Identifying the Old English exponent for the semantic prime LIVE

The aim of this article is to identify the Old English exponent for the semantic prime LIVE following the principles of the Natural Semantic Metalanguage theory (Wierzbicka 1996, Goddard & Wierzbicka 2002, Goddard 2011). The methodology applied in the study is based on previous research in Old English semantic primes. In these terms, a search for those Old English words conveying the meaning of the semantic prime LIVE is made. This search selects the verbs (ge)buan, drohtian, (ge)eardian, (ge)libban, and wunian as candidate words for prime exponent. Then, these verbs are analysed in terms of morphological, textual, semantic, and syntactic criteria. With this purpose, relevant information on these words has been gathered from different lexicographical and textual sources in Old English, such as the Dictionary of Old English, the Dictionary of Old English Corpus, and the lexical database of Old English Nerthus. After the analysis of these verbs, the conclusion is drawn that the Old English verb (ge)libban is selected as prime exponent, as it satisfies the requirements proposed by each criterion.

Las distintas vidas de un edificio. El Palacio de Don antonio de Mendoza

<p>The appearance of buildings is the result of a historical process that has left its imprint on them in at all its stages, particularly when this process has involved a constant change of uses, entailing continuous refurbishments and extensions. The building studied here is unusual in that it is the result of contributions by three major architects in the history of Spanish architecture: Lorenzo Vázquez, who introduced the Renaissance into Spain; Alonso de Covarrubias, one of its leading architects, and Ricardo Velázquez Bosco, perhaps the prime exponent of Spanish eclecticism. Their work, and that of others, mainly linked to the uses to which the building has been put, have created the structure as it stands today. This paper provides an overview of its history, how it has been enriched and how it has suffered irreparable losses, and examines how those changes led to the constant urban transformation of the surrounding area, in the urban fabric of the city.</p>

Semantic primes in historical languages. The identification of the Old English exponent for DO

This journal article follows the research line opened on the search for semantic primes’ exponents in Old English within the frame of the Natural Semantic Metalanguage theory (Goddard 1997, 2012; Goddard and Wierzbicka 2002). The aim of this study is to complete the line of research on prime identification opened on the category Actions, Events, Movement, Contact by establishing the Old English exponent of the prime DO. With this purpose, this paper discusses the adequacy of different OE verbs as possible prime exponent on the basis of textual frequency, morphology, semantics and syntactic complementation. Relevant data of analysis have been retrieved mainly from the lexical database of Old English Nerthus, the Dictionary of Old English (Healey et al. 2018) and the Dictionary of Old English Corpus (Healey et al. 2009).

Symbol length of p-algebras of prime exponent

We prove that if the maximal dimension of an anisotropic homogeneous polynomial form of prime degree [Formula: see text] over a field [Formula: see text] with [Formula: see text] is a finite integer [Formula: see text] greater than 1 then the symbol length of [Formula: see text]-algebras of exponent [Formula: see text] over [Formula: see text] is bounded from above by [Formula: see text], and show that every two tensor products of symbol algebras of lengths [Formula: see text] and [Formula: see text] with [Formula: see text] can be modified so that they share a common slot. For [Formula: see text], we obtain an upper bound of [Formula: see text] for the symbol length, which is sharp when [Formula: see text].

Frobenius Distribution for Quotients of Fermat Curves of Prime Exponent

Let denote the Fermat curve over ℚ of prime exponent ℓ. The Jacobian Jac() of splits over ℚ as the product of Jacobians Jac(k), 1 ≤ k ≤ ℓ −2, where k are curves obtained as quotients of by certain subgroups of automorphisms of . It is well known that Jac(k) is the power of an absolutely simple abelian variety Bk with complex multiplication. We call degenerate those pairs (ℓ, k) for which Bk has degenerate CM type. For a non-degenerate pair (ℓ, k), we compute the Sato–Tate group of Jac(Ck), prove the generalized Sato–Tate Conjecture for it, and give an explicit method to compute the moments and measures of the involved distributions. Regardless of whether (ℓ, k) is degenerate, we also obtain Frobenius equidistribution results for primes of certain residue degrees in the ℓ-th cyclotomic field. Key to our results is a detailed study of the rank of certain generalized Demjanenko matrices.

Central simple algebras of prime exponent and divided power operations

Let p be a prime and F a field of characteristic different from p. Suppose all p-primary roots of unity are contained in F. Let α ∈ pBr(F) which has a cyclic splitting field. We prove that γi(α) = 0 for all i ≥ 2, where γi : pBr(F) → K2i(F)/pK2i(F) are the divided power operations of degree p. We also show that if char F ≠ 2, √−1 ∈ F*. D ∈2 Br(F), indD = 8 and a ∈ F* such that ind DF(√a) = 4, then γ3(D) = {a,s}γ2(D) for some s ∈ F*. Consequently, we prove that if D, considered as a division algebra, has a subfield of degree 4 of certain type, then γ3(D) = 0. At the end of the paper we pose a few open questions.