A new heap game

AbstractGiven k⩾3 heaps of tokens. The moves of the 2-player game introduced here are to either take a positive number of tokens from at most k−1 heaps, or to remove the same positive number of tokens from all the k heaps. We analyse this extension of Wythoff's game and provide a polynomial-time strategy for it

Respectus Philologicus, 2009 Nr. 16 (21) A

CONTENTS I. DISCOURSE: THE RESEARCH PROBLEMS OF GENERATION, PERCEPTION AND IMPACTAgnieszka Miksza (Poland). The Politics of Reading and Writing. Jeanette Winterson’s Dialogue with Herself and the Reader... 11Olga Glebova (Poland). Recontextualisation as an Interpretive Strategy in Contemporary Novelistic Discourse ... 19Wojciech Majka (Poland).Understanding as Context for Disclosure ... 30Jurgita Vaičenonienė (Lithuania). Cultural Translation and Linguistic Metaphor: A Case Study of Verbal Metaphor Translation ... 38Regina Koženiauskienė (Lithuania). The Manipulation of Headlines: The Opposition of Text and Context... 50Erika Rimkutė, Neringa Pakalnytė (Lithuania). Topics and Linguistic Features of Social Advertisements...57Dovilė Vengalienė (Lithuania). The Cultural Aspects of Auto-Ironic Blends Referring to Lithuania and America in News Headlines ... 73Solveiga Sušinskienė (Lithuania). Nominalization as a Micro-Structural Item of English Scientific Discourse ...84 II. LITERARY FICTION: INTERPRETATION POSSIBILITIESUgnius Keturakis (Lithuania). Two Ways Leading to Modern National Culture: Vincas Kudirka and Jurgis Baltrušaitis... 93Marek Smoluk (Poland). The English Royal Court through the Eyes of Erasmus ... 105Ingrida Žindžiuvienė (Lithuania). Location and Space in Don Delillo’s Cosmopolis and Antanas Škėma’s Balta drobulė ... 112 III. CONTEMPORARY RESEARCH INTO LITHUANIAN LINGUISTICS: LINGUISTIC AND EXTRALINGUISTIC APPROACHESJonas Andrijauskas, Lina Bačiūnaitė-Lužinienė, Vytas Kriščiūnas (Lithuania). The Employment of New Technologies in Diachronic Toponymy ... 123Saulė Juzelėnienė, Giedrė Baranauskaitė (Lithuania). The Expression of Semantic Group of Movement in the Air in the Lithuanian and English Languages... 135Robertas Kudirka (Lithuania). The Formant Structure of the Accented Long and Short Vowels in the Lithuanian Standard Language... 141Jurga Kerevičienė (Lithuania). Dativus iudicantis in Lithuanian and its Equivalents in English ... 153Daiva Aliūkaitė (Lithuania). Accuracy of Standard Language Images: the Problem of Quasistandard... 160Nijolė Tuomienė (Lithuania). Declension of the ā- and iā Stem nouns in the Peripheral Ramaškonys Subdialect... 188Rima Bacevičiūtė (Lithuania). Tendencies and problems of instrumental analysis of sounds in lithuanian dialectology... 202 IV. SCIENTIFIC LIFE CHRONICLEBirutė Briaukienė (Lithuania). 110 Years to “Lietuviška gramatikėlė”...216Daiva Aliūkaitė, Gabija Bankauskaitė-Sereikienė (Lithuania). Young Linguists of the Lithuanian Language Gathering — a Part of Jubilee Events at VU KHF ...221 V. REQUIREMENTS FOR PUBLICATION... 226VI. OUR AUTHORS... 234TURINYS / SPIS TREŚCI I. DISKURSAS: GENERAVIMO, SUVOKIMO IR POVEIKIO TYRIMO PROBLEMOSAgnieszka Miksza (Lenkija). The Politics of Reading and Writing. Jeanette Winterson’s Dialogue with Herself and the Reader... 11Olga Glebova (Lenkija). Recontextualisation as an Interpretive Strategy in Contemporary Novelistic Discourse ... 19Wojciech Majka (Lenkija).Understanding as Context for Disclosure ... 30Jurgita Vaičenonienė (Lietuva). Cultural Translation and Linguistic Metaphor: A Case Study of Verbal Metaphor Translation ... 38Regina Koženiauskienė (Lietuva). Manipuliavimas antraštėmis: teksto ir konteksto opozicija...50Erika Rimkutė, Neringa Pakalnytė (Lietuva). Socialinių reklamų tematika ir kalbinės ypatybės... 57Dovilė Vengalienė (Lietuva). The Cultural Aspects of Auto-Ironic Blends Referring to Lithuania and America in News Headlines ... 73Solveiga Sušinskienė (Lietuva). Nominalization as a Micro-Structural Item of English Scientific Discourse ...84 II. MENINIS TEKSTAS: INTERPRETAVIMO GALIMYBĖSUgnius Keturakis (Lietuva). Du keliai į moderniąją nacionalinę kultūrą: V. Kudirka ir J. Baltrušaitis... 93Marek Smoluk (Lenkija). The English Royal Court through the Eyes of Erasmus ... 105Ingrida Žindžiuvienė (Lietuva). Location and Space in Don Delillo’s Cosmopolis and Antanas Škėma’s Balta drobulė ... 112 III. ŠIUOLAIKINIAI LIETUVIŲ KALBOTYROS TYRIMAI: LINGVISTINĖS IR EKSTRALINGVISTINĖS PROBLEMOSJonas Andrijauskas, Lina Bačiūnaitė-Lužinienė, Vytas Kriščiūnas (Lietuva). The Employment of New Technologies in Diachronic Toponymy ... 123Saulė Juzelėnienė, Giedrė Baranauskaitė (Lietuva). Judėjimo ore semantinės grupės raiška ...135Robertas Kudirka (Lietuva). Lietuvių bendrinės kalbos kirčiuotų ilgųjų ir trumpųjų balsių formantinė struktūra... 141Jurga Kerevičienė (Lietuva). Dativus iudicantis in Lithuanian and its Equivalents in English ... 153Daiva Aliūkaitė (Lietuva). Bendrinės kalbos vaizdiniai: kvazistandarto problema... 160Nijolė Tuomienė (Lietuva). Periferinės Ramaškonių šnektos a, ia kamienų daiktavardžių linksniavimas. ...188Rima Bacevičiūtė (Lietuva). Instrumentinio garsų tyrimo kryptys ir problemos lietuvių dialektologijoje... 202 IV. MOKSLINIO GYVENIMO KRONIKABirutė Briaukienė (Lietuva). „Lietuviškai gramatikėlei“ — 110 metų... 216Daiva Aliūkaitė, Gabija Bankauskaitė-Sereikienė (Lietuva). Jaunųjų Lietuvos tyrėjų lituanistų mokslinis sambrūzdis — VU KHF jubiliejinių renginių dalis ... 221 V. REIKALAVIMAI STRAIPSNIAMS ... 226Vi. MŪSŲ AUTORIAI ... 23

Mathematics Education and Language Diversity

This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapter draws on research from two or more countries to illustrate important research findings, theoretical developments and practical strategies. This open access book examines multiple facets of language diversit

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Aspects of emergent cyclicity in language and computation

This thesis has four parts, which correspond to the presentation and development of a theoretical framework for the study of cognitive capacities qua physical phenomena, and a case study of locality conditions over natural languages. Part I deals with computational considerations, setting the tone of the rest of the thesis, and introducing and defining critical concepts like ‘grammar’, ‘automaton’, and the relations between them . Fundamental questions concerning the place of formal language theory in linguistic inquiry, as well as the expressibility of linguistic and computational concepts in common terms, are raised in this part. Part II further explores the issues addressed in Part I with particular emphasis on how grammars are implemented by means of automata, and the properties of the formal languages that these automata generate. We will argue against the equation between effective computation and function-based computation, and introduce examples of computable procedures which are nevertheless impossible to capture using traditional function-based theories. The connection with cognition will be made in the light of dynamical frustrations: the irreconciliable tension between mutually incompatible tendencies that hold for a given dynamical system. We will provide arguments in favour of analyzing natural language as emerging from a tension between different systems (essentially, semantics and morpho-phonology) which impose orthogonal requirements over admissible outputs. The concept of level of organization or scale comes to the foreground here; and apparent contradictions and incommensurabilities between concepts and theories are revisited in a new light: that of dynamical nonlinear systems which are fundamentally frustrated. We will also characterize the computational system that emerges from such an architecture: the goal is to get a syntactic component which assigns the simplest possible structural description to sub-strings, in terms of its computational complexity. A system which can oscillate back and forth in the hierarchy of formal languages in assigning structural representations to local domains will be referred to as a computationally mixed system. Part III is where the really fun stuff starts. Field theory is introduced, and its applicability to neurocognitive phenomena is made explicit, with all due scale considerations. Physical and mathematical concepts are permanently interacting as we analyze phrase structure in terms of pseudo-fractals (in Mandelbrot’s sense) and define syntax as a (possibly unary) set of topological operations over completely Hausdorff (CH) ultrametric spaces. These operations, which makes field perturbations interfere, transform that initial completely Hausdorff ultrametric space into a metric, Hausdorff space with a weaker separation axiom. Syntax, in this proposal, is not ‘generative’ in any traditional sense –except the ‘fully explicit theory’ one-: rather, it partitions (technically, ‘parametrizes’) a topological space. Syntactic dependencies are defined as interferences between perturbations over a field, which reduce the total entropy of the system per cycles, at the cost of introducing further dimensions where attractors corresponding to interpretations for a phrase marker can be found. Part IV is a sample of what we can gain by further pursuing the physics of language approach, both in terms of empirical adequacy and theoretical elegance, not to mention the unlimited possibilities of interdisciplinary collaboration. In this section we set our focus on island phenomena as defined by Ross (1967), critically revisiting the most relevant literature on this topic, and establishing a typology of constructions that are strong islands, which cannot be violated. These constructions are particularly interesting because they limit the phase space of what is expressible via natural language, and thus reveal crucial aspects of its underlying dynamics. We will argue that a dynamically frustrated system which is characterized by displaying mixed computational dependencies can provide straightforward characterizations of cyclicity in terms of changes in dependencies in local domains