On the Jager-Kaul theorem concerning harmonic maps

In 1983, Jager and Kaul proved that the equator map u*(x) = (x/\x\,0) : B-n --> S-n is unstable for 3 less than or equal to n less than or equal to 6 and a minimizer for the energy functional E(u, B-n) = integral B-n \del u\(2) dx in the class H-1,H-2(B-n, S-n) with u = u* on partial derivative B-n when n greater than or equal to 7. In this paper, we give a new and elementary proof of this Jager-Kaul result. We also generalize the Jager-Kaul result to the case of p-harmonic maps.

Heat flow for Yang-Mills-Higgs fields, part I

The Yang-Mills-Higgs field generalizes the Yang-Mills field. The authors establish the local existence and uniqueness of the weak solution to the heat flow for the Yang-Mills-Higgs field in a vector bundle over a compact Riemannian 4-manifold, and show that the weak solution is gauge-equivalent to a smooth solution and there are at most finite singularities at the maximum existing time.

Heat flow for the Yang-Mills-Higgs field and the Hermitian Yang-Mills-Higgs metric

For a parameter lambda > 0, we study a type of vortex equations, which generalize the well-known Hermitian-Einstein equation, for a connection A and a section phi of a holomorphic vector bundle E over a Kahler manifold X. We establish a global existence of smooth solutions to heat flow for a self-dual Yang-Mills-Higgs field on E. Assuming the lambda -stability of (E, phi), we prove the existence of the Hermitian Yang-Mills-Higgs metric on the holomorphic bundle E by studying the limiting behaviour of the gauge flow.

On the minimality of the p-harmonic map - x/vertical bar x vertical bar : B-n -> Sn-1

We prove that for any real number p with 1 p less than or equal to n - 1, the map x/\x\ : B-n --> Sn-1 is the unique minimizer of the p-energy functional integral(Bn) \delu\(p) dx among all maps in W-1,W-p (B-n, Sn-1) with boundary value x on phiB(n).

Truncation of the GABA(A)-receptor gamma 2 subunit in a family with generalized epilepsy with febrile seizures plus

Recent findings from studies of two families have shown that mutations in the GABA(A)-receptor gamma2 subunit are associated with generalized epilepsies and febrile seizures. Here we describe a family that has generalized epilepsy with febrile seizures plus (GEFS(+)), including an individual with severe myoclonic epilepsy of infancy, in whom a third GABA(A)-receptor gamma2-subunit mutation was found. This mutation lies in the intracellular loop between the third and fourth transmembrane domains of the GABA(A)-receptor gamma2 subunit and introduces a premature stop codon at Q351 in the mature protein. GABA sensitivity in Xenopus laevis oocytes expressing the mutant gamma2(Q351X) subunit is completely abolished, and fluorescent-microscopy studies have shown that receptors containing GFP-labeled gamma2(Q351X) protein are retained in the lumen of the endoplasmic reticulum. This finding reinforces the involvement of GABA(A) receptors in epilepsy.

A peptide-binding motif for I-A(g7), the class II major histocompatibility complex (MHC) molecule of NOD and Biozzi AB/H mice

The class II major histocompatibility complex molecule I-A(g7) is strongly linked to the development of spontaneous insulin-dependent diabetes mellitus (IDDM) in non obese diabetic mice and to the induction of experimental allergic encephalomyelitis in Biozzi AB/H mice. Structurally, it resembles the HLA-DQ molecules associated with human IDDM, in having a non-Asp residue at position 57 in its beta chain. To identify the requirements for peptide binding to I-A(g7) and thereby potentially pathogenic T cell epitopes, we analyzed a known I-A(g7)-restricted T cell epitope, hen egg white lysozyme (HEL) amino acids 9-27. NH2- and COOH-terminal truncations demonstrated that the minimal epitope for activation of the T cell hybridoma 2D12.1 was M12-R21 and the minimum sequence for direct binding to purified I-A(g7) M12-Y20/K13-R21. Alanine (A) scanning revealed two primary anchors for binding at relative positions (p) 6 (L) and 9 (Y) in the HEL epitope. The critical role of both anchors was demonstrated by incorporating L and Y in poly(A) backbones at the same relative positions as in the HEL epitope. Well-tolerated, weakly tolerated, and nontolerated residues were identified by analyzing the binding of peptides containing multiple substitutions at individual positions. Optimally, p6 was a large, hydrophobic residue (L, I, V, M), whereas p9 was aromatic and hydrophobic (Y or F) or positively charged (K, R). Specific residues were not tolerated at these and some other positions. A motif for binding to I-A(g7) deduced from analysis of the model HEL epitope was present in 27/30 (90%) of peptides reported to be I-A(g7)-restricted T cell epitopes or eluted from I-A(g7). Scanning a set of overlapping peptides encompassing human proinsulin revealed the motif in 6/6 good binders (sensitivity = 100%) and 4/13 weak or non-binders (specificity = 70%). This motif should facilitate identification of autoantigenic epitopes relevant to the pathogenesis and immunotherapy of IDDM.

Two estimates concerning asymptotics of the minimizations of a Ginzburg-Landau functional

We prove two asymptotical estimates for minimizers of a Ginzburg-Landau functional of the form integral(Omega) [1/2 \del u\(2) + 1/4 epsilon(2) (1 - \u\(2))(2) W (x)] dx.

A novel group of allenic hydrocarbons from five Australian (Melolonthine) beetles

Allenic hydrocarbons, previously unknown as a molecular class from insects, are represented by CH3(CH2)(n)-CH=. =CH-(CH2)(7)CH3 (n = 11-15, 17, 19) in several Australian melolonthine scarab beetles and with demonstrated (R)-chirality when n = 11 and 13.

The human temporal cortex: Characterization of neurons expressing nitric oxide synthase, neuropeptides and calcium-binding proteins, and their glutamate receptor subunit profiles

Immunocytochemical techniques were used to examine the distribution of neurons immunoreactive (-ir) for nitric oxide synthase (nNOS), somatostatin (SOM), neuropeptide Y (NPY), parvalbumin (PV), calbindin (CB) and calretinin (CH), in the inferotemporal gyros (Brodmann's area 21) of the human neocortex. Neurons that colocalized either nNOS or SOM with PV, CB or CR were also identified by double-labeling techniques. Furthermore, glutamate receptor subunit profiles (GluR1, GluR2/3, GluR2/4, GluR5/6/7 and NMDAR1) were also determined for these cells. The number and distribution of cells containing nNOS, SOM, NPY, PV, CB or CR differed for each antigen. In addition, distinct subpopulations of neurons displayed different degrees of colocalization of these antigens depending on which antigens were compared. Moreover, cells that contained nNOS, SOM, NPY, PV, GB or CR expressed different receptor subunit profiles. These results show that specific subpopulations of neurochemically identified nonpyramidal cells may be activated via different receptor subtypes. As these different subpopulations of cells project to specific regions of pyramidal calls, facilitation of subsets of these cells via different receptor subunits may activate different inhibitory circuits. Thus, various distinct, but overlapping, inhibitory circuits may act in concert in the modulation of normal cortical function, plasticity and disease.

Bis(diethylenetriamine)mercury(II) bis(thiocyanate)

Mercury(II) in the title compound, [Hg(C4H13N3)2](SCN)2, is six-coordinated with two diethylenetriamine (dien) ligands in a sym-facial configuration. The complex cation has a twofold axis of symmetry, and the secondary amine groups are in trans positions.