Narrower Class Research Articles

On some functional calculus of closed operators in a Banach space

We develop a functional calculus for a class of closed operators in a Banach space. We establish several properties of the calculus under consideration such as continuity, stability, and uniqueness theorems, the spectral mapping theorem, the inversion theorem, and some others. In our preceding work we developed an analogous functional calculus for a narrower class of operators.

Stimulation of Ideas through Compound‐Based Bibliometrics: Counting and Mapping Chemical Compounds for Analyzing Research Topics in Chemistry, Physics, and Materials Science

Counting compounds (rather than papers or citations) offers a new perspective for quantitative analyses of research activities. First of all, we can precisely define (compound-related) research topics and access the corresponding publications (scientific papers as well as patents) as a measure of research activity. We can also establish the time evolution of the publications dealing with specific compounds or compound classes. Moreover, the mapping of compounds by establishing compound-based landscapes has some potential to visualize the compound basis of research topics for further research activities. We have analyzed the rare earth compounds to give an example of a broad compound class. We present the number of the currently existing compounds and of the corresponding publications as well as the time evolution of the papers and patents. Furthermore, we have analyzed the rare earth cuprates (copper oxides) as an example of a narrower compound class to demonstrate the potential of mapping compounds by compound-based landscapes. We have quantified the various element combinations of the existing compounds and revealed all element combinations not yet realized in the synthesis within this compound class. Finally, we have analyzed the quasicrystal compound category as an example of a compound class that is not defined by a specific element combination or a molecular structure.

A very strong difference property for semisimple compact connected lie groups

Let G be a topological group. For a function f: G → ℝ and h ∈ G, the difference function Δhf is defined by the rule Δhf(x) = f(xh) − f(x) (x ∈ G). A function H: G → ℝ is said to be additive if it satisfies the Cauchy functional equation H(x + y) = H(x) + H(y) for every x, y ∈ G. A class F of real-valued functions defined on G is said to have the difference property if, for every function f: G → ℝ satisfying Δhf ∈ F for each h ∈ G, there is an additive function H such that f − H ∈ F. Erdős’ conjecture claiming that the class of continuous functions on ℝ has the difference property was proved by N. G. de Bruijn; later on, F. W. Carroll and F. S. Koehl obtained a similar result for compact Abelian groups and, under the additional assumption that the other one-sided difference function ∇hf defined by ∇hf(x) = f(xh) − f(x) (x ∈ G, h ∈ G) is measurable for any h ∈ G, also for noncommutative compact metric groups. In the present paper, we consider a narrower class of groups, namely, the family of semisimple compact connected Lie groups. It turns out that these groups admit a significantly stronger difference property. Namely, if a function f: G → ℝ on a semisimple compact connected Lie group has continuous difference functions Δhf for any h ∈ G (without the additional assumption concerning the measurability of the functions of the form ∇hf), then f is automatically continuous, and no nontrivial additive function of the form H is needed. Some applications are indicated, including difference theorems for homogeneous spaces of compact connected Lie groups.

On Banach spaces whose norm-open sets are [formula omitted]-sets in the weak topology

We investigate non-separable Banach spaces whose norm-open sets are countable unions of sets closed in the weak topology and a narrower class of Banach spaces with a network for the norm topology which is σ-discrete in the weak topology. In particular, we answer a question of Arhangel'skii exhibiting various examples of non-separable function spaces C ( K ) with a σ-discrete network for the pointwise topology and (consistently) we answer some questions of Edgar and Oncina concerning Borel structures and Kadec renormings in Banach spaces.

Convergence acceleration of orthogonal series

The aim of this paper is to verify efficiency of two acceleration methods for orthogonal series (more strictly, for series defined at the beginning of Section 1). These methods are quite different although they use the same transform of such a series given there. The first method (Section 3) has some features common with Levin’s and Weniger’s methods. It may be profitably used in numerical calculations for a vast class of series. The second one (Sections 4 and 5) is somewhat similar to the Euler–Knopp transform of power series. Also this method is numerically realizable but more important is that for a narrower class of series, including some ones having applications in physics, it gives explicit analytic formulae of their transform.

Local or Global Minima: Flexible Dual-Front Active Contours

Most variational active contour models are designed to find local minima of data-dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a "desirable" local minimum as opposed to an undesirable configuration due to noise or complex image structure. As such, there has been much research into the design of complex region-based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge-based energy functionals whose sensitivity to noise and texture is significantly worse. Unfortunately, most of these more "robust" region-based energy functionals are applicable to a much narrower class of imagery compared to typical edge-based energies due to stronger global assumptions about the underlying image data. Devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image-based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima. Such implementations have been proposed for capturing global minima. However, sometimes the completely-global minimum is just as undesirable as a minimum that is too local. In this paper, we propose a novel, fast, and flexible dual front implementation of active contours, motivated by minimal path techniques and utilizing fast sweeping algorithms, which is easily manipulated to yield minima with variable "degrees" of localness and globalness. By simply adjusting the size of active regions, the ability to gracefully move from capturing minima that are more local (according to the initial placement of the active contour/surface) to minima that are more global allows this model to more easily obtain "desirable" minimizers (which often are neither the most local nor the most global). Experiments on various 2D and 3D images and comparisons with some active contour models and region-growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications.

On the commutative factorization of n × n matrix Wiener–Hopf kernels with distinct eigenvalues

In this article, we present a method for factorizing n × n matrix Wiener–Hopf kernels where n >2 and the factors commute. We are motivated by a method posed by Jones (Jones 1984 a Proc. R. Soc. A 393 , 185–192) to tackle a narrower class of matrix kernels; however, no matrix of Jones' form has yet been found to arise in physical Wiener–Hopf models. In contrast, the technique proposed herein should find broad application. To illustrate the approach, we consider a 3×3 matrix kernel arising in a problem from elastostatics. While this kernel is not of Jones' form, we shall show how it can be factorized commutatively. We discuss the essential difference between our method and that of Jones and explain why our method is a generalization. The majority of Wiener–Hopf kernels that occur in canonical diffraction problems are, however, strictly non-commutative. For 2×2 matrices, Abrahams has shown that one can overcome this difficulty using Padé approximants to rearrange a non-commutative kernel into a partial-commutative form; an approximate factorization can then be derived. By considering the dynamic analogue of Antipov's model, we show for the first time that Abrahams' Padé approximant method can also be employed within a 3×3 commutative matrix form.

Cosmological evolution of heavy-element andH2abundances

Spectroscopic observations of distant quasars have resulted in the detection of molecular hydrogen in intervening damped Lyman α absorption clouds (DLAs). We use observations compiled from different experimental groups to show that the molecular hydrogen abundance exhibits a dramatic increase over a cosmological time period corresponding to 13 to 24 per cent of the age of the Universe. We also tentatively show that the heavy-element abundances in the same gas clouds exhibit a faster and more well-defined cosmological evolution compared with the general DLA population over the same time baseline. We argue that this latter point is unsurprising, because the general DLA population arises in a wide variety of galaxy types and environments, and thus a spans broad range of ISM gas-phases and abundances at the same cosmic time. DLAs exhibiting H2 absorption may therefore circumvent this problem, efficiently identifying a narrower class of objects, and provide a more sensitive probe of cosmological chemical evolution.

Sexual ratio in populations of Sparisoma radians and Sparisoma atomarium at Los Roques Archipelago, Venezuela: An evolutionary approach

A comparative study of two populations of Sparisoma radians and one population of Sparisoma atomarium indicates significant differences in the overall and size-specific adult sex ratio, as well as in the width of the critical size class for sex change of these hermaphrodite marine fish species. Sparisoma atomarium shows an overall sex ratio more biased to females and a rather sharp change in size-specific sex ratio than S. radians, revealing a narrower critical size class for sex change. The differences observed between species agree with that reported in another study, which outlines an evolutionary explanation based on the different mating systems of these species. Significant differences were detected in the form and central localization of size distribution between the two samples of S. radians, accompanied with a displacement in the respective size class for sex change and the constancy in overall sex ratio. This result, in addition to the condition of sex ratio biased to females in the three populations, agrees with predictions of evolutionary models of sequential hermaphroditism.

Generalized piecewise linear histograms

We extend the concept of piecewise linear histogram introduced recently by Beirlant, Berlinet and Györfi. The disadvantage of that histogram is that in many models it takes on negative values with probability close to 1. We show that for a wide set of models, the extended class of estimates contains a bona fide density with probability tending to 1 as the sample size n increases to infinity. The mean integrated absolute error in the extended class of estimators decreases with the same rate n–2/5 as in the original narrower class.

Can robots without Hebbian plasticity make good models of adaptive behaviour?

No. Animals' primary problem is the shaping of movements, guided by and adapting to sensory signals. This requires a narrower class of biorobotic models than that spanned by Webb's dimensions and examples. We claim that all model variables and mechanisms must have real counterparts, input vectors must model known sensor fields, internal state vectors and transformations must model neurophysiological processes, and output vectors must model coordinated muscle signals.

Monsters Among Us

There are monsters that scare children and monsters that scare grownups, and then there are monsters that scare philosophers of mind. This paper is concerned with this third sort of monster, whose primary representative is the zombie – a living being, physically just like a person but lacking consciousness. Though zombies act like normal people and appear to have normal brains, everything is blank inside. Unfortunately, the term ‘zombie’ covers a narrower class of deficits than is convenient, failing to cover apparently normal human beings lacking propositional attitudes. Davidson's (1987) “Swampman” is supposed to be an example of such a creature, so I will dub individuals who are apparently normal but lack all propositional attitudes ‘swampfolk,’ though this is non-standard terminology. In what follows, I will refer to both zombies and swampfolk as ‘monsters,’ and will similarly designate animals lacking in consciousness or propositional attitudes.

Richard Peterson and cultural theory: From genetic, to integrated, and synthetic approaches

To trace the importance of Richard Peterson for theories of culture in effect this article maps developments over the past thirty years. Initially, Peterson introduced the production-of-culture approach as a grounded theoretical perspective, rather than a formal theory. Theoretically, this perspective was undergirded by assumptions about culture as genetic code. From this point of departure, Peterson subsequently moved to consider cultural consumption. Specifically, his analysis of ‘culture classes’ and characterization of cultural ‘omnivores’ moved beyond narrower structuralist class theories of consumption. Given these two strands of cultural analysis - of production and consumption - the question arose of how to arrive at an integrated theory of relations between the two. A review of the sociologies of Wendy Griswold and Howard S. Becker suggests two central issues: overcoming the binary division of production versus consumption, and incorporating theories of meaning formation and deployment. But these issues in turn require a synthetic theory rather than simply the integration of production and consumption approaches. Recent developments toward a synthetic theory of culture reach a point anticipated by Peterson in the 1970s, in that they theorize the production of meaning in the course of social life.

Services of General Interest in EC Law: Matching Values to Regulatory Technique in the Public and Privatised Sectors

All the European Union Member States have long traditions of state activity in providing key services (such as the utilities, health and education) to their citizens and underpinning both such direct provision and provision of services by non‐state actors with certain administrative or legal guarantees. In European Community doctrines they are referred to as ‘services of general interest’ within which is a narrower class of ‘services of general economic interest’. The diverse national public service traditions have been challenged both by the requirements of the single market and by other pressures such as fiscal crisis and broader public sector reform. This article examines the means by which services to which special principles should be applied can be identified and focuses on the range of sometimes contradictory values denoted by the term ‘services of general interest’, examining the range of regime types (based on hierarchical, competition‐based and community forms) by which those values might be pursued. The concluding section suggests that the matching of values to techniques should not be made according to the importance of the values to be pursued, but rather by reference to which techniques are likely to be effective given the configuration of interests and capacities and existing culture within the target domain.

EVOLUTIONARY STABILITY OF INEQUALITY STRUCTURES

This paper studies the evolution of a population whose members compare their relative income to coordinate actions in a simple bargaining game. Two alternative customs are considered: one in which difference in income (i.e. difference in social class) is large enough to justify difference in behavior, and another in which difference in income is perceived as not sufficient to justify a difference in behavior. Although we constrain agents to these bargaining strategies, reference class boundaries are subjectively determined. Our model yields the following conclusions. If individuals form fixed, unambiguous images of their position in the social structure, then social inequality will eventually disappear, as the income of each individual converges to a uniform level. On the other hand, if social images vary from individual to individual (and evolve through some learning process), then social inequality may persist, with class consciousness (i.e. narrower subjective class boundaries) being most pronounced in those who occupy the extreme positions (either very rich or very poor) of the social ranking.

Minimizing the Rounding Error from Point Sample Estimates of Tree Frequencies

Abstract Three solutions are presented for estimating stems per acre when trees are tallied by diameter class with horizontal point sampling. The first solution is based on the arithmetic mean of the diameter-class limits. The second is based on the geometric mean of the diameter-class limits and is unbiased for uniform within-class diameter distributions. The third is a harmonic mean solution; it is derived from the ratio of the geometric mean squared and the arithmetic mean. If the within-class distribution is linear, then the solution based on the geometric mean is preferable. Any of these solutions may be adequate provided diameter-class widths are minimized, particularly for small trees. The geometric-mean solution is the recommended solution in instances where uniformity can be assumed within diameter classes. Observed frequencies in two stands, however, provided inconsistent results. In estimating tree frequency, errors resulting from grouping become smaller as tree diameter increases. For large trees, estimation of frequency can be obtained with much wider diameter limits than with small trees for a fixed level of grouping error. Rather than fixing diameter-class width, it may be advantageous to consider a narrower class width or exact measurement for trees in smaller diameter classes. West. J. Appl. For. 12(4):108-114.

The Existence of a Short Sequence of Admissible Pivots to an Optimal Basis in LP and LCP

We say an LP (linear programming) is fully nondegenerate if both the primal and the dual problems are nondegenerate. In this paper, we prove the existence of a sequence of |B∖B| admissible pivot from any basis B (not necessarily feasible) to the unique optimal basis B, if the given LP has an optimal solution and is fully nondegenerate. Here admissible pivots are those pivots (satisfying certain sign conditions) that exist if the current LP dictionary is not terminal, i.e., neither optimal, inconsistent nor dual inconsistent. A natural extension of the result to LCPs (linear complementarity problems) with sufficient matrices is given. The existence itself does not yield a strongly polynomial pivot algorithm for LPs but provides us with a good motivation to study the class of admissible pivot methods for LPs, as opposed to the narrower class of simplex methods for which the shortest sequence of pivots is not known to be polynomially bounded.

The existence of a short sequence of admissible pivots to an optimal basis in LP and LCP

We say an LP (linear programming) is fully nondegenerate if both the primal and the dual problems are nondegenerate. In this paper, we prove the existence of a sequence of |B ∗βB| admissible pivot from any basis B (not necessarily feasible) to the unique optimal basis B ∗ , if the given LP has an optimal solution and is fully nondegenerate. Here admissible pivots are those pivots (satisfying certain sign conditions) that exist if the current LP dictionary is not terminal, i.e., neither optimal, inconsistent nor dual inconsistent. A natural extension of the result to LCPs (linear complementarity problems) with sufficient matrices is given. The existence itself does not yield a strongly polynomial pivot algorithm for LPs but provides us with a good motivation to study the class of admissible pivot methods for LPs, as opposed to the narrower class of simplex methods for which the shortest sequence of pivots is not known to be polynomially bounded.

Inconsistencies in paranoid functioning, premorbid adjustment, and chronicity: question of diagnostic criteria.

Despite the widely held belief that paranoid behavior is associated with good premorbid adjustment, low chronicity, and high current functioning in psychiatric inpatients, inconsistencies in the literature suggest that supportive evidence may be an artifact of the measurement model commonly used to index paranoid status. In a sample of 497 nonorganic inpatients selected from 19 treatment units, paranoid behavior, when measured by a dimensional/cumulative model, was not found to indicate higher functioning and associated relationships, but simply to reflect a narrower class of problem behavior. Only when paranoid status was defined using a traditional model based on the predominance of the defining class of behavior did paranoid subjects demonstrate better premorbid adjustment, lower chronicity, and higher levels of functioning than nonparanoid subjects. Serious problems exist in the use of information obtained from traditional predominance/class models for either theoretical or practical purposes.

A Generalized Compositional Approach for Reservoir Simulation

Abstract A procedure for solving compositional model equations is described. The procedure is based on the Newton-Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated readily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered are (1) a conventional waterflood problem, (2) displacement of oil by CO2, and (3) the displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems.