Killing spinors on Lorentzian manifolds

The aim of this paper is to describe some results concerning the geometry of Lorentzian manifolds admitting Killing spinors. We prove that there are imaginary Killing spinors on simply connected Lorentzian Einstein–Sasaki manifolds. In the Riemannian case, an odd-dimensional complete simply connected manifold (of dimension n≠7) is Einstein–Sasaki if and only if it admits a non-trivial Killing spinor to . The analogous result does not hold in the Lorentzian case. We give an example of a non-Einstein Lorentzian manifold admitting an imaginary Killing spinor. A Lorentzian manifold admitting a real Killing spinor is at least locally a codimension one warped product with a special warping function. The fiber of the warped product is either a Riemannian manifold with a real or imaginary Killing spinor or with a parallel spinor, or it again is a Lorentzian manifold with a real Killing spinor. Conversely, all warped products of that form admit real Killing spinors.     

IsoscalarE2 transition strengths in 10≦A≦48 nuclei

Electric quadrupole transition strengths for the 2 ₁ ⁺ ,T=1→0 ₁ ⁺ ,T=1γ-decay branches are summarized for 10≦A≦42 nuclei. In¹⁰B the corresponding branch has been remeasured by use of the⁹Be(p, γ)¹⁰B resonance reaction atE _p =320 keV; an upper limit of 0.6% is found. The variation of theE2 strengths within each individualT=1 isobaric multiplet reveals the particleor hole-character of the levels involved. The isoscalar 2 ₁ ⁺ →0 ₁ ⁺ transition strengths in 10≦A≦48 nuclei vary between 2 and 20 Weißkopf units showing drastic shell effects. Results for the ratio of neutron and proton matrix elements deduced from analogγ-decay studies and from inelastic pion scattering are compared.     

Spectral curves for Cauchy-Riemann operators on punctured elliptic curves

We show that one can define a spectral curve for the Cauchy-Riemann operator on a punctured elliptic curve under appropriate boundary conditions. The algebraic curves thus obtained arise, for example, as irreducible components of the spectral curves of minimal tori with planar ends in ?³. It turns out that these curves coincide with the spectral curves of certain elliptic KP solitons studied by Krichever.     

Salicylaldiminato derivatives of cyclotriveratrylene: flexible strategy for new rim-metalated CTV complexes

The amino-derivatized cyclotriveratrylene analogue, triaminotrimethoxytribenzocyclononene [CTV(NH2)3(OMe)3], 1, is readily converted into triply substituted imine compounds [CTV(sal)3(OMe)3], 2, in high yield by treatment of the acid salt of 1 with a variety of substituted salicylaldehydes. Cleavage of the protecting methoxy group generates the tristridentate chelate CTV(sal)3(OH)3, 3, which is readily converted into new rim-metalated species CTV(sal)3(ONiL)3, 4a (a, L = pyrrolidine; b, L = 1-n-butyl-imidazole). Taken together, these results illustrate the remarkable synthetic flexibility that is possible for the CTV-based metal complexes by alteration of the metal, the salicylaldehyde component of the CTV ligand, or the ancillary ligands coordinated to the metal.     

Effect of Pr-Ca substitution on the transport and magnetic behavior of LaMnO3 perovskite

The effect of simultaneous substitution of a fluctuating cation and a divalent cation in LaMnO₃ perovskite modifies the properties of the material to exhibit large valence colossal magnetoresistance (CMR) effect. A good example of these properties is (La_1−2x Pr _x Ca _x )MnO₃ (LPCMO) type CMR material. In this communication it is reported that, with the increase in x (for x=0.1, 0.15, 0.2), the T _c varies between 100 and 120 K with improvisation in metal-insulator transition. Interestingly, resistance increases with x from few hundred ohms to few kilo ohms with corresponding decrease in the unit cell volume. The results of the studies using X-ray diffraction (XRD), electrical resistivity, magnetoresistance and ac susceptibility measurements on LPCMO samples for understanding the structural, transport and magnetic properties are discussed in detail.     

A robust optimization approach to wine grape harvesting scheduling

Optimization models are increasingly being used in agricultural planning. However, the inherent uncertainties present in agriculture make it difficult. In recent years, robust optimization has emerged as a methodology that allows dealing with uncertainty in optimization models, even when probabilistic knowledge of the phenomenon is incomplete. In this paper, we consider a wine grape harvesting scheduling optimization problem subject to several uncertainties, such as the actual productivity that can be achieved when harvesting. We study how effective robust optimization is solving this problem in practice. We develop alternative robust models and show results for some test problems obtained from actual wine industry problems.     

The Chiral Trimer and a Metastable Chiral Dimer of Achiral Hexafluoroisopropanol: A Multi‐Messenger Study

1,1,1,3,3,3‐hexafluoro‐propan‐2‐ol aggregates preferentially into an achiral dimer of achiral monomers, but the trimer is found to prefer three metastable chiral monomer units arranged into a strained OH???O hydrogen‐bonded ring, which is reinforced by secondary CH???FC interactions. This is shown by a combination of infrared, microwave, and Raman spectroscopy in supersonic jet expansions and supported by high‐level quantum chemical calculations. It involves an activation of the monomers by >15 kJ mol^?1, clearly driven by the much stronger hydrogen‐bond interaction available to the gauche and even more to the cis monomer units.