A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas

The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol–Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge–Kutta method. The presence of chaotic limit cycles is pointed out.

Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On weak and strong Peano theorems

We say that the Peano theorem holds for a topological vector space $E$ if, for any continuous mapping $f : {\Bbb R}\times E \to E$ and any $(t(0), x(0))$ is an element of ${\Bbb R}\times E$, the Cauchy problem $\dot x(t) = f(t,x(t))$, $x(t(0)) = x(0)$, has a solution in some neighborhood of $t(0)$. We say that the weak version of Peano theorem holds for $E$ if, for any continuous map $f : {\Bbb R}\times E \to E$, the equation $\dot x(t) = f (t, x(t))$ has a solution on some interval. We construct an example (answering a question posed by S. G. Lobanov) of a Hausdorff locally convex topological vector space E for which the weak version of Peano theorem holds and the Peano theorem fails to hold. We also construct a Hausdorff locally convex topological vector space E for which the Peano theorem holds and any barrel in E is neither compact nor sequentially compact.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Controls on the contemporary distribution of lake thecamoebians (testate amoebae) in the Greater Toronto Area and their potential as water quality indicators.

Thecamoebians were examined from 71 surface sediment samples collected from 21 lakes and ponds in the Greater Toronto Area to (1) elucidate the controls on faunal distribution in modern lake environments; and (2) to consider the utility of thecamoebians in quantitative studies of water quality change. This area was chosen because it includes a high density of kettle and other lakes which are threatened by urban development and where water quality has deteriorated locally as a result of contaminant inputs, particularly nutrients. Fifty-eight samples yielded statistically significant thecamoebian populations. The most diverse faunas (highest Shannon Diversity Index values) were recorded in lakes beyond the limits of urban development, although the faunas of all lakes showed signs of sub-optimal conditions. The assemblages were divided into five clusters using Q-mode cluster analysis, supported by Detrended Correspondence Analysis. Canonical Correspondence Analysis (CCA) was used to examine species-environment relationships and to explain the observed clusterings. Twenty-four measured environmental variables were considered, including water property attributes (e.g., pH, conductivity, dissolved oxygen), substrate characteristics, sediment-based phosphorus (Olsen P) and 11 environmentally available metals. The thecamoebian assemblages showed a strong association with phosphorus, reflecting the eutrophic status of many of the lakes, and locally to elevated conductivity measurements, which appear to reflect road salt inputs associated with winter de-icing operations. Substrate characteristics, total organic carbon and metal contaminants (particularly Cu and Mg) also influenced the faunas of some samples. A series of partial CCAs show that of the measured variables, sedimentary phosphorus has the largest influence on assemblage distribution, explaining 6.98% (P < 0.002) of the total variance. A transfer function was developed for sedimentary phosphorus (Olsen P) using 58 samples from 15 of the studied lakes. The best performing model was based on weighted averaging with inverse deshrinking (WA Inv, r jack 2= 0.33, RMSEP = 102.65 ppm). This model was applied to a small modern thecamoebian dataset from a eutrophic lake in northern Ontario to predict phosphorus and performed satisfactorily. This preliminary study confirms that thecamoebians have considerable potential as quantitative water quality indicators in urbanising regions, particularly in areas influenced by nutrient inputs and road salts.

Electron impact excitation of Kr XXXII

Collision strengths (Ω) have been calculated for all 7750 transitions among the lowest 125 levels belonging to the View the MathML source, and 2p23ℓ configurations of boron-like krypton, Kr XXXII, for which the Dirac Atomic R -matrix Code has been adopted. All partial waves with angular momentum J⩽40 have been included, sufficient for the convergence of Ω for forbidden transitions. For allowed transitions, a top-up has been included in order to obtain converged values of Ω up to an energy of 500 Ryd. Resonances in the thresholds region have been resolved in a narrow energy mesh, and results for effective collision strengths (ϒ) have been obtained after averaging the values of Ω over a Maxwellian distribution of electron velocities. Values of ϒ are reported over a wide temperature range below View the MathML source, and the accuracy of the results is assessed. Values of ϒ are also listed in the temperature range View the MathML source, obtained from the nonresonant collision strengths from the Flexible Atomic Code.

Breit-Pauli R-matrix calculation of fine-structure effective collision strengths for the electron impact excitation of Mg V

Context. Electron-impact excitation collision strengths are required for the analysis and interpretation of stellar observations.
Aims. This calculation aims to provide effective collision strengths for the Mg V ion for a larger number of transitions and for a greater temperature range than previously available, using collision strength data that include contributions from resonances.
Methods. A 19-state Breit-Pauli R-matrix calculation was performed. The target states are represented by configuration interaction wavefunctions and consist of the 19 lowest LS states, having configurations 2s22p4, 2s2p5, 2p6, 2s22p33s, and 2s22p33p. These target states give rise to 37 fine-structure levels and 666 possible transitions. The effective collision strengths were calculated by averaging the electron collision strengths over a Maxwellian distribution of electron velocities.
Results. The non-zero effective collision strengths for transitions between the fine-structure levels are given for electron temperatures in the range = 3.0 - 7.0. Data for transitions among the 5 fine-structure levels arising from the 2s22p4 ground state configurations, seen in the UV range, are discussed in the paper, along with transitions in the EUV range – transitions from the ground state 3P levels to 2s2p5?3P levels. The 2s22p4?1D–2s2p5?1P transition is also noted. Data for the remaining transitions are available at the CDS.

Bimodules over nest algebras and Deddens'

We generalise Dedden's Theorem for nest algebras to nest algebra bimodules. We define an object which extends the Jacobson radical of a nest algebra, and characterose it generalising a theorem of Erdos.

Effective collision strengths for transitions of Ni XVII

Electron impact excitation collision strengths are required for the analysis and interpretation of stellar observations. This calculation aims to provide fine structure effective collision strengths for the Ni XVII ion using a method which includes contributions from resonances. A DARC calculation has been performed, involving 37 J pi states. The effective collision strengths are calculated by averaging the electron collision strengths over a Maxwellian distribution of electron velocities. The non-zero effective collision strengths for transitions between the fine structure levels are given for electron temperatures (T(e)) in the range log(10) T(e)(K) = 4.5 - 8.5. Data for several transitions from the ground state are discussed in this paper.

Effective collision strengths for electron-impact excitation of S X

Effective collision strengths computed by the R-matrix method are presented for the electron-impact excitation of nitrogen-like S X. The total wave function used in the expansion includes the lowest 11 eigenstates of S X which arise from the 2s(2)2p(3), 2s2p(4), 2p(5) and 2s(2)2p(2)3s configurations. These 11 LS target states correspond to 22 fine-structure levels, giving 231 possible transitions. All the effective collision strengths for these transitions are tabulated in the range log T(K) = 4.6 to log T(K) = 6.7. The energy level values and oscillator strengths for allowed transitions are also tabulated. The effective collision strengths were calculated by averaging the electron collision strengths over a Maxwellian distribution of velocities. The present effective collision strengths are the only results currently available for these fine-structure transition rates. (C) 2000 Academic Press.

Robust Dynamic Pricing Over Infinite Horizon in The Presence of Model Uncertainty( 2* Journal)

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.