Lang maps and Harris’s conjecture

We show that any variety in characteristic 0 possesses a universal dominant rational map, which we callthe Lang map, to a variety of general type. We discuss a conjecture of J. Harris regarding the relation between rational points and Lang maps. Partially supported by NSF grant DMS-9503276.     

Microheterogeneity of benzene solutions of cyclohexane, 1,4-dioxane,and morpholine

Data obtained in molecular light scattering, adiabatic compressibility, and molar volume studies of benzene solutions of cyclohexane, 1,4-dioxane, and morpholine were used to suggest a model of the structure of these solutions and show that microheterogeneity of solutions was caused by the presence of agglomerates comprising benzene molecules in the benzene-cyclohexane system and conglomerates including heteromolecular interactions in the other systems.     

Novel vinyl phosphonates and vinyl boronates by halogenation, allylation, and propargylation of alpha-boryl- and alpha-phosphonozirconacyclopentenes

[structure: see text] Alpha-phosphonozirconacyclopentenes or alpha-borylzirconacyclopentenes react by bromination, iodination, allylation, and propargylation to generate unique vinyl boronates and vinyl phosphonates not obtainable by other methods. The reaction proceeds in two steps, with both high regio- and stereoselectivity. With the vinyl boronates, the Zr-Csp2 bond is initially cleaved by 1 equiv of electrophile. With the phosphonates, either the Zr-Csp2 bond (allyl bromide, Br(2)) or the Zr-Csp3 bond (I(2), propargyl bromide) may be initially cleaved. The addition of a second equivalent of an electrophile results in disubstitution.     

Analysis of experimental data on the key thermonuclear reactions going within the low energy range

A comparative analysis of experimental data on hydrogen and helium isotope interaction with deuterons and tritons at low energy is performed. If the energy of an incident particle falls to several keV, the astrophysical factor S(E) rises sharply, indicating that there is an electron screening effect for such interaction. The values of electron screening potentials and enhancement factors are given for key thermonuclear reactions. It is important to allow for the electron screening effect in calculations performed during astrophysical research and in designing different thermonuclear facilities.     

Relationship between spontaneous generation of voltage and structural features in a single crystal of Pr0.6Ca0.4MnO3

Spontaneous generation of electrical voltage U was found for the perovskite-like single crystal of Pr_0.6Ca_0.4MnO₃, wherein the charge and orbital orderings occur at T _CO = 240 K and the antiferromagnetic one occurs at the Neel point T _N = 174 K. With decreasing the temperature, the U value increases first slowly (in the temperature range of 300 K-T _CO) and then more rapidly (T _CO-T _N). Starting from T _N, U increases exponentially and, at 85 K, reaches the value of 115 mV (in the ab plane) and 6.5 mV (along the c axis). The magnetic field has a different effect on the U value in different temperature ranges: in the temperature range of 85–130 K, it decreases U and, in the range of 130–240 K, increases U. The spontaneous voltage is thought to be caused by the existence of ferromagnetic and charge-orbital-ordered clusters of different topology in the sample. The latter clusters have own features and their structure are described by the non-centrosymmetric space group P2₁ nm.     

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.

     

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.