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Notes: The SL(3,R) theory of projective transformations of the plane is applied to the Lagrangians of all one-dimensional Newtonian linear systems. Noether and non-Noether equivalent Lagrangians, as well as the associated Noether and non-Noether constants of motion, are thus obtained in a completely general and systematic way. Complete unification is achieved by this group-theoretic approach to Lagrangians of one-dimensional linear systems.

Notes: Shoal position can have a strong influence on individual fitness. Individuals in front positions of shoals were observed to have higher feeding rates than individuals elsewhere. Manipulation of nutritional state showed that hungry individuals had a stronger preference for front positions and that the duration of food-deprivation was positively correlated with the degree of the position preference. On the other hand, front positions (like other peripheral positions) probably incur costs in terms of increased predation risks. Experiments with Schreckstoff showed that frightened individuals seek the central part of the shoal. This suggests that individuals rotate their shoal positions according to the tradeoff between energy intake and predation risk.

Notes: Single sticklebacks (Gasterosteus aculeatus) were presented with a choice between (a) a shoal and an empty compartment, and (b) two different sized shoals of conspecifics. The choice of hungry test fish (food-deprived for 24 h and 72 h, respectively) was compared to that of fish which were fed to satiation once a day. It was hypothesized that due to the increased level of competition for food in large shoals, hungry fish would spend less time with the larger of two shoals than their well-fed conspecifics. The results showed that there was indeed a significant trend for test fish to spend a decreasing amount of time near the compartment with the larger number of fish with increasing duration of food deprivation.

Notes: Abstract: The influence of deprivation of the neurotransmitter dopamine (DA) on the development of [Met5]-enkephalin (ME) and substance P (SP) neuropeptide systems of the stria-turn was investigated in Sprague-Dawley rats. The neurotoxin 6-hydroxydopamine (6-OHDA) was used to induce DA deficiency on postnatal day 3 in rats, and the animals were killed at different postnatal time points until 35 days of age. The levels of ME and SP were determined by radioimmu-noassay, and the abundance of preproenkephalin (PPE) and preprotachykinin (PPT) mRNA in the striatum was assessed by Northern blot hybridization analysis. The concentrations of DA, 5-hydroxytryptamine (5-HT), and their acid metabolites were determined by HPLC with electrochemical detection. The postnatal development of the PPE-derived pep-tide ME and the PPT-derived peptide SP closely paralleled the appearance of the respective mRNAs coding for these peptides. The dopaminergic lesion with 6-OHDA led to a marked depletion of DA and its metabolites but produced an increase in content of 5-HT and its metabolite in the striatum. The lesion did not affect the ME and PPE mRNA levels in the striatum up to 25 days but increased the levels at 35 days. In contrast, a decreased developmental expression in SP and PPT mRNA was observed throughout the observation period. The lesion failed to influence the development of the mRNA coding for the structural protein β-actin. The results indicate that the normal development of enkephalin, tachy-kinin, and 5-HT systems of the striatum is dependent on the availability of DA, the integrity of dopaminergic neurons, or both. The studies provide evidence for an interrelationship and interdependence between the development of neurotransmitter and neuropeptide systems. It is suggested that an early developmental abnormality in the DA system could permanently alter the neuropeptide systems, which in turn could influence the progression and expression of the DA-deficiency state parkinsonism, Lesch-Nyhan disease, or both.

Notes: Abstract: The aim of the study was to test whether the synthesis of substance P (SP) and that of its receptor (also known as NK1 receptor) are coordinately regulated after chronic pharmacologic intervention in two neural systems, the spinal cord and basal ganglia. In one set of experiments, capsaicin was administered subcutaneously during the early postnatal period (day 3 after birth) to induce degeneration of afferent sensory neurons in the spinal cord. In the other set of experiments, interruption of dopaminergic transmission was achieved by two methods: (a) The neurotoxin 6-hydroxydopamine was used to denervate dopaminergic neurons during the early postnatal period, and (b) haloperidol was used in adult animals to block dopaminergic transmission by receptor blockade. The spinal cord, striatum, or both were used for the quantification of tachykinin [SP and neurokinin A (NKA)] and opioid peptides [[Met5]-enkephalin (ME) and dynorphin A (1–8) (DYN)] by radioimmunoassays. The abundance of total SP-encoding preprotachykinin (PPT) mRNA and SP receptor (SPR) mRNA in spinal cord (C5 to T1 segments), striatum, or microdissected substantia nigra was determined by northern blot or solution hybridization analysis. Amines and their acid metabolites were quantified by HPLC. Capsaicin administration (subcutaneously) during the early postnatal period increased latency in a hot-plate test, decreased SP and NKA levels, increased levels of PPT mRNAs, and did not affect SPR mRNA levels in the spinal cord. Intraspinal SP systems may attempt to compensate for the loss of afferent SP input, whereas spinal cord receptor mRNA levels do not appear to be altered. Neonatal dopaminergic denervation or haloperidol blockade of dopamine receptors in adult rats decreased PPT mRNA levels in the striatum as previously reported but did not alter the abundance of SPR mRNA in the striatum or substantia nigra. The presence of SPR mRNA levels in microdissected substantia nigra and the lack of alteration in its levels as a consequence of dopamine denervation suggest that the receptor is expressed within nondopaminergic neurons, possibly GABAergic neurons. In both spinal cord and basal ganglia systems, regardless of increases or decreases in SP or SP-encoding mRNA levels, SPR mRNA levels were not altered. We conclude that the regulation of the presynaptic biosynthesis of SP and the postsynaptic regulation of the SPR mRNA can be modulated independently of each other in spinal cord and basal ganglia SP systems.

Notes: A rather strong concept of symmetry is introduced in classical mechanics, in the sense that some mechanical systems can be completely characterized by the symmetry laws they obey. Accordingly, a "complete symmetry group'' realization in mechanics must be endowed with the following two features: (1) the group acts freely and transitively on the manifold of all allowed motions of the system; (2) the given equations of motion are the only ordinary differential equations that remain invariant under the specified action of the group. This program is applied successfully to the classical Kepler problem, since the complete symmetry group for this particular system is here obtained. The importance of this result for the quantum kinematic theory of the Kepler system is emphasized.

Notes: The formalism of non-Abelian group quantization is briefly revisited, within the regular representation of noncompact Lie groups. It is shown that some of such r-dimensional groups have a set of r basic quantum-kinematic invariants, which substantially differ from the traditional invariants. The relation of the traditional invariants of the Lie algebra with the new quantum-kinematic invariants is also briefly examined. This paper contains two miscellaneous examples of quantum-kinematic invariant operators.