Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Electron acceleration and parallel electric fields due to kinetic Alfvén waves in plasma with similar thermal and Alfvén speeds

We investigate electron acceleration due to shear Alfven waves in a collissionless plasma for plasma parameters typical of 4–5RE radial distance from the Earth along auroral field lines. Recent observational work has motivated this study, which explores the plasma regime where the thermal velocity of the electrons is similar to the Alfven speed of the plasma, encouraging Landau resonance for electrons in the wave fields. We use a self-consistent kinetic simulation model to follow the evolution of the electrons as they interact with a short-duration wave pulse, which allows us to determine the parallel electric field of the shear Alfven wave due to both electron inertia and electron pressure effects. The simulation demonstrates that electrons can be accelerated to keV energies in a modest amplitude sub-second period wave. We compare the parallel electric field obtained from the simulation with those provided by fluid approximations.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Let λ1,…,λn be real numbers in (0,1) and p1,…,pn be points in Rd. Consider the collection of maps fj:Rd→Rd given by fj(x)=λjx+(1−λj)pj. It is a well known result that there exists a unique nonempty compact set Λ⊂Rd satisfying Λ=∪nj=1fj(Λ). Each x∈Λ has at least one coding, that is a sequence (ϵi)∞i=1 ∈{1,…,n}N that satisfies limN→∞fϵ1…fϵN(0)=x. We study the size and complexity of the set of codings of a generic x∈Λ when Λ has positive Lebesgue measure. In particular, we show that under certain natural conditions almost every x∈Λ has a continuum of codings. We also show that almost every x∈Λ has a universal coding. Our work makes no assumptions on the existence of holes in Λ and improves upon existing results when it is assumed Λ contains no holes.

On univoque points for self-similar sets

Let K⊆R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence, we can show that the set of points with a unique coding is a graph-directed self-similar set in the sense of Mauldin and Williams (1988). The theory of Mauldin and Williams then provides a method by which we can explicitly calculate the Hausdorff dimension of this set. Our algorithm can be applied generically, and our result generalises the work of Daróczy, Kátai, Kallós, Komornik and de Vries.

Are the magnetic fields of millisecond pulsars similar to 10(8) G?

It is generally assumed that the magnetic fields of millisecond pulsars (MSPs) are similar to 10(8) G. We argue that this may not be true and the fields may be appreciably greater. We present six evidences for this: (1) The similar to 10(8)G field estimate is based on magnetic dipole emission losses which is shown to be questionable; (2) The MSPs in low mass X-ray binaries (LMXBs) are claimed to have < 10(11) G on the basis of a Rayleygh-Taylor instability accretion argument. We show that the accretion argument is questionable and the upper limit 10(11) G may be much higher; (3) Low magnetic field neutron stars have difficulty being produced in LMXBs; (4) MSPs may still be accreting indicating a much higher magnetic field; (5) The data that predict similar to 10(8) G for MSPs also predict ages on the order of, and greater than, ten billion years, which is much greater than normal pulsars. If the predicted ages are wrong, most likely the predicted similar to 10(8) G fields of MSPs are wrong; (6) When magnetic fields are measured directly with cyclotron lines in X-ray binaries, fields a parts per thousand << 10(8) G are indicated. Other scenarios should be investigated. One such scenario is the following. Over 85% of MSPs are confirmed members of a binary. It is possible that all MSPs are in large separation binaries having magnetic fields > 10(8) G with their magnetic dipole emission being balanced by low level accretion from their companions.

Exercise-stimulated GLUT4 Expression is Similar in Normotensive and Hypertensive Rats

The effects of exercise training on systolic blood pressure (BP), insulin sensitivity, and plasma membrane GLUT4 protein content in spontaneously hypertensive (SHR) and normotensive Wistar-Kyoto (WKY) rats were compared. 16 SHR and 16 WKY male rats, aged 6 months, were randomized into sedentary and trained (tread-mill running, 5 days/week, 60 min/day for 10 weeks) groups (n = 8/group). At baseline, SHR had lower insulin sensitivity than WKY rats, however, there were no differences between WKY and SHR GLUT4 expression. The 10-week training reduced BP by similar to 19% in SHR, improved insulin sensitivity by similar to 24% in SHR, but not in WKY, and increased GLUT4 expression in both animal models. Compared to the sedentary group, there was an increase of GLUT4 in WKY rats by similar to 25% in the heart, by similar to 23% in the gastrocnemius, and by similar to 15% in the fat tissue. Trained SHR presented an increase in GLUT4 of similar to 21%, similar to 20%, and similar to 14%, in the same tissues, respectively. There were no differences between SHR and WKY rats in post-training GLUT4 expression. We conclude that training determined BP and insulin resistance reduction in SHR, and increased GLUT4 expression in both normotensive and hypertensive rats. However, considering the similar rise in GLUT4-induced training in SHR and WKY, it is possible that GLUT4 levels in plasma membrane fraction do not have a pivotal role in the exercise-induced improvement of insulin sensitivity in SHR.

CD4(+) CD25(+) Foxp3(+) Regulatory T Cells, Dendritic Cells, and Circulating Cytokines in Uncomplicated Malaria: Do Different Parasite Species Elicit Similar Host Responses?

Clearing blood-stage malaria parasites without inducing major host pathology requires a finely tuned balance between pro- and anti-inflammatory responses. The interplay between regulatory T (Treg) cells and dendritic cells (DCs) is one of the key determinants of this balance. Although experimental models have revealed various patterns of Treg cell expansion, DC maturation, and cytokine production according to the infecting malaria parasite species, no studies have compared all of these parameters in human infections with Plasmodium falciparum and P. vivax in the same setting of endemicity. Here we show that during uncomplicated acute malaria, both species induced a significant expansion of CD4(+) CD25(+) Foxp3(+) Treg cells expressing the key immunomodulatory molecule CTLA-4 and a significant increase in the proportion of DCs that were plasmacytoid (CD123(+)), with a decrease in the myeloid/plasmacytoid DC ratio. These changes were proportional to parasite loads but correlated neither with the intensity of clinical symptoms nor with circulating cytokine levels. One-third of P. vivax-infected patients, but no P. falciparum-infected subjects, showed impaired maturation of circulating DCs, with low surface expression of CD86. Although vivax malaria patients overall had a less inflammatory cytokine response, with a higher interleukin-10 (IL-10)/tumor necrosis factor alpha (TNF-alpha) ratio, this finding did not translate to milder clinical manifestations than those of falciparum malaria patients. We discuss the potential implications of these findings for species-specific pathogenesis and longlasting protective immunity to malaria.

Extensions of homogeneous polynomials ON c(0)(l(2)(i))

We show that a 2-homogeneous polynomial on the complex Banach space c(0)(l(2)(i)) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c(0)(l(2)(i)).

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

Homogeneous polynomials of degree 2 on the complex Banach space c(0)(l(n)(2)) are shown to have unique norm-preserving extension to the bidual space. This is done by using M-projections and extends the analogous result for c(0) proved by P.-K. Lin.

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.

Clonagem e caracterização parcial de cDNA de glândula salivar de Boophilus microplus (Acari:Ixodidae) similar a glutationa s-transferase

O carrapato Boophilus microplus é um ectoparasita hematófago de bovino que causa sérias perdas econômicas. Estudos para o desenvolvimento de formas alternativas de controle do carrapato tem sido realizados para diminuir ou substituir a aplicação de agentes químicos, que contaminam o ambiente, os derivados da carne, além dos problemas de resistência das gerações de carrapatos aos acaricidas. As vacinas são uma forma alternativa de controle do carrapato. As enzimas glutationa S-transferase (GSTs) são alvo potencial para intervenção imunológica contra alguns parasitas. Este trabalho teve como objetivo isolar e caracterizar parcialmente um cDNA de B. microplus similar a GST da classe Mu. O clone SG2 foi isolado dentre aproximadamente 8 x 103 pfu de fagos recombinantes de uma biblioteca de cDNA de glândula salivar de partenógina, sondada com anti-soro de coelho contra glândula salivar. O clone SG2 contendo um inserto de 864 pb teve sua seqüência determinada e a fase de leitura aberta corresponde a 220 amino ácidos. A análise desta seqüência indicou que o gene clonado codifica uma GST de B. microplus (BmGST) com um motivo altamente conservado entre os resíduos 60 e 68 que compreende o sítio de ligação a glutationa (GSH) e outro motivo SLAILRYL, centrado no resíduo 78 da seqüência. No alinhamento múltiplo da AgSG2 com outras GSTs foi observada uma similaridade de até 41% com GSTs da classe Mu de outros organismos e inclusive com outra GST da classe Mu isolada de larva de B. microplus (HE et al., 1999). A proteína recombinante AgSG2 purificada apresentou atividade enzimática contra o substrato cromogênico CDNB. Ensaios de atividade enzimática com extratos de tecidos, secreções e excreções foram realizados para verificar a presença de GST. Ensaios de RT-PCR com tecidos de B. microplus indicaram que os sítios de síntese de BmGST são glândulas salivares e intestino de partenógina e teleógina.

Affine processes, arbitrage-Free Term structures of legendre polynomials,and option pricing

Multivariate Affine term structure models have been increasingly used for pricing derivatives in fixed income markets. In these models, uncertainty of the term structure is driven by a state vector, while the short rate is an affine function of this vector. The model is characterized by a specific form for the stochastic differential equation (SDE) for the evolution of the state vector. This SDE presents restrictions on its drift term which rule out arbitrages in the market. In this paper we solve the following inverse problem: Suppose the term structure of interest rates is modeled by a linear combination of Legendre polynomials with random coefficients. Is there any SDE for these coefficients which rules out arbitrages? This problem is of particular empirical interest because the Legendre model is an example of factor model with clear interpretation for each factor, in which regards movements of the term structure. Moreover, the Affine structure of the Legendre model implies knowledge of its conditional characteristic function. From the econometric perspective, we propose arbitrage-free Legendre models to describe the evolution of the term structure. From the pricing perspective, we follow Duffie et al. (2000) in exploring Legendre conditional characteristic functions to obtain a computational tractable method to price fixed income derivatives. Closing the article, the empirical section presents precise evidence on the reward of implementing arbitrage-free parametric term structure models: The ability of obtaining a good approximation for the state vector by simply using cross sectional data.