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1. |
Record Nr. |
UNINA9910953751903321 |
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Autore |
Throm Sebastian |
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Titolo |
Uniqueness of Fat-Tailed Self-Similar Profiles to Smoluchowski's Coagulation Equation for a Perturbation of the Constant Kernel |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2021 |
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©2021 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (118 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.271 |
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Classificazione |
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Disciplina |
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Soggetti |
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Statistical mechanics |
Integro-differential equations |
Integral equations -- Integro-partial differential equations -- Integro-partial differential equations |
Statistical mechanics, structure of matter -- Time-dependent statistical mechanics (dynamic and nonequilibrium) -- Interacting particle systems |
Integral transforms, operational calculus -- Integral transforms, operational calculus -- Laplace transform |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Cover -- Title page -- Chapter 1. Introduction -- 1.1. Smoluchowski's equation -- 1.2. Long-time behaviour and self-similarity -- 1.3. The equation for self-similar profiles -- 1.4. Finite mass, fat-tailed profiles and scale invariance -- 1.5. Existence and uniqueness of self-similar profiles -- 1.6. The constant kernel =2 -- 1.7. Assumptions on the kernel -- 1.8. Preliminary work and main result -- 1.9. The boundary layer at zero -- 1.10. Outline of the main ideas and strategy of the proof -- Chapter 2. Functional setup and preliminaries -- 2.1. Function spaces and norms -- 2.2. Transforming the equation to Laplace variables -- 2.3. Notation and elementary properties of \T -- Chapter 3. Uniqueness of profiles -Proof of Theorem 1.12 -- 3.1. Key ingredients for the proof -- 3.2. Proof of Theorem 1.12 -- Chapter 4. Continuity estimates -- 4.1. Proof of \cref{Lem:est:Arho,Lem:est:B2} -- 4.2. Proof of Proposition 3.5 -- 4.3. Estimates for differences -Proof of |
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Proposition 3.6 -- Chapter 5. Linearised coagulation operator -Proof of Proposition 3.7 -- Chapter 6. Uniform bounds on self-similar profiles -- 6.1. A priori estimates for self-similar profiles -- 6.2. Uniform convergence in Laplace variables -- 6.3. Proof of \cref{Prop:norm:boundedness,Prop:closeness:two:norm} -- Chapter 7. The boundary layer estimate -- 7.1. Boundary layer equation -- 7.2. Preliminary estimates -- 7.3. Proof of Proposition 3.10 -- Chapter 8. The representation formula for ₀(⋅, ) -- 8.1. Analyticity properties -- 8.2. Proof of Proposition 7.11 -- Chapter 9. Integral estimate on \Qo₀(⋅, ) -- 9.1. Proof of Proposition 7.12 -- Chapter 10. Asymptotic behaviour of several auxiliary functions -- 10.1. Bounds on moments -- 10.2. Asymptotic behaviour of _{ } and Φ -- 10.3. Regularity properties close to zero -- Appendix A. Useful elementary results. |
Appendix B. The representation formula for -- B.1. Proof of Proposition 1.2 -- B.2. Integral estimates on \Ker -- Appendix C. Existence of profiles -- Acknowledgments -- Bibliography -- Back Cover. |
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Sommario/riassunto |
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"This article is concerned with the question of uniqueness of self-similar profiles for Smoluchowski's coagulation equation which exhibit algebraic decay (fat tails) at infinity. More precisely, we consider a rate kernel which can be written as The perturbation is assumed to have homogeneity zero and might also be singular both at zero and at infinity. Under further regularity assumptions on we will show that for sufficiently small there exists, up to normalisation of the tail behaviour at infinity, at most one self-similar profile. Establishing uniqueness of self-similar profiles for Smoluchowski's coagulation equation is generally considered to be a difficult problem which is still essentially open. Concerning fat-tailed self-similar profiles this article actually gives the first uniqueness statement for a non-solvable kernel"-- |
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2. |
Record Nr. |
UNINA9911049101703321 |
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Autore |
Panda Minati |
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Titolo |
Exploring Interactions Between Linguistic Theories, Language Learning and Pedagogy / / edited by Minati Panda, Suneeta Mishra, Judit Baranyiné Kóczy |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
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ISBN |
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Edizione |
[1st ed. 2025.] |
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Descrizione fisica |
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1 online resource (640 pages) |
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Collana |
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Second Language Learning and Teaching, , 2193-7656 |
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Altri autori (Persone) |
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MishraSuneeta |
Baranyiné KóczyJudit |
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Disciplina |
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Soggetti |
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Psycholinguistics |
Language and languages - Study and teaching |
Applied linguistics |
Education and state |
Psycholinguistics and Cognitive Lingusitics |
Language Education |
Applied Linguistics |
Educational Policy and Politics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Chapter 1: ‘Language’ and ‘Learning’ as objects of Inquiry: A transdisciplinary historiography of theories and practices -- Chapter 2: Meaningful Grammar: Theories and Practices -- Chapter 3: Universal Grammar and Language Pedagogy: What we know that we do not know -- Chapter 4: Generative Foundation of Multilingualism in Language Learning -- Chapter 5: The acquisition of frozen expressions: Challenging the generative framework -- Chapter 6: Cultural-Cognitive Foundations of Language Pedagogy for a Multilingual Society -- Chapter 7: Plurilingual-pluricultural identity and language learning: The contribution of cognitive corpus linguistics and cultural studies -- Chapter 8: Perspectives on Social Life of Language -- Chapter 9: A Cultural Linguistics approach to language pedagogy: The role of Cultural conceptualizations -- Chapter 10: Translanguaging: From language praxis to language pedagogy -- Chapter 11: Situating the |
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teacher in the acquisition-learning debate -- Chapter 12: Metatext and cognitive linguistics: Inputs for language pedagogy -- Chapter 13: Motivation for the choice of complements in predicate-argument structure: The role of image schemas, metaphors and metonymies -- Chapter 14: Toward an adaptive system of language acquisition: Dialogue between Generative and Functional linguistics -- Chapter 15: Ethno-syntax in language learning: Evidentiality in Finno-Ugric Languages -- Chapter 16: Conceptualizing time in terms of space and motion in Japanese using Cognitive Metaphor Theory -- Chapter 17: Understanding the acquisition of non-literal constructions using usage-based approach -- Chapter 18: Narratives and theory of mind: A cultural-cognitive turn in language pedagogy -- Chapter 19: Internal State Terms & Narratives: What they mean for language pedagogy -- Chapter 20: Perfecting Imperfections: Pragmatic Competence for Preschool Teachers of English Language in a Multicultural Environment -- Chapter 21: The bottom-up perspective and less commonly taught languages: the case of Swahili -- Chapter 22: Combinatorial Variability as a Model: Managing classrooms for minority children -- Chapter 23: Language, Learner, and Learning: Issues in Language Pedagogy and Language -- Chapter 24: Language Acquisition and Language Pedagogy: A Transdisciplinary Dialogue between three Scholars. |
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Sommario/riassunto |
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The book explores the theoretical and philosophical groundings of various frameworks of language acquisition, pedagogy and practices. Central to its inquiry are foundational questions such as: How do different theories look at the nature of language and its acquisition, and how do they generate a two-way process of influencing pedagogical practices in different socio-cultural contexts and receive information back from the practices for its theoretical reflections? Structured in five parts—(i) Linguistic structure, language use, and cognitive processes; (ii) Cultural embeddedness of linguistic structures; (iii) The acquisition-learning debate and contemporary language pedagogy; (iv) Multilingual contexts of language use and instruction; and (v) The socio-political epistemology of language use—the book engages in a socio-political and critical-historical analysis. It traces the evolution of linguistic concepts and their influence on educational practices, explores their transdisciplinary migration across linguistics, psychology, and education, and interrogates the conceptual tensions that continue to challenge and reshape the field of language learning and pedagogy. "Traversing diverse and conflicting linguistic theories, contributors have tried to achieve an equilibrium in proposing language pedagogic practices most appropriate to multilingual societies. An unusual compendium of transdisciplinary dialogue between scholars from different sub-disciplines of linguistics, psychology, and education”.---Anvita Abbi “This timely volume insightfully explores the multiple intersections between linguistic theories, language learning, and instructional practices in ways that contribute significantly to current understandings of the central role that language plays in all facets of human existence”.--- Jim Cummins “This immensely exciting book explores the intricate relationship between language, cognition, and pedagogy, moving beyond traditional views of language to highlight its culturally embedded nature and provides insights that can be leveraged for effective language education, particularly in multilingual societies”.---Ajit K. Mohanty “This volume is a welcome contribution to the articulation of interdisciplinary language sciences as social practices/theories of learning and teaching in a postcolonial world”.--- Christopher Sinha. |
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