Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Zeros of orthogonal polynomials generated by canonical perturbations of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Interpretação eletrostática e a conjectura se Smale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interpretação eletrostática e zeros de polinômios

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Electrostatic force microscopy and potentiometry of realistic nanostructured systems

We investigate the dependency of electrostatic interaction forces on applied potentials in electrostatic force microscopy (EFM) as well as in related local potentiometry techniques such as Kelvin probe microscopy (KPM). The approximated expression of electrostatic interaction between two conductors, usually employed in EFM and KPM, may loose its validity when probe-sample distance is not very small, as often realized when realistic nanostructured systems with complex topography are investigated. In such conditions, electrostatic interaction does not depend solely on the potential difference between probe and sample, but instead it may depend on the bias applied to each conductor. For instance, electrostatic force can change from repulsive to attractive for certain ranges of applied potentials and probe-sample distances, and this fact cannot be accounted for by approximated models. We propose a general capacitance model, even applicable to more than two conductors, considering values of potentials applied to each of the conductors to determine the resulting forces and force gradients, being able to account for the above phenomenon as well as to describe interactions at larger distances. Results from numerical simulations and experiments on metal stripe electrodes and semiconductor nanowires supporting such scenario in typical regimes of EFM investigations are presented, evidencing the importance of a more rigorous modeling for EFM data interpretation. Furthermore, physical meaning of Kelvin potential as used in KPM applications can also be clarified by means of the reported formalism. © 2009 American Institute of Physics.

A Model to Understand the Oxygen Vacancy Formation in Zr-Doped CeO2:Electrostatic Interaction and Structural Relaxation

Using density functional theory with the inclusion of on-site Coulomb Correction, the O vacancy formation energies of CexZr1-xO2 solid solutions with a series of Ce/Zr ratios are calculated, and a model to understand the results is proposed. It consists of electrostatic and structural relaxation terms, and the latter is found to play a vital role in affecting the O vacancy formation energies. Using this model, several long-standing questions in the field, such as why ceria with 50% ZrO2 usually exhibit the best oxygen storage capacity, can be explained. Some implications of the new interpretation are also discussed.

Foil rolling : a new interpretation of experimental results

This paper explores a new interpretation of experiments on foil rolling. The assumption that the roll remains convex is relaxed so that the strip profile may become concave, or thicken in the roll gap. However, we conjecture that the concave profile is associated with phenomena which occur after the rolls have stopped. We argue that the yield criterion must be satisfied in a nonconventional manner if such a phenomenon is caused plastically. Finite element analysis on an extrusion problem appears to confirm this conjecture.

A phenomenological explication of dream interpretation among rural and urban Nguni people

Psychologists investigating dreams in non-Western cultures have generally not considered the meanings of dreams within the unique meaning-structure of the person in his or her societal context. The majority of dream studies in African societies are no exception. Researchers approaching dreams within rural Xhosa and Zulu speaking societies have either adopted an anthropological or a psychodynamic orientation. The latter approach particularly imposes a Western perspective in the interpretation of dream material. There have been no comparable studies of dream interpretation among urban blacks participating in the African Independent Church Movement. The present study focuses on the rural Xhosa speaking people and the urban black population who speak one of the Nguni languages and identify with the African Independent Church Movement. The study is concerned with understanding the meanings of dreams within the cultural context in which they occur. The specific aims of the study are: 1. To explicate the indigenous system of dream interpretation as revealed by acknowledged dream experts. 2. To examine the commonalities and the differences between the interpretation of dreams in two groups, drawn from a rural and urban setting respectively. 3. To elaborate upon the life-world of the participants by the interpretations gained from the above investigation. One hundred dreams and interpretations are collected from two categories of participants referred to as the Rural Group and the Urban Group. The Rural Group is made up of amagqira [traditional healers] and their clients, while the Urban Group consists of prophets and members of the African Independent Churches. Each group includes acknowledged dream experts. A phenomenological methodology is adopted in explicating the data. The methodological precedure involves a number of rigorous stages of expl ication whereby the original data is reduced to Constituent Profiles leading to the construction of a Thematic Index File. By searching and reflect ing upon the data, interpretative themes are identified. These themes are explicated to provide a rigorous description of the interpretative-reality of each group. Themes explicated w i thin the Rural Group are: the physiognomy of the dreamer's life-world as revealed by ithongo, the interpretation of ithongo as revealed through action, the dream relationship as an anticipatory mode-of-existence, iphupha as disclosing a vulnerable mode-of-being, human bodiliness as revealed in dream interpretations and the legitimation of the interpretative-reality within the life-world. Themes explicated within the Urban Group are: the phys iognomy of the dreamer's life-world revealed in their dream-existence, the interpretative-reality revealed through the enaction of dreams, tension between the newer Christian-based cosomology and the traditional cultural-based cosmology, a moral imperative, prophetic perception and human bodiliness, as revealed in dream interpretations and the legitimation of the interpretative-reality within the life-world. The essence of the interpretative-reality of both groups is very similar and is expressed in the notion of relatedness to a cosmic mode-of-being. The cosmic mode-of-being includes a numinous dimension which is expressed through divine presence in the form of ancestors, Holy Spirit or God. These notions cannot be apprehended by theoretical constructs alone but may be grasped and given form in meaning-disclosing intuitions which are expressed in the lifeworld in terms of bodiliness, revelatory knowledge, action and healing. Some differences b e tween the two groups are evident and reveal some conflict between the monotheistic Christian cosmology and the traditional cosmology. Unique aspects of the interpetative-reality of the Urban Group are expressed in terms of difficulties in the urban social environment and the notion of a moral imperative. It is observed that cul tural self-expression based upon traditional ideas continues to play a significant role in the urban environment. The apparent conflict revealed between the respective cosmologies underlies an integration of the aditional meanings with Christian concepts. This finding is consistent with the literature suggesting that the African Independent Church is a syncretic movement. The life-world is based upon the immediate and vivid experience of the numinous as revealed in the dream phenomenon. The participants' approach to dreams is not based upon an explicit theory, but upon an immediate and pathic understanding of the dream phenomenon. The understanding is based upon the interpreter's concrete understanding of the life-world, which includes the possibility of cosmic integration and continuity between the personal and transpersonal realms of being. The approach is characterized as an expression of man's primordial attunement with the cosmos. The approach of the participants to dreams may not b e consistent with a Western rational orientation, but neverthele ss, it is a valid approach . The validity is based upon the immediate life-world of experience which is intelligible, coherent, and above all, it is meaning-giving in revealing life-possibility within the context of human existence.

An experiment in mixed compilation/interpretation

One of the classic forms of intermediate representation used for communication between compiler front-ends and back-ends are those based on abstract stack machines. It is possible to compile the stack machine instructions into machine code by means of an interpretive code generator, or to simulate the stack machine at runtime using an interpreter. This paper describes an approach intermediate between these two extremes. The front-end for a commercial Modula 2 compiler was ported to the "industry standard PC", and a partially compiling back-end written. The object code runs with the assistance of an interpreter, but may be linked with libraries which are fully compiled. The intent was to provide a programming environment on the PC which is identical to that of the same compilers on 32-bit UNIX machines. This objective has been met, and the compiler is available to educational institutions as free-ware. The design basis of the new compiler is described, and the performance critically evaluated.