On the simultaneous existence of eastward and westward flowing equatorial electrojet currents

The counter-electrojet currents are evidenced by the disappearance of theq type ofEs layer (Es-q) or the appearance of the blanketing type ofEs (Es-b) at Kodaikanal, associated with the depression of the geomagneticH field and the reveisal of ionospheric drift at Thumba. The necessary condition for such an event is not the decrease of theH field below the night level but that the difference of theH field between an equatorial and a non-equatorial station should decrease below its night level. The different kinds of association between the disappearance ofEs-q and the depression in theH field are suggested due to superimposition over theSq current system (at about 107 km) of a separate westward current system at a lower level (about 100 km). The source of the reversed current over the dip equator during the daytime hours is sought in the current system generated by the lunar tides or in various magnetospheric processes generating the polar substorms. Large day-to-day variations of the solar daily range ofH at the equator independent ofSq variation at tropical latitudes are suggested to be due to superimposition at the equator of the two rather independent current systems.     

Transition from spiral wave to target wave and other coherent structures in the networks of Hodgkin-Huxley neurons

Transition of spiral wave in the regular networks of Hodgkin-Huxley (H-H) neurons is simulated and discussed in detail when the effect of membrane temperature and forcing current is considered. Neurons are distributed in the sites of two-dimensional array, neurons are connected with complete nearest-neighbor connections, no-flux boundary conditions, appropriate initial values and physiological parameters are used to develop a stable rotating spiral wave. A statistic factor of synchronization is defined to discuss the transition and development of spiral wave in the two parameters space (membrane temperature T and forcing current I), and it is found that spiral wave keeps alive due to positive current forcing and the spiral wave can be removed completely when the temperature is increased to a threshold about T = 22.3 °C at a fixed current intensity. Periodical forcing current is imposed on the networks of neurons globally and locally, respectively. It is found that spiral wave could be suppressed by the new generated traveling wave or target wave when periodical forcing current is imposed on the border of networks of neurons, and the most effective frequency of the external forcing current is close to the intrinsic frequency of the spiral wave of the networks.     

Bifurcation phenomena in FitzHugh's nerve conduction equations

We consider the second order nonlinear ordinary differential equations developed by FitzHugh to simplify the fourth order current clamped Hodgkin-Huxley nerve conduction equations. We demonstrate the bifurcation, direction, and stability of a family of small periodic solutions as the current parameter I passes through a critical value. Arguments are given which suggest that this family grows to become a large periodic solution, then shrinks, collapsing onto the steady state as I passes through a second critical value. The usefulness of these results in studying the Hodgkin-Huxley equations is discussed.     

Sur l'existence du nombre de Lelong d'un courant positif fermé défini sur une variété presque complexe

Let (M,J) be an almost complex manifold. By using local coordinate system adapted to the structure J, we prove that every closed positive current on M possesses a Lelong number at any point. In case the manifold is equipped with an integrable complex structure, this Lelong number coincides with the usual Lelong number of a closed positive current.     

Synchrony of two uncoupled neurons under half wave sine current stimulation

Two uncoupled Hindmarsh–Rose neurons under different initial discharge patterns are stimulated by the half wave sine current; and the synchronization mechanism of the two neurons is discussed by analyzing their membrane potentials and their interspike interval (ISI) distribution. Under the half wave sine current stimulation, the two uncoupled neurons under different initial conditions, whose parameter r (the parameter r is related to the membrane penetration of calcium ion, and reflects the changing speed of the slow adaptation current) is different or the same, can realize discharge synchronization (phase synchronization) or the full synchronization (state synchronization). The synchronization characteristics are mainly related to the frequency and the amplitude of the half wave sine current, and are little related to the parameter r and the initial state of the two neurons. This investigation shows the mechanism of the current’s amplitude and its frequency affecting the synchronization process of neurons, and the neurons’ discharge patterns and synchronization process can be adjusted and controlled by the current’s amplitude and its frequency. This result is of far reaching importance to study synchronization and encode of many neurons or neural network, and provides the theoretic basis for studying the mechanism of some nervous diseases such as epilepsy and Alzheimer’s disease by the slow wave of EEG.     

Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs

We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n+1 rungs. Such an assignment yields an index one current graph with current group Z_12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K_12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+7. We use our characterization to construct Skolem sequences that give rise to such current assignments. These produce many nonisomorphic orientable biembeddings of cyclic Steiner triple systems of order 12n+7.     

Reducing the bandwidth of a sparse matrix with tabu search

The bandwidth of a matrix A={a_ij} is defined as the maximum absolute difference between i and j for which a_ij≠0. The problem of reducing the bandwidth of a matrix consists of finding a permutation of the rows and columns that keeps the nonzero elements in a band that is as close as possible to the main diagonal of the matrix. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the nonzero elements of the corresponding symmetrical matrix. Many bandwidth reduction algorithms have been developed since the 1960s and applied to structural engineering, fluid dynamics and network analysis. For the most part, these procedures do not incorporate metaheuristic elements, which is one of the main goals of our current development. Another equally important goal is to design and test a special type of candidate list strategy and a move mechanism to be embedded in a tabu search procedure for the bandwidth reduction problem. This candidate list strategy accelerates the selection of a move in the neighborhood of the current solution in any given iteration. Our extensive experimentation shows that the proposed procedure outperforms the best-known algorithms in terms of solution quality consuming a reasonable computational effort.     

Finite dams with double level of release

We considered a finite dam with discrete additive input and double level of release. If the current dam content is not greater than a certain boundM, the release is one unit unless the dam is empty; and if the current dam content is greater thanM, the release isr (? 1) units provided it is available, otherwise the whole content will be withdrawn. We derive all the expressions of the distributions of first emptiness with and without overflow, the distributions of emptiness with and without overflow, the time dependent distributions of dam content with and without overflow, and the distributions of overflow times and quantities. IfM is equal to the dam capacity, the results are reduced to the case of unit release; and ifM=0, the results are reduced to the case of releaser.     

A uniqueness theorem in the inverse problem for the integrodifferential electrodynamics equations

Under study is the problem of finding the kernel and the index of dielectric permeability for the system of integrodifferential electrodynamics equations with wave dispersion. We consider a direct problem in which the external pulse current is a dipole located at a point y on the boundary ?B of the unit ball B. The point y runs over the whole boundary and is a parameter of the problem. The information available about the solution to the direct problem is the trace on ?B of the solution to the Cauchy problem given for the times close to the time when a wave from the dipole source arrives at a point x. The main result of the article consists in obtaining some theorems related to the uniqueness problems for a solution to the inverse problem.     

An iterative algorithm for sparse and constrained recovery with applications to divergence-free current reconstructions in magneto-encephalography

We propose an iterative algorithm for the minimization of a ? ₁-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the data misfit part and in the penalty term of the functional). None of the three matrices must be invertible. Convergence is proven in a finite-dimensional setting. We apply the algorithm to a synthetic problem in magneto-encephalography where it is used for the reconstruction of divergence-free current densities subject to a sparsity promoting penalty on the wavelet coefficients of the current densities. We discuss the effects of imposing zero divergence and of imposing joint sparsity (of the vector components of the current density) on the current density reconstruction.     

Fast local search methods for solving limited memory influence diagrams

Limited memory influence diagrams are graph-based models that describe decision problems with limited information such as planning with teams and/or agents with imperfect recall. Solving a (limited memory) influence diagram is an NP-hard problem, often approached through local search. In this work we give a closer look at k-neighborhood local search approaches. We show that finding a k-neighboring strategy that improves on the current solution is W[1]-hard and hence unlikely to be polynomial-time tractable. We also show that finding a strategy that resembles an optimal strategy (but may have low expected utility) is NP-hard. We then develop fast schema to perform approximate k-local search; experiments show that our methods improve on current local search algorithms both with respect to time and to accuracy.     

Sur l'existence du nombre de Lelong d'un courant positif psh défini sur une variété presque complexe

The goal of this Note is to extend to an almost complex manifold the existence of the Lelong number of a positive plurisubharmonic (psh) current. In this way, we generalize results of Lelong and Skoda established in the case of an integrable complex structure, and of Haggui in the non-integrable case, but only for a closed positive current. The main point is to establish a Lelong–Jensen formula for a positive psh current defined on an almost complex manifold, which generalizes a formula proved by Demailly when the structure is integrable. To cite this article: F. Elkhadhra, S.K. Mimouni, C. R. Acad. Sci. Paris, Ser. I 344 (2007).     

Gravitation and Electromagnetism as Geometrical Objects of a Riemann-Cartan Spacetime Structure

In this paper we first show that any coupled system consisting of a gravitational plus a free electromagnetic field can be described geometrically in the sense that both Maxwell equations and Einstein equation having as source term the energy-momentum of the electromagnetic field can be derived from a geometrical Lagrangian proportional to the scalar curvature R of a particular kind of Riemann-Cartan spacetime structure. In our model the gravitational and electromagnetic fields are identified as geometrical objects of the structure.We show moreover that the contorsion tensor of the particular Riemann-Cartan spacetime structure of our theory encodes the same information as the one contained in Chern-Simons term ${{\bf A} \wedge {\it d}{\bf A}}$ that is proportional to the spin density of the electromagnetic field. Next we show that by adding to the geometrical Lagrangian a term describing the interaction of a electromagnetic current with a general electromagnetic field plus the gravitational field, together with a term describing the matter carrier of the current we get Maxwell equations with source term and Einstein equation having as source term the sum of the energy-momentum tensors of the electromagnetic and matter terms. Finally modeling by dust charged matter the carrier of the electromagnetic current we get the Lorentz force equation. Moreover, we prove that our theory is gauge invariant. We also briefly discuss our reasons for the present enterprise.     

Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces

The existence of common fixed points is established for three mappings where T is either generalized (f,g)-nonexpansive or asymptotically (f,g)-nonexpansive on a nonempty subset of a Banach space. As applications, the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained. Our results unify and substantially improve several recent results existing in the current literature.     

The complexity of node blocking for dags

We consider the following modification of annihilation games called node blocking. Given a directed graph, each vertex can be occupied by at most one token. There are two types of tokens, each player can move only tokens of his type. The players alternate their moves and the current player i selects one token of type i and moves the token along a directed edge to an unoccupied vertex. If a player cannot make a move then he loses. We consider the problem of determining the complexity of the game: given an arbitrary configuration of tokens in a planar directed acyclic graph (dag), does the current player have a winning strategy? We prove that the problem is PSPACE-complete.     

Stability of a cylindrical plasma in the presence of a monotonic field—II

The stability of an incompressible inviscid, perfectly conducting cylindrical plasma against azimuthal disturbances in the presence of a monotonic decreasing magnetic field having a constant pitch is discussed by using energy principle. The results obtained by this principle are compared form = 1 mode (which is a dangerous mode in which there is a lateral shift of the entire column) with that obtained by normal mode analysis. It is found thatm = 1 mode is always unstable. Further, an axial line current, external axial field and the surface tension tend to stabilisem ≠ modes.     

Numerical investigation of a three-dimensional four field model for collisionless magnetic reconnection

In this paper we present the numerical investigation of a three-dimensional four field model for magnetic reconnection in collisionless regimes. The model describes the evolution of the magnetic flux and vorticity together with the perturbations of the parallel magnetic and velocity fields. We explored the different behavior of vorticity and current density structures in low and high β regimes, β being the ratio between the plasma and magnetic pressure. A detailed analysis of the velocity field advecting the relevant physical quantities is presented. We show that, as the reconnection process evolves, velocity layers develop and become more and more localized. The shear of these layers increases with time ending up with the occurrence of secondary instabilities of the Kelvin-Helmholtz type. We also show how the β parameter influences the different evolution of the current density structures, that preserve for longer time a laminar behavior at smaller β values. A qualitative explanation of the structures formation on the different z-sections is also presented.     

A local convergence proof for the iterative aggregation method

The iterative aggregation method for the solution of a system of linear algebraic equations x = Ax + b, where A ≥ 0, b ≥ 0, s > 0, and s ′ A < s ′, is proved to be locally convergent. It is shown that the method can be considered a consistent nonstationary iterative method, where the iteration matrix depends on the current iterate, and that some norm of the iteration matrix is less than one in the vicinity of the solution.     

Struktur der Grenzschicht zwischen einem feldfreien Plasma und einem Magnetfeld im Vakuum

Self-consistent solutions of Vlasov's equations describing a plane boundary layer without shear are given. The currents within the layer are due to free and trapped electrons. The ion current is neglected sincem _e ?m _i . The free electrons and the ions are assumed Maxwellian at infinity. For the trapped electrons a one parameter family of distribution functions is assumed. Profiles are computed for potentials, fields, densities and currents for different numbers of trapped electrons. Numerical solutions are obtained by applying the method of finite elements to a variational formulation of the problem.