Let M and N be non-zero finitely generated modules over a local (Noetherian) ring (R,m). Assume that TorRi (M,N) = 0 for i >> 0, and let q = qR(M,N) be the largest integer i for which TorRi (M,N) 6= 0. For the case q = 0, Auslander [A, Theorem 1.2] found a useful formula relating the depths of M , N and R. In view of the Auslander-Buchsbaum formula [BH,Thm. 1.3.3] Auslander’s theorem goes as fo...

The storage of high level radioactive waste is still an unresolved problem of the nuclear industry, being geological disposal the most favoured option and, naturally, the one requiring the strongest geo-mechanical input. Most conceptual designs for the deep geological disposal of nuclear waste envisage placing the canisters containing the waste in horizontal drifts or vertical boreholes. The em...

Triple-helical microchannel (THM) constitutes a unique configuration for implementing parallel flows with enhanced interfacial mass transfer through torsion-induced advection in the bulk phases. Key operational aspects include identifying stable regimes of flow respect to phase rates and characterizing intensification achieved secondary flow. The current work investigates two-phase flow, typica...

S[ and Sg are then said to separate (or: to screen) S± and S2. Finally, Sf is called a binary subbase if each linked system S^ (zS^ (i.e., a subcollection S^' of ^ of which any two members meet) satisfies ς\Sf'φ 0. It is well-known that a binary subbase is TΊ (cf. van Mill [9, Lemma 1]), that a space carrying a binary subbase is compact (use Alexander's lemma), and that a space is completely re...

Abstract. About fifty years ago Mahler [M] proved that if α > 1 is rational but not an integer and if 0 < l < 1, then the fractional part of α is > l apart from a finite set of integers n depending on α and l. Answering completely a question of Mahler, we show (Thm. 1) that the same conclusion holds for all algebraic numbers which are not d-th roots of Pisot numbers. By related methods we also ...

An mtroductlon to the theory of the amsotroplc magnetoresistance effect m ferromagnetic thm films IS given, endmg m a treatment of the mmlmahzatlon of the free energy which IS the result of the lntnnslc and extnnslc anlsotroples of the thm-film structure The amsotroplc magnetoreslstance effect m long stnps IS revlewed Attention IS given to problems hke the formation of domains and measures hke ...

OBJECTIVES Ideal treatment for achalasia permanently eliminates the dysfunctional lower oesophageal sphincter, relieving dysphagia and regurgitation. The aim of this study was to review the results in a series of patients undergoing video-imaged thoracoscopic Heller's myotomy (THM). METHODS Records of all patients undergoing THM by a single surgeon at one institution were analysed. Follow-up ...

(3) a. ∃y. ∣y∣=2 ∧ *man(y) ∧ ∀z. z ∈ y ∧ AT(z) → ∃e. ∃x. ∣x∣=3 ∧ *bag(x) ∧ *carry(e) ∧ *Thm(e)=x ∧ *Ag(e)=z There is a pair of men y, and every atomic member of y carried three (possibly different) bags. b. ∃e. ∀e’. e’ ∈ e ∧ AT(e) → ∃y. ∣y∣=2 ∧ *man(y) ∧ ∃x. ∣x∣=3 ∧ *bag(x) ∧ *carry(e’) ∧ *Thm(e’)=x ∧ *Ag(e’)=y There is an event e, and every atomic subevent e’ of e is an event of two men (colle...

We show that a maximal curve over Fq2 defined by the affine equation y = f(x), where f(x) ∈ Fq2 [x] has degree coprime to n, is such that n is a divisor of q+1 if and only if f(x) has a root in Fq2 . In this case, all the roots of f(x) belong to Fq2 ; cf. Thm. 1.2, Thm. 4.3 in [J. Pure Appl. Algebra 212 (2008), 2513–2521]. In particular, we characterize certain maximal curves defined by equatio...