Divergent Conditions Research Articles

Towards New Economic Cooperation in Northeast Asia:Lessons from the Franco-German Coalition

Towards New Economic Cooperation in Northeast Asia:Lessons from the Franco-German Coalition

Energy-conserved splitting FDTD methods for Maxwell’s equations

In this paper, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations in two dimensions are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the discrete divergence of electric fields for these two schemes. For the EC-S-FDTDII scheme, we prove that the discrete divergence is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes are non-dissipative. Numerical experiments confirm well the theoretical analysis results.

A Silicon-Based Approach to Oligoarenes by Iterative Cross-Coupling Reactions of Halogenated Organo[(2-hydroxymethyl)phenyl]dimethylsilanes

Highly efficient synthesis of silyl-substituted oligoarenes with defined structures is achieved by an iterative cross-coupling reaction and deprotection sequence using organo[(2-hydroxymethyl)phenyl]dimethylsilanes. The excellent stability of the tetraorganosilicon compounds as well as mild and divergent conditions for cross-coupling and deprotection steps allows preparation of highly conjugated oligoarenylsilanes such as unsymmetrically disilylated quinquethiophenes.

A high-order implicit finite element method for integrating the two-fluid magnetohydrodynamic equations in two dimensions

We describe a new method for solving the time-dependent two-fluid magnetohydrodynamic (2F-MHD) equations in two dimensions that has significant advantages over other methods. The stream-function/potential representation of the velocity and magnetic field vectors, while fully general, allows accurate description of nearly incompressible fluid motions and manifestly satisfies the divergence condition on the magnetic field. Through analytic manipulation, the split semi-implicit method breaks the full matrix time advance into four sequential time advances, each involving smaller matrices. The use of a high-order triangular element with continuous first derivatives (C1 continuity) allows the Galerkin method to be applied without introduction of new auxiliary variables (such as the vorticity or the current density). These features, along with the manifestly compact nature of the fully node-based C1 finite elements, lead to minimum size matrices for an unconditionally stable method with order of accuracy h4. The resulting matrices are compatible with direct factorization using SuperLU_dist. We demonstrate the accuracy of the method by presenting examples of two-fluid linear wave propagation, two-fluid linear eigenmodes of a tilting cylinder, and of a challenging nonlinear problem in two-fluid magnetic reconnection.

On a generalized resolvent estimate for the Stokes system with Robin boundary condition

We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the L q framework ( 1 ν = h on the boundary of the domain with α , β ≥ 0 and α + β = 1 , where u denotes a velocity vector, p a pressure, T ( u , p ) the stress tensor for the Stokes flow, and ν the unit outer normal to the boundary of the domain. It presents the slip condition when β = 1 and the non-slip one when α = 1 , respectively.

On the kinematics of 2+1-dimensional motions of a fibre-reinforced fluid. Integrable connections

Summary Evolution of foliations of the plane is shown, under a condition of constant divergence, to be linked to the scattering problem for the integrable modified Korteweg–de Vries hierarchy. This result is applied to a set of kinematic relations which arise in the theory of ideal fibre-reinforced fluids. In particular, it is established that the fibres, which are convected with the fluid, constitute generalized tractrices.

Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data

We investigate the nonstationary Navier-Stokes equations for an exterior domain Ω ⊂ R 3 in a solution class L s ( 0 , T ; L q ( Ω ) ) of very low regularity in space and time, satisfying Serrin's condition 2 s + 3 q = 1 but not necessarily any differentiability property. The weakest possible boundary conditions, beyond the usual trace theorems, are given by u | ∂ Ω = g ∈ L s ( 0 , T ; W - 1 / q , q ( ∂ Ω ) ) , and will be made precise in this paper. Moreover, we suppose the weakest possible divergence condition k = ÷ u ∈ L s ( 0 , T ; L r ( Ω ) ) , where 1 3 + 1 q = 1 r .

Global attraction and stability for Cohen–Grossberg neural networks with delays

We consider a class of Cohen-Grossberg neural networks with delays. We prove the existence and global asymptotic stability of an equilibrium point and estimate the region of existence. Furthermore, we show that the trajectories of the neural networks with positive initial data will stay in the positive region if the amplification function satisfies a divergent condition. We also establish the existence of a globally attracting compact set for more general networks. We estimate this compact set explicitly in terms of the network parameters from physiological and biological models. Our results can be applied to neural networks with a wide range of activation functions which are neither bounded nor globally Lipschitz continuous such as the Lotka-Volterra model. We also give some examples and simulations.

Estimating vegetation water content with hyperspectral data for different canopy scenarios: Relationships between AVIRIS and MODIS indexes

Three linked leaf and canopy radiative transfer models were used to assess uncertainties in three vegetation architectures for the relationships between canopy water content and Equivalent Water Thickness (EWT). The leaf radiative transfer model PROSPECT was linked to SAILH, rowMCRM, and FLIM canopy reflectance models to generate synthetic spectra for a range of leaf and canopy parameters under closed, row-structured, and forest canopy architectures, respectively. Leaf water content ( C w) and leaf area index (LAI) were used to calculate canopy water content. Leaf and canopy parameters that affect the retrieval of EWT, estimated by the MODTRAN-based fitting technique, were used to investigate their influence on the water content estimates. Results showed a consistent relationship between retrieved EWT and canopy water content for the different simulated architectural scenarios. It was shown that EWT was negatively affected by leaf dry matter and soil background. Retrievals of EWT from hyperspectral Advanced Visible Infrared Imaging Spectrometer (AVIRIS) imagery at three study sites were then used for cross-validation of the Moderate Resolution Imaging Spectrometer (MODIS) data, assessing the behavior of NDVI, EVI, NDWI, and SIWSI as potential indicators of vegetation water content. All four MODIS indexes showed consistent agreement with retrievals of EWT from AVIRIS imagery at the agricultural site and the savanna–shrub site, with EVI having the highest correlation. However, at the conifer forest study site the two water indexes, NDWI and SIWSI, yielded better agreement with retrievals of EWT than NDVI and EVI. The performance of NDVI was inconsistent across sites. This manuscript demonstrates the importance of canopy architecture when estimating EWT by showing that large errors are obtained when EWT estimates derived from absorption feature curve-fitting are applied to different canopy types. These errors are propagated in simple indexes that produce inconsistent results when applied to divergent vegetation conditions.

Comments on the coordination number models and equations of state of Tsai and Chen [Fluid Phase Equilibria 187–188 (2001) 39–59 and 232 (2005) 100–112

This paper notes typographical errors in the coordination number model of Tsai and Chen [Fluid Phase Equilib. 232 (2005) 100–112] for square-well mixtures and in the equations of state of Tsai and Chen [Fluid Phase Equilib. 187–188 (2001) 39–59; Fluid Phase Equilib. 232 (2005) 100–112] for pure square-well fluids and their mixtures. In addition, the divergence condition and applicable range of the coordination number model of Tsai and Chen (2005) for mixtures are described.

Dynamics of grazing policy and practice: environmental and social impacts in three communal areas of southern Africa

This paper traces the history of grazing policy, its conceptual basis, practical implementations and outcomes, in three southern African countries. In spite of the divergent environmental conditions facing pastoralists in the Highlands of Lesotho, Botswana's southern Kalahari and the Namaqualand succulent karoo in South Africa, they have all been subjected to similar grazing and rangeland management policies. The theoretical underpinnings of such policies have their origins in a development paradigm and ecological theory derived from northern temperate environments and are directly related to two persistent and powerful narratives: ‘land degradation’ and ‘the tragedy of the commons’. Policy and development initiatives were implemented in order to overcome the perceived causes of these negative scenarios, such as overstocking, open access tenure and low output subsistence production. They typically ignored the multi-purpose goals of traditional pastoral systems and emphasized commercialisation of livestock farming and privatisation of communal land, which resulted in the weakening or destruction of local, traditional land management institutions. Such policies have survived the transitions from colonial rule to independence and from apartheid to democracy. We argue that these powerful and pervasive ideas, when applied to grazing policies, have caused the very problems they were formulated to prevent.

Importance of the Life Cycle in Sympatric Host Race Formation and Speciation of Pathogens

ABSTRACT Numerous morphological species of pathogenic fungi have been shown to actually encompass several genetically isolated lineages, often specialized on different hosts and, thus, constituting host races or sibling species. In this article, we explore theoretically the importance of some aspects of the life cycle on the conditions of sympatric divergence of host races, particularly in fungal plant pathogens. Because the life cycles classically modeled by theoreticians of sympatric speciation correspond to those of free-living animals, sympatric divergence of host races requires the evolution of active assortative mating or of active host preference if mating takes place on the hosts. With some particular life cycles with restricted dispersal between selection on the host and mating, we show that divergence can occur in sympatry and lead to host race formation, or even speciation, by a mere process of specialization, with strong divergent adaptive selection. Neither active assortative mating nor active habitat choice is required in these cases, and this may explain why the phylo-genetic species concept seems more appropriate than the biological species concept in these organisms.

The effect of three-dimensional glottal geometry on intraglottal quasi-steady flow distributions and their relationship with phonation

Vocal fold geometry plays an important role in human phonation. The intraglottal quasi-steady pressure and velocity distributions depend upon the shape, size, and diameter of the glottis. This study reports the effects of the variation of glottal shapes on intraglottal pressures and velocities using a Plexiglas model with a glottis having nine symmetric glottal angles (uniform, as well as convergent and divergent 5 degrees, 10 degrees, 20 degrees and 40 degrees), while the minimal glottal diameter was held constant at 0.06 cm. The empirical data were supported by penalty finite element computational results. The results suggest that larger convergent glottal angles correspond to increased pressures and decreased velocities in the glottis upstream of the minimum glottal location, with a reversal of this pattern at the minimal glottal diameter location. The pressure dip near the glottal entrance for divergent glottal angles was greatest for the 10 degrees divergence angle condition, and was sequentially less for 5 degrees, 20 degrees, and 40 degrees. Flow resistance was greater for a convergent angle than a divergent angle of the same value, and least for the 10 degrees divergent condition. Pressure recovery in the glottis suggested that the optimal glottal diffuser angle was near 10 degrees. Results suggest that the glottal geometry has a critical relationship with phonation (especially for vocal efficiency), and therefore important significance to understanding artistic voice and clinical voice management.

$L_p$-$L_q$ maximal regularity and viscous incompressible flows with free surface

We prove the $L_p$-$L_q$ maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. And as an application, we consider a free boundary problem for the Navier-Stokes equation. We prove a locally in time unique existence of solutions to this problem for any initial data and a globally in time unique existence of solutions to this problem for some small initial data.

RESORPTION EFFICIENCY DECREASES WITH INCREASING GREEN LEAF NUTRIENTS IN A GLOBAL DATA SET

To investigate effects of green-leaf nutrient status on senesced-leaf nutrient concentrations and resorption efficiency, we developed a database of nitrogen (N) and phosphorus (P) concentrations in green and senesced leaves from 92 published studies. We fit power functions (i.e., [nutrient]sen = A [nutrient]grB) separately for N and P. The database encompassed 297 perennial species of different life-forms. Across these divergent species and conditions, a major control on senesced-leaf nutrient concentration was green-leaf nutrient status; nutrient concentrations in senesced leaves were positively associated with green-leaf nutrient concentrations (r2 values from 51% to 84%). Within-species variation as well as species differences contributed to the overall variation in nutrient concentrations. Moreover, N and P resorption efficiency decreased, respectively, with increased N and P green-leaf status; fitted power functions indicated that a disproportionate amount of nutrient remained in senesced leaves of h...

On convergence of generalized continued fractions and Ramanujan's conjecture

We consider continued fractions (CF) − a 1 1 − a 2 1 − a 3 1 − ⋯ with real coefficients a i converging to a limit a. Ramanujan claimed that if a ≠ 1 4 , then the fraction converges if and only if a < 1 4 . The statement of convergence was proved by Van Vleck in 1904 for complex a i converging to a ∈ C ∖ [ 1 4 , + ∞ ) . Gill proved the divergence of (CF) under the assumption that a i → a > 1 4 fast enough, more precisely, whenever ∑ i | a i − a | < ∞ . The Ramanujan's conjecture saying that (CF) always diverges whenever a i → a > 1 4 remained, up to now, an open question. In the present Note we disprove it. We show that for any a > 1 4 there exists a real sequence a i → a such that (CF) converges. Moreover, we show that Gill's sufficient divergence condition is the optimal condition on the speed of convergence of the a i 's. To cite this article: A.A. Glutsyuk, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

Competitive divergence in non-random mating populations

A haploid model of frequency-dependent selection and assortative mating is introduced and analyzed for the case of a single multiallelic autosomal locus. Frequency-dependent selection is due to intraspecific competition mediated by a quantitative character under stabilizing or directional selection. Assortment is induced by the same trait. We analyze the equilibrium structure and the local stability properties of all possible equilibria. In the limit of weak selection we obtain global stability properties by finding a Lyapunov function. We provide necessary and sufficient conditions for the maintenance of polymorphism in terms of the strength of stabilizing selection, intraspecific competition and assortment. Our results also include criteria for the ability of extreme types to invade the population. Furthermore, we study the occurrence of disruptive selection and provide necessary and sufficient conditions for intraspecific divergence to occur.

Mappings of finite distortion: discreteness and openness for quasi-light mappings

Let f∈W1,n(Ω,Rn) be a continuous mapping so that the components of the preimage of each y∈Rn are compact. We show that f is open and discrete if |Df(x)|n⩽K(x)Jf(x) a.e. where K(x)⩾1 and Kn−1/Φ(log(e+K))∈L1(Ω) for a function Φ that satisfies ∫1∞1/Φ(t)dt=∞ and some technical conditions. This divergence condition on Φ is shown to be sharp.

Comparative Perspectives on the Ethical Orientations of Human Resources, Marketing and Finance Functional Managers

The human resources profession emphasizes the personal and interpersonal aspects of work, that make it conscious of complex ethical issues in relationships in the workplace, while finance specialists are conversant with routine compliance with regulations. Marketing professionals are under pressure to produce revenue results. Thus, this research hypothesized that human resources managers would be more disapproving of unethical conduct than both finance and marketing functional managers, and that finance managers would be more disapproving than marketing managers. When asked to evaluate instances of unethical behavior in vignettes, human resources and finance managers were both significantly more disapproving than marketing managers. However, human resources managers were not significantly more disapproving than finance managers. Explanations for the results lie in the divergent antecedent conditions, objectives, perceptions of ethical problems and demands of the various functions. Alternative behavior patterns to resolve ethical dilemmas and expected consequences by the different functions also define their ethical orientations. Average responses on the disapproving side from all three functional groups are explained by two complementary trends that promote ethical awareness among all functional managers. One is the adoption of homogeneous conventions in ethical business practice. The other trend is the increase in ethical awareness specific to each of the functional professions.

Hydrostatic Stokes equations with non-smooth data for mixed boundary conditions

The main subject of this work is to study the concept of very weak solution for the hydrostatic Stokes system with mixed boundary conditions (non-smooth Neumann conditions on the rigid surface and homogeneous Dirichlet conditions elsewhere on the boundary). In the Stokes framework, this concept has been studied by Conca [Rev. Mat. Apl. 10 (1989)] imposing non-smooth Dirichlet boundary conditions.In this paper, we introduce the dual problem that turns out to be a hydrostatic Stokes system with non-free divergence condition. First, we obtain strong regularity for this dual problem (which can be viewed as a generalisation of the regularity results for the hydrostatic Stokes system with free divergence condition obtained by Ziane [Appl. Anal. 58 (1995)]). Afterwards, we prove existence and uniqueness of very weak solution for the (primal) problem.As a consequence of this result, the existence of strong solution for the non-stationary hydrostatic Navier-Stokes equations is proved, weakening the hypothesis over the time derivative of the wind stress tensor imposed by Guillén-González, Masmoudi and Rodrı́guez-Bellido [Differential Integral Equations 50 (2001)].