Maximin share and minimax envy in fair-division problems

For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the values are probability measures) maximin-share and minimax-envy inequalities are derived for both continuous and discrete measures. The tools used include classical and recent basic convexity results, as well as ad hoc constructions. Examples are given to show that the envy-minimizing criterion is not Pareto optimal, even if the values are mutually absolutely continuous. In the discrete measure case, sufficient conditions are obtained to guarantee the existence of envy-free partitions.     

CuPc molecules adsorbed on Au(1 1 0)-(1 × 2): growth morphology and evolution of valence band states

We present the growth morphology, the long-range ordering, and the evolution of the valence band electronic states of ultrathin films of copper phthalocyanine (CuPc) deposited on the Au(1 1 0)-(1 × 2) reconstructed surface, as a function of the organic molecule coverage. The low energy electron diffraction patterns present a (5 × 3) reconstruction from the early adsorption stages. High-resolution UV photoelectron spectroscopy data show the disappearance of the Au surface states related to the (1 × 2) reconstruction, and the presence of new electronic features related to the molecule-substrate interaction and to the CuPc molecular states. The CuPc highest occupied molecular orbital gradually emerges in the valence band, while the interface electronic states are quenched, upon increasing the coverage.     

Gamow Vectors in Exactly Solvable Models

Through two examples: the Friedrichs model and a particular case of central potential scattering, we illustrate the way of constructing Gamow vectors.     

Variety of LaSrMnO structures induced by growth conditions and laser irradiation

Crystallographic phase transitions in perovskite-like LaSrMnO metallic oxides are studied. The transitions are induced when internal stresses generated during film synthesis (at temperatures between 450 and 730°C) vary (decrease or increase) upon subsequent irradiation by a KrF laser emitting in the UV range. As the synthesis temperature T _s grows, the rhombohedral-to-orthorhombic phase transition occurs at 650–670°C. The resistivity is shown to be either temperature-independent, ρ(T)=const, at T<T _crit, or varies and reaches a maximum, ρ(T)=ρ_max, at the Curie temperature T _c. Optical transmission spectra taken at photon energies ℏω=0.5–2.5 eV exhibit both a high (0.8–0.9) and low (0.1–0.3) transmission coefficient t, depending on the synthesis temperature. As follows from X-ray diffraction data, the laser irradiation causes a phase transition only in LaSrMnO films grown at T _s<650°C. Phases of different size scales appear: the long-range-order orthorhombic matrix and mesoscopic-range-order rhombohedral clusters are observed in the films grown at T _s=450–550°C and the rhombohedral matrix with orthorhombic clusters, in the films grown at T _s=550–650°C.     

Magnetic hysteresis of the magnetoresistance and the critical current density in polycrystalline YBa2Cu3O7−δ–Ag superconductors

A systematic study of the magnetic hysteresis in transport properties of polycrystalline YBa₂Cu₃O_7−δ–Ag compounds has been made based on two kinds of measurements at 77 K and under applied magnetic fields up to 30 mT: critical current density J_c(B_a) and magnetoresistance R(B_a). The R(B_a) curves show a minimum in their decreasing branch occurring at B=B_min which was found to be both the excitation current I_ex and the maximum applied magnetic field B_am dependent. In addition, for a certain value of B_am>5 mT, we have observed that B_min increases with increasing I_ex and reaches a saturation value. The J_c(B_a) curves show a maximum in decreasing applied magnetic fields occurring at B=B_max. We have also found that B_max increases with increasing B_am and reaches a saturation value. The minimum in the R(B_a) and the maximum in J_c(B_a) curves were found to be related to the trapped flux within the grains. All the experimental results are discussed within the context of the flux dynamics and transport mechanisms in these high-T_c materials.     

Van der waals waves in free-surface liquids

It is shown that, along with gravity waves, surface and internal waves caused by van der Waals forces may exist in a liquid with a horizontal free surface. A dispersion relation is found by using the stepwise approximation for the coefficients of a wave equation derived for these waves. The surface waves are similar to surface gravity waves in dispersion and amplitude distribution but differ in frequency by several orders of magnitude. Another sequence of roots in the spectrum corresponds to internal van der Waals waves that have an upper frequency bound and the dispersion law typical of a multimode waveguide.     

Reaction of Methylmalonyl Dichloride with Unsaturated Carboxamides

Methylmalonyl dichloride reacts with (2E)-3-phenylacrylamides and (2E)-3-(2-furyl)acrylamide to give the corresponding E-isomeric 2-substituted 4-hydroxy-5-methyl-6H-1,3-oxazin-6-ones. The reaction of methylmalonyl dichloride with acrylamide afforded N-(3-chloropropionyl)-2-methylmalonamic acid. The structure of the products was confirmed by the ¹H and ¹³C NMR, IR, and UV spectra.     

NMR excitation by an electric field as a dynamic manifestation of magnetoelectric and antiferroelectric interactions

The possibility of excitation of NMR signals by an ac electric field in magnetically ordered crystals is discussed. Such signals can be recorded using the time-dependent component of the electric polarization vector. It is assumed that the electric and magnetic characteristics are coupled to each other through magnetoelectric and antiferroelectric interactions. Several types of magnetic structures are analyzed in which these interactions are not forbidden by symmetry. Such structures include two-sublattice single-position ferro-and antiferromagnetic phases in centrosymmetrical crystals, two-sublattice magnetic crystals without a center of symmetry (such as KNiPO₄), and four-sublattice antiferromagnetic crystals with three types of antiferromagnetism vectors (such as Cr₂O₃ and α-Fe₂O₃).     

The minimizing of the Nielsen root classes

Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M ₂)−χ(M ₁0/(1−χ(M ₂)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M ₂)−χ(M ₂)/(1−χ(M ₂)). Also we construct, for each integer n≥3, an example of a map f: K _n →N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time.     

Effects of tributyltin(IV) chloride on the gametes and fertilization of Ascidia malaca (Ascidiacea: Tunicata)

Ascidia malaca gametes before fertilization incubated in 10^?5 or 10^?7 M solutions of tributyltin(IV) chloride, TBTCl, for 3 h appear highly damaged under transmission electron microscopy observation. Also, the fertilization process is affected by the compound: the damaged spermatozoa are present in the vitelline coat and the egg does not cleave. An increase of microbodies, structurally similar to peroxisomes, have been detected in the egg peripheral cytoplasm, probably in relation to their role in alleviating damage to some cellular components. The results have shown that the reproduction of ascidians under unfavourable environmental conditions is prevented. Copyright © 2003 John Wiley & Sons, Ltd.