Multiple solutions for Neumann and periodic problems with singular ?-Laplacian

We use the critical point theory for convex, lower semicontinuous perturbations of C¹-functionals to establish existence of multiple radial solutions for some one parameter Neumann problems involving the operator . Similar results for periodic problems are also provided.     

On the Birch and Swinnerton-Dyer conjecture for abelian varieties attached to Hilbert modular forms

In this paper we prove that if the Birch and Swinnerton-Dyer conjecture holds for abelian varieties attached to Hilbert newforms of parallel weight 2 with trivial central character, then the Birch and Swinnerton-Dyer conjecture holds for abelian varieties attached to Hilbert newforms of parallel weight 2 with trivial central character regarded over arbitrary totally real number fields.     

Numerical block diagonalization of matrix *-algebras with application to semidefinite programming

Semidefinite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms. In this paper we propose a new pre-processing technique for SDP instances that exhibit algebraic symmetry. We present computational results to show that the solution times of certain SDP instances may be greatly reduced via the new approach.     

Metallophilic bonding and agostic interactions in gold(I) and silver(I) complexes bearing a thiotetrazole unit

Gold(I) and silver(I) complexes of 1-methyl-5-thio-tetrazole (1) have been prepared and the coordination chemistry of this ligand toward metal-phosphine frameworks has been explored. As indicated by IR and Raman data, ligand 1 is deprotonated and the resulted anion acts as a bidentate (S,N)-tetrazole-5-thiolato unit in the new gold(I) complexes, [Au(SCN(4)Me)(PPh(3))] (2), [{Au(SCN(4)Me)}(2)(μ-dppm)] (3), and [{Au(SCN(4)Me)}(2)(μ-dppe)] (4), while it is coordinated only through the sulfur atom as its neutral tetrazole-5-thione form in the silver(I) derivative, [Ag(HSCN(4)Me)(PPh(3))](2)(OTf)(2) (5). Further characterization of the new compounds was performed using multinuclear ((1)H, (13)C, (31)P, (19)F) NMR spectroscopy, mass spectrometry, and DSC measurements. Single-crystal X-ray diffraction studies revealed basically linear P-M-S arrangements in complexes 3-5. The bidentate (S,N) coordination pattern results in a T-shaped (S,N)PAu core in 3 and 4, whereas, in 5, a similar coordination geometry is achieved in the dimer association based on S-bridging ligand 1. Herein, weak (C)H···Au and (C)H···Ag agostic interactions were observed. An intramolecular Au···Au contact occurs in 3, while in 4 intermolecular aurophilic bonds lead to formation of a chain polymer. An intermolecular Ag···Ag contact is also present in the dimer unit of 5. Low-temperature (31)P NMR data for 5 evidenced the presence of monomer and dimer units in solution. Theoretical calculations on model of the complexes 2 and 4 are consistent with the geometries found by X-ray diffraction studies.     

4‐(Azulen‐1‐yl) six‐membered heteroaromatics substituted with thiophen‐2‐yl or furan‐2‐yl moieties in 2 and 6 positions

Pyranylium perchlorates with azulen‐1‐yl moiety in 4‐position and thiophen‐2‐yl or furan‐2‐yl in 2 and 6‐positions were obtained by the substitution of 4‐chloro corresponding salts with azulenes. The pyranylium salts are used as starting materials for the synthesis of pyridine and pyridinium salts. The products were characterized and for pyridines pKa was spectroscopically determined. Several attempts were made for pyridine complexation with metal cations as Hg²⁺ or Ag⁺. J. Heterocyclic Chem., (2011).     

Synthesis and characterization of [PW11O39Ir(H2O)]4-: successful incorporation of Ir into polyoxometalate framework and study of the substitutional lability at the Ir(III) site

The first Keggin-type heteropolyanion, [PW(11)O(39)Ir(H(2)O)](4-) (1), was synthesized by hydrothermal reaction from two different polytungstate precursors and [IrF(6)](2-). It was isolated as (Bu(4)N)(4)[PW(11)O(39)Ir(H(2)O)] (1a), which was completely characterized by multinuclear (31)P and (183)W NMR, ESI-mass spectrometry and cyclic voltammetry. A rapid screening methodology to ascertain the intrinsic substitutional lability at the Ir site is also presented, based on ESI-MS.     

Assembly of 2D ionic layers by reaction of alkali halides with the organic electrophile 7,7,8,8-tetracyano-p-quinodimethane (TCNQ)

Sublimation of alkali halides (NaCl and LiCl) onto a pre-assembled hydrogen-bonded layer of TCNQ on Au(111) resulted in the formation of 2D ionic layers via a direct charge-transfer reaction without involvement of the substrate. The presented approach allows for the fabrication of different ionic layers, decoupled from the substrate and offering new, potentially interesting properties.     

Cluster analysis of an Ising-Preisach interacting particle system

The paper deals with the analysis of clusters' size in diverse magnetization states of a system of ferromagnetic particles organized in a perfect 2D array with all the anisotropy axes perpendicular to the plane (perpendicular medium) following the evolution of the clusters in correlation with various parameters like applied field or interaction strength. We present numerical simulations for a two-level Ising-type model each magnetic entity being characterized by a Stoner-Wohlfarth nonlinear energy barrier and a rectangular hysteresis loop (Ising-Preisach hysteron). In the simulations we took into account, the long-range inter-particle magnetostatic interactions in an attempt to mimic as accurately as possible with a still simple model, materials like Bit-Patterned media that are now considered as good candidates for the magnetic memories of the future.     

Direct probes of linearly polarized gluons inside unpolarized hadrons

We show that linearly polarized gluons inside unpolarized hadrons can be directly probed in jet or heavy quark pair production in electron-hadron collisions. We discuss the simplest cos2? asymmetries and estimate their maximal value, concluding that measurements of the unknown linearly polarized gluon distribution in the proton should be feasible in future Electron-Ion Collider or Large Hadron electron Collider experiments. Analogous asymmetries in hadron-hadron collisions suffer from factorization breaking contributions and would allow us to quantify the importance of initial- and final-state interactions.