Exclusive Regions Research Articles

The Weakest Libera! Preconditions of Nondeterministic Machines and Robust Programs

Abstract The weakest liberal precondition (wlp) of a nondeterministic machine S for a desired postcondition R may be defined as wlp(S, R)=–wp(S, T)⋁wp(S,R), where wp(S, R) is the weakest precondition of S for R. Some of the errors in Dijkstra’s predicates for describing the seven mutually exclusive regions of the initial state of nondeterministic machine are pointed out in this paper with their corrections given. It is shown that the concept of weakest liberal precondition is also useful in defining program robustness.

Distribution of external cuneate nucleus afferents to the cerebellum: I. Notes on the projections from the main cuneate and other adjacent nuclei. An experimental study with radioactive tracers in the cat.

Transport of radioactive leucine was used to demonstrate cerebellar projections from the external cuneate nucleus (NCE) and from adjacent portions of the main cuneate nucleus (NC), of the spinal trigeminal nucleus (N.tr.sp.V) and of the vestibular nuclei. Projections from NCE and NC in part terminate over exclusive regions and in part overlap. After injections limited to NCE, labeling is found in all regions of the anterior lobe and lobule VI, in vermal lobules VII, VIII, and IX, and in medial regions of central folia of the paramedian lobule. Afferents from NC are observed in intermediate and lateral regions of lobules IV-VI, in lobules VIII and IX, in medial portions of crura I and II, and in lateral parts of central folia of the paramedian lobule as well as in its rostral folia. Afferents from N.tr.sp.V are distributed in lateral regions of lobules II-VI, in the rostral folium of lobule IX, in medial parts of crura I and II, and in rostral folia of the paramedian lobule. Afferents from the vestibular nuclei are present in vermal lobules VII, IX, and X and in the paramedian lobule. Projections from NCE are bilateral with ipsilateral predominance, whereas those from NC and N.tr.sp.V are ipsilateral. Projections from NCE are generally much denser than those from the other nuclei. Throughout the projection area, afferents from NCE are distributed in greater amounts in folia close to the medullary core and are much less dense near the surface. Afferents from the other nuclei do not show surface-to-depth density differences.

Identified motoneurons and their innervation of axial muscles in the zebrafish

The organization of spinal cord motoneurons and their innervation of axial (white) muscles in the zebrafish were studied. Motoneurons can be divided into 2 classes, primary and secondary, on the basis of their cell-body sizes and positions. Each side of each spinal segment contains 3 primary motoneurons that are uniquely identifiable as individuals by their stereotyped cell-body positions and peripheral branching patterns. Moreover, these motoneurons precisely innervate cell-specific subsets of contiguous muscle fibers in mutually exclusive regions of their own body segment. Individual muscle fibers receive inputs from a single primary motoneuron and, in addition, from up to 3 secondary motoneurons. The results demonstrate that the precision of innervation previously described in invertebrates is also present in some vertebrates.

Potential model for fusion and angular momentum localisation

The elastic scattering and fusion cross sections for ten different heavy-ion systems with (A1+A2)<100 have been successfully described with an interaction potential obtained from the double-folding model. Similarly, the (9Be, 8Be) reaction as a representative example for direct processes in the system 9Be+28Si is well reproduced by a DWBA calculation which in turn leads to a localisation of fusion and direct processes in mutually exclusive regions of the angular momentum space.

Double-pomeron decoupling and the relation of exclusive to inclusive experiments with the dual resonance model

The double-pomeron coupling strength in the dual resonance model is found in both the inclusive and exclusive regions by comparison with experiments. Double-pomeron coupling occurs in inclusive experiments in the Mueller diagram for the central plateau region. Its strength can also be bounded from its non-observation in the two-particle to four-particle exclusive experiments. The dual resonance model is used to perform the analytic continuation of a six-point amplitude between these regions. The results show that the coupling strength for two forward pomerons in the exclusive region must be less than 1 300 of that in the inclusive region. This is experimental evidence for substantial forward double-pomeron decoupling in exclusive processes.

KLEIN–DUNHAM POTENTIAL ENERGY FUNCTIONS IN SIMPLIFIED ANALYTICAL FORM

A simple formula, based originally on the work of Klein and Rees, is developed for calculating potential energy curves, except near the dissociation limit, for electronic states of diatomic molecules. Classical turning points r1,2 are given as functions of vibrational quantum number (V ≡ ν + 1/2), with coefficients depending on observed spectroscopic constants, in the form[Formula: see text]where[Formula: see text]For most states convergence is rapid, but as a rule more so for heavy molecules than for light molecules. Assuming it to be close to the 'true' potential, such a representation affords a convenient means of assessing the accuracy of the Morse or other empirical potential function. Morse curves have also been fitted by least squares to Klein–Rees turning points.Term-by-term comparison between the inverted Dunham series and an equivalent form of the above has led to the surprising discovery that if Dunham's small correction terms are neglected, Klein and Dunham potentials are mathematically identical. This is contrary to the generally held belief that the two should be used in mutually exclusive regions. In the present form these series exhibit better behavior over a wider range than a series giving potential energy as a function of internuclear separation.

Multiple Objectives in Mathematical Programming

The abstraction from a real situation to a model suitable for mathematical programming often raises the dilemma of multiple objective functions, and of the arbitrary roles of objective functions and restrictions. This dilemma is resolved by formulating a more general model of the total objective function. This formulation includes (1) defining a subobjective space, (2) defining a set of mutually exclusive regions in subobjective space, (3) defining an individual objective function for each such region, (4) indicating an order of preference for the regions. Examples are given for the problems of optimal product mix and military aircraft design.