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Academic literature on the topic 'Zeta Chapter'

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Published: 26 July 2024
Last updated: 27 July 2024

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Journal articles on the topic "Zeta Chapter"

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Geštautas, Andrius, and Antanas Laurinčikas. "On Universality of Some Beurling Zeta-Functions." Axioms 13, no. 3 (February 23, 2024): 145. http://dx.doi.org/10.3390/axioms13030145.

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Let P be the set of generalized prime numbers, and ζP(s), s=σ+it, denote the Beurling zeta-function associated with P. In the paper, we consider the approximation of analytic functions by using shifts ζP(s+iτ), τ∈R. We assume the classical axioms for the number of generalized integers and the mean of the generalized von Mangoldt function, the linear independence of the set {logp:p∈P}, and the existence of a bounded mean square for ζP(s). Under the above hypotheses, we obtain the universality of the function ζP(s). This means that the set of shifts ζP(s+iτ) approximating a given analytic function defined on a certain strip σ^<σ<1 has a positive lower density. This result opens a new chapter in the theory of Beurling zeta functions. Moreover, it supports the Linnik–Ibragimov conjecture on the universality of Dirichlet series.For the proof, a probabilistic approach is applied.
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Müller, Wolfgang. "The mean square of the Dedekind zeta function in quadratic number fields." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 3 (November 1989): 403–17. http://dx.doi.org/10.1017/s0305004100068134.

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Let K be a quadratic number field with discriminant D. The aim of this paper is to study the mean square of the Dedekind zeta function ζK on the critical line, i.e.It was proved by Chandrasekharan and Narasimhan[1] that (1) is at most of order O(T(log T)2). As they noted at the end of their paper, it ‘would seem likely’ that (1) behaves asymptotically like a2T(log T)2, with some constant a2 depending on K. Applying a general mean value theorem for Dirichlet polynomials, one can actually proveThis may be done in just the same way as this general mean value theorem can be used to prove Ingham's classical result on the fourth power moment of the Riemann zeta function (cf. [3], chapter 5). In 1979 Heath-Brown [2] improved substantially on Ingham's result. Adapting his method to the above situation a much better result than (2) can be obtained. The following Theorem deals with a slightly more general situation. Note that ζK(s) = ζ(s)L(s, XD) where XD is a real primitive Dirichlet character modulo |D|. There is no additional difficulty in allowing x to be complex.
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Tomlinson, J. L., A. W. Hahn, G. M. Constantinescu, Colette Wagner-Mann, and N. Williams. "Heat Conduction of Fixator Pins with Polymethylmethacrylate External Fixation." Veterinary and Comparative Orthopaedics and Traumatology 10, no. 03 (1997): 153–59. http://dx.doi.org/10.1055/s-0038-1632587.

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SummaryThe purpose of this study was to determine the degree of thermal conduction along the fixation pins associated with acrylic external fixators and to develop a means of minimizing the potential for thermal injury. The data suggest that the degree of temperature conducted with 1.9 cm diameter acrylic external fixators was of minimal clinical significance if maintained a distance of one centimeter from the patient’s tissues. Larger diameter columns increase the potential for injury, however, this can be minimized with the use of a constant saline drip at the pin-acrylic interface to facilitate heat loss.This article describes the evaluation of thermal properties of polymethylmethacrylate external skeletal fixators. The data demonstrate heat conduction along the fixation pins. Thermal injury is theoretically minimized if columns are maintained a distance of at least one centimeter from the patient’s tissue.Research supported in part by and presented for the University of Missouri Pi Chapter of the Honor Society of Phi Zeta in coordination with SmithKline Beecham Animal Health, April 7, 1994
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Trajković Filipović, Stefan. "“Oh, Vladimir, King of Dioclea, Hard Headed, Heart Full of Pride!” Isaiah Berlin and Nineteenth Century Interpretations of the Live of Saint Vladimir of Dioclea." Issues in Ethnology and Anthropology 9, no. 3 (February 26, 2016): 723. http://dx.doi.org/10.21301/eap.v9i3.10.

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Saint Vladimir of Dioclea (i.e. Zeta) (c. 990–1016) left very few traces in medieval sources, and yet, for centuries now, he is present throughout the Balkans, notably in the areas of modern Albania, Bulgaria, Montenegro, Macedonia and Serbia. Compared to other notable medieval holy kings (e.g. Saint Stefan of Dečani), Saint Vladimir is a “vague” character; he was never as popular and his representations were never fully standardized nor uniformed – he is often simultaneously addressed with few names (Vladimir/Jovan/Jovan Vladimir) and with more than one title (an emperor/Tsar, king or prince). However, this “vagueness“, and yet persistence of the story about this saint makes an interesting research topic. The first elaborated narrative about the saint, the Life of Saint Vladimir of Dioclea, was published in 1601 as part of the Annals of the Priest of Dioclea, a chronicle depicting the history of an imagined early medieval Slavic dynasty and used as an introductory chapter to the Kingdom of Slavs by Mauro Orbini. The Life represents a developed hagiographic narrative with two main lessons – the value of (Saint Vladimir’s) martyrdom (following the model of Christ’s Passion) and of divine punishment awaiting the sinners. Furthermore, as part of the Annals of the Priest of Diocela (and of the Kingdom of Slavs), the Life depicts Vladimir as a Slavic holy king. Since its first edition, the Life remains the main source of inspiration and a starting point for most of the later interpretations of the story of Saint Vladimir’s life and death. In the focus of the article is a specific transformation that occurred in the nineteenth century regarding the story, within Serbian romantic literature. The approach to the transformation is based on the interpretation of the Romantic Movement provided by Isaiah Berlin in his 1965 Mellon lectures delivered in Washington DC (The Roots of Romanticism). I observe the transformation through the analysis of three representative nineteenth century interpretations of the story of Saint Vladimir: the historical dramas Vladimir and Kosara (1829, by Lazar Lazarević) and Vladislav (1843, by Jovan Sterija Popović) and the short story Vladimir of Dioclea (1888, by Stevan Sremac). Comparison of the Life with these narratives reveals significant shifts in main motives and lessons one finds in the story. Thus, instead of focusing on the notions of a holy man who serves as a tool of God’s will and of a Slavic holy king, one finds in nineteenth century interpretations the notions of man’s will, desire and utter loyalty to his own principles and values, one of them being his (Serbian) nation, as key ideas and supreme virtues. In spite of keeping certain hagiographic traits, these romantic interpretations bring reversals of main lessons of the story of Saint Vladimir and thus contribute to Berlin’s observation about the process of conscious creation of new mythologies within Romantic Movement with long-term consequences.
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Brzegowy, Tadeusz. "Los słowa Bożego w sercach słuchaczy (Iz 6,1-13)." Verbum Vitae 13 (January 14, 2008): 29–52. http://dx.doi.org/10.31743/vv.1456.

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Le récit d’Is 6 est rédigé selon le schème des récits de la vocation. Il se compose de la vision (vv. 1-7) et de l’audience (8-13). La liturgie chrétienne propose aux auditeurs seulement la premières partie du chapitre en terminant par le v. 8: «Me voici, envoie-moi». Mais un vrai problème du chapitre se trouve dans sa deuxième partie où Dieu révèle au prophète une inefficacité de sa prediction. Les impératifs «appesantis le coeur de ce peuple» font l’impression que la prédication du messager divin causera l’endurcissement des Israelites, le manque de la conversion et du salut. Cependant ces impératifs sont à entendre comme futurs: ils dévoilent au prophète les difficultés au cours de sa mission, qui a pour but évidemment le salut du peuple. Et ce salut est bien visible dans le denier verset du récit qui parle de la survivance, après une punition terrible, d’un Reste, de la Semence Sainte. Ainsi la vocation finit non seulement par vision de la survivance d 'une petite partie du peuple, mais aussi de sa sanctification. Il est aussi très probable que dans l’appellatif zera’ qodes est compris le Messie personnel, du Rejeton de Jesse du chapitre 11, l et Ie Germe de Yahvé (semah Yahvé) du chapitre 4,2.Selon le récit de vocation d’Isaïe (Is 6, 1-13) l’aventure de la parole de Dieu se déploie dans le coeur humain. C’est pourquoi il vaut la peine de lire et de mediter toute la narration de la vocation d’Isaïe: la parole de Dieu entre dans le coeur de l’homme, le libère de l’endurcissement, et le conduit finalement à la conversion et la sainteté.
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Korac, Vojislav. "Prilog poznavanju jednobrodnih crkava sa kupolom na dubrovackom podrucju." Zbornik radova Vizantoloskog instituta, no. 44 (2007): 129–43. http://dx.doi.org/10.2298/zrvi0744129k.

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(francuski) L?objet du travail sont les dessins architectoniques du groupe d??glises a une nef du haut moyen ?ge dans la r?gion de Dubrovnik. Les dessins sont accompagnes de br?ves descriptions des monuments. L?auteur les publie en les destinant a une meilleure connaissance des monuments gr?ce aux dessins plus complets et faits avec plus de pr?cision que les dessins publies. Ils sont le fruit des recherches faites en 1962 et ils n?ont pas ?t? publies en raison du changement d?orientation de l?auteur vers des th?mes que la pratique lui imposait. Un texte bref explique la raison de la publication des dessins avec citation de la litt?rature sur les monuments. Le plus en vue de ces monuments est l??glise de Saint Michel a Stone, ?uvre du roi de Zeta Mihailo (Michel). Dans leur ensemble ces monuments repr?sentent un chapitre important de l?histoire de l?architecture serbe m?di?vale, ou l??glise a une nef avec la coupole, d?origine byzantine, ?tait dominante. Le fait que les historiens de l?art aussi bien serbes que croates ont accorde leur attention a ces ?uvres indiquent toute l?importance de ces monuments.
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Nassir, Aqeelnasssir, Abbas Mishall, and Ahmad mohammed. "Soil Compaction Induced by Different Tillage Systems and its Impact on Growth and Yield of Maize (Zea Mays L.)." University of Thi-Qar Journal of agricultural research 13, no. 1 (June 1, 2024): 185–200. http://dx.doi.org/10.54174/utjagr.v13i1.302.

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Abstract: Maize (Zea Mays L.) cultivation faces challenges from mechanized tillage-induced compaction, impacting soil physical properties crucial for growth. This compaction, stemming from machinery-soil interactions during tillage, alters bulk density, root penetration resistance, and water infiltration rates. Tractive tires play a central role in this process. The chapter explores the intricate relationship, emphasizing its adverse effects on maize root development, nutrient availability, and overall grain yield. While studies report significant yield reductions under severe compaction, a universally agreed-upon critical level remains elusive, necessitating further research into dynamic soil factors influencing maize productivity. This insight informs strategies for optimizing cultivation practices amid mechanized tillage challenges. Soil compaction, a critical concern in maize cultivation, profoundly impacts plant growth. Mechanized tillage-induced compaction alters soil properties, affecting bulk density, root penetration, and water movement. Compacted soil restricts air and water availability, hindering root respiration and nutrient uptake. This multifaceted constraint leads to poor seed germination, reduced yields, and increased vulnerability to root diseases. Mitigation strategies include low tillage machine loads, precision agriculture, conservation tillage, bioturbation, and deep tillage. While some compaction may benefit water retention, excessive levels pose risks. A holistic approach involves soil assessments, controlled traffic farming, cover crops, mechanical aeration, optimized equipment design, and ongoing monitoring. Education and adaptive practices are crucial for sustainable soil compaction management.
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Books on the topic "Zeta Chapter"

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Boone, William R. 113 Calhoun Street: The early years of the Beta Zeta Chapter of Alpha Gamma Rho. [S.l: s.n.], 2003.

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Chapter, Zeta Omicron Omega. History, Heritage and Timeless Service 1955-2013: Alpha Kappa Alpha Sorority, Inc. Zeta Omicron Omega Chapter Mid-Atlantic Region. AuthorHouse, 2014.

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Zeta, Omicron Omega Chapter. History, Heritage and Timeless Service 1955-2013: Alpha Kappa Alpha Sorority, Inc. Zeta Omicron Omega Chapter Mid-Atlantic Region. AuthorHouse, 2014.

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Keating, Jon P. Random matrices and number theory: some recent themes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0008.

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The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and rather selective introduction to the theory of the Riemann zeta function, in particular to those parts needed to understand the connections with random matrix theory. The second section focuses on the value distribution of the zeta function on its critical line, specifically on recent progress in understanding the extreme value statistics gained through a conjectural link to log–correlated Gaussian random fields and the statistical mechanics of glasses. The third section outlines some number-theoretic problems that can be resolved in function fields using random matrix methods. In this latter case, random matrix theory provides the only route we currently have for calculating certain important arithmetic statistics rigorously and unconditionally.
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Crown Jewels and Cultured Pearls along the Ivy Vine : The Mid -Atlantic Region, and the Timeless History and Timeless Service of Zeta Chi Omega Chapter from 1956-2013: The Enduring Legacy of Alpha Kappa Alpha Sorority, Inc. Alpha Kappa Alpha Sorority, Incorporated Zeta Chi Omega Chapter, 2014.

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Bakan, Michael B. Zena Hamelson. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190855833.003.0002.

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When we first meet ten-year-old Zena Hamelson, she is sitting in a chair staring blankly at the wall, flapping her hands, repeatedly straightening and bending her legs, compulsively twisting and pulling on her fingers as her Artism Ensemble bandmates make joyful music all around her. Zena is stimming, that is, she is practicing a personal repertoire of self-stimulatory behaviors that align precisely with the symptomatic profile of her diagnosed autism spectrum disorder: Asperger’s syndrome. Stimming, autism researchers tell us, is associated with some dysfunctional system in the brain; its reduction or elimination is a target goal of many therapeutic interventions and autism studies. Yet as the chapter unfolds, Zena’s stimming is revealed as something else entirely: a meaningful mode of music-making, creative expression, and social experience unto itself.
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Algebraic Geometry Codes: Advanced Chapters. American Mathematical Society, 2019.

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Book chapters on the topic "Zeta Chapter"

1

Cornelissen, Gunther, and Norbert Peyerimhoff. "Spectra, Group Representations and Twisted Laplacians." In Twisted Isospectrality, Homological Wideness, and Isometry, 17–30. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27704-7_3.

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AbstractIn this chapter, we review basic notions about spectra, group representations, and twisted Laplace operators. We first recall how to define the spectrum and the spectral zeta function for a general symmetric second order elliptic differential operator acting on smooth sections of a Hermitian line bundle. We prove that the non-zero spectrum (i.e., the spectral zeta function) determines the entire spectrum on an odd-dimensional manifold, but also give an example showing that this is not always true for even-dimensional manifolds; the example is obstructed by the non-vanishing of some topological genus. After setting up some notation from representation theory, we discuss G-sets and weak conjugacy (“Gaßmann equivalence”) of subgroups of a group, explaining the interrelations. In the final sections, we introduce twisted Laplacians, corresponding to unitary representations of the fundamental group. After this, we focus on the case of a twisted Laplacian arising from a finite Galois cover of manifolds and we relate the spectrum on the top manifold to that of the induced representation on the bottom manifold. We relate the multiplicity of zero in the spectrum to the multiplicity of the trivial representation in the given representation, and finally we show that, contrary to the general case, the multiplicity of zero in the spectrum of a twisted Laplacian is determined from the non-zero spectrum, provided one also knows the usual Laplace spectrum of the manifold.
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Cornelissen, Gunther, and Norbert Peyerimhoff. "Homological Wideness, “Class Field Theory” for Covers, and a Number Theoretical Analogue." In Twisted Isospectrality, Homological Wideness, and Isometry, 85–90. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-27704-7_10.

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AbstractIn a previous chapter, we have constructed a particular Riemannian covering realising a wreath product. In this chapter, we first return to that example and use class field theory for Riemannian coverings (à la Sunada) to study the behaviour of geodesic in such covers. We then relate, in the general case, homological wideness of a group G acting on a manifold M (i.e., the question whether the first homology of M contains the regular representation of G) to the existence of geodesics with certain splitting behaviour. In exact analogy to an classical argument in analytic number theory, we use the Ruelle zeta function to show the existence of infinitely many totally split geodesics for a given covering in the negative curvature case. Finally, the analogy with class field theory allows us to study an analogue of homological wideness in the theory of extensions of number fields.
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Chabannon, Christian, and Chiara Bonini. "Structure of and Signalling Through Chimeric Antigen Receptor." In The EBMT/EHA CAR-T Cell Handbook, 3–5. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-94353-0_1.

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AbstractChimeric antigen receptor (CAR) is a synthetic transmembrane protein expressed at the surface of immune effector cells (IECs) that are reprogrammed either in vitro or in vivo (June et al. 2018; June and Sadelain 2018). Techniques for genetic engineering of autologous or allogeneic IECs are described in the next chapter. The synthetic CAR incorporates several functional domains. The extracellular domain is composed of a single chain variable fragment (ScFV) of immunoglobulin and recognizes the “tumour” antigen. The clinical relevance of the selected tumour antigen—with a view to minimize “on-target/off-tumour” side effects—is discussed in the third chapter of this section. Bispecific and trispecific CARs are currently being evaluated in preclinical and early clinical trials (Bielamowicz et al. 2018; Shah et al. 2020). The use of an immunoglobulin domain as the ligand of the target antigen means that recognition is not restricted to HLA antigens and that CAR-T cells are universally applicable as opposed to T cell receptor (TCR) transgenic T cells that recognize antigenic peptides presented in the context of a defined major histocompatibility complex (MHC), limiting clinical applications to subsets of patients with defined HLA typing. The intracellular domain is composed of the intracellular domain of the zeta chain of the CD3 component of the TCR, which will trigger signalling when the CAR engages the targeted ligand. The transmembrane region links the two extracellular and intracellular domains through the cell membrane and plays an important role in determining the conformation and flexibility of the CAR and its ability to efficiently bind the targeted antigen/epitope. Association of only these three functional domains characterized first generation CARs, as described in the original publications (Kuwana et al. 1987; Eshhar et al. 1993). However, full activation of T cells requires the addition of one (second generation CARs) or two (third generation CARs) domains from costimulatory molecules, such as CD28, 4-1BB/CD137, or OX40/CD134, that provide the T cell costimulatory signal. Currently approved CAR-T cells are second generation CAR-T cells; as an illustration, the CAR in tisagenlecleucel contains a 4-1BB domain, while the CAR in axicabtagene ciloleucel contains a CD28 domain. The nature of the costimulatory domain influences the ability of CAR-T cells to expand or persist (limit T cell exhaustion) in vivo after infusion into the patient, although it is unclear how this translates clinically and affects disease control, occurrence of adverse events, and overall survival due to the lack of head-to-head comparison between approved products. Finally, fourth generation CAR-T cells have been developed for preclinical projects. These cells, named armoured CAR cells or T cells redirected for universal cytokine-mediated killing (TRUCKS), encode not only a CAR (usually with one costimulatory domain, such as in second generation CARs) but also a cytokine, interleukin, pro-inflammatory ligand, or chemokine that will counteract the immune suppressive microenvironment that prevails in most solid tumours (Eshhar et al. 1993; Chmielewski and Abken 2015).
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Dobre, Mihnea. "Chapter 1: Introduction." In zeta-descartes, 17–66. Zeta Books, 2017. http://dx.doi.org/10.5840/zeta-descartes20173.

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Dobre, Mihnea. "Chapter 5: Conclusions." In zeta-descartes, 376–95. Zeta Books, 2017. http://dx.doi.org/10.5840/zeta-descartes20177.

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Simionescu-Panait, Andrei. "Chapter 2. Inchoate movement." In zeta-reconciledbody, 53–112. Zeta Books, 2021. http://dx.doi.org/10.5840/zeta-reconciledbody20214.

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Simionescu-Panait, Andrei. "Chapter 3. Postured movement." In zeta-reconciledbody, 113–70. Zeta Books, 2021. http://dx.doi.org/10.5840/zeta-reconciledbody20215.

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Simionescu-Panait, Andrei. "Chapter 1. Phenomenological toolkit." In zeta-reconciledbody, 27–52. Zeta Books, 2021. http://dx.doi.org/10.5840/zeta-reconciledbody20213.

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Telegdi-Csetri, Áron. "Chapter 7: Cosmopolitanism or Cosmopolitics?" In zeta-kantc, 174–94. Zeta Books, 2020. http://dx.doi.org/10.5840/zeta-kantc20208.

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Telegdi-Csetri, Áron. "Chapter 5: Cosmopolitanism, Deliberation and Right." In zeta-kantc, 123–57. Zeta Books, 2020. http://dx.doi.org/10.5840/zeta-kantc20206.

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