The Spread Relation and Its Applications

Beginning with Valiron [262], the value distribution theory of algebroid functions of one complex variable has been studied extensively. A few contributions are listed under references. The Nevalinna theory of meromorphic functions on a complex manifold M or meromorphic mappings from M into a projective variety has been studied (see Griffith-King [75], Stoll [239], Vitter [265]). Here we will concentrate on the value distribution theory and its application of algebroid functions in several complex variables.

The measurement of quality in auditorium acoustics by subjective scaling methods—A review of developments in theory and practice

In this paper a review of the recent developments in the theory of a slowly oscillating low aspect ratio, pointed wing at sonic speed is presented, using the concepts of the parabolic method, the equivalence rule and a iteration method to approximately incorporate the thickness effect in the analysis.

3R29. Theory of Porous Media: Highlights in Historical Development and Current State. - R de Boer (Inst fur Mechanik, Univ Essen, Fachbereich 10 Bauwesen, Essen, D-45117, Germany). Springer-Verlag, Berlin. 2000. 618 pp. ISBN 3-540-65982-X. $95.00. Reviewed by N Katsube (Dept of Mech Eng, Ohio State Univ, 206 W 18th Ave, Columbus, OH 43210).This book consists of historical and recent development of porous material theory, can be used as a reference book in this area. In the early and classical era, general development of continuum mechanics such as Cauchy's formulation of the stress concept, the development of linear elasticity theory, and the foundation of thermodynamics are summarized. At the end of each chapter, biographical notes of the important contributors are outlined. There the readers could learn about the lives of these prominent researchers, including their characters, and the nature of scholarly debates. The readers can also learn about how the lives of these researchers were influenced by the historical events, and how failure in one event had led to success in another. In the modern era, the emphasis is placed on the porous materials. The historical review includes the controversy between Fillunger and von Terzaghi and the subsequent development of the theory by Biot and others. Further development of elasticity and plasticity theories and a more modern framework of continuum mechanics and mixture theory are also discussed. The current state of porous material theory reflects the author's work as well as the related work developed mostly in Europe. It is based on the assumption that the deformation gradient of the constituent can be separated into the part due to the real material and the part due to the change of the pores in size and shape through a multiplicative decomposition process. In developing constitutive theories, the principle of material objectivity as well as entropy inequality is employed. An extensive development of a porous material theory is presented based on these theoretical frameworks.Theory of Porous Media: Highlights in Historical Development and Current State is a great book to have if you would like to know about the historical development of porous material theory since many of the letters and articles written by the researchers in early days are not available in English. In addition, if you would like to follow the recent development of porous material theory, which is consistent with the above stated assumptions, this book will provide an extensive review. However, the reader should be aware that this is not the only approach available in the area of porous materials. There are a number of different approaches available for the development of constitutive behavior of porous materials. These other approaches are more phenomenologically based and often motivated by experimental observations. The developed models are verified by experimental data and used to solve important practical problems.

We investigate the uniqueness of transcendental analytic fun- ctions that share three values DM in one angular domain instead of the whole complex plane. 1. Introduction and main results In this paper, a transcendental meromorphic (analytic) function is mero- morphic (analytic) in the whole complex plane C and not rational. We as- sume that the reader is familiar with the Nevanlinna's theory of meromorphic functions and the standard notations such as m(r, f ), T (r, f ). For references, see (2). We say that two meromorphic functions f and g share the value a (a ∈ C = C ∪ {∞}) in X ⊆ C provided that in X, we have f (z) = a if and only if g(z) = a. We will state whether a shared value is by DM (differential mul- tiplicities), or by IM (ignoring multiplicities). R. Nevanlinna (see (4)) proved that if two meromorphic functions f and g have five distinct IM shared values in X = C, then f (z) ≡ g(z). After his very work, the uniqueness of meromor- phic functions with shared values in the whole complex plane attracted many investigations (for references, see (7)). E. Mues consider DM shared values and proved the following theorem.

Today most scholars agree that Rameau was the founder of modern harmonic theory. As we have seen in the previous chapter, Rameau attempted to synthesize in his many writings a multiplicity of ideas – both old and new, speculative and practical – into a unified theory of tonal harmony grounded upon a single underlying principle, the corps sonore (see Chapter 24, pp. 759–71). If he did not succeed in creating a truly systematic and stable theory of harmony owing to his many differing and often contradictory theoretical arguments and intellectual borrowings, he nonetheless bequeathed to the nineteenth century a number of compelling and richly suggestive ideas that would inspire theorists in their own efforts. In this chapter, we will look at the evolution of harmonic theory in the nineteenth century. This is of course a vast and complex topic. Given the profound changes in harmonic language between 1800 and 1900 – a period covering the end of Viennese Classicism and closing with Schoenberg’s first tentative steps beyond the tonal system – it is not surprising that theorists expended extraordinary energy and efforts in their attempts to rationalize this shifting practice. As it is impossible here to describe all of these efforts in detail, we will limit our scope to the development of Austro-German harmonic theory, a tradition which arguably encompasses some of the most innovative and influential writings on this topic for the entire century. Within this tradition, three individual trajectories can be traced back by differing routes to Rameau’s own theory: scale-degree ( Stufen ) theory, fundamental-bass theory, and function theory.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTComments upon Recent Developments in Theory of FiltrationB. F. Ruth, R. E. Montonna, and G. H. MontillonCite this: Ind. Eng. Chem. 1931, 23, 7, 850–851Publication Date (Print):July 1, 1931Publication History Published online1 May 2002Published inissue 1 July 1931https://doi.org/10.1021/ie50259a036RIGHTS & PERMISSIONSArticle Views57Altmetric-Citations3LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (326 KB) Get e-Alerts

Theories of generation of acoustic and magnetohydrodynamic waves are briefly reviewed with a special emphasis on their applicability to stellar convection zones. Recent developments in these theories and possible directions for future studies are discussed. A new approach allowing to extend the Lighthill-Proudman theory of sound generation to a non-isothermal medium is also presented.

The purpose of this paper is to lay the groundwork for the development of a scientific theory of complex human functioning. We first discuss the assumptions on which our thinking is based, then advance the argument that behavior, and human activity in general, may be more fully understood in light of current data on the structural organization of the central nervous system. The brain is organized as a modular, distributed, self-organizing system, which is in constant transaction with the environment. Because of its plasticity, structural and functional change occurs in the brain as a result of experience throughout life. It is our thesis that complex human behavior is organized in a similar manner - that is, human personality and behavior manifest themselves as modular systems. The insights provided by an understanding of the relationship of brain and behavior may enhance the capacity to explain both normal and pathological personality functioning.

The author articulates his most recent formulation of Specificity Theory. He offers personal and professional influences that have contributed to his apprehension of psychoanalytic therapeutic process depicted by this theory. Specificity Theory arises from a psychoanalytic tradition that prioritizes therapeutic efficacy. This tradition began with Ferenczi and unfolded in the clinical perspectives of Balint, Alexander, Winnicott, Bion, and Kohut. Contemporary findings in ancillary fields, such as the infant research of Sander and Tronick, the hermeneutic philosophy of Hans-Georg Gadamer, and the neurobiological theories of brain development and function offered by Gerald Edelman, are confirmatory of the process of understanding emergent uniqueness that Specificity Theory describes. Specificity Theory holds that therapeutic effectiveness is a function of the specific capability for requisite responsiveness of a particular analytic dyad. Specificity Theory is a process theory that recognizes that an analyst's formal psychoanalytic structure theory is only one constituent of that analyst's unique capacity to respond optimally to his particular patient.

The Solow-Swan model which was built under the influence of Harrod’s and Domar’s works on economic growth opened a new way to modeling economic growth (Solow, 1956, Swan, 1956, Burmeister and Dobell, 1970, Zhang, 1990). The standard neoclassical growth model initiated a new course of development of economic growth theory by using the neoclassical production function and neoclassical production theory, still maintaining the traditional way in handling with consumers behaviors in the dynamic analysis. This book is supposed to construct a comprehensive economic theory under the influence of the neoclassical growth theory, even though I will model consumers’ behavior in a way different from the Solow-Swan model. Using the utility function specified in Section 2.1, I am able to solve many important dynamic economic issues which are difficult to be analyze by the traditional economic theories in a consistent manner.

In this paper, we will give suitable conditions on differential polynomials [Formula: see text] such that they take every finite nonzero value infinitely often, where [Formula: see text] is a meromorphic function in complex plane. These results are related to Problems 1.19 and 1.20 in a book of Hayman and Lingham [Research Problems in Function Theory, preprint (2018), https://arxiv.org/pdf/1809.07200.pdf ]. As consequences, we give a new proof of the Hayman conjecture. Moreover, our results allow differential polynomials [Formula: see text] to have some terms of any degree of [Formula: see text] and also the hypothesis [Formula: see text] in [Theorem 2 of W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11(2) (1995) 355–373] is replaced by [Formula: see text] in our result.

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if <TEX>$f^m$</TEX> is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type <TEX>$$f^n+P(f)=be^{sz}+Q(e^z)$$</TEX>, where P(f) is a differential polynomial in f of degree at most n-1, and Q(<TEX>$e^z$</TEX>) is a polynomial in <TEX>$e^z$</TEX> of degree k <TEX>$\leqslant$</TEX> max {n-1, s(n-1)/n} with small functions of <TEX>$e^z$</TEX> as its coefficients.

Reviews - Selected papers of Abraham Robinson. Volume 1. Model theory and algebra. Edited and with an introduction by H. J. Keisler. Yale University Press, New Haven and London1979, xxxvii + 694 pp. - George B. Selioman. Biography of Abraham Robinson, pp. xiii–xxxii. - H. J. Keisler. Introduction, pp. xxxiii–xxxvii. - Abraham Robinson. On the application of symbolic logic to algebra, pp. 3–11. A reprint of XVIII 182. - Abraham Robinson. Recent developments in model theory, pp. 12–31. A reprint of XL 269. - Abraham Robinson. On the construction of models, pp. 32–42. A reprint of XL 506. - Abraham Robinson, Metamathematical problems, pp. 43–59. (Reprinted from The journal of symbolic logic, vol. 38 (1973), pp. 500–516.) - Abraham Robinson. Model theory as a framework for algebra, pp. 60–83. (Reprinted from Studies in model theory, edited by M. D. Morley, Studies in mathematics, vol. 8, The Mathematical Association of America, Washington, D.C., 1973, pp. 134–157.) - Abraham Robinson. A result on consistency and its application to the theory of definition, pp. 87–98. A reprint of XXV 174. - Abraham Robinson. Ordered structures and related concepts, pp. 99–104. A reprint of XXV 170. - Volume 47 Issue 1

Recent developments in value distribution theory for Schrödinger operators on the half line