On unitals in PG(2,q^2) stabilized by a homology group

The linear collineation group of a classical unital of $\mathrm{PG}(2,q^2)$ contains a group of homologies of order $q+1$ . In this paper we prove that if $\mathcal{U }$ is a unital of PG $(2,q^2)$ stabilized by a homology group of order $q+1$ and $q$ is a prime number, then $\mathcal{U }$ is classical.     

3-Nets realizing a group in a projective plane

In a projective plane $\mathit{PG}(2,\mathbb{K})$ defined over an algebraically closed field $\mathbb{K}$ of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky (Compos. Math. 140:1614–1624, 2004), arises from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky (Adv. Math. 219:672–688, 2008), comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzúa’s 3-nets (Adv. Geom. 10:287–310, 2010) realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds in characteristic p>0 apart from three possible exceptions $\rm{Alt}_{4}$ , $\rm{Sym}_{4}$ , and $\rm{Alt}_{5}$ . Motivation for the study of finite 3-nets in the complex plane comes from the study of complex line arrangements and from resonance theory; see (Falk and Yuzvinsky in Compos. Math. 143:1069–1088, 2007; Miguel and Buzunáriz in Graphs Comb. 25:469–488, 2009; Pereira and Yuzvinsky in Adv. Math. 219:672–688, 2008; Yuzvinsky in Compos. Math. 140:1614–1624, 2004; Yuzvinsky in Proc. Am. Math. Soc. 137:1641–1648, 2009).     

Dysregulation of chemo-cytokine production in schizophrenic patients versus healthy controls

Background  

The exact cause of schizophrenia is not known, although several aetiological theories have been proposed for the disease, including developmental or neurodegenerative processes, neurotransmitter abnormalities, viral infection and immune dysfunction or autoimmune mechanisms. Growing evidence suggests that specific cytokines and chemokines play a role in signalling the brain to produce neurochemical, neuroendocrine, neuroimmune and behavioural changes. A relationship between inflammation and schizophrenia was supported by abnormal cytokines production, abnormal concentrations of cytokines and cytokine receptors in the blood and cerebrospinal fluid in schizophrenia. Since the neuropathology of schizophrenia has recently been reported to be closely associated with microglial activation we aimed to determined whether spontaneous or LPS-induced peripheral blood mononuclear cell chemokines and cytokines production is dysregulated in schizophrenic patients compared to healthy subjects. We enrolled 51 untreated first-episode schizophrenics (SC) and 40 healthy subjects (HC) and the levels of MCP-1, MIP-1α, IL-8, IL-18, IFN-γ and RANTES were determined by Elisa method in cell-free supernatants of PBMC cultures.     

Twist points of planar domains

We establish a potential theoretic approach to the study of twist points in the boundary of simply connected planar domains.

     

One-step synthesis of labeled sugar nucleotides for protein O-GlcNAc modification studies by chemical function analysis of an archaeal protein

Herein we present the chemical function analysis of a recombinant sugar nucleotidyltransferase from the hyperthermophile Pyrococcus furiosus and its use in the one-pot synthesis of chloroacetyl- and alkyne-tagged analogues of uridinediphospho-N-acetylglucosamine (UDP-GlcNAc). The gene was originally annotated as a glucose-1-phosphate deoxythymidylyltransferase; however, kinetic analysis of a panel of sugar-1-phosphates with the protein shows that it is better described as a bifunctional protein that synthesizes UDP-GlcNAc from glucosamine-1-phosphate and acetyl coenzyme A (CoA). A new mass-spectrometry-based assay for the rapid analysis of the acyltransferase activity demonstrates that the enzyme can also accept cheaper truncated N-acetylcysteamine thioester substrates in place of the natural acetyl CoA. The enzyme can tolerate alkyne or chloride substitutions in the acyl moiety, thereby allowing the facile synthesis of tagged sugar nucleotides for future use in protein O-GlcNAc modification studies.     

The hydration of sodium dehydrocholate micelles

The hydration of micellised sodium dehydrocholate molecules was determined by viscosity measurements. It was found that there are 39 water molecules for each micellised surfactant molecule. About ten water molecules may be attributed to the hydration of the sodium carboxylate group. By assignation of two water molecules to each of the three carbonyl groups, the total hydration of a micellised sodium dehydrocholate molecule was estimated as about 16 water molecules. The remaining 23 water molecules per micellised sodium dehydrocholate molecule may be attributed to water trapped in the structure of micelles.     

Photophysical properties of ruthenium(II) tris(2,2'-bipyridine) complexes bearing conjugated thiophene appendages

A small series of ruthenium(II) tris(2,2'-bipyridine) complexes has been synthesized in which ethynylated thiophene residues are attached to one of the 2,2'-bipyridine ligands. The photophysical properties depend on the conjugation length of the thiophene-based ligand, and in each case, dual emission is observed. The two emitting states reside in thermal equilibrium at ambient temperature and can be resolved by emission spectral curve-fitting routines. This allows the properties of the two states to be evaluated in both fluid butyronitrile solution and a transparent KBr disk. It is concluded that both emitting states are of metal-to-ligand charge-transfer (MLCT) character, and despite the presence of conjugated thiophene residues, there is no indication for a low-lying pi,pi*-triplet state that promotes nonradiative decay of the excited-state manifold. A key feature of these systems is that the conjugation length imposed by the thiophene-based ligand helps to control the rate constants for both radiative and nonradiative decay from the two MLCT triplet states.