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For an oriented graph G with n vertices, let f(G) denote the minimum number of transitive subtournaments that decompose G. We prove several results on f(G). In particular, if G is a tournament then f(G)n2/3000. For general G we prove that f(G)⩽⌊n2/3⌋ and this is tight. Some related parameters are also considered.

We prove that a tournament with n vertices has more than 0.13 n 2 ( 1 + o ( 1 ) ) edge-disjoint transitive triples. We also prove some results on the existence of large packings of k-vertex transitive tournaments in an n-vertex tournament. Our proofs combine probabilistic arguments and some powerful packing results due to Wilson and to Frankl and Rodl.

Transitive Expletive Constructions adduced in the Paston Letters have the following characteristics: the subject is not extraposed, acceptable only in the negative form, and always preceded by modals, or other auxiliaries. The problems I pose in this article are (I) does anything move from its original position? (II) if so, where does it move? (III) why does it have to move? I conclude that the subject leaves its original position [spec, VP] and moves to [spec, NegP] in order to check the negative features of the spec and the head.

A ∗-compactification of a T1 quasi-uniform space (X, U ) is a compact T1 quasi-uniform space (Y, V ) that has a T ( V ∗ ) -dense subspace quasi-isomorphic to (X, U ), where V ∗ denotes the coarsest uniformity finer than V . With the help of the notion of T1 ∗-half completion of a quasi-uniform space, which is introduced and studied here, we show that if a T1 quasi-uniform space (X, U ) has a ∗-compactification, then it is unique up to quasi-isomorphism. We identify the ∗-compactification of (X, U ) with the subspace of its bicompletion ( X , U ) consisting of all points which are closed in ( X , T ( U )) and prove that (X, U ) is ∗-compactifiable if and only if it is point symmetric and ( X , U ) is compact. Finally, we discuss some properties of locally fitting T0 quasi-uniform spaces, a large class of quasi-uniform spaces whose bicompletion is T1, and, hence, they are T1 ∗-half completable.

It is proved that each infinite completely regular Hausdorff space admits a nontransitive totally bounded quasi-uniformity.  2002 Elsevier Science B.V. All rights reserved. AMS classification: 54E15; 54A25

For a given transitive binary relation e on a set E, the transitive closures of open (i.e., co-transitive in e) sets, called the regular closed subsets, form an ortholattice Reg(e), the extended permutohedron on e. This construction, which contains the poset Clop(e) of all clopen sets, is a common generalization of known notions such as the generalized permutohedron on a partially ordered set on the one hand, and the bipartition lattice on a set on the other hand. We obtain a precise description of the completely join-irreducible (resp., completely meet-irreducible) elements of Reg(e) and the arrow relations between them. In particular, we prove that (1) Reg(e) is the Dedekind-MacNeille completion of the poset Clop(e); (2) Every open subset of e is a set-theoretic union of completely join-irreducible clopen subsets of e; (3) Clop(e) is a lattice iiff every regular closed subset of e is clopen, iff e contains no "square" configuration, iff Reg(e)=Clop(e); (4) If e is finite, then Reg(e) is pseudocomplemented iff it is semidistributive, iff it is a bounded homomorphic image of a free lattice, iff e is a disjoint sum of antisymmetric transitive relations and two-element full relations. We illustrate the strength of our results by proving that, for n greater than or equal to 3, the congruence lattice of the lattice Bip(n) of all bipartitions of an n-element set is obtained by adding a new top element to a Boolean lattice with n2^{n-1} atoms. We also determine the factors of the minimal subdirect decomposition of Bip(n)., 25 pages

We investigate the structure of (minimal) n -transitive semigroups of matrices of rankat most n in M k ( F ) , by considering an equivalent problem regarding certain families of (n−k) -dimensional subspaces of F k .

There are several applications of maximal intersecting families (MIFs) and different notions of fairness. We survey known results regarding the enumeration of MIFs, and we conclude the enumeration of the 207,650,662,008 maximal families of intersecting subsets of X whose group of symmetries is transitive for |X

I will try to illustrate the dynamics of the passage as described by metabasis in a few stoic texts and several grammatical analysis of Apollonius Dyscolus. I believe the concept of « décrochement », which I borrow from Claude Lévi-Strauss, helps to clarify it. The adjective metabatikos qualifies the type of human representation, logical representation, which, in as much as it is « transitive », allows an information to open into another, as well as their mutual articulation, therefore founding the conception of the sign « if this, then this » and the possibility of the conditional « if it is day, there is light ». According to the grammarian Apollonius Dyscolus, metabasis intervenes in the analysis of the transitive diathesis and in the definition of the person. I will procède to show the part played by metabasis in the grammatical treatment of conjunction and how it allows to throw some light upon the obscure part of the definition of conjunction in the Technè Grammatikè attributed to Dionysus the Thrax., résumé : Je chercherai à illustrer, dans quelques textes stoïciens et dans certaines analyses grammaticales, la dynamique du passage que décrit la metabasis. Le concept de « décrochement », que j'emprunte à Claude Lévi-Strauss, permet à mon sens de l'éclairer. L'adjectif metabatikos qualifie chez les stoïciens le type de la représentation humaine, représentation logique, qui, en tant que « transitive », permet l'ouverture d'une information sur une autre et leur articulation entre elles, fonde la pensée du signe (« si ceci, alors ceci ») et la possibilité du conditionnel (« s'il fait jour, il y a de la lumière »). Chez le grammairien Apollonius Dyscole, la metabasis intervient dans l'analyse de la dia- thèse transitive ainsi que dans la définition de la personne. Je montrerai enfin comment la metabasis intervient dans le traitement grammatical de la conjonction, et comment elle peut permettre d'expliciter la partie obscure de la définition de la conjonction dans la Technè Grammatikè attribuée à Denys le Thrace., Ildefonse Frédérique. Petite histoire de la Metabasis. In: Histoire Épistémologie Langage, tome 20, fascicule 2, 1998. Théories des cas. pp. 63-80.

[EN] We prove that the minimal number of matrices on Cn required to forma hypercyclic abelian semigroup on Cn is n+1. We also prove that theaction of any abelian semigroup finitely generated by matrices on Cnor Rn is never k-transitive for k 2. These answer questions raised byFeldman and Javaheri.

Let X be a vector field on a closed smooth manifold M. In this paper, we show that if X belongs to the C 1 Open image in new window-interior of the set of all vector fields having the limit shadowing property, then it is transitive Anosov.

This paper presents an experiment that demonstrates syntactic priming in three- and four-year-old children, exploring the effect the relative frequency of a construction has on children‟s structural experience in language acquisition. We selected a priming paradigm in the form of a „snap‟ game in an attempt to elicit both forms of transitive and ditransitive alternations. While children have been shown to frequently produce both forms of the ditransitive alternation, the passive form of the transitive alternation is very infrequent in both children‟s own productions, and child-directed speech. Participants described a set of cards that depicted both transitive and ditransitive events after hearing the experimenter describe a lexically unrelated transitive or ditransitive event. We found priming for both children and our adult control group; however children showed stronger priming for the less frequent construct, while showing relatively weak priming for the more frequent ditransitive construct. Results provide further evidence for an implicit learning theory; children were more susceptible to priming of an infrequent structure and this effect was robust and increased over a significant period of time. Thus, frequency plays a significant role in children's experience during language acquisition.

The present paper demonstrates the relevance of the semantic approach to transitivity(going back to Hopper and Thompson 1980) for the analysis of Vedic causative verbs. It argues that in terms of this approach it is possible to explain a number of constraints on causative derivation (which cannot be explained in terms of the traditional, syntactic, definition) and to offer a unified account of the semantics of these verbs. The paper also briefly discusses some theoretical implications of this analysis of causative verbs in Vedic for a diachronic typology of transitivity.

A tournament is a complete graph with its edges directed, and colouring a tournament means partitioning its vertex set into transitive subtournaments. For some tournaments H there exists c such that every tournament not containing H as a subtournament has chromatic number at most c (we call such a tournament H a hero); for instance, all tournaments with at most four vertices are heroes. In this paper we explicitly describe all heroes., Simons Foundation (Fellowship)

A very simple, short and self-contained proof is presented of Burnside's Theorem that every proper algebra of matrices over an algebraically closed field has a non-trivial invariant subspace.

Let f be a diffeomorphism of a closed n-dimensional C ∞ manifold. In this article, we show that C1-generically, if f has the C1-stably asymptotic average shadowing property on a closed set then it admits a dominated splitting. Mathematical Subject Classification: 34D05; 37C20; 37D30.

En este trabajo se reconstruye la demostración del teorema principal del artículo [Mor07] del profesor Carlos Morales de la Universidad Federal de Rio de Janeiro. Se presentan y se demuestran resultados conocidos sobre conjuntos hiperbólicos y parcialmente hiperbólicos. Además se enuncian y demuestran los resultados que se obtienen a partir de este teorema principal. / Abstract. In this paper we reconstructs the proof of the theorem of the Carlos Morales�s paper [Mor07] professor at the Federal University of Rio de Janeiro. We introduce and prove known results on hyperbolic sets and partially hyperbolic sets. Also set forth and show the results obtained from this main theorem. Maestría

In the present work the interconnections between various notions of transitivity for Abelian p-groups and the recently introduced concepts of socle-regular and strongly socle-regular groups are studied.

Three main issues are touched upon in this paper: (a) main morphological types of Georgian verbs in correlation with verb form, on one hand, and with the categories of telicity, stativeness, and transitivity, on the other; (b) peculiarities of case alternating objects of medial verbs; (c) and formal features of medial verbs as the basis for identification of the medial verb class (along with semantic features).This paper is based on Hopper & Thompson’s (1980) hypothesis that considers transitivity not as a strict dichotomy but as a continuum where various degrees of semantic transitivity may be distinguished. Differences expressed on semantic and syntactical levels mark one class of Georgian verbs, Class III, as intermediate between transitives and intransitives. Labile transitives, a term suggested by Melikishvili (2001), is used in this paper to indicate peculiarities of Class III verbs with respect to transitivity. This term expresses the nature of Class III verbs in terms of transitivity more accurately than the labeling of these verbs as intransitive, transitive, stative voiceless, or active intransitive verbs. It is demonstrated in this paper that various degrees of semantic transitivity as well as the category of telicity have their morphological expression in Georgian. Semantically, a case-alternating object of labile transitive verbs is often an inconcrete, non-definite object and/or is not affected by the action described in the verb. Syntactically, the difference is expressed by the lack of ability to assign a third person object marker to a verb. Case alternating objects of both Class I and Class III verbs are marked by the dative case in the tenses of series I. But the difference is that the dative marked, case alternating object of telic verbs (Class I) is usually marked by a prefix on verbs in old Georgian and in several modern dialects of East Georgia (ს-თლის s-tlis ‘s/he is peeling it’). In contrast, the dative marked, case alternating third person object of Class III verbs (atelic, labile transitives) cannot trigger a person marker on a verb (თამაშობს tamashobs but not *ს-თამაშობს *s-tamashobs ‘s/he is playing’). The latter forms are not attested, not even in those dialects where the person marking of the dative marked third person direct object is still preserved.As is described above, besides semantic peculiarities, this verb class, standing in an intermediate position between transitives and intransitives, exhibits morphological and syntactical features of its own.

In this paper, we give a characterization of hypercyclic abelian affine group G. If G is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by n affine maps on C^n has a dense orbit.

Tese de Mestrado em Arquitectura A presente dissertação aborda a arquitectura na sua vertente pragmática e transitória, tendo como fundamento o conceito de Emergência. Tomando como ponto de partida questões como a da Qualidade de Vida - Mobilidade e Sustentabilidade – numa procura de esclarecimento sobre o papel que o arquitecto tem na criação de soluções transitórias que garantam as condições mínimas de dignidade e habitabilidade às populações vítimas de eventos cataclísmicos ou de conflitos sociais e políticos. A emergência é neste sentido abordada no seu carácter efémero e temporário, constituindo uma resposta da Arquitectura à necessidade de abrigo das vítimas de catástrofe, revelando as atitudes reflexivas, oníricas e criativas da habilidade do arquitecto, que interpreta a Arquitectura de Emergência como solução actual e operativa em cenários de contingência. Deste modo, a emergência na arquitectura, denota especificidades de mutabilidade, pragmatismo e rapidez de resposta a um conjunto de premissas fundamentais. A Habitabilidade é assegurada pela protecção contra as agressões externas (condicionantes climáticas); o armazenamento e protecção dos bens materiais; e o equilíbrio emocional e satisfação da necessidade de intimidade. A Mobilidade, quer dos utilizadores, quer do próprio objecto arquitectónico, é possibilitada pela acessibilidade entre as habitações e os lugares de trabalho (mobilidade pendular); a flexibilidade na configuração espacial (divisões interiores e ampliações); e a utilização de materiais reutilizáveis, recicláveis e autóctones. E por fim, a Sustentabilidade depende da integração de equipamentos complementares de fácil aplicação e aceitação cultural; da autonomia energética; e da gestão de recursos hídricos. ABSTRACT - This dissertation discusses the architecture in its pragmatic and transitional measure, having as a basis the concept of Emergency. Taking as point of departure issues such as the quality of life - Mobility and sustainability - a demand for clarification on the role of the architect has in the creation of transitional solutions to guarantee the minimum conditions of dignity and liveability for victims of natural disasters or social and political conflicts. The emergency is in this sense addressed in her nature ephemeral and temporary, constituting a response from the Architecture to need for shelter for victims of disaster, revealing the reflective, idealist and creative attitudes of the architect, which interprets the architecture of Emergency as current solution and operative scenarios of contingency. Thus, the emergency in architecture shows specificities of mutability, pragmatism and rapidity of response to a set of basic preconditions. The Liveability is ensured by protection against external damage (climatic constraints); the storage and protection of material goods; and emotional balance and satisfaction of the need of intimacy. Mobility, either of users, either the own subject architectural, is made possible by accessibility between the dwellings and the places of work (mobility); the flexibility in shaping spatial (divisions interiors and extensions); and the use of materials which are reusable, recyclable and indigenous. AND lastly, the sustainability depends on the integration of additional equipment easily applied and cultural acceptance; energy autonomy; and the management of water resources.

We prove that the minimal number of matrices on C^n required to form a hypercyclic abelian semigroup on C^n is n + 1. We also prove that the action of any abelian semigroup nitely generated by matrices on Cn or Rn is never k-transitive for k >=2.; We prove that the minimal number of matrices on C^n required to form a hypercyclic abelian semigroup on C^n is n + 1. We also prove that the action of any abelian semigroup nitely generated by matrices on C^n or R^n is never k-transitive for k>= 2. These answer questions raised by Feldman and Javaheri.

Nosotros conocemos que dos clases homoclínicas diferentes contenidas en un conjunto hiperbólico son disjuntas. Además un conjunto transitivo singular-hiperbólico con orbitas periódicas densas y una única singularidad es transitivo o es unión de dos clases homoclínicas diferentes. De estos resultados se puede preguntar si dos clases homoclínicas diferentes contenidas en un conjunto singular hiperbólico son disjuntas o si la segunda alternativa no puede ocurrir. Aquí se da una respuesta negativa a la pregunta. / Abstract. We know that two different homoclinic classes contained in the hyperbolic set are disjoint. Moreover singular-hyperbolic attracting set whit dense periodic orbits and unique equilibrium is either transitive or the union of two different homoclinic classes. These results motivate the questions of if two different homoclinic classes contained in the same singular-hyperbolic set are disjoint or if second alternative in cannot. Here it give a negative the answer for both questions. Maestría

Estudiamos las soluciones de un sistema no lineal de ecuaciones, conocido como el sistema Lorenz, cuyas soluciones reposan en una región de atracción del espacio de fases y analizamos la evolución en el tiempo, cuando sus parámetros toman los valores: σ=10, b=8/3, y r=24.74, donde los valores propios complejos cruzan el eje imaginario perdiendo su estabilidad, lo que implica que el sistema exhibe una bifurcación tipo Hopf. Dicho sistema inspiró la elaboración de un modelo geométrico, conocido como el atractor geométrico de Lorenz, de donde analizamos su estructura y las propiedades que comparte con el sistema Lorenz, además de reconstruir la demostración del por qué el atractor geométrico de Lorenz, siendo uno de los ejemplos más importantes de conjunto singular hiperbólico, es una clase homoclínica. / Abstract. We study the solutions of a nonlinear system of equations, known as the Lorenz systems, whose solutions lie in a region of attraction in phase space and analyze the evolution in time, when its parameters take the values: σ =10, b=8/3, y r=24.74, where complex eigenvalues cross the imaginary axis losing its stability, which implies that the system exhibits a Hopf bifurcation type. Such a system inspired the development of a geometric model, known as the geometric Lorenz attractor, where we analyze its structure and properties it shares with the Lorenz system, in addition to rebuilding the demonstration of why the geometric Lorenz attractor, one of the most important examples of singular hyperbolic set, is a homoclinic class. Maestría

International audience

L'une des caractéristiques du système verbal, en chamito-sémitique, est d'opposer un thème simple à des thèmes dérivés, l'une des dérivations les mieux représentées dans les diverses branches du phylum chamito-sémitique étant celle qui est utilisée dans la formation des causatifs-factitifs. En berbère, c'est le préfixe ‘S' (et ses variantes) qui sert à cette dérivation, très productive dans tous les parlers. L'article porte spécifiquement sur le berbère zénaga de Mauritanie qui tend à se distinguer sur deux points. D'une part, le préfixe présente une série de réalisations particulièrement variées, à tel point qu'il est souvent difficile de décider a priori si la première consonne du verbe est un élément morphématique ou un élément radical. D'autre part, le nom d'action des verbes dérivés à préfixe ‘S' se caractérise par la présence d'une laryngale, après l'élément vocalique a- caractéristique des noms masculins. Je commence, dans une première partie, par faire un tableau des problèmes rencontrés au plan morpho-sémantique. Dans la seconde partie de mon exposé, j'étudie spécifiquement les variations du préfixe ‘S' à travers un inventaire de toutes les formes relevées en zénaga et j'établis les règles de variation (assimilation, dissimilation, gémination...).

If X is a convex-transitive Banach space and 1\leq p\leq \infty then the closed linear span of the simple functions in the Bochner space L^{p}([0,1],X) is convex-transitive. If H is an infinite-dimensional Hilbert space and C_{0}(L) is convex-transitive, then C_{0}(L,H) is convex-transitive. Some new fairly concrete examples of convex-transitive spaces are provided., Corrected version

This report is essentially an upgrade of the results of Audu (see [1] and [2]) on some finite permutation groups. It consists of the basic procedure for computing wreath product of groups. We also discussed the conditions under which the wreath products of permutation groups are faithful, transitive and primitive. Further, the centre of the stabilizer and the centre of wreath products was investigated, and finally, an illustration was supplied to support our findings

In every separable Banach space the set of smooth points of the unit ball is a G&#948 dense subset of the unit sphere (see [12]). In this paper, we find some conditions in order to obtain a similar result for rotund points. For instance, we prove that if the unit ball of a smooth and separable Banach space is free of rotund points then the set of non-norm-attaining functionals of norm 1 is residual in the unit sphere of the dual. Furthermore, by taking profit of these techniques we provide positive approaches to the Banach-Mazur conjecture for rotations.Keywords: Rotund, smooth, Gδ-dense, transitive, separableQuaestiones Mathematicae 30(2007), 85–96

Türkçede, “Sözlüksel özne, yüzey yapıda olsa da olmasa da, yüklemde yer alan kişi ekleri, bize özneyi verir.” söylemi yaygındır. Aldım, gönderdik, vurdun vb. Ancak bu durum, yalnız etken çatılı eylemler için geçerlidir. Edilgen çatıda durum değişir. Geçişsiz-edilgen çatılı eylemler, oluş ifade ettiklerinden yalnız üçüncü teklik kişiyle çekimlenmesin karşın, geçişli-edilgen çatılı eylemler kılış bildirdiklerinden kişi eklerinin tümüyle çekimlenebilirler. Edilgen eylemin geçişli oluşu, çevresinde eksiz belirtme durumuna girmiş ad değerindeki bir birimin bulunmasını zorunlu kılar. İşte, geçişli-edilgen çatılı eylem çekiminde (alındım, gönderildik, vuruldun vb.) yer alan kişi eki, eylemi yapana (özneye) değil, eylemden etkilenen eksiz belirtme durumuna girmiş bu birime (nesneye) gönderme yapar. Bu da, yüklem içinde her zaman öznenin barınmadığına, bazı durumlarda nesnenin de barındığına işaret eder. In Turkish, it is widely known expression that "no matter if the subject exists in the surface structure of the sentence or not, the personal suffixes in the verb reveal the subject"; such as, “I took”, “we sent”, “you hit” etc. This, however, is only the case with the active verbs. In passive verbs, this situation changes. While the intransitive-passive verbs can just be conjugated by the third person singular pronouns since they Express “happening”, transitive-passive verbs can be conjugated by all personal pronoun suffixes. The transitive aspect of the passive verb necessitates the presence of a unit in the form of defining noun that is without any suffixes. Therefore, the personal pronoun suffix present in the conjuction of transitive passive verbs, such as “I was taken”, “we were sent”, “you were shot” etc. doesn’t refer refer to subject, but refers to this unit in the form of a noun-suffixed defining word (object). This demonstrates that the verb doesn’t always contain the subject within itself and in some cases there is the object in it.

Let $G$ be a permutation group on a set $\Omega$ with no fixed points in $\Omega$ and let $m$ be a positive integer. Then we define the movement of $G$ as, $m:=move(G):=sup_{\Gamma}\{|\Gamma^{g}\setminus\Gamma | | g\in G\}$. Let $p$ be a prime, $p\geq 5$, and let $move(G)=m$. We show that if $G$ is not a 2-group and $p$ is the least odd prime dividing $|G|$, then $n:=|\Omega|\leq 4m-p$. Moreover for an infinite family of groups the maximum bound $n=4m-p$ is attained.

TEZ5943 Tez (Yüksek Lisans) -- Çukurova Üniversitesi, Adana, 2006. Kaynakça (s.72-76) var. viii, 81 s. ; 29 cm. The aim of this study is to find out what kind of errors Turkish learners of EFL make in passivising the verbs. We focus on the sources of errors in passivisation and find out whether Turkish learners of EFL make more errors in passivising certain verbs. We analyzed the grammatical and semantic characteristics of the verbs which are passivised incorrectly. The participants of the study are selected from pre-intermediate level students at YADIM in Çukurova University. In Chapter One, the statement of the problem, background to the study, research questions, hypotheses, operational definition, assumptions and limitations are presented. Related literature on passivisation in English and Turkish is reviewed in Chapter Two. Chapter Three provides the research design, subjects, materials and tasks, data collection and data analysis. Chapter Four contains grammatical and semantic analyses of the errors on passivization. Conclusion is drawn in Chapter Five. Bu çalısmanın amacı, Ingilizceyi yabancı dil olarak ögrenen Türk ögrencilerin eylemleri edilgenlestirirken ne tür hatalar yaptıklarını saptamak ve bu hataların kaynaklarını bulmaktır. Bu nedenle, Ingilizceyi yabancı dil olarak ögrenen Türklerin yaptıkları hataların belirli sözcüklerde daha fazla olup olmadıgını arastırdık. Yanlıs edilgenlestirilen eylemlerin dilbilgisel ve anlambilimsel özelliklerini inceledik. Katılımcılar, Çukurova Üniversitesi Yabancı Diller Merkezindeki alt-orta seviyedeki ögrenciler arasından seçildi. Birinci bölümde, problemin tanımı, geçmiste bu konuda yapılan çalısmalar hakkında bilgi, arastırma soruları, hipotezler, tanımlar ve sınırlılıklar verilmistir. Ikinci bölümde bu konuda daha önce yapılan Ingilizce ve Türkçe arastırmalara deginilmis ve kuramsal açıklamalara yer verilmistir. Üçüncü bölümde arastırma modeli, katılımcılar, veri toplama araçları, verilerin toplanması, çözümü ve yorumu açıklanmıstır. Dördüncü bölümde edilgenlestirme hatalarının dilbilgisel ve anlambilimsel analizi yapılmıstır. Sonuç, besinci bölümde verilmistir. Bu çalışma Ç.Ü. Bilimsel Araştırma Projeleri Birimi Tarafından Desteklenmiştir. Proje No

It is known that transitive and subtractive groupoids are geometrically interesting and important in defining a group by its inverse operation. We are discussing different possibilities for postulating such groupoids.

Ancient Indo-European verbal syntax, as attested in early Vedic Sanskrit, exhibits numerous examples of the labile syntactic pattern: several verbal forms can show valence alternation with no formal change in the verb; cf. pres. svadate 'he makes sweet' / 'he is sweet'; perf. vavrdhuH ~ 'they have grown' (intr.) / 'they have increased' (tr.). It is argued that the labile patterning of the Vedic verb, however common it may appear, is mostly of a secondary character. There are a limited number of reasons which give rise to labile syntax: (i) the polyfunctionality of the middle inflection (which can be used to mark the anticausative, passive and reflexive functions, on the one hand, and the self-beneficent meaning of the transitive forms, on the other); (ii) the homonymy of some middle participles "shared" by passive (medio-passive aorist, stative) and nonpassive formations; (iii) the syntactic reanalysis of intransitive constructions with the accusative of parameter/scope (content accusative) as transitive-causative. As to the perfect, it could probably be employed both intransitively and transitively already in Proto-Indo-European, although the intransitive usages were prevalent. In the historical period the newly-built perfect middle forms have largely taken over the intransitive function, but active perfects are still quite common in the (more archaic) intransitive usages in early Vedic .