Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Higher identities for the ternary commutator

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc - acb - bac + bca + cab - cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation theory of the symmetric group to demonstrate the existence of new identities in degree 11. The only irreducible representations of dimension <400 with new identities correspond to partitions 2(5), 1 and 2(4), 1(3) and have dimensions 132 and 165. We construct an explicit new multilinear identity for partition 2(5), 1 and we demonstrate the existence of a new non-multilinear identity in which the underlying variables are permutations of a(2)b(2)c(2)d(2)e(2) f.

A substantive theory of the realization of stroke patients’ dignity in hospital care

Dignity is seen important in health care context but considered as a controversial and complex concept. In health care context, it is described as being influenced by for example autonomy, respect, communication, privacy and hospital environment. Patient dignity is related to satisfaction with care, reduced stress, better confidence in health services, enhanced patient outcomes and shorter stay in a hospital. Stroke patients may struggle for dignity as being dependent on other people has impact on the patients’ self-image. In all, stroke patients are very specific patient group and considered vulnerable from emotional aspect. Therefore study findings from other patient groups in the area of ethical problems cannot be transferred to the stroke patients. This master’s thesis consists of two parts. The first part is the literature review of patients’ dignity in hospital care. The literature defined dignity and described factors promoting and reducing it. The results were ambiguous and thus a clear understanding was not able to create. That was the basis for the second part of the master’s thesis, the empirical study. This part aimed to develop theoretical construction to explore the realization of stroke patients’ dignity in hospital care. The data of the second part was collected by interviewing 16 stroke patients and analyzed using the constant comparison of Grounded Theory. The result was ‘The Theory of Realization of Stroke Patients’ Dignity in Hospital Care’ which is described not only in this master’s thesis but also as a scientific article. The theory consists of the core category, four generic elements and five specific types on realization. The core category emerged as ‘dignity in a new situation’. After a stroke, dignity is defined in a new way which is influenced by the generic elements: life history, health history, individuality and a stroke. Stroke patient’s dignity is realized through five specific types on realization: person related dignity type, control related dignity type, independence related dignity type, social related dignity type and care related dignity type. The theory points out possible special characteristics of stroke patients’ dignity in control related dignity type and independence related dignity type. Before implementing the theory, the relation between the core category, generic elements and specific types on realization needs to be studied further.

A Moral Stakeholder Theory of the Firm

To be a coherent and genuinely alternative conception to the shareholder model, any moral stakeholder theory must meet the following conditions: (1) It must be an ethical theory; (2) It must identify a limited group as stakeholders; (3) The group must be identified on morally relevant grounds; (4) Stakeholder claims must be non-universal; (5) And not held against everyone. A principle for identifying the stakeholder is suggested as a person who has much to lose – financially, socially, or psychologically – by the failure of the firm. The emerging picture contrasts sharply with the conventional conception of the firm.

An axiomatic characterization of the MVSHN group fitness ordering

In order to analyze a unicellular-multicellular evolutionary transition, a multicellular organism is identified with the vector of viabilities and fecundities of its constituent cells. The Michod–Viossat–Solari–Hurand–Nedelcu index of group fitness for a multicellular organism is a function of these cell viabilities and fecundities. The MVSHN index has been used to analyze the germ-soma specialization and the fitness decoupling between the cell and organism levels that takes place during the transition to multicellularity. In this article, social choice theory is used to provide an axiomatic characterization of the group fitness ordering of vectors of cell viabilities and fecundities underlying the MVSHN index.

On the algebraic K theory of the massive D8 and M9-branes

In this paper we review some basic relations of algebraic K theory and we formulate them in the language of D-branes. Then we study the relation between the D8-branes wrapped on an orientable, compact manifold W in a massive Type IIA, supergravity background and the M9-branes wrapped on a compact manifold Z in a massive d = 11 supergravity background from the K-theoretic point of view. By interpreting the D8-brane charges as elements of K-0(C(W)) and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of K-0(C(Z) x ((k) over bar*) G) where G is a one-dimensional compact group, a connection between charges and gauge fields is argued to exists. This connection could be realized as a composition map between the corresponding algebraic K theory groups.

Holomorphic Automorphisms of Danielewski Surfaces II: Structure of the Overshear Group

We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces and investigate their group of holomorphic automorphisms. Our main result states that the overshear group, which is known to be dense in the identity component of the holomorphic automorphism group, is a free product.

An evolutionary theory of the family.

An evolutionary framework for viewing the formation, the stability, the organizational structure, and the social dynamics of biological families is developed. This framework is based upon three conceptual pillars: ecological constraints theory, inclusive fitness theory, and reproductive skew theory. I offer a set of 15 predictions pertaining to living within family groups. The logic of each is discussed, and empirical evidence from family-living vertebrates is summarized. I argue that knowledge of four basic parameters, (i) genetic relatedness, (ii) social dominance, (iii) the benefits of group living, and (iv) the probable success of independent reproduction, can explain many aspects of family life in birds and mammals. I suggest that this evolutionary perspective will provide insights into understanding human family systems as well.

On some Finite-Dimensional Representations of Artin Braid Group

Валентин В. Илиев - Авторът изучава някои хомоморфни образи G на групата на Артин на плитките върху n нишки в крайни симетрични групи. Получените пермутационни групи G са разширения на симетричната група върху n букви чрез подходяща абелева група. Разширенията G зависят от един целочислен параметър q ≥ 1 и се разцепват тогава и само тогава, когато 4 не дели q. В случая на нечетно q са намерени всички крайномерни неприводими представяния на G, а те от своя страна генерират безкрайна редица от неприводими представяния на групата на плитките.

Systematic Revision of the granulatus Group of Urophonius Pocock, 1893 (Scorpiones, Bothriuridae), with Description of a New Species from Central Chile

A systematic revision of the granulatus group of the bothriurid scorpion genus Urophonius Pocock, 1893 is presented. Urophonius pizarroi, n. sp., a new species from central Chile, is described. Urophonius granulatus Pocock, 1898, Urophonius somuncura Acosta, 2003, and Urophonius tregualemuensis Cekalovic, 1981, are redescribed using modern standards. The adult males of U. somuncura and U. tregualemuensis are described for the first time. A distribution map and key to the species of the granulatus group are provided, along with a discussion of their phenology.

Half-Filled Layered Organic Superconductors and the Resonating-Valence-Bond Theory of the Hubbard-Heisenberg Model

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta('), kappa, and lambda phases of (BEDT-TTF)(2)X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)(2)X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a d(x)(2)-y(2) superconductor with a small superfluid stiffness and a pseudogap with d(x)(2)-y(2) symmetry.