Analytical formulae for electromechanical effective properties of 3-1 longitudinally porous piezoelectric materials

A unidirectional fiber composite is considered here, the fibers of which are empty cylindrical holes periodically distributed in a transversely isotropic piezoelectric matrix, The empty-fiber cross-section is circular and the periodicity is the same in two directions at an angle pi/2 or pi/3. Closed-form formulae for all electromechanical effective properties of these 3-1 longitudinally periodic porous piezoelectric materials are presented. The derivation of such expressions is based on the asymptotic homogenization method as a limit of the effective properties of two-phase transversely isotropic parallel fiber-reinforced composites when the fibers properties tend to zero. The plane effective coefficients satisfy the corresponding Schulgasser-Benveniste-Dvorak universal type of relations, A new relation among the antiplane effective constants from the solutions of two antiplane strains and potential local problems is found. This relation is valid for arbitrary shapes of the empty-fiber cross-sections. Based on such a relation, and using recent numerical results for isotropic conductive composites, the antiplane effective properties are computed for different geometrical shapes of the empty-fiber cross-section. Comparisons with other analytical and numerical theories are presented. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

1.° Anonymi tractatus algorismi de fractionibus, sive methodus calculandi minutias : praemittitur calendarium. — 2.° Anonymus de nominibus instrumentorum in astrolabio. — 3.° Liber de operatione astrolabii. — 4.° Anonymi canones, sive regulae tabularum astronomiae : accedunt tabulae. — 5.° Centiloquium Ptolomaei de judiciis astrorum : accedit Haly commentarius. — 6.° Epistola Messahallae de conjunctionibus planetarum. — 7.° Albumasaris tractatus inscriptus : flores de judiciis astrorum. — 8.° Scholium de potestate planetarum et signorum, et de formis eorum. — 9.° Anonymi opusculum de tuendae valetudinis ratione. — 10.° Formulae collationum ecclesiasticarum.

Colbertinus

Generalization of Vélu’s formulae for isogenies between elliptic curves

Given an elliptic curve E and a finite subgroup G, V ́lu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P + G as the difference between the abscissa of IG (P ) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstraß coefficients of E ′ as polynomials in the coefficients of E and two additional parameters: w0 = t and w1 = w. We generalize this by defining parameters wn for all n ≥ 0 and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in P +G. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when G is a rational group.

Do standard burn mortality formulae work on a population of severely burned children and adults?

Accurate prediction of mortality following burns is useful as an audit tool, and for providing treatment plan and resource allocation criteria. Common burn formulae (Ryan Score, Abbreviated Burn Severity Index (ABSI), classic and revised Baux) have not been compared with the standard Acute Physiology and Chronic Health Evaluation II (APACHEII) or re-validated in a severely (≥20% total burn surface area) burned population. Furthermore, the revised Baux (R-Baux) has been externally validated thoroughly only once and the pediatric Baux (P-Baux) has yet to be. Using 522 severely burned patients, we show that burn formulae (ABSI, Baux, revised Baux) outperform APACHEII among adults (AUROC increase p<0.001 adults; p>0.5 children). The Ryan Score performs well especially among the most at-risk populations (estimated mortality [90% CI] original versus current study: 33% [26-41%] versus 30.18% [24.25-36.86%] for Ryan Score 2; 87% [78-93%] versus 66.48% [51.31-78.87%] for Ryan Score 3). The R-Baux shows accurate discrimination (AUROC 0.908 [0.869-0.947]) and is well-calibrated. However, the ABSI and P-Baux, although showing high measures of discrimination (AUROC 0.826 [0.737-0.916] and 0.848 [0.758-0.938]) in children), exceedingly overestimates mortality, indicating poor calibration. We highlight challenges in designing and employing scores that are applicable to a wide range of populations.

A Collation of Recently published Western European Formulae for Age Estimation of Subadult Skeletal Remains: Recommendations For Forensic Anthropology and Osteoarchaeology

The aim of this study is to provide an effective and quick reference guide based on the most useful European formulae recently published for subadult age estimation. All of these formulae derive from studies on postnatal growth of the scapula, innominate, femur, and tibia, based on modern skeletal data (173 ♂, 173 ♀) from five documented collections from Spain, Portugal, and Britain. The formulae were calculated from Inverse Regression. For this reason, these formulae are especially useful for modern samples from Western Europe and in particular on 20th century human remains from the Iberian Peninsula. Eleven formulae were selected as the most useful because they can be applied to individuals from within a wide age range and in individuals of unknown sex. Due to their high reliability and because they derive from documented European skeletal samples, we recommend these formulae be used on individuals of Caucasoid ancestry from Western Europe.

Noves consideracions sobre la inscripció tarraconense de la beata Thecla (segle V)

S’estudia una inscripció funerària d’una verge consagrada anomenada Thecla d’origen egipci que va ser enterrada en una de les basíliques funeràries que existien en el segle v a ponent de Tarraco. Es revisa el que s’ha escrit sobre aquesta important inscripció els darrers vint anys, i s’analitzen de nou les característiques de l’epígraf (paleografia, formulari, etc.). Finalment, es conclou que no hi ha relació entre aquesta Thecla i el culte implantat en època medieval a santa Tecla com a patrona de Tarragona, en contra del que han proposat alguns autors.

Formulae generales de solidis regularibus

Invokaatio: I.N.S.B.

1.° Codicis Theodosiani, sive potius breviarii Aniani interpretationum fragmenta. — 2.° Theodosii Junioris et Valentiniani III. novellae constitutiones. — 3.° Gaii Institutionum fragmenta. — 4.° Julii Pauli sententiarum fragmenta. — 5.° Gregoriani, Hermogeniani et Papianei codicum fragmenta. — 6.° Formulae veteres : finis desideratur

Colbertinus

1.° M. Pauli Veneti libri tres de conditionibus et consuetudinibus orientalium regionum : interprete Francisco Pipino, Bononiensi, ordinis Fratrum Praedicatorum. — 2.° Epistola Presbyteri Joannis, quam misit Imperatori Frederico Barba-rubea. — 3.° Vita Machometi ; qualiter seduxit Terram sanctam, sive, Ecclesiam Orientalem. — 4.° Gesta Romanorum, sive potiùs, fabulae aniles et insulsae sub nominibus Romanorum Imperatorum. — 5.° Formulae variarum orationum, tam Presbyteri, quàm cujuscumque fidelis. — 6.° Confessio multùm spiritualis, composita per Cardinalem sancti Sixti. — 7.° Decretum Concilii Florentini super unione Graecorum, anno 1439. — 8.° Eugenii, Papae IV. bulla de unione Graecorum ; data eodem anno. — 9.° Ejusdem bulla super reductione Armenorum.

Ludovici de Targny

Tree Inscriptions: restoring a lost facet of the Graeco-Roman epigraphic habit

This article for the first time considers all extant ancient evidence for the habit of carving inscriptions on tree trunks. It emerges a picture that bears remarkable resemblances to what is known from the habit of graffiti writing (with important addition to that latter field to be derived from the findings), for individual and technical texts.

Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.