THE QUALITATIVE CONTENT OF RENEWABLE RESOURCE MODELS

This paper analyzes the extent to which standard dynamic renewable resource models possess refutable implications. Both the steady state comparative static and local comparative dynamic properties of the standard model are studied. A unified framework is developed which enables one to analyze the qualitative properties of any standard renewable resource model. This is achieved by explicitly linking the local stability, steady state comparative static, and local comparative dynamic properties of the model.     

Tagging of the Magnetization with the Transition Zones of 360° Rotations Generated by a Tandem of Two Adiabatic DANTE Inversion Sequences

A new technique is presented for generating myocardial tagging using the signal intensity minima of the transition zones between the bands of 0° and 360° rotations, induced by a tandem of two adiabatic delays alternating with nutations for tailored excitation (DANTE) inversion sequences. With this approach, the underlying matrix corresponds to magnetization that has experienced 0° or 360° rotations. The DANTE sequences were implemented from adiabatic parent pulses for insensitivity of the underlying matrix to B₁ inhomogeneity. The performance of the proposed tagging technique is demonstrated theoretically with computer simulations and experimentally on phantom and on the canine heart, using a surface coil for both RF transmission and signal reception. The simulations and the experimental data demonstrated uniform grid contrast and sharp tagging profiles over a twofold variation of the B₁ field magnitude.     

Eye tissue structure and refraction alterations upon nondestructive laser action

A new approach to alterations in eye refraction upon nondestructive laser action on the sclera and cornea is studied. It is demonstrated in in vivo experiments on rabbit eyes that sequential laser irradiation of the sclera and cornea yields a significant alteration in the eye refraction. The collagen structure of the sclera and cornea is studied after the nondestructive laser action with noninvasive polarization-sensitive optical coherence tomography. It is demonstrated that collagen fibers that provide for the cornea tension and applanation partially survive in the zone of the local denaturation of sclera. An irradiation mode that corresponds to an increase in the cornea’s plasticity and does not cause visible structural changes is chosen. The simplest theoretical model for alterations in the eye refraction upon the nonablative laser action on sclera is analyzed. The alteration in the cornea curvature upon stretching resulting from the local sclera coagulation and the corresponding decrease in its volume is calculated. The model makes it possible to approximately estimate the laser irradiation modes that provide the desired alterations in eye refraction.     

Every diassociative A-loop is Moufang

An A-loop is a loop in which every inner mapping is an automorphism. A problem which had been open since 1956 is settled by showing that every diassociative A-loop is Moufang.

     

The Linear Fokker-Planck Equation for the Ornstein-Uhlenbeck Process as an (Almost) Nonlinear Kinetic Equation for an Isolated N-Particle System

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are functionals of the solution itself rather than being prescribed, describes the kinetic evolution (in the N→∞ limit) of an isolated N-particle system with certain stochastic interactions. Here we discuss in detail this recently discovered interpretation. An erratum to this article can be found at     

Constructing Invariant Fairness Measures for Surfaces

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined.     

Bis(μ6‐cis‐2,4,6,8,10,12,14,16‐octa­methyl­cyclo­octa­siloxane‐2,4,6,8,10,12,14,16‐octolato)octa­kis[(dimethyl­formamide)copper(II)] dimethyl­formamide solvate enclosing a pyrazine mol­ecule

The title compound, [Cu₈(C₈H₂₄O₂Si)₂(C₃H₇NO)₈]·C₄H₄N₂·C₃H₇NO, features a sandwich‐like cage enclosing a pyrazine mol­ecule, both situated on a centre of inversion. In addition, the crystal structure contains one dimethyl­formamide mol­ecule which is disordered over a centre of inversion. The copper layer, containing eight atoms, is located between two siloxanolate fragments. The whole structure of Cu atoms and siloxanolate rings is distorted by the pyrazine mol­ecule, leading to an oval form. As a result, the angles between the Cu atoms differ at the copper layer. The difference in the angles could lead to some deviations in the Cu–Cu exchange inter­actions within the copper ring, which is of inter­est for mol­ecular magnetism.     

Ricci and Matter Collineations of Locally Rotationally Symmetric Space-Times

A new method is presented for the determination of Ricci Collineations (RC) and Matter Collineations (MC) of a given spacetime, in the cases where the Ricci tensor and the energy momentum tensor are non-degenerate and have a similar form with the metric. This method reduces the problem of finding the RCs and the MCs to that of determining the KVs whereas at the same time uses already known results on the motions of the metric. We employ this method to determine all hypersurface homogeneous locally rotationally symmetric spacetimes, which admit proper RCs and MCs. We also give the corresponding collineation vectors. These results conclude a long due open problem, which has been considered many times partially in the literature.