Validación del software educativo Poliestudio 1.0: informe de investigación

PoliEstudio 1.0 is a computational tool, with free license, created to work with polynomial expressions in one variable and it was created by a team in which the authors of this article are part of. This article documents the qualitative validation performed to this software which main objective was to bring to the Costa Rican Educational System a validated educational software that can solve, partially, the problems that nowadays exists in the mathematic education of secondary students, particularly in the topics related to polynomial expressions in one variable and specifically to those students who are in eighth grade.

Keys on the Formation and Human Development in Pedagogy

This paper is based on the experiences of the author, who has worked in the various levels of the Venezuelan educational system. This has been a very important platform to understand the ideas of education and human development within the Venezuelan institutionality in the educational field. The idea of education that we have, as teachers, should be rethought in order to consider the personal stories of those who share with us their time, interests and willingness: children, young people or adults, all with particular identities, differences and coincidences. The teachers, the schools and the State cannot consider an education for someone they do not know. In this sense, we provide some reflections resulting from our ethnographic work, based on the school life, interviews, class analysis, observations, and stories, among others. Our thoughts are classified as formation, hope, dialogue, attitude, and school life.

Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

ASSOCIATIVE IDENTITIES OF OCTONIONS

We work to find a basis of identities for an octonion algebra modulo an associator ideal of a free alternative algebra, or, in other words, a basis for an associative replica of an ideal of identities of an octonion algebra.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Three-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of L-tartaric acid with the associative-group monosubstituted pyridines 3-minopyridine, 3-carboxypyridine (nicotinic acid) and 2-carboxypyridine (picolinic acid).

The 1:1 proton-transfer compounds of L-tartaric acid with 3-aminopyridine [3-aminopyridinium hydrogen (2R,3R)-tartrate dihydrate, C5H7N2+·C4H5O6-·2H2O, (I)], pyridine-3-carboxylic acid (nicotinic acid) [anhydrous 3-carboxypyridinium hydrogen (2R,3R)-tartrate, C6H6NO2+·C4H5O6-, (II)] and pyridine-2-carboxylic acid [2-carboxypyridinium hydrogen (2R,3R)-tartrate monohydrate, C6H6NO2+·C4H5O6-·H2O, (III)] have been determined. In (I) and (II), there is a direct pyridinium-carboxyl N+-HO hydrogen-bonding interaction, four-centred in (II), giving conjoint cyclic R12(5) associations. In contrast, the N-HO association in (III) is with a water O-atom acceptor, which provides links to separate tartrate anions through Ohydroxy acceptors. All three compounds have the head-to-tail C(7) hydrogen-bonded chain substructures commonly associated with 1:1 proton-transfer hydrogen tartrate salts. These chains are extended into two-dimensional sheets which, in hydrates (I) and (III) additionally involve the solvent water molecules. Three-dimensional hydrogen-bonded structures are generated via crosslinking through the associative functional groups of the substituted pyridinium cations. In the sheet struture of (I), both water molecules act as donors and acceptors in interactions with separate carboxyl and hydroxy O-atom acceptors of the primary tartrate chains, closing conjoint cyclic R44(8), R34(11) and R33(12) associations. Also, in (II) and (III) there are strong cation carboxyl-carboxyl O-HO hydrogen bonds [OO = 2.5387 (17) Å in (II) and 2.441 (3) Å in (III)], which in (II) form part of a cyclic R22(6) inter-sheet association. This series of heteroaromatic Lewis base-hydrogen L-tartrate salts provides further examples of molecular assembly facilitated by the presence of the classical two-dimensional hydrogen-bonded hydrogen tartrate or hydrogen tartrate-water sheet substructures which are expanded into three-dimensional frameworks via peripheral cation bifunctional substituent-group crosslinking interactions.

Composing maternal identities : the living realities of mothers with young adult-children in twenty-first century Australia

There is an abundance of books available on the topic of motherhood and mothering; the majority of these books focus on the vulnerability of babies and young children and the motherwork such vulnerability demands. In particular they focus on what it is right to do in the interests of the child, and particularly his or her growth and development. Such a focus is consistent in Western culture with modern moral frameworks where understandings of goodness have been assimilated to dimensions of human action rather than dimensions of human being, selfhood, or specific forms of life. As Charles Taylor has observed, much modern moral philosophy has focused =on what it is right to do rather than the nature of the good life‘ (1989, 13). The master narratives of motherhood and the prevailing social discourses of intensive1 and sacrificial2 mothering exemplify this view as such narratives and discourses depict =what mothers are expected to do [and] how mothers are supposed to be‘ (Nelson 2001, 140). From such infant/child-focused accounts a canonical maternal identity can be discerned; arguably, it is a restricted one. The majority of these books fail to address questions related to what it means be a mother in particular situated, existing, living realities. For instance, ask a mother with young children what being a mother means to her and she may speak of the challenges she faces balancing paid employment and her role as a mother, or the impact of the demands being made on her time and energy. However, ask a mother with young adult-children3 what being a mother means to her and she may speak in similar tones, but she may also speak in differing tones. For example, a "mature" mother may speak of the "empty nest", the "crowded house" and/or "its revolving front door". She may speak of issues related to the vulnerability of the long term marriage, elder care, or grandparenting, or even disillusionment and disenchantment. The purpose of this research is to explore the identity challenges and prospects of some mothers with young adult-children aged between 18 and 30 years of age in twenty-first century Australia. In interpreting the identity challenges and prospects this particular cohort of mothers encounter in their ordinary, everyday living, a diverse and particular range of maternal experiences.my own included5.have been traced, along with the social and ethical meanings ascribed in them. With an understanding and appreciation of voice as the medium which connects one's inner and outer worlds, this research illuminates the plurality of voices and the multiple layers of meaning in each of these mother's particular living and existing realities. Specifically, this research addresses the narrowly constructed, canonical maternal identity through a critical exploration and reflection on stories, shared in a research context, of the living realities of a group of self-identified "mature", middle-class, Australian mothers with children aged between 18 and 30 years of age6. By appraising the broader familial, historical, social, cultural, institutional, and, importantly, moral contexts in which these mothers are situated, 'thick descriptions' (Geertz 1973, 27)7 of maternal identities, and the challenges and prospects these mothers are negotiating, are provided. In terms of its ethical orientation, the frameworks which support and frame this research reject, repudiate and contest (Nelson 2001) the reduction of ethical concerns to individual or intellectual problems or dilemmas to be solved through the application of a theory derived from reasoned thinking. In dismissing deductive and =theoretical-juridical‘8 approaches, the individualistic orientation entrenched in contemporary Western moral thinking, expressed in the notion of '"what ought I to do" when faced with a problem, issue or dilemma of practical urgency' (Isaacs & Massey 1994, 1), is simultaneously rejected, repudiated and contested (Nelson 2001). In countering such understandings, this research reorients us to the illumination and articulation of who it is good to be, for each of these mothers, in allegiance with those goods which guide and inspire her orientations towards living a good life—a life which embraces and enhances the flourishing of herself and her significant others. With an understanding and appreciation that 'mind is never free of precommitment[—t]here is no innocent eye, nor is there one that penetrates aboriginal reality' (Bruner 1987, 32), this thesis is written with the voices of other interlocutors9. These interlocutors include the voices of my research participants whom I refer to as "research interlocutors", my textual "friends" — those scholars whose work resonates strongly with my orientations—as well as the myriad other voices that speak to mothers, for mothers and about mothers, such as those found in popular and mainstream press and culture. Sometimes these voices resonate; other times dissonance may be heard. In situating this research within these complementary frameworks, this research invites readers to join with me in considering, appreciating and appraising the narrow construction of maternal identity. I seek for this engagement, like the engagements with my research interlocutors, to be 'a meeting of voices, an authentic dialogue that is inclusive of the voices of all concerned participants' (Isaacs 2001, 6). I hope that the voices in this thesis resonate with yours (although, at times, you may feel some dissonance) and that together we can draw closer to the accounting, re-counting and re-stor(y)ing of maternal identities; like concentric circles of witness, the dialogue, ...will thus be expanded rippling into corners where one might both imagine, and least expect. Possibilities, then, are vast; the future exciting (Smith 2007, 397). This research is also shaped and guided by maternal scholarship, a relatively new field of inquiry known as 'motherhood studies' (O'Reilly 2011, xvii) which has its origins within the broader terrain of feminist scholarship. As a work of maternal scholarship, this thesis draws upon and continues the tradition of examining motherhood as it is experienced 'in a social context, as embedded in a political institution: in feminist terms' (Rich 1995, ix). It values mothers, their experiences, their stories, their lives. As such, this research is oriented towards 'matricentric feminism', a particular form of feminist inquiry, politics and theory which is consistent with and receptive to feminist frameworks of care and equal rights (O‘Reilly 2011, 25). A number of complementary conceptual frameworks have been engaged in this research with the thesis presented in three parts: the pre-figurative, configurative and re-configurative. As my particular living experiences provided the initial motivation for this research, an account of the challenges I experienced as a mother with young adult-children are outlined as a Prelude to this thesis. Attention then turns to Part One – Pre-figuring Maternal Identities in which the contextual, conceptual and methodological foundations underpinning this research are explored and outlined. In Chapter One, the prevailing cultural narratives and social discourses supporting and shaping the construction of the canonical maternal identity are outlined. Next, in setting the scholarly context, the critiques — arising from feminist and maternal scholarship — of motherhood as a patriarchal institution, mothering as experience, and mothering as work, are explored. As this research engaged with participants who are embedded in particular middle-class, heterosexual, familial and cultural structures, an exploration of family life cycle theory and main stream media accounts are also incorporated. The terrain in which "mature" mothering within an Australian context is experienced is also outlined, including the notions of "empty nests" and "crowded houses", grandparenting, elder care and women's midlife transition. Chapter Two gives an account of the conceptual ontological, ethical, identity and narrative frameworks underpinning this research. In setting the context for rich interpretations, the characteristics of being human10 are outlined before attention turns to our embodiment and embeddedness in our shared human condition11. From this point, attention then turns to understanding the moral form of human living12. In appreciating the vulnerability inherent in our shared human condition, the ways in which we may experience trouble in our lives is noted. The framing of identity constitution13 as complex, multi-faceted, relationally negotiated and composed is then outlined, followed by an understanding of why narrative is a valuable interpretive tool for interpreting and understanding human experiences. This chapter concludes with an appreciation of the ethical significance of storytelling. The research methodology is then outlined in Chapter Three. The rationale underpinning the adoption of the narrative interviewing technique of in-depth interviewing is explored. In exploring these methodological frameworks, the recruitment and interview processes involved in gathering and interpreting the recorded transcripts of ten Australian mothers with young adult-children are outlined. The method of analysis known as the Listening Guide14 best complements the multi-layered, pluri-vocal nature of narrative accounting. The final section of Chapter Three outlines The Guide, with one mother's recorded transcript used to illustrate this method's step-by-step process. Having gathered an understanding and appreciation of the pluri-vocal, multi-layered nature of narrative and identity constitution, the tone of this thesis changes in Part Two . Configuring Maternal Identities. This section consists of Chapters Four and Five and seeks to find meaning in, and make sense of, the differences and commonalities across these particular accounts. Chapter Four explores the living realities of four Australian mothers with young adult-children: Poppy, Honey, Lily and Heather. In presenting a thick description of these mothers' situated realities, the frameworks.the familial, social, cultural, historical and institutional backgrounds.which have supported and shaped each mother's experiences are illuminated. Simultaneously revealed through these particular accounts are the plurality of goods focusing and moving each mother to the moral form of life, a life of meaning and purpose. The harms challenging some mothers' moral motivations are also revealed in this chapter. Specifically illustrated in Chapter Four are the unique and qualitative differences of particular maternal identity configurations. Chapter Five reveals the commonalities amongst all of the research interlocutors' accounts. This chapter contests the individualistic orientation of many contemporary accounts of motherhood which are aimed at defining or contesting what a "good" mother ought to do. By turning away from such individualistic orientations, the chapter does not seek to define 'the content of obligation' (Taylor 1989, 3) but rather seeks to illuminate and articulate a richer, deeper understanding and appreciation of maternal be-ing and be-coming - that is, who it is good to be, for each of these mothers - in allegiance with those goods that focus and inspire her moral motivations. Part Three - Re-Configuring Maternal Identities, which is comprised of Chapter Six, draws this thesis to a close. In this final chapter, the preconceptions, conditions and aspirations for this mother-centred account of the living realities of a small, local cohort of mothers are reiterated. The insights gathered from the rich, descriptive accounts are illuminated and articulated, and the chapter closes with some suggestions for future research. In a Postlude, I reflect on how this research has been a transformative learning experience in my own life.an experience in which I have been able to not only deeply understand and appreciate the challenges and disorientation I was experiencing but also to identify and reorient my stance in relation to the good. In a practical sense, by offering thick descriptions of the living realities of this cohort of "mature" mothers, this research challenges the canonical maternal identity and questions its relevance for, and effect on, "mature" mothers' identity constitution. By bringing to light the complex existing realities of these particular mothers, this research critiques the canonical maternal identity by illustrating that each mother's life and her identity constitutions are complex, relationally negotiated and composed and that motherhood is an enduring way of being. Through these illustrations, this research engages with and extends understandings of difference feminism. This research, however, not only rejects, repudiates and contests (Nelson 2001) the narrowly defined canonical maternal identity. By illuminating and articulating the goods which shape and inspire these "mature" mothers' motherwork, this research offers a matricentric account which is consistent with and respectful of the particular, situated realities—the broader familial, social, institutional, but most importantly, moral values and frameworks—in which each mother‘s life is embedded and her motherwork oriented. By understanding and appreciating the complex and multiple webs of relationships in which each mother exists, this matricentric re-stor(y)ing of maternal experiences not only understands and appreciates the unique nature of each mother‘s existing realities, it is oriented to the continuing enhancing of the shared pursuit of the good which underpins particular maternal practices and particular maternal ways of being.

Decomposition construction for secret sharing schemes with graph access structures in polynomial time

The purpose of this paper is to describe a new decomposition construction for perfect secret sharing schemes with graph access structures. The previous decomposition construction proposed by Stinson is a recursive method that uses small secret sharing schemes as building blocks in the construction of larger schemes. When the Stinson method is applied to the graph access structures, the number of such “small” schemes is typically exponential in the number of the participants, resulting in an exponential algorithm. Our method has the same flavor as the Stinson decomposition construction; however, the linear programming problem involved in the construction is formulated in such a way that the number of “small” schemes is polynomial in the size of the participants, which in turn gives rise to a polynomial time construction. We also show that if we apply the Stinson construction to the “small” schemes arising from our new construction, both have the same information rate.

Unitary Processes with Independent Increments and Representations of Hilbert Tensor Algebras

The aim of this article is to characterize unitary increment process by a quantum stochastic integral representation on symmetric Fock space. Under certain assumptions we have proved its unitary equivalence to a Hudson-Parthasarathy flow.

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Working with Identities Promoting Student Teachers Professional Development

The starting point of the study was that good teaching requires a teacher to be aware of the sources of his or her pedagogical decisions; that is, personal values, beliefs and understandings. From this perspective, a teacher s professional development refers to a process of extending one s self-knowledge. The aim of this study was to promote student teachers' professional development with the help of identity work. Identity work refers to reflecting on both personal and professional experiences. Identity work consists of student teachers self-reflection on their life experiences (self-identity) and video diary-based reflection on their classroom practice (professional identity). The research questions of the study were 1) how is identity work manifested by the participants? and 2) what is the potential of identity work in promoting student teachers professional development? The research data was collected from four student teachers in the academic year 2007-2008; the research group had 24 meetings during the research process. Student teachers take part in a multimode teacher education programme, where students work as ordinary teachers in schools during their university studies. The data collection was conducted by using two methods: participants narratives based on autobiographical writings and video diaries based on participants lessons. Narrative research data was analysed by employing qualitative methods and strategies as they were needed in the research. The research results revealed four different ways of working with identities, each of them revealing different aspects of and approaches to identity work. The results also showed that identity work has the potential to promote professional development. As the research progressed, there were visible changes in the participants reflection. However, despite encouraging results, some issues should be critically questioned. Although reflection sounds attractive and fruitful as a tool for promoting professional development, there are also difficulties and obstacles. On the basis of the results, a proposal for promoting student teachers professional development is offered. Keywords: Teacher identity, identity work, reflection, teacher professional development

Uncertainty analysis of vibrational frequencies of an incompressible liquid in a rectangular tank with and without a baffle using polynomial chaos expansion

Polynomial chaos expansion (PCE) with Latin hypercube sampling (LHS) is employed for calculating the vibrational frequencies of an inviscid incompressible fluid partially filled in a rectangular tank with and without a baffle. Vibration frequencies of the coupled system are described through their projections on the PCE which uses orthogonal basis functions. PCE coefficients are evaluated using LHS. Convergence on the coefficient of variation is used to find the orthogonal polynomial basis function order which is employed in PCE. It is observed that the dispersion in the eigenvalues is more in the case of a rectangular tank with a baffle. The accuracy of the PCE method is verified with standard MCS results and is found to be more efficient.

A polynomial algorithm for the three-machine open shop with a bottleneck machine

The paper considers the three‐machine open shop scheduling problem to minimize themakespan. It is assumed that each job consists of at most two operations, one of which is tobe processed on the bottleneck machine, the same for all jobs. A new lower bound on theoptimal makespan is derived, and a linear‐time algorithm for finding an optimalnon‐preemptive schedule is presented.

A fully polynomial approximation scheme for the single machine weighted total tardiness problem with a common due date

We develop a fully polynomial-time approximation scheme (FPTAS) for minimizing the weighted total tardiness on a single machine, provided that all due dates are equal. The FPTAS is obtained by converting an especially designed pseudopolynomial dynamic programming algorithm.