Half twists and the cohomology of hypersurfaces

A Hodge structure V of weight k on which a CM field acts defines, under certain conditions, a Hodge structure of weight , its half twist. In this paper we consider hypersurfaces in projective space with a cyclic automorphism which defines an action of a cyclotomic field on a Hodge substructure in the cohomology. We determine when the half twist exists and relate it to the geometry and moduli of the hypersurfaces. We use our results to prove the existence of a Kuga-Satake correspondence for certain cubic 4-folds. Received: 25 August 2000; in final form: 8 January 2001 / Published online: 18 January 2002     

The study and applications of photochemical-dynamical gravity wave model II

A nonlinear, compressible, non-isothermal gravity wave model that involves photochemistry is used to study the effects of gravity wave on atmospheric chemical species distributions in this paper. The changes in the distributions of oxygen compound and hydrogen compound density induced by gravity wave propagation are simulated. The results indicate that when a gravity wave propagates through a mesopause region, even if it does not break, it can influence the background distributions of chemical species. The effect of gravity wave on chemical species at night is larger than in daytime.     

Linear nonstationary optical dimensional resonances in atomic nanostructures

The existence of linear nonstationary optical resonances in a diatomic nanostructural object with a dipole-dipole atomic interaction has been proved. A new solution to the joint system of modified Bloch optical equations and nonlocal field equations is obtained for time intervals much shorter than the times of phase and energy relaxation. Formulas for effective polarizabilities of the object’s atoms, which have a set of dimensional resonances, are derived. The frequencies of these resonances significantly differ from the eigenfrequencies of the object’s atoms, and their properties depend on the interatomic distance, light-pulse duration, initial atomic inversions, and the orientation of the object’s axis relative to the direction of incidence of the external light wave.     

On the critical exponents of random k‐SAT

There has been much recent interest in the satisfiability of random Boolean formulas. A random k‐SAT formula is the conjunction of m random clauses, each of which is the disjunction of k literals (a variable or its negation). It is known that when the number of variables n is large, there is a sharp transition from satisfiability to unsatisfiability; in the case of 2‐SAT this happens when m/n → 1, for 3‐SAT the critical ratio is thought to be m/n ≈ 4.2. The sharpness of this transition is characterized by a critical exponent, sometimes called ν = ν_k (the smaller the value of ν the sharper the transition). Experiments have suggested that ν₃ = 1.5 ± 0.1. ν₄ = 1.25 ± 0.05, ν₅ = 1.1 ± 0.05, ν₆ = 1.05 ± 0.05, and heuristics have suggested that ν_k → 1 as k → ∞. We give here a simple proof that each of these exponents is at least 2 (provided the exponent is well defined). This result holds for each of the three standard ensembles of random k‐SAT formulas: m clauses selected uniformly at random without replacement, m clauses selected uniformly at random with replacement, and each clause selected with probability p independent of the other clauses. We also obtain similar results for q‐colorability and the appearance of a q‐core in a random graph. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 182–195, 2002     

A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.     

Illumination dependence of I-V and C-V characterization of Au/InSb/InP(1 0 0) Schottky structure

The effects of surface preparation and illumination on electric parameters of Au/InSb/InP(100) Schottky diode were investigated, in the later diode InSb forms a fine restructuration layer allowing to block In atoms migration to surface. In order to study the electric characteristics under illumination, we make use of an He-Ne laser of 1 mW power and 632.8 nm wavelength. The current-voltage I(V_G), the capacitance-voltage C(V_G) measurements were plotted and analysed. The saturation current I_s, the serial resistance R_s and the mean ideality factor n are, respectively, equal to 2.03 × 10⁻⁵ A, 85 Ω, 1.7 under dark and to 3.97 × 10⁻⁵ A, 67 Ω, 1.59 under illumination. The analysis of I(V_G) and C(V_G) characteristics allows us to determine the mean interfacial state density N_ss and the transmission coefficient θ_n equal, respectively, to 4.33 × 10¹² eV⁻¹ cm⁻², 4.08 × 10⁻³ under dark and 3.79 × 10¹² eV⁻¹ cm⁻² and 5.65 × 10⁻³ under illumination. The deep discrete donor levels presence in the semiconductor bulk under dark and under illumination are responsible for the non-linearity of the C⁻²(V_G) characteristic.     

Balancing a Rotor with Two Coupled Perfectly Rigid Bodies

The steady motions of a vertical rotor balanced by two coupled perfectly rigid bodies (PRBs) are analyzed for stability. The rotor executes plane-parallel motions. The PRBs can rotate together about the rotor axis and about its transverse axes through equal angles but in opposite directions. It is established that when the mass of the PRBs is much less than that of the rotor and the rotor spins with a superresonant speed, only the basic steady motions, which are those of the best-balanced rotor, are asymptotically stable.