Original Hierarchy Research Articles

A Microscopic Hierarchy Theory of the Fractional Quantum Hall Effect

In this paper we present a microscopic hierarchy theory of the fractional quantum Hall effect. The wave functions of the ground state and the collective excitation states are obtained in terms of the electron coordinates. Working in the subspace spanned by the quasiparticles of the 1/m L Laughlin ground state, with m L an odd integer, it is shown that there exists a simple mapping between electron states in the quasiparticle subspace and states of an auxiliary boson system which is defined such that the number of the bosons is the same as that of the quasiparticles and the total magnetic flux quanta seen by the bosons equals the number of electrons. For the auxiliary boson system, one can write down the Laughlin state as well as the density wave states, analogous to the electron system at filling factor 1/m L . By mapping these states onto the quasiparticle subspace of the electrons, we find that the resulting wave functions provide a quite good description for the ground state and the collective excitations respectively of the original electron system at filling factor ν=1/(m L (± 1/2p)) with p a positive integer. This construction of the ground state and the collective excitation states can be repeated for higher filling factors. The theory presented in this paper can be viewed as a microscopic realization of Haldane's original hierarchy picture.

Instability of motor unit firing rates during prolonged isometric contractions in human masseter

The firing patterns of up to 4 concurrently active masseter motor units were studied with intramuscular electrodes during a continuous isometric contraction of 15 min duration, in which the subject maintained the mean firing rate of one selected unit at 10 Hz. With this paradigm the net excitation (i.e. mean firing rate) of one unit in the muscle was controlled. This served as the reference for the functional state of other active units during the prolonged contraction. With the mean firing rate of one unit in the muscle fixed, 58% of other active units showed a slow, statistically-significant change in mean firing rate over the 15 min. The initial firing rate of the units did not influence the change in rate. The original firing rate hierarchy, which in short-term contractions reflects the recruitment order, was altered during the prolonged contraction. The explanation for these differential changes in motoneuron net excitation is not clear; they could be intrinsic to the motoneurons or perhaps mediated by reflex pathways. The selective facilitation or suppression of some motor units with continuous activation means that the original size-structured combination of motor units can be modified during a prolonged contraction.

A Remark on the Commuting Flows Defined by Lax Equations

The Lax forms of many soliton· like equations such as the Burgers equation, the Dym equation, etc. are given. Relaxing the conditions imposed on the formal pseudo·differential operator in Sato theory of the KP-hierarchy, we obtain hierarchies of soliton-like equations. The Burgers hierarchy or the Dym hierarchy is obtained by a reduction of the original hierarchy of differential equations. We can also obtain many other hierarchies of soliton-like equations.

The influence of social experience on the behavior of male cockroaches,Nauphoeta cinerea

The influence of social experience on rates of agonistic behavior was investigated in a cockroach, Nauphoeta cinerea. Social experience was manipulated by establishing three types of groups of four identically aged males: (1) ran-domly chosen, socially naive males (control); (2) males of similar status and activity level (from treatment 1); and (3) males returned to their original hierarchy after experiencing treatment 2. In the control groups, we found stable hierarchies, significant differences in the rate of agonistic behaviors exhibited among different status males, and a significant relationship between social status and level of agonism. We also compare activity levels within and among groups after males had novel social experiences. Among similar status individuals, we found less activity than when they wereintheir original groups. When males were returned to their original groups, the level of activity increased compared to the level of activity before treatment. The social status of males was unstable after these treatments. Losing tended to result in relatively more subordinate behavior, and winning in relatively more dominant behavior by a male. Within groups, the rate of agonism also increased over 5 days in groups of males that had no previous interactions with each other, while the rate of agonism remained the same in groups of familiar males. We interpret these results in light of male-male assessment and the maintenance of social status in this species.

A Model to Exhibit the Interdependence of the Cognitìve and Affective Domains of Objectives for Use in Science and Technical Teacher Training

Abstract A diagrammatic model connecting the cognitive and affective domains of educational objectives is proposed. It abandons the original (Krathwohl) hierarchy of affective objectives for one based solely on the arousal of interest as a positive dimension. A negative dimension for this affective hierarchy is also suggested. This bipolar affective axis is set at an acute angle to the conventional cognitive hierarchy with the implication that success in the cognitive domain is related to positive affective outcomes of instruction and lack of success therein results from situations where, for a variety of reasons, the affective outcomes of instruction are in the negative dimension. Research evidence supporting the model is quoted. A list of 21 antithetic teaching strategies and pupils’ personal and social characteristics reputed to contribute positively or negatively to success in the affective dimension is given.

EFFECTS OF COLONY DIVISION ON FOUNDRESS ASSOCIATIONS IN POLISTES FUSCATUS (HYMENOPTERA: VESPIDAE)

AbstractThree colonies of Polistes fuscatus (Fabricius), each with two foundresses, were bisected during the pre-emergence stage and separated for 20 days. In the absence of the dominant, each subordinate foundrss became an egg-laying queen on her half of the nest. The dominant foundress did not exhibit superior reproductive productivity. The split colonies were reunited by placing the nests approximately 4.0 cm apart in a single nest box. Each foundress and all workers were observed tending both half-colonies, and the original dominance hierarchy was apparently restored in two of the three colonies.

On the nonequivalence of correlations and clusters in phonon systems

It is shown that for the anharmonic lattice, the nature of the correlations depends upon the scale Q of the macroscopic inhomogeneity. It is only for the zero-soundregime of large Q that an asymptotically valid kinetic description follows from the usual cluster definition of correlations. For the hydrodynamic limit Q → 0 of first sound, modifications are indispensable, and certain clusters are to be considered as forming part of the correlation vacuum. The existence of such vacuum clusters considerably complicates the kinetic description: the vacuum state no longer satisfies a single closed equation, but is determined by a complete hierarchy of coupled equations, analogous to the original hierarchy of the exact description.

Resolution of the Hierarchy of Many-Body Green's Functions

The rigorous evolution equations for the one-body Green's functions ( g > , g < ) describing an imperfect gas in a finite volume are not closed (an analogue of B–B–G–K–Y hierarchy for the many-body distribution functions). The analysis of these equations are made in terms of proper connected diagrams. It is shown that in the bulk limit: N (particle number)→∞, \(\varOmega\)(volume)→∞ such that N /Ω=constant, these equations can be reduced to the closed equations, which are however, non-linear and non-Markoffian, in contrast to the original hierarchy equations.

Properties of the functional formalism and their application to the theory of classical fluids

A general formalism is derived relating any generating functional of a hierarchy of functions to some other functionals yieldingUrsell, Husimi, and similar expansions of the original hierarchy and vice versa. There are two expansions starting with an equation of the O.-Z. type. This formalism is applied to the grand partition function with an external potential which is a generating functional for the molecular distribution functions. When the external potential is induced by adding particles to the system we obtain several hierarchies of integral equations related to each other in a simple fashion. As the Kirkwood-Salsburg, Mayer-Montroll, Green equations, the P. Y., HNC and a HNC similar approximation with their extensions are special cases of these hierarchies the relations between them become transparent. At the same time the heuristic feature in the choice of functionals and independent functions in earlier derivations of some of these equations is removed.