DERIVE and Linear Algebra

This work describes an experience with a methodology for learning based on competences in Linear Algebra for engineering students. The experience has been based in autonomous team work of students. DERIVE tutorials for Linear Algebra topics are provided to the students. They have to work with the tutorials as their homework. After, worksheets with exercises have been prepared to be solved by the students organized in teams, using DERIVE function previously defined in the tutorials. The students send to the instructor the solution of the proposed exercises and they fill a survey with their impressions about the following items: ease of use of the files, usefulness of the tutorials for understanding the mathematical topics and the time spent in the experience. As a final work, we have designed an activity directed to the interested students. They have to prepare a project, related with a real problem in Science and Engineering. The students are free to choose the topic and to develop it but they have to use DERIVE in the solution. Obviously they are guided by the instructor. Some examples of activities related with Orthogonal Transformations will be presented.

A toolbox with DERIVE: calculus on several variables, Applications of Computer Algebra

A toolbox is a set of procedures taking advantage of the computing power and graphical capacities of a CAS. With these procedures the students can solve math problems, apply mathematics to engineering or simply reinforce the learning of certain mathematical concepts. From the point of view of their construction, we can consider two types of toolboxes: (i) the closed box, built by the teacher, in which the utility files are provided to the students together with the respective tutorials and several worksheets with proposed exercises and problems,

Libro primero, de Arithmetica Algebratica, enel qual se contiene el arte Mercantiuol, con otras muchas Reglas del arte menor, y la Regla del Algebra, vulgarmente llamada Arte mayor, o Regla de la cosa ... [Texto impreso] ...]

Marca tip. en v. de port. y en v. de última h.

Two-dimensional freezing in the liquid–vapor interface of a dilute Pb:Ga alloy

We report the results of x-ray reflectivity and grazing incidence x-ray diffraction studies of the liquid–vapor interface of a dilute alloy of Pb in Ga over the temperature range of 23–76°C. Our data show that the liquid–vapor interface of this alloy is stratified for several atomic diameters into the bulk liquid and that a monolayer of Pb forms the outermost stratum of the interface. Over the temperature range of 23–56°C, the monolayer of Pb is in an ordered hexagonal phase. At about 58°C, this monolayer undergoes a first-order transition to a hexatic phase, which remains stable to 76°C. An analogy between the observed transition and the first-order melting transition in a one-component classical plasma is suggested.

Subcellular Localization of Myosin-V in the B16 Melanoma Cells, a Wild-type Cell Line for the dilute Gene

The discovery that the dilute gene encodes a class V myosin led to the hypothesis that this molecular motor is involved in melanosome transport and/or dendrite outgrowth in mammalian melanocytes. The present studies were undertaken to gain insight into the subcellular distribution of myosin-V in the melanoma cell line B16-F10, which is wild-type for the dilute gene. Immunofluorescence studies showed some degree of superimposed labeling of myosin-V with melanosomes that predominated at the cell periphery. A subcellular fraction highly enriched in melanosomes was also enriched in myosin-V based on Western blot analysis. Immunoelectron microscopy showed myosin-V labeling associated with melanosomes and other organelles. The stimulation of B16 cells with the α-melanocyte-stimulating hormone led to a significant increase in myosin-V expression. This is the first evidence that a cAMP signaling pathway might regulate the dilute gene expression. Immunofluorescence also showed an intense labeling of myosin-V independent of melanosomes that was observed within the dendrites and at the perinuclear region. Although the results presented herein are consistent with the hypothesis that myosin-V might act as a motor for melanosome translocation, they also suggest a broader cytoplasmic function for myosin-V, acting on other types of organelles or in cytoskeletal dynamics.

Cultured melanocytes from dilute mutant mice exhibit dendritic morphology and altered melanosome distribution

Mutant alleles at the dilute unconventional myosin heavy chain locus cause diluted coat color, opisthotonic seizures, and death. The dilute coat color phenotype is caused by irregular clumping of pigment in the hair, but amounts of melanin are unchanged from wild-type controls. The melanocyte phenotype has been described as adendritic, since hair bulb and Harderian gland melanocytes appear to be rounded in tissue sections. These observations do not exclude the possibility that the processes lack pigment, since the melanocyte shape was judged by the distribution of melanin. We have tested this hypothesis by culturing primary melanocytes from dilute mutant and wild-type mice. The mutant melanocytes do not lack processes; instead, they exhibit a concentrated perinuclear distribution of melanosomes, while wild-type melanocytes have a very uniform cytoplasmic distribution of melanosomes. Electron micrographs show no detectable differences in melanosome morphology or maturation between dilute and wild-type melanocytes. Immunofluorescence experiments indicate that the dilute protein is concentrated in regions of the cytoplasm that contain melanosomes. These experiments show that the dilute myosin is necessary for the localization of melanosomes, either by active transport or tethering.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Novel phenomena in dilute electron systems in two dimensions

For the past two decades, all two-dimensional systems of electrons were believed to be insulating in the limit of zero temperature. Recent experiments provide evidence for an unexpected transition to a conducting phase at very low electron densities. The nature of this phase is not understood and is currently the focus of intense theoretical and experimental attention.

Cloning and characterization of myr 6, an unconventional myosin of the dilute/myosin-V family.

We have isolated cDNAs encoding a second member of the dilute (myosin-V) unconventional myosin family in vertebrates, myr 6 (myosin from rat 6). Expression of myr 6 transcripts in the brain is much more limited than is the expression of dilute, with highest levels observed in choroid plexus and components of the limbic system. We have mapped the myr 6 locus to mouse chromosome 18 using an interspecific backcross. The 3' portion of the myr 6 cDNA sequence from rat is nearly identical to that of a previously published putative glutamic acid decarboxylase from mouse [Huang, W.M., Reed-Fourquet, L., Wu, E. & Wu, J.Y. (1990) Proc. Natl. Acad. Sci. USA 87, 8491-8495].

Critical behavior of the dilute antiferromagnet in a magnetic field

We study the critical behavior of the diluted antiferromagnet in a field with the tethered Monte Carlo formalism. We compute the critical exponents (including the elusive hyperscaling violations exponent θ). Our results provide a comprehensive description of the phase transition and clarify the inconsistencies between previous experimental and theoretical work. To do so, our method addresses the usual problems of numerical work (large tunneling barriers and self-averaging violations).

Quantum simulation of a topological Mott insulator with Rydberg atoms in a Lieb lattice

We propose a realistic scheme to quantum simulate the so-far experimentally unobserved topological Mott insulator phase-an interaction-driven topological insulator-using cold atoms in an optical Lieb lattice. To this end, we study a system of spinless fermions in a Lieb lattice, exhibiting repulsive nearest-and next-to-nearest-neighbor interactions and derive the associated zero-temperature phase diagram within mean-field approximation. In particular, we analyze how the interactions can dynamically generate a charge density wave ordered, a nematic, and a topologically nontrivial quantum anomalous Hall phase. We characterize the topology of the different phases by the Chern number and discuss the possibility of phase coexistence. Based on the identified phases, we propose a realistic implementation of this model using cold Rydberg-dressed atoms in an optical lattice. The scheme, which allows one to access, in particular, the topological Mott insulator phase, robustly and independently of its exact position in parameter space, merely requires global, always-on off-resonant laser coupling to Rydberg states and is feasible with state-of-the-art experimental techniques that have already been demonstrated in the laboratory.

An introduction to alysidal algebra (IV)

Purpose – Deontical impure systems are systems whose object set is formed by an s-impure set, whose elements are perceptuales significances (relative beings) of material and/or energetic objects (absolute beings) and whose relational set is freeways of relations, formed by sheaves of relations going in two-way directions and at least one of its relations has deontical properties such as permission, prohibition, obligation and faculty. The paper aims to discuss these issues. Design/methodology/approach – Mathematical and logical development of human society ethical and normative structure. Findings – Existence of relations with positive imperative modality (obligation) would constitute the skeleton of the system. Negative imperative modality (prohibition) would be the immunological system of protection of the system. Modality permission the muscular system, that gives the necessary flexibility. Four theorems have been formulated based on Gödel's theorem demonstrating the inconsistency or incompleteness of DISs. For each constructed systemic conception can happen to it one of the two following things: either some allowed responses are not produced or else some forbidden responses are produced. Responses prohibited by the system are defined as nonwished effects. Originality/value – This paper is a continuation of the four previous papers and is developed the theory of deontical impure systems.

An introduction to alysidal algebra (V): phenomenological components

Purpose – This paper aims to refer to a subjective approach to a type of complex system: human ecosystems, referred to as deontical impure systems (DIS) to capture a set of properties fundamental to the distinction between human and natural ecosystems. There are four main phenomenological components: directionality, intensity, connection energy and volume. The paper establishes thermodynamics of deontical systems based on the Law of Zipf and the temperature of information. Design/methodology/approach – Mathematical and logical development of human society structure. Findings – A fundamental question in this approach to DIS is the intensity or forces of a relation. Concepts are introduced as the system volume and propose a system thermodynamic theory. It hints at the possibility of adapting the fractal theory by introducing the fractal dimension of the system. Originality/value – This paper is a continuation of other previous papers and developing the theory of DIS.

Un receuil: containing painting, penmanship, algebra and pieces selected from various authors in prose and verse, with a few pieces in French with their translation / by Phebe Folger of Nantucket : manuscript, 1797-1806

Written mostly in a copperplate hand in black ink, and illustrated with watercolor drawings.

Algebra, or universal mathematics: revived 1738 with notes and additions : manuscript, [after 1738]

Instructional book in algebra with exercises.