Torification and factorization of birational maps

Building on work of the fourth author and Morelli's work, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field of characteristic zero is a composite of blowings up and blowings down with nonsingular centers.

     

A recyclable chiral Ru catalyst for enantioselective olefin metathesis. Efficient catalytic asymmetric ring-opening/cross metathesis in air

The synthesis and structure of a new chiral bidentate imidazolinylidene ligand and a derived chiral Ru-based carbene are disclosed. The Ru complex is stereogenic at the metal center; it can be prepared in >98% diastereoselectivity and purified by silica gel chromatography with undistilled solvents. The air-stable Ru complex efficiently catalyzes ring-closing and ring-opening metathesis and is recyclable. The chiral complex is highly effective (0.5-10 mol % loading) in promoting enantioselective ring-opening/cross metathesis reactions (up to >98% ee). These enantioselective transformations can be effected in air, with unpurified solvent and with substrates that would only polymerize with Mo-based catalysts.     

Peculiarities of the magnetic,galvanomagnetic, elastic,and magnetoelastic properties of Sm<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>x</Subscript>MnO<Subscript>3</Subscript> manganites

Manganites of the Sm1?xSr_xMnO₃ system (x=0.33, 0.4, and 0.45) possess giant negative values of the magnetoresistance Δρ/ρ and the volume magnetostriction ω near the Curie temperature T_C. In the compound with x=0.33, the isotherms of Δρ/ρ, ω, and magnetization σ exhibit smooth variation and do not reach saturation up to maximum magnetic field strengths (120 kOe) studied (according to the neutron diffraction data, this substance comprises a ferromagnetic (FM) matrix with distributed clusters of a layered antiferromagnetic (AFM) structure of the A type). In the compounds with x=0.4 and 0.45 containing, besides the FM matrix and A-type AFM phase, a charge-ordered AFM phase of the CE type (thermally stable to higher temperatures as compared to the A-type AFM and the FM phases), the same isotherms measured at T ≥ T_C show a jumplike increase in the interval of field strengths between H_c1 and H_c2 and then reach saturation. In the interval H_c1 > H > H_c2, the σ, ω, and Δρ/ρ values exhibit a metastable behavior. At temperatures above T_C, the anisotropic magnetostriction changes sign, which is indicative of rearrangements in the crystal structure. The giant values of ω and Δρ/ρ observed at T ≥ T_C for all compounds, together with excess (relative to the linear) thermal expansion and a maximum on the ρ(T) curve, are explained by the phenomenon of electron phase separation caused by a strong s-d exchange. The giant values of magnetoresistance and volume magnetostriction (with ω reaching ～10^?3) are attributed to an increase in the volume of the FM phase induced by the applied magnetic field. In the compound with x=0.33, this increase proceeds smoothly as the FM phase grows through the FM layers in the A-type AFM phase. In the compounds with x=0.4 and 0.45, the FM phase volume increases at the expense of the charge-ordered CE-type AFM structure (in which spins of the neighboring manganese ions possess an AFM order). The jumps observed on the σ(H) curves, whereby the magnetization σ reaches ～70% of the value at T=1.5 K, are indicative of a threshold character of the charge-ordered phase transition to the FM state. Thus, the giant values of ω and Δρ/ρ are inherent in the FM state, appearing as a result of the magnetic-field-induced transition of the charge-ordered phase to the FM state, rather than being caused by melting of this phase.     

On parallel asynchronous high-order solutions of parabolic PDEs

In achieving significant speed-up on parallel machines, a major obstacle is the overhead associated with synchronizing the concurrent processes. This paper presents high-orderparallel asynchronous schemes, which are schemes that are specifically designed to minimize the associated synchronization overhead of a parallel machine in solving parabolic PDEs. They are asynchronous in the sense that each processor is allowed to advance at its own speed. Thus, these schemes are suitable for single (or multi) user shared memory or (message passing) MIMD multiprocessors. Our approach is demonstrated for the solution of the multidimensional heat equation, of which we present a spatial second-order Parametric Asynchronous Finite-Difference (PAFD) scheme. The well-known synchronous schemes are obtained as its special cases. This is a generalization and expansion of the results in [5] and [7]. The consistency, stability and convergence of this scheme are investigated in detail. Numerical tests show that although PAFD provides the desired order of accuracy, its efficiency is inadequate when performed on each grid point.In an alternative approach that uses domain decomposition, the problem domain is divided among the processors. Each processor computes its subdomain mostly independently, while the PAFD scheme provides the solutions at the subdomains' boundaries. We use high-order finite-difference implicit scheme within each subdomain and determine the values at subdomains' boundaries by the PAFD scheme. Moreover, in order to allow larger time-step, we use remote neighbors' values rather than those of the immediate neighbors. Numerical tests show that this approach provides high efficiency and in the case which uses remote neighbors' values an almost linear speedup is achieved. Schemes similar to the PAFD can be developed for other types of equations [3].This research was supported by the fund for promotion of research at the Technion.     

A study of the reactions π−p → K1X, K1Σ and K1Y11(1385) at 3.93 GeV/c

We have investigated the final states K¹⁰(890)Σ, $\text{K}{}^{10}\text{(890)Σ}{}^0$ and K¹⁰(890) Y₁¹⁰(1385) produced in π^?p interactions at 3.93 GeV/c. We present the differential cross sections and spin density matrix elements for the resonances as functions of momentum transfer, as well as the gL and Σ⁰ polarizations. The Σ⁰ polarization is found to be positive and maximal. An amplitude analysis is performed for the K¹ Λ and $\text{K}{}^1\text{Σ}{}^0$ reactions, and it is found that one natural parity transversity amplitude is dominant for the latter.     

Critical behavior of light in mode-locked lasers

Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.     

Faraday rotation in a two-dimensional photonic crystal with a magneto-optic defect

We study the magneto-optic (MO) Faraday rotation in a two-dimensional square-lattice photonic crystal with a central MO defect layer in the optical wavelength range. We show that when a TM plane wave is incident upon a photonic crystal, an enhancement of Faraday rotation takes place in a region where a resonance peak appears in the photonic bandgap. In this region the mode conversion is high.     

Cu-catalyzed asymmetric allylic alkylations of aromatic and aliphatic phosphates with alkylzinc reagents. An effective method for enantioselective synthesis of tertiary and quaternary carbons

Efficient enantioselective Cu-catalyzed allylic alkylations of aromatic and aliphatic allylic phosphates bearing di- and trisubstituted olefins are disclosed. Enantioselective C-C bond forming reactions are promoted in the presence of 10 mol % readily available chiral amino acid-based ligand (5 steps, 40% overall yield synthesis) and 5 mol % (CuOTf)2 x C6H6. Reactions deliver tertiary and quaternary stereogenic carbon centers regioselectively and in 78-96% ee. Data regarding the effect of variations in ligand structure on the efficiency and enantioselectivity of the alkylation process, as well as a mechanistic working model, are presented. The suggested model involves a dual role for the chiral Cu complex: association of the Cu(I) center to the olefin is facilitated by a two-point binding between the carbonyl of the ligand's amide terminus and the P=O of the substrate.