bluuebunny/crossref_metadata_2025 huggingface dataset:
Combining Anerobic Degradation and Chemical Precipitation for the Treatment of High Strength, Strong Nitrogenous Landfill Leachate
Authors: Gunay Ahmet , Karadag Dogan , Tosun Ismail , Ozturk Mustafa
Published: November 2008

Treatment of organics and ammonium from sanitary landfill leachate was investigated using a combination of anaerobic treatment and magnesium ammonium phosphate precipitation (MAP) processes. The effect of organic loading rate (OLR) was evaluated for the removal of COD and BOD5 in an anaerobic treatment by anaerobic sludge blanket (UASB) reactor. The UASB reactor removed organics successfully. OLR has a significant effect on the reactor performance and the maximum COD removal was 90% at an OLR of 9 kg COD/(m3d). On average, 86.3% of COD and 95.3% of BOD5 were removed at a steady state of anaerobic treatment. MAP precipitation was performed in order to decrease the ammonium concentration of anaerobically‐treated leachate. Furthermore, the effect of pH and the molar ratio of MAP constituents on the removal of ammonium were evaluated. The maximum ammonium removal was observed as 98% at a pH of 8.5 and a stoichometric ratio of NH4/PO4/Mg = 1/1/1. The results obtained indicate that a combination of UASB and MAP can be successfully used for the removal of organics and ammonium from sanitary landfill leachate.
Topology and symmetry analysis of rare earth borocarbides structural family, analogy to hexaferrites and relation to properties
Authors: Belokoneva E. L. , Mori Takao
Published: November 2008

The topology and symmetry analysis was applied to a series of rare earth borocarbide compounds, which have been gaining increasing interest due to their magnetic and thermoelectric properties. Using principles of OD theory, the crystal structures were deconvoluted into L(1) (B12 icosahedra and C‐B‐C chain) layers and L(2) (rare earth and B6 octahedral) layers. The arrangement of B12 icosahedra in the L(1) layer is equal to close packed spheres, however, symmetry of the B12 block lowers symmetry of the resulting layer from P 6/mmm to P 3m1. Both layers, L(1) and L(2) possess symmetry P 3m1 and the conjugation of L(1) with L(2) layers occurs in accordance with the symmetry elements. No disorder may appear here because of equal symmetry of single layers and layer pairs and it is not a classical OD family. Only the increasing of the amount of one type of layers, namely L(1), provides the structural variations. Close analogy to the hexagonal ferrites family has been found. Topology and symmetry analysis reveals principles in the building up of the structural family, gives an insight into the particular order‐disorder formation mechanism/criteria of these homologous borocarbide compounds and as the result relation to the properties (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Estimating Euler equations with noisy data: two exact GMM estimators
Authors: Alan Sule , Attanasio Orazio , Browning Martin
Published: November 2008

In this paper we exploit the specific structure of the Euler equation and develop two alternative GMM estimators that deal explicitly with measurement error. The first estimator assumes that the measurement error is log‐normally distributed. The second estimator drops the distributional assumption at the cost of less precision. Our Monte Carlo results suggest that both proposed estimators perform much better than conventional alternatives based on the exact Euler equation or its log‐linear approximation, especially with short panels. An empirical application to the PSID yields plausible and precise estimates of the coefficient of relative risk aversion and the discount rate. Copyright © 2008 John Wiley & Sons, Ltd.
Adjustment of high‐order sliding‐mode controllers
Authors: Levant Arie , Michael Alon
Published: November 2008

Long‐lasting problems of high‐order sliding‐mode (HOSM) design are solved. Only local uncertainty suppression was previously obtained in the case when the dynamic system uncertainties are unbounded. This restriction is removed in this paper. A universal method is proposed for the proper controller parameter adjustment based on the homogeneity approach. The method allows making the finite‐time convergence arbitrarily fast or slow. In addition, a HOSM regularization procedure is proposed diminishing chattering. Computer simulation confirms the theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.
Kranbahnträger aus warmgewalzten Mannesmann‐Stahlhohlprofilen (MSH)
Authors: Dittmann Cornelius , Herion Stefan , Josat Ole , Sunder Philipp
Published: November 2008

Für den Neubau einer Hofkranbahn des Werks Düsseldorf der Vallourec & Mannesmann Deutschland GmbH sollte für den Einsatz von quadratischen warmgefertigten Hohlprofilen ein neues Designkonzept untersucht und umgesetzt werden. Bis dahin wurden Kranbahnträger für größere Stützweiten und höhere Beanspruchungen durch Hohlkastenträger oder individuelle Sonderkonstruktionen realisiert. Sowohl die Fertigung dieser Träger als auch die spätere Montage auf der Baustelle ist komplex, zeit‐ und kostenintensiv. In enger Zusammenarbeit aller an dem Projekt Beteiligten und unter Federführung des Ingenieurbüros Dittmann & Pollmann in Hagen ist es gelungen, die technischen Herausforderungen des Projekts zu bewältigen und einen neuen Kranbahntyp zu realisieren, wie der folgende Beitrag zeigt.
A Liberal Nation In Spite of Itself
Authors: Kazin Michael
Published: November 2008

All praise to Jeff Cowie and Nick Salvatore. They've dared to look deep into the pit of progressive hopes in modern US history and have emerged with something important and new to say about that much debated, much lamented subject. And they get certain big things right. The hegemony of individualism, the historic weakness of the labor movement, divisions of race, and the ways in which most white Christians apply their religious faith have all interacted to limit what, in Europe, are called the prospects of social-democracy and, in this country, usually go under the name of modern liberalism. Their concluding suggestion that reformers may find in “the fluid alliances of the Progressive Era” a more helpful analogy than in the class-based coalition led by FDR is a welcome provocation, although they don't choose to elaborate on it.
Christ and the CIO: Blue-Collar Evangelicalism's Crisis of Conscience and Political Turn in Early Cold-War California
Authors: Dochuk Darren
Published: November 2008

This article explores tensions within the Democratic Party's uneasy alliance of grassroots labor and blue-collar evangelicalism that collapsed in heated confrontation during California's postwar political realignment. The context in which this played out is Ham and Eggs, one of California's largest old-age welfare movements during the 1930s which, in the midst of economic reconstruction, found new (but short-lived) relevance in the late 1940s. From spring 1945 until summer 1946 Ham and Eggs rallied workers behind its message of economic redistribution and Christian Americanism in hopes of forcing new legislation on behalf of pensions for the elderly. In the process, it stirred a political storm that thrust it into a significance exceeding its original intent. At issue was the “labor question,” the vexing uncertainty animating American politics at this juncture about the extent to which New Deal liberalism's labor-friendly initiatives and progressive impulses for economic freedom, racial equality, and social justice would be extended. Caught between a labor-Left movement within the Democratic Party that looked to extend New Deal liberalism and a galvanized Christian Right, which looked to roll it back, blue-collar evangelicals affiliated with Ham and Eggs confronted a new political reality that compelled them to choose between their class and faith commitments. With reluctance they chose the latter over the former. The decision marked the beginning of blue-collar evangelicalism's shift to the Right and ultimately the formation of a broader evangelical political alliance that would prove instrumental in the rise of California's conservative Republican movement.
The relevance of spoken features in English as a foreign language (EFL)
Authors: Markus Manfred
Published: November 2008

An analysis of the need for attention to the spoken word and phonetics in the teaching of English world-wide. It is a truism that English is increasingly becoming a world language. Even in China a ‘craze for English’ has been, in view of the fact that over 200 million children (about 20% of all children in the world) now1 learn English in Chinese schools. McArthur has estimated that c.250 million Indians use English every day. All these speakers of English use it their own way. This localisation of English has been variously detected, for example in Hong Kong. It is also well known from versions of African English and, in fact, from most English varieties that have been attributed to the ‘Outer’ or ‘Extended. However, as early as 1983 Kachru voiced a caveat: ‘A large majority of the non-native speakers of institutionalised varieties of English use a local variety of English, but when told so, they are hesitant to accept the fact’.
Soil and light effects on the sapling performance of the shade-tolerant speciesBrosimum alicastrum(Moraceae) in a Mexican tropical rain forest
Authors: Lopez-Toledo Leonel , Martínez Mariana , van Breugel Michiel , Sterck Frank J.
Published: November 2008

Many studies conclude that light is the most important resource that determines plant performance of tree saplings in tropical rain forests, and implicitly suggest that soil resources are less important. To provide a quantitative test for soil versus light effects on sapling performance, we studied how saplings of the shade-tolerant tree speciesBrosimum alicastrumresponded to contrasting levels of light availability and soil fertility in a Mexican tropical rain forest. Therefore saplings were selected from ten low-light exposure (crown position index <1.5) and ten high-light exposure (crown position index ≥2.5) sites either on productive alluvial soils, or on poor sandy soils on adjacent hills. Annual growth responses were scored for 58 saplings. The soil–light interaction had a strong positive effect on branching rate and leaf area production, rather than light or soil alone. Height growth only increased at higher light availability. Herbivore damage was higher on the more productive soil and, to a lesser extent, at higher light availability. Our results suggest that saplings (1) responded differently to soil and light availability, (2) expanded in overall size when both soil and light limitations are released, but only increased in height with increasing light intensity (3) and faced a trade-off between expansion and defence along both soil and light gradients. This study emphasizes the role of soil resources, in interaction with light availability, on the plastic responses in saplings living in a tropical forest understorey.
Linguistic Input and Conversational Strategies in L1 and L2
Authors: McLaughlin Barry
Published: November 2008

There has been a great deal of discussion in the literature on second-language acquisition about the relationship between first-(L1) and second-language (L2) acquisition. I believe that the dust is beginning to settle and that it is now possible to move beyond this debate. I would like to do so in this paper, and examine in particular the role of linguistic input in L1 and L2 and the nature of conversational strategies in both processes.
Intercultural Differences and Communicative Approaches to Foreign Language Teaching in the Third World
Authors: Osterloh Karl-Heinz
Published: November 2008

Language is not simply a formal system of sounds, words, and syntactical structures; language also reaches into the domain of human interaction, which for its own part follows certain rules. Every native speaker assimilates individual social experiences characteristic of his own culture. These experiences inhere in statements that obtain their communicative significance through interpretation: “Die Bedeutung eines sprachlichen Zeichens kennen heisst wis en, wie es verwendet werden kann, d.h. wie man mit ihm handeln kann, welche Regeln für seinen Gebrauch gelten” (Heringer, 1977). Each society accumulates rules according to which concrete statements are interpreted abstractly and which are valid among communicating partners through common usage.
English Reference Grammar for Polish Learners
Authors: Krzeszowski Tomasz P.
Published: November 2008

English Reference Grammar for Polish Students or shortly Polish English Grammar (PEG) is a pedagogical contrastive grammar. It is written on contrastive principles and is based on the results of investigations conducted by a team of Polish linguists within the Polish-English Contrastive Project, sponsored by Center for Applied Linguistics at Arlington, Virginia and the Polish Ministry of Science, Technology and Higher Education. The Project is managed by Professor Jacek Fisiak, Director of the Institute of English Studies at Adam Mickiewicz University in Poznan. Two volumes of the studies have already been published and two more are in preparation. (Fisiak 1973, 1974). The studies are conducted in the theoretical framework of generative transformational grammar, covering the most recent developments of the theory, without priority given to any specific version of the theory. Case grammar, generative semantics, extended standard theory, natural phonology, natural generative grammar and even language-in-the-context versions are all considered in the studies. Being basically theoretically oriented, the Project is not directly applicable in pedagogical practice, although a considerable amount of work is also being done along the didactic lines.
Abdication and Responsibility in Language Teaching
Authors: Allwright Dick
Published: November 2008

It is easy for learner-centred approaches to classroom method to fall into the trap of appearing to advocate the virtual abdication of the teacher. The purpose of this paper is to try to redress the balance by setting out an approach (in Section II), initially quite neutral with respect to the ‘teacher-centred or learner-centred’ issue, that instead simply specifies the ‘things that have to happen’ in a classroom if the experience is to have any chance of being a profitable one for the learners. These things are necessary but not sufficient, because attempting to ensure that they happen entails running a number of major risks (to be specified in Section II) that threaten to destroy the value of the classroom experience.
Incipient creolization in Gastarbeiterdeutsch?: An experimental sociolinguistic study
Authors: Pfaff Carol W.
Published: November 2008

From the point of view of linguists interested in pidginization, creolization, or other language contact phenomena, the continued presence of large numbers of southern European and North African foreign workers (called Gastaibeitei in Germany) and their families in northern European countries presents almost laboratory conditions for the investigation of the initial and subsequent stages of foreign language acquisition and development. Of particular interest is the fact that many of the languages involved here (Turkish, Arabic, Greek, Serbo-Croatian, Spanish, Italian, Portuguese) are typologically and genetically distinct; thus the situation is ideal for the study of common features of language development. If a Creole were to develop here, it would provide extremely valuable evidence for or against proposed universals.
Learner feedback and its effects in communication tasks: a pilot study
Authors: Gaies Stephen J.
Published: November 2008

This article reports on a pilot investigation of learner feedback and its effects on teacher/ learner interactions in second language learning. In twelve ESL (English as a Second Language) dyads and triads, tapes were made of the performance by the participants of a pair of tasks in referential communication. In these tasks, the teacher described verbally a series of six graphic designs in such a way that the learner(s), who had the designs reproduced on a sheet of paper, could determine the order in which the designs were described. Data analysis involved classification of both learner feedback and teachers' post-feedback responses.
Beyond output: the analysis of interlanguage development
Authors: Kohn Kurt
Published: November 2008

One of the main challenges faced by second langague acquisition research is to find an answer to the question of which processes and strategies guide the learner's attempt to acquire a foreign language. Whereas most investigations are based on the learner's output, this paper argues in favor of a more comprehensive approach. It tries to close the speculative gap between output and the underlying processes by integrating three types of questions:

(a) What requirements do learners impose on their own interlanguage output?

(b) What linguistic knowledge concerning the fulfillment of their requirements do learners have stored in their memories?

(c) What linguistic forms do learners actually use in their interlanguage output and how do these comply with their underlying knowledge?

An analysis which goes beyond the bounds of output by combining what learners want with what they know along with what they produce leads to insights into their interlanguage processes.

Quantitative procedures are introduced which measure learners' knowledge with respect to their requirement of correctness and also the extent to which their output complies with what they know. Three empirical studies are presented. They demonstrate that an analysis which combines information about requirements, knowledge and output can deal effectively with some of the dynamic aspects of interlanguage behavior.
Language lateralization in adult bilinguals
Authors: Wesche Marjorie B. , Schneiderman Eta I.
Published: November 2008

Recent experimental studies of bilinguals have provided evidence of less left lateralization (i.e. greater right hemisphere participation) for verbal tasks in the second language than in the first. Other clinical and experimental studies of adults suggest that the normal adult right hemisphere has certain residual language-related capacities and that it plays a role in the early stages of both child and adult language acquisition. These findings lead us to postulate a link between right hemisphere involvement in the early stages of first and second language acquisition.

Two studies were designed to investigate this issue. The subjects of the studies were adult French-English bilinguals, with one group dominant in English and a second in French. A single word dichotic listening paradigm was employed in both studies. Following Obler (1981), the hypotheses were 1) that the second language dichotic task would show less left lateralization (greater right hemisphere involvement) than the first and 2) that greater proficiency in the second language would correlate with a higher degree of left lateralization (less right hemisphere involvement) on the dichotic test in that language. The studies provide some support for these hypotheses and thus, indirectly, for a unified theory of first and second language acquisition.
Classroom Interaction and Discourse Options
Authors: Kramsch Claire J.
Published: November 2008

This article takes a social-theoretical view of the reality created by a foreign language in the classroom. It examines the interaction of teacher and learners in their various activities along a continuum that extends from instructional to natural discourse and is determined by the way participants present themselves to one another and negotiate turns-at-talk, topics, and repairs. Suggestions are made for broadening and diversifying the discourse options in the classroom to enrich the social context of the language learning experience.
Some Assumptions about Second Language Text Comprehension
Authors: Wolff Dieter
Published: November 2008

In an empirical investigation, the results of which are reported elsewhere in greater detail (Wolff, 1985), an attempt was made to discover more about the strategies and processes specific to second language (L2) comprehension. On the assumption that information processing is of a universal cognitive nature, no differences in the cognitive processes themselves involved in first language (L1) and L2 comprehension were expected. It was, however, expected that differences would emerge in the way common strategies and processes were applied in the decoding of texts and utterances. We assumed that the differences would be of degree and not of kind, and that the extent and exploitation of these processes in L2 comprehension could be distinguished from L1 comprehension. The experimental design closely followed that developed by L1 comprehension research. A text was presented to an informant followed by the instruction to recall it. We adopted this type of experiment for two reasons: (a) It has proved its reliability in L1 research, and (b) our results could be compared to those obtained in L1 research. The similarities and differences between L1 and L2 results were thus quite easy to analyze.
Second Language Acquisition: Possible Insights from Studies on How Birds Acquire Song
Authors: Neapolitan Denise M. , Pepperberg Irene M. , Schinke-Llano Linda
Published: November 2008

Research into general linguistic and cognitive processes in humans has been aided by studies of analogous processes in animals. Studies on how birds develop their species-specific song have been of particular interest to researchers seeking to identify critical variables and universels in first language acquisition in humans. Because of recent studies onexceptionalsong acquisition, that is, time-independent. learning of second dialects or song by birds generally thought to acquire a single song during a limited sensitive period, we suggest that there also exist significant parallels between human second language acquisition and avian bilingualism. The purpose of this paper is to highlight these parallels and to demonstrate that such interspecies comparisons may provide new insights into the processes of second language acquisition.
A Proposed Framework for Testing the Oral Language of Second/Foreign Language Learners
Authors: Shohamy Elana
Published: November 2008

Within the proposed framework, oral tests consist of several different speech interactions, each of which encompasses a variety of contextual variables that affect its output. These interactions are performed as simulations in order to tap unmonitored language, which approximates the most stable discourse style, namely, the vernacular. The sample of speech interactions included on an oral test is randomly selected from specifications of those interactions most relevant to the specific context and purpose of the assessment. The language samples are then assessed with rating scales, whose criteria vary according to the intended use of the test results. The accuracy of the scores, the quality of the test as a whole, and the assumptions made about oral language are examined through the relevant types of reliability and validity as well as through extensive research.
Second Language Acquisition and Language Universals Research
Authors: Comrie Bernard
Published: November 2008

To the extent that language universals represent internal properties of human beings, one would expect them to manifest themselves in first language (L1) acquisition. Whether they should also manifest themselves in second language (L2) acquisition depends on whether or not language universals remain accessible to adults. The relation between L2 acquisition and language universals research is examined with respect to three phenomena: extraction, where the subset principle makes interesting predictions, although the second language data are far from clear; structure dependence, where there is evidence for the continuation beyond puberty of a general formal property of language; and the distribution of overt reflexives, which has a functional basis and therefore poses the interesting question whether or not this functional basis is accessible to language learners.
Acquisition Theory and Experimental Design
Authors: Beck Maria-Luise , Eubank Lynn
Published: November 2008

In their recent contribution on the Garden Path Technique, Tomasello and Herron (1989) suggested that the experimental results they obtained on this means of providing negative feedback lend support to a “cognitive comparison model” of second language (L2) acquisition, and they further hypothesize that it may be useful in eliminating other L2 overgeneralizations. The results Tomasello and Herron (henceforth TH) present are clearly interesting, for they appear to show that negative evidence—here, a special type of error correction—may be crucial in L2 learning. As promising as the TH results may be, however, there is reason to believe that they also should be viewed with caution. In the following, we provide some of the reasons why caution should be taken.
The Mechanism of the Rusting of Iron
Authors: Evans U. R.
Published: November 2008

In a previous paper it has been shown that the corrosion of zinc, cadmium, iron and lead is connected with electric currents set up through unequal distribution of oxygen; the currents have been measured and compared with the weight of metal corroded away. The “unaerated” areas are anodic, and thus the attack tends to become concentrated upon the points relatively inaccessible to oxygen. When a drop of salt water is placed on an iron sheet, the central part of the drop suffers anodic corrosion, giving rise to ferrous salts, whilst the marginal ring over which oxygen has ready access to the metal becomes cathodic, alkali being produced there. Where the ferrous salt and alkali come into contact, ferrous hydroxide is precipitated, which oxidises to ferric hydroxide; after a few hours we get a membrane of brown ferric hydroxide extending right over the drop, but surrounded by a ring of clear alkaline liquid. All the actual corrosion of the metal is confined to the area within the membrane; the metal below the external ring of clear liquid, to which oxygen has access, suffers no attack.
Hankel Transforms
Authors: Titchmarsh E. C.
Published: November 2008

I have to correct the proof of the assertion on p. 471 of my paper that if f (t) is integrable over (0, a) and ν ≥ – ½, then
Reducibility of differential operators some: examples
Authors: Fishel B. , Denkel N.
Published: November 2008

A symmetric operator on a Hilbert space, with deficiency indices (m; m) has self-adjoint extensions. These are ‘highly reducible’. The original operator may be irreducible, (see example (i), below). Can the mechanism whereby reducibility is achieved be understood? The concrete examples most readily studied are those associated with differential operators. It is easy to obtain operators, associated with a formal linear differential operator, having deficiency indices (m; m). What of reducibility? Nothing seems to be known. In the case of the first-order operator we were able, using the Volterra operator, to establish irreducibility of the associated minimal operator. To investigate symmetric operators associated with a second-order differential operator, different methods had to be developed. They apply also to the first-order operator, and we employ them to demonstrate the irreducibility of the associated minimal operator. In the second-order case the minimal operator proves reducible, and we also exhibit examples of reducibility of associated symmetric operators. It would clearly be of interest to elucidate the influence of the boundary conditions on reducibility.
The Pettis integration of a perturbed wave equation
Authors: Fink James P.
Published: November 2008

In this paper, we investigate the integrability of the vector field of the initial-value problem associated with certain nonlinear wave equations. This vector field involves translations and as such is not a strongly continuous or even strongly measurable L∞-valued function. It is shown that such a vector field, although not generally Pettis integrable, does turn out to be so in an important situation. We then indicate how this result can be used to obtain pseudo-solutions of the initial-value problem.
On the transitivity of the orthogonal and symplectic groups in projective space
Authors: Dye R. H.
Published: November 2008

1.Introduction. Let Ω be a non-singular quadric in ann-dimensional projective spacePG(n, K) whose coordinate field isK. With respect to Ω the linear subspaces ofPG(n, K) fall into various types: the subspaces of a given type each have the same dimension and the same geometrical kind of quadric section with Ω. Each element of the collineation group Γ preserving Ω takes a subspace into one of the same type, but Γ may divide the subspaces of a given type into several transitivity classes or orbits.
The isotropic scattering of radiation from an asymmetric spherical source in a finite atmosphere
Authors: Smith M. G.
Published: November 2008

A singular integral equation is derived for the three-dimensional Fourier transform of the source function, when the scattering atmosphere is contained in a finite convex volume.

This equation is shown to reduce to the usual equation in the case of an isotropic point source in a finite spherical atmosphere of radius R0, and is used to solve the same problem when the source is anisotropic.

It is shown that in the latter case an expansion in Legendre polynomials results, in which the coefficients are obtained from the integral equations of a similar construction to those for an isotropic source. The error in taking the dominant part is now however of order 1/R0 and not e–R0.
On a certain class of group presentations
Authors: Edjvet M.
Published: November 2008

In [8] and [9] S. J. Pride has initiated a study of group presentations in which each defining relator involves exactly two members of the generating set. The methods there involve the use of graphs and so-called edge groups – the building blocks of such presentations. In this paper we replace ‘graph’ by ‘set of finite subsets of a given set’, and ‘edge group’ by ‘face group’ in order to study a larger class of presentations. This way we are able to extend to this larger class a Freiheitssatz and a result on diagrammatic asphericity which appear in the references cited above.
Ringing the cosets. II
Authors: White Arthur T.
Published: November 2008

Hamiltonian circuits with associated word an n-cycle, in Schreier right coset graphs for symmetric groups Sn mod cyclic groups Zn, correspond to change ringing principles on n bells for which the plain course is the extent; that is, neither bobs nor singles are required. This connection is made explicit for the general case, and then specialized to the cases n = 4 (minimus) and n= 5 (doubles). In particular, all 102 no-call doubles principles on three generators are found and catalogued.
Lifting results for sequences in Banach spaces
Authors: Gonzalez M. , Onieva V. M.
Published: November 2008

Several important classes of Banach spaces are characterized by means of convergence properties of sequences. For example, if X is a Banach space, then X belongs to the class Nl1 of spaces without copies of l1, the class R of reflexive spaces or the class F of finite-dimensional spaces if and only if each bounded sequence has respectively a weakly Cauchy (w-Cauchy), weakly convergent (w-convergent) or convergent subsequence. Similarly X is in the class WSC of weakly sequentially complete spaces, or the class SCH of spaces with the Schur property if and only if each w-Cauchy sequence is w-convergent, or convergent, respectively; note that X ∈ SCH if and only if each w-convergent sequence of X is convergent (see [12], p. 47).
Isometries of self-adjoint complex function spaces
Authors: Ellis A. J.
Published: November 2008

By a complex function space A we will mean a uniformly closed linear space of continuous complex-valued functions on a compact Hausdorff space X, such that A contains constants and separates the points of X. We denote by S the state-space

endowed with the w*-topology. If A is self-adjoint then it is well known (cf. [1]) that A is naturally isometrically isomorphic to , and re A is naturally isometrically isomorphic to A(S), where (respectively A(S)) denotes the Banach space of all complex-valued (respectively real-valued) continuous affine functions on S with the supremum norm.
An ‘excursion’ approach to an annealing problem
Authors: Chan Terence , Williams David
Published: November 2008

The following problem is the simplest of a group of problems motivated by work of Durran and Truman [1] on planetesimals.
A distance formula and Bourgain algebras
Authors: Younis R. , Zheng D.
Published: November 2008

In this paper, a distance formula to a Douglas algebra is established. We use this distance formula to show that the distance of an L∞ function to the intersection of arbitrary Douglas algebras is equivalent to the supremum of the distance of that function to these algebras. As an application, we prove that the Bourgain algebra of the intersection of two Douglas algebras is equal to the intersection of the Bourgain algebras of these two algebras.
Multifractal dimensions of product measures
Authors: Olsen L.
Published: November 2008

We study the multifractal structure of product measures. for a Borel probability measure μ and q, t Є , let and denote the multifractal Hausdorff measure and the multifractal packing measure introduced in [O11] Let μ be a Borel probability merasure on k and let v be a Borel probability measure on t. Fix q, s, t Є . We prove that there exists a number c > 0 such that

for E ⊆k, F ⊆l and Hk+l provided that μ and ν satisfy the so-called Federer condition.

Using these inequalities we give upper and lower bounds for the multifractal spectrum of μ × ν in terms of the multifractal spectra of μ and ν
Abstract Definitions for the Symmetry Groups of the Regular Polytopes, in Terms of Two Generators. Part I: The Complete Groups
Authors: Coxeter H. S. M. , Todd J. A.
Published: November 2008

The groups of rotations that transform the regular polygons and polyhedra into themselves have. been studied for many years. Lately, increasing interest has been shown in the “extended” groups, which include reflections (and other congruent transformations of negative determinant). Todd has proved that every such group can be defined abstractly in the form

This group is denoted by [k1, k2, …, kn−1], and is the complete (extended) group of symmetries of either of the reciprocal n.-dimensional polytopes {k1, k2,…, kn−1}, {kn−1, kn−2,…, k1}. There is a sense in which these statements hold for arbitrarily large values of the k's. But here we are concerned only with the cases where the groups and the polytopes are finite. The finite groups are

[k] is simply isomorphic with the dihedral group of order 2k (e.g. [2], the Vierergruppe). [3, 3,…, 3] with n − 1 threes, or briefly [3n−1], is simply isomorphic with the symmetric group of order (n + 1)!.
Canonical Forms of the Quaternary Cubic associated with arbitrary Quadrics
Authors: Turnbull H. W.
Published: November 2008

§ 1. The general quaternary cubic

can be expressed in various interesting canonical forms involving suitably chosen linear forms Xi, Yi, Ai. Thus, referred to the pentahedron. X1X2X3X4X5 of Sylvester the cubic becomes the sum of five cubes

with its Hessian in the form

where the coefficients ai may if necessary be taken as equal to unity and the five linear forms Xi each contain four independent parameters, making a total of twenty parameters which is the number of coefficients aijk in the given cubic C3
The Integral Expansions of Arbitrary Functions connected with Integral Equations
Authors: Hyslop J.
Published: November 2008

The following paper aims at a more general treatment than has hitherto been given, of the integral expansions of arbitrary functions, from the point of view of integral equation theory.
On Five Lines, in Space of Four Dimensions, which lie upon a, Quadric Threefold and the Normal Quartic Curves of which they are Chords
Authors: Bath F.
Published: November 2008

The connexion between the conditions for five lines of S4

(i) to lie upon a quadric threefold,

and (ii) to be chords of a normal quartic curve,

leads to an apparent contradiction. This difficulty is explained in the first paragraph below and, subsequently, two investigations are given of which the first uses, mainly, properties of space of three dimensions.
A preliminary note on a direct determination of the distribution of intensity in the natural β-ray Spectrum of RaB and RaC
Authors: Curtiss L.F.
Published: November 2008

Many investigations bave sbown the presence of a “continuous” β-ray spectrum accompanying tbe β-ray lines in tbe naturai spec-trum of Ra B and Ra C. The existence of sucb a spectrum is not easily accounted for if one is to regard the nucleus as existing in sharply quantised states. It has been pointed out that this spectrum may be a spurious effect, arising from scattering from the walls of the apparatus and not from within the atom itself. Therefore it is of importance to obtain accurate information regarding the continuous spectrum and its relation to the line spectrum.
A characterization of universally measurable sets
Authors: Darst R. B.
Published: November 2008

The purpose of this note is to complement some recent results of R. O. Davies and H.G.Eggleston.
On Appell's function F2
Authors: Manocha H. L.
Published: November 2008

1. It has been observed that certain problems in quantum mechanics have their exact solutions which can be expressed in terms of Appell's function F2 as defined by (e.g. (7), p. 211)

Having regard to this fact, Srivastava (5) proved a summation formula

where R(λ) > 1, R(α) > − 1 and x⇌y indicates the presence on the right of a second term that originates from the first by interchanging x and y.
On the function
Authors: Meligy A. S. , EL Gazzy E. M.
Published: November 2008

In a previous paper (3) one of us reported an expansion for the exponential integral

in terms of Bessel functions. In this note, we shall obtain the more general formula

where n is any positive integer, γ is Euler's constant and

It reduces to that in (3) when n = 1.
On the relative merits of correlated and importance sampling for Monte Carlo integration
Authors: Halton John H.
Published: November 2008

Given a totally finite measure space (S, S, μ) and two μ-integrable, non-negative functions f(x) and φ(x) defined in S, such that when

then

we define correlated sampling as the technique of estimating

by sampling an estimator function

where ξ is uniformly distributed in S with respect to μ (i.e. for any T ∈ S, p(T) = μ(T)/μ(S) is the probability that ξ lies in T): and importance sampling as estimating L by sampling the estimator function

where η is distributed in S with probability density φ(x)/Φ

Then, clearly,

It follows that υ(ξ) and ν(η) are both unbiased estimators of L, and that their variances can both be made to approach zero arbitrarily closely by making φ(x) a sufficiently close approximation to f(x).
An approximate solution for two-dimensional transonic flow past thin airfoils
Authors: Evans T.
Published: November 2008

The transonic, two-dimensional flow past a thin airfoil is treated by approximating the transonic small perturbation equation by a linear equation valid in the neighbourhood of the airfoil. The solution is derived by representing the body by a line of suitable sources. Pressure distributions are given for airfoils with maximum thickness both forward and aft, and agreement with experiment improves as the position of maximum thickness moves aft.
On the idea of frequency
Authors: Burnside W.
Published: November 2008

A statistical table is in effect a classification of a finite number, N, of objects in respect of a finite number of different classes, A, B, C, … It is assumed that unambiguous rules have been laid down by which it is possible to determine whether any particular one of the objects does or does not belong to any particular one of the classes. The application of these rules to a particular object does not depend on the fact that that object is one of a finite number of N objects, so that the process of classification may be started on a non-finite collection of objects. When the collection of objects is non-finite the process can never end. On the other hand when the collection is finite the process must end; and when completed it will determine how many of the objects belong to any particular class. If in this way it is found that N1 (≤ N) of the objects belong to class A, the proper fraction N1/N is spoken of as the frequency of class A in the collection. In particular cases it may be zero or unity. In general it is a rational proper fraction. For its determination in complicated cases it may be convenient to suppose the collection to be arranged in some special way, but its value is absolutely independent of any such particular arrangement.
Intersection-complexes. I. Combinatory Theory
Authors: Newman M. H. A.
Published: November 2008

The theory of the intersection-complex Ch · Ck, due originally to Veblen, Weyl, Alexander and Lefschetz, has recently been extended by Flexner to cover intersections on a “topological n-manifold” (locally Cartesian n-space) in the case h + k = n. In his theory the whole of Lefschetz's work for ordinary simplicial manifolds is presupposed, including the rather difficult approximations. The object of the present paper is to provide a combinatory theory of the general intersection, (h + k ≥ n), which would serve equally well as a basis for Flexner's work, and avoids the wasteful process of using two independent approximations.
Some relations connecting the freedoms of manifolds
Authors: Room T. G.
Published: November 2008

The word “freedom” is used in this paper with the same meaning as “Konstantenzahl"—the number of free constants—and corresponds very roughly to the term “degrees of freedom” as used in elementary mechanics. “Freedom of a manifold” is used as a convenient abbreviation for “freedom of the class of manifolds of the same specification as the given one”. At the outset the idea is rather vague; in the background there is an intuitive notion of a definite number associated with any given manifold—the number of conditions that manifolds of the same specification can be made to satisfy. This paper is intented to give some precision to this idea, and to formulate rules which will enable the freedom of a given manifold to be calculated.
A Method of Continuous Observation of the Equivalent Height of the Kennelly-Heaviside Layer
Authors: White E. L. C.
Published: November 2008

A development of the “echo” method of observation of the height of the Kennelly-Heaviside layer is described. Short wave-trains of radiation lasting sec. are transmitted at regular sec. intervals, and observed stroboscopically, together with their echoes, by means of a cathode ray oscillograph. Details of the transmitting and receiving apparatus are given. The rapid fluctuation in amplitude of the echoes is easily studied by this method.
On Summable Trigonometric Integrals
Authors: Verblunsky S.
Published: November 2008

1. The analogue for trigonometric integrals of de la Vallée Poussin's classical theorem concerning the uniqueness of the trigonometrical development has recently been obtained by M. Jacob in the following form.
Some series and integrals involving associated Legendre functions
Authors: Bailey W. N.
Published: November 2008

1. In a recent paper I have given some definite integrals involving Legendre functions which, as a limiting case, give known results involving Bessel functions. In another paper I have shown how some integrals involving Bessel functions can be obtained from Bateman's integral

and the well-known expansion
A condensation diagram
Authors: Dee P. I.
Published: November 2008

When a mass of air, saturated with water vapour at room temperature θ1, is expanded adiabatically, the temperature falls to a lower temperature θ2. In general the resulting density of water vapour is greater than the equilibrium value at the temperature θ2and condensation commences. This condensation causes heating of the gas and the temperature rises until finally at some temperature θ3the density of uncondensed vapour is equal to the equilibrium vapour density at θ3. (θ1> θ3> θ2.) Condensation then ceases and the air rises slowly to room temperature by heat conduction through the walls of the apparatus.
On Gauss's proof of the normal law of errors
Authors: Jeffreys Harold
Published: November 2008

Gauss gave a well-known proof that under certain conditions the postulate that the arithmetic mean of a number of measures is the most probable estimate of the true value, given the observations, implies the normal law of error. I found recently that in an important practical case the mean is the most probable value, although the normal law does not hold. I suggested an explanation of the apparent discrepancy, but it does not seem to be the true one in the case under consideration.
A theorem on transitive groups
Authors: Birkhoff Garrett
Published: November 2008

Let be any transitive permutation group on the n symbols 1, …, n. Let be the subgroup of whose elements leave i fixed. Let ′ be the normalizer of , i.e., the subgroup of the symmetric group on 1, …, n transforming into itself. Let G′, G′1, G′2, etc., denote elements of ′. Finally, let ″ be the centralizer of , i.e., the subgroup in transforming every element of into itself.
Slow rotation of a circular cylinder in a viscous fluid bounded by parallel walls
Authors: Howland R. C. J. , Knight R. C.
Published: November 2008

Solutions of the bi-harmonic equation valid in the region bounded externally by parallel lines and internally by a circle midway between the lines have been given by one of the Authors in a recent paper [2]. These solutions were adapted to the requirements of certain problems in the theory of elasticity, but modified solutions satisfying the boundary conditions characteristic of viscous fluid motion are easily derived. These modified solutions will here be given and will be used to find the stream function corresponding to the slow rotation of a cylinder placed symmetrically between parallel walls.
Lines and Planes in a Metrical Space
Authors: Hunter W.
Published: November 2008

§ 1. “Stretches” joining Points in a Metrical Space.

If x, y, z are any points in a metrical space, then by definition

Regarding x and y as fixed, we may define the set of points z for which

as the “stretch joining the points xy” or more shortly the stretch xy*. Then for points z not on the stretch,

The stretch xy always contains the points x and y themselves, which we may call the “end-points” of the stretch. In particular cases, it may contain no other points: e.g. with the function δ0(x, y) = 1 when xǂy, each stretch contains only its end-points †.
The surface ionisation of potassium on molybdenum
Authors: Evans R. C.
Published: November 2008

Some experiments are described in which the efficiency of ionisation of potassium at a hot molybdenum surface was investigated. The degree of ionisation observed is consistent with the most recent measurements of the electron work function of molybdenum.
On the Figure of Pappus' Theorem
Authors: Rao C. V. Hanumanta
Published: November 2008

When a triangle ABC is in perspective with A′B′C′ and with B′C′A′, so is it also in perspective with C′A′B′, and the two triangles may then be said to be in cyclic perspective. The centres of perspective then form a third triangle XYZ, such that, of the three triangles, every two are in cyclic perspective with the vertices of the third for centres. The figure thus arising is the figure of Pappus' Theorem with nine points and nine lines incident by threes.
The absorption spectra of “saturated” and “unsaturated” organic substances
Authors: Purvis J. E.
Published: November 2008

This investigation is to discuss some of the conditions which influence the absorption spectra of various “saturated” and “unsaturated” organic compounds. A condensed cadmium spark was used as the source of radiant energy; alcoholic solutions of the substances were employed, except for stearic acid, which was dissolved in ether. The vapours were examined in a quartz tube 200 mm. long, placed in a bath which could be heated to various temperatures.