One-sided Conditions Research Articles

The galactic motion field of K0-5 giants from Hipparcos data

We have investigated the motions of all K0-5 stars which have a proper motion in the Hipparcos catalogue and a known luminosity class III (due to the incompleteness of the ongoing classification, the distribution of these stars at the celestial sphere is rather uneven). We have used the apparent magnitudes and colours together with adopted means and dispersions of the absolute values in order to estimate distances. The fulfilment of two one-sided conditions has been ensured: the stars should only be reddened and their photometric parallaxes should be consistent with the trigonometric ones; this is practically a one-sided condition, if, as usual, the trigonometric parallax is near zero (every condition to be demanded within s dispersions). Our final total sample contains 8349 stars. We did not demand the knowledge of radial velocities or metallicities, nor did we use them in the rather small fraction of our stars which they were known for. The estimated photometric distances have a logarithmic mean of 280 pc and an error of typically 25%. The proper motions were represented by a kind of ‘adaptive’ model, using a three dimensional expansion in a series of orthogonal functions of galactic latitude, longitude and of the logarithm of the distance. Our programme searches automatically for significant functions. Usually, we have selected those which could arise by chance with a 5% probability only or less than 5% (in some cases we additionally have treated the data with a corresponding limit of 1%). Most of the found significant functions belong to exact or approximate equivalents of known standard motions, especially the average ensemble motion and the two first order parameters of galactic rotation. The data were treated first for each spectral subclass separately and then - since the differences were not pronounced - as a united sample. For the united sample, the ensemble motion with respect to the sun is (U0, V0, W0) = (—9.0 ± 0.5, —21.0 ± 0.5, —7.7 ± 0.4) km/s and with respect to the local standard of rest (U, V, W)LSR = (+1, —16, —1) km/s As galactic rotation parameters we obtain Q = —1.81 ± 0.51 mas/yr, P = +2.92 ± 0.32 mas/yr (the first being corrected for asymmetric drift with the aim to represent the circular velocity). Beyond these standard motions, three non-standard functions appear. One of those has a 4 s coefficient and corresponds to a distance dependent galactic shear parameter C. If we were to demand that this term vanishes, Q would change towards —2.60 mas/yr - in agreement with the value from Hipparcos Cepheids. The residuals against the systematic motions are used to obtain the 3 axes of a velocity ellipsoid (assumed to be aligned to the galactic axes) σ(U) = 37.5 ± 0.3 km/s, σ(V) = 26.9 ± 0.4 km/s, σ(W) = 20.1 ± 0.7 km/s. The two quantities V0 and σ(U) mutually fulfill the asymmetric drift relation. From the total dispersion an age of the order 4 · 109 years can be obtained. These figures agree with those of nearby old giants, but they now refer to a much larger volume and number of stars. All dispersions depend on the distance z perpendicular to the galactic plane. Most distinctly, the dispersion perpendicular to the galactic plane cannot be described by one isothermal component. σ(W) increases with |z|; the distribution of the W-velocities near the galactic plane is non-Gaussian in the sense that the central peak is more populated. Thus at least 3 components would be required if a description with isothermal components were wanted.

The galactic motion field of K0-5 giants from Hipparcos data

We have investigated the motions of all K0-5 stars which have a proper motion in the Hipparcos catalogue and a known luminosity class III (due to the incompleteness of the ongoing classification, the distribution of these stars at the celestial sphere is rather uneven). We have used the apparent magnitudes and colours together with adopted means and dispersions of the absolute values in order to estimate distances. The fulfilment of two one-sided conditions has been ensured: the stars should only be reddened and their photometric parallaxes should be consistent with the trigonometric ones; this is practically a one-sided condition, if, as usual, the trigonometric parallax is near zero (every condition to be demanded within s dispersions). Our final total sample contains 8349 stars. We did not demand the knowledge of radial velocities or metallicities, nor did we use them in the rather small fraction of our stars which they were known for. The estimated photometric distances have a logarithmic mean of 280 pc and an error of typically 25%. The proper motions were represented by a kind of ‘adaptive’ model, using a three dimensional expansion in a series of orthogonal functions of galactic latitude, longitude and of the logarithm of the distance. Our programme searches automatically for significant functions. Usually, we have selected those which could arise by chance with a 5% probability only or less than 5% (in some cases we additionally have treated the data with a corresponding limit of 1%). Most of the found significant functions belong to exact or approximate equivalents of known standard motions, especially the average ensemble motion and the two first order parameters of galactic rotation. The data were treated first for each spectral subclass separately and then - since the differences were not pronounced - as a united sample. For the united sample, the ensemble motion with respect to the sun is (U0, V0, W0) = (—9.0 ± 0.5, —21.0 ± 0.5, —7.7 ± 0.4) km/s and with respect to the local standard of rest (U, V, W)LSR = (+1, —16, —1) km/s As galactic rotation parameters we obtain Q = —1.81 ± 0.51 mas/yr, P = +2.92 ± 0.32 mas/yr (the first being corrected for asymmetric drift with the aim to represent the circular velocity). Beyond these standard motions, three non-standard functions appear. One of those has a 4 s coefficient and corresponds to a distance dependent galactic shear parameter C. If we were to demand that this term vanishes, Q would change towards —2.60 mas/yr - in agreement with the value from Hipparcos Cepheids. The residuals against the systematic motions are used to obtain the 3 axes of a velocity ellipsoid (assumed to be aligned to the galactic axes) σ(U) = 37.5 ± 0.3 km/s, σ(V) = 26.9 ± 0.4 km/s, σ(W) = 20.1 ± 0.7 km/s. The two quantities V0 and σ(U) mutually fulfill the asymmetric drift relation. From the total dispersion an age of the order 4 · 109 years can be obtained. These figures agree with those of nearby old giants, but they now refer to a much larger volume and number of stars. All dispersions depend on the distance z perpendicular to the galactic plane. Most distinctly, the dispersion perpendicular to the galactic plane cannot be described by one isothermal component. σ(W) increases with |z|; the distribution of the W-velocities near the galactic plane is non-Gaussian in the sense that the central peak is more populated. Thus at least 3 components would be required if a description with isothermal components were wanted.

One-sided convergence conditions for Hermite-Fejér interpolation of higher order of Lagrange type

The authors investigate the Hermite-Fejer interpolation of higher order of Lagrange type for continuous functions on the Jacobi abscissas. A uniform convergence theorem is stated, generalizing a previous result for Lagrange interpolation.

Tauber-Bedingungen für Verfahren Mit Abschnittskonvergenz

We consider a summability matrix A with sectional convergence (in the null-domain) and use sectional submethods B. If (I - B)s has small oscillation (for a suitable B), then s also has small oscillation. Employing a set of such B, we obtain Tauberian results yielding convergence (also with one-sided conditions). In particular this analysis applies to weighted means. Thus we have a new approach to results given by Moricz and Rhoades [3].

Controlled H Systems and Chomsky Hierarchy

This paper is an up-to-dated survey of results about the power of controlled extended H systems of various types. Such systems are finite generative devices based on the splicing operation, which, in turn, is a model of the DNA recombination. When no control is imposed on the splicing operation, we get a characterization of regular languages. When a control is considered, we obtain characterizations of recursively enumerable languages. We briefly discuss here H systems with control mechanisms similar to those in regulated rewriting area in formal language theory. We do not present proofs, but only definitions, results, and bibliographical information. Looking for characterizations of families in Chomsky hierarchy other than those of regular and of recursively enumerable languages, we closely investigate the H systems with permitting context conditions. We disprove a conjecture of Chakaravarthy and Krithivasan: such systems of radius one and using only one-sided context conditions can generate all context-free languages (the conjecture was that a characterization of linear languages is obtained). Some open problems are also mentioned.

On a Family of Summability Methods and One-Sided Tauberian Conditions

We discuss a large family of summability methods including power series methods, generalized Nörlund means, running means and investigate Abelian and Tauberian relations in this family. The main goal is to find weakest possible one-sided Tauberian conditions for the Tauberian conclusions. From these results we can derive strong laws and Erdős-Rényi laws for all the methods in question when applied to i.i.d. random variables.

Biomass production, structural deformation, selfthinning and thinning mechanisms in monocultures

Consideration is given to the production of biomass in three of the possible growth phases that may be experienced by plants at various spacings in stand monocultures. The amount of radiant energy available for this is related to canopy surface area, volume, and slenderness, and the efficiency with which the operation is performed. The unified non-dimensional formulae established describe normal natural growth, growth with plastic deformation, and growth subject to the self-thinning process, which occurs when individuals are packed too closely together. The formulae define growth surfaces for the life-lines followed by individual plants, and for the rounding and smoothing of these lines that occurs, at the otherwise sharply defined growth phase boundaries, as a result of the statistical uncertainties in specifying plant dimensions and numbers in spacetime. The results provide an explanation of features of the self-thinning process and the values of the constants and parameters associated with approximate power law descriptions of the phase boundary on which it takes place. A quasi-static analysis of growth and thinning mechanisms indicates one-sided competition coexistence conditions for plants in distributions with uniformly augmented and diminished biomass, and the boundaries separating and distinguishing diminished biomass states from which recovery to further growth is, or is not, possible. Because of the dependence of events in the growth process on canopy shape and volume a preliminary classification of suitable geometric forms is given, together with formulae for evaluating the required quantities, for several cases of interest.

Two-level system coupled to a boson mode.

The thermodynamics of a two-level system coupled to a boson field is investigated by means of a functional-integral method. The model can be used to describe the motion of a small polaron between two sites on a molecule, or a spin-1/2 magnetic moment coupled to a phonon bath. The model is also relevant to the problem of dissipation in macroscopic quantum phenomena. We use a functional-integral method to investigate a two-level electronic system coupled linearly to a harmonic oscillator. The density matrix is cast as a functional integral over paths obeying one-sided boundary conditions at either 0 or \ensuremath{\beta}=1/${\mathit{k}}_{\mathit{B}}$T. The integration variables are c numbers for the oscillator and Grassmann numbers for the electrons. The oscillator variables are integrated out, leaving an effective density matrix for the electrons containing retarded interactions. The partition function is then calculated up to second order of an expansion about the exact fermionic classical paths. Then, the free energy, specific heat, and average hopping energy are obtained. We find that the most significant reduction in the hopping energy is manifested at intermediate temperatures.

Existence of multiple solutions for some nonlinear boundary value problems

By imposing one-sided conditions on the nonlinearity, where neither regularity nor uniformity is required, we prove the existence of either a nonnegative or a nonpositive solution for first and second order ordinary differential equations with periodic, Neumann, or Dirichlet boundary conditions. Positone and nonpositone problems are considered. Some nonexistence results are also obtained. When using generalized Ambrosetti-Prodi type conditions we get the existence of nonnegative and nonpositive solutions for first and second order periodic or Neumann boundary value problems. Our method of proof makes use of topological degree arguments in Cones.

One-sided conditions for quasilinear Jacobi differential equations

One-sided conditions for quasilinear Jacobi differential equations

One-Sided Smoothness Conditions and Conformal Mapping

One-Sided Smoothness Conditions and Conformal Mapping

One-sided conditions for the Navier-Stokes equations

One-sided conditions for the Navier-Stokes equations

Circuitry analysis of the outer plexiform layer in the rabbit retina: I. Extension of analysis of circuits interpreted to be associated with directional sensitivity and edge detection

The earlier analysis of the circuitry of the outer plexiform layer in the rabbit retina [ Sjostrand, 1969 , Sjostrand, 1974 , Sjostrand, 1976 , Sjostrand, 1976 ] has been extended with respect to the circuitry that was proposed to be associated with directional sensitivity and edge detection. This circuitry involved one bipolar cell, here referred to as bipolar cell 1, which was connected to horizontal cells according to a characteristic pattern that appeared suitable for a detector for directional sensitivity and for an edge. The same characteristics of the pattern of connections were found repeated at the contacts of this bipolar cell at a second photoreceptor cell of the β type (α and β type cells are usually identified with rod and cone cells, respectively). The similarities involve the presence of collateral branches of bipolar cell 1 that contact horizontal cell processes outside the subsynaptic neuropil, connections in the subsynaptic neuropil which involve both bipolar cell and horizontal cell processes, contacts with efferent bipolar cells in the subsynaptic neuropil, contact relations with horizontal cell processes at synaptic ribbon complexes, and contacts with the photoreceptor cells. Collateral branches are a unique feature of bipolar cell 1 among all bipolar cells contacting these two photoreceptor cells. As in the previous papers, the interpretation of the functional significance of the circuitry was based on distinguishing between two types of horizontal cell-bipolar cell connections. Horizontal cells were thus classified as contributing either processes that showed a structural polarity or processes that were lacking any structural polarity. In five synaptic ribbon complexes analyzed at photoreceptor cell β2, one of the two horizontal cell endings of each complex was contributed by a horizontal cell process with structural polarity, while the other was contributed by a process lacking structural polarity. This is in agreement with the most common arrangement observed in earlier analysis ( Sjostrand, 1974 ). It could also be confirmed that the bipolar cell process to a synaptic ribbon complex was a side branch of the end branch which itself was received in a separate invagination of the plasma membrane of the terminal. There were five horizontal cell processes with structural polarity that contacted or were contacted by bipolar cell 1 in synaptic ribbon complexes, in the subsynaptic neuropil, and outside the subsynaptic neuropil. All these processes showed the same polarity which agreed with the polarity of corresponding horizontal cell processes' contacts at photoreceptor cell β1. The systematic repetition of similar contact relations of bipolar cell 1 at both photoreceptor cells and the fact that the similarities involved a characteristic, nonrandom but rather specific type of contact pattern support the concept that the neurons are connected according to well-defined patterns designed for a particular type of information processing. As a consequence, circuit analysis of this kind together with electrophysiological analysis should form a concrete basis for revealing how information is processed in nervous centers. The subsynaptic neuropil showed an even more complex circuitry at this photoreceptor cell than at photoreceptor cell β1, supporting the earlier conclusion that the subsynaptic neuropil is the site of a major part of retinal circuitry ( Sjostrand, 1974 , Sjostrand, 1976 , Sjostrand, 1976 ). A pairing of contacts of endings of neurons was observed to be a general rule for contacts not only in the synpatic ribbon complexes but also in the subsynaptic neuropil and outside the subsynaptic neuropil. For horizontal cells this pairing involved one horizontal cell process with polarity paired with one lacking polarity like the most common combination at synaptic ribbon complexes. From a functional point of view the horizontal cell processes lacking structural polarity were interpreted to be involved in neural adaptation of the retina while the horizontal cell processes with structural polarity were interpreted to act in an inhibitory way on bipolar cells on the basis of local, one-sided conditions of illumination of the retina. This functional interpretation was the basis for proposing that the observed circuitry could be associated with directional sensitivity and edge detection. These proposals appear to have gained additional support from the fact that the same type of connections were found at both photoreceptor cell β1 and β2.

A necessary condition for the iterated logarithm law

both {X.} and { X , } obey one-sided Iterated Logarithm Laws. A particular category of interest is the so-called weighted i.i.d, case consisting of sequences {o' ,Y,,n>l} where {I1,} are i.i.d, random variables with EYI=0 and {o-,} are constants with 2_ , s. Z1 a2 ~ oo. In [5], a necessary and separately, sufficient conditions were given for the twosided LIL to hold for independent random variables {X,}. These, in turn, yielded in the weighted i.i.d, case (and certain specific choices of weights {a,}) a necessary and sufficient condition for a two-sided LIL in terms of the distribution of Y. Here, a necessary condition (Theorem 1) is obtained for the general one-sided case and alternative sufficient conditions (Theorem 2) are provided for the twosided case which simplify to Theorem 3 in the weighted i.i.d, case and permit an enlargement of the class of weightings for which a (simultaneous) necessary and sufficient condition may be given (Section 3).

On the Contract of Employment of the Shipping Crew in"Edo"Era

With respect to Japan's shipping business in modern times, studies have been made in such ways that there are only few problems yet to be inves-tigated further regarding vessels, routes, ports and shipping systems and management. But, with respect to the main constituent of management, shipping operators, and practical workers, the crew, still further studies should be made. Above other things, without the thorough investigation of the human-relationship between operators and crew-men, practical under-takers of the business, the perfection of the study of shipping business can not be expected.The present writer tried to make some study on the contract of employ-ment of the crew with an intention of supplying a deficiency of the study mentioned above.The contract of employment of the crew in those times was the contract of service for supplying continual labor. The contract is divided into three kinds, whose subjects are respectively apprentice-sailors, sailors and captains.The conclusion of the contract of service was in reality the agreement of employees to the one-sided conditions offered by employers ; it was also attained through three due formalities, i. e., an interview, the delivery and receipt of advanced money, and drawing and delivery of the deed of contract.The contract consisted mainly of the kinds and the volume of labor and the amount of pay. These conditions of employment were again restricted largely by arrangements made among shipping operators and the routine of the shipping business world in those times. In the contract of service, employees were obliged to swear to perform their duties faithfully, and their responsibilities for the loss of property due to their negligence of service were described in details. The payment as the reward for their service was calculated according to the following four systems : the base-pay, the interest distribution, the Kiridashi, and the Homachi.As in other contracts of service, employees were at the mercy of their employers. They could be fired one-sidedly when they were judged to be guilty or ineligible from the point of view of employers alone, or even for personal reasons on the part of employers. And besides, in case employees violated the laws established by the feudal government, or arrangements made among employers, they were inflicted punishment and were incapable of being employed by other shipping operators.