin stretching problem. Using these techniques, we improve the best lower bound for this problem to 19/14. We explain the technique and show that it can be generalized to compute lower bounds for any online or semi-online packing or scheduling problem.