Algebraic nonsolvability of the problem of existence of holomorphic first integrals

We prove that the existence of a holomorphic first integral of an analytic differential equation is an algebraically nonsolvable problem. Moreover, we prove a perturbation lemma showing that a nilpotent singularity of a differential equation in the plane cannont have a holomorphic first integral independently of the prolongation of anynth-order jet. We give an application to the case of nilpotent centers.     

An Example of a Vector Field with the Oriented Shadowing Property

Journal of Dynamical and Control Systems - We consider shadowing properties for vector fields corresponding to different type of reparametrizations. We give an example of a vector field which has...     

The determination of unknown thermal coefficients through phase change process with temperature-dependent thermal conductivity

We study the determination of unknown thermal coefficient of a semi-infinite material through a phase-change process with an overspecified condition on the fixed face with temperature-dependent thermal conductivity. We determine necessary and sufficient conditions on data in order to obtain the existence of the solution. We also give formulae for the unknown coefficients.     

Approximate weak invariance for differential inclusions in Banach spaces

We give here criteria for a given set K to be approximately weakly invariant with respect to approximate or exact solutions of the differential inclusion x′(t) ∈ F(x(t)) in Banach spaces, using the concept of a tangent set to another set. We give an application regarding the Lipschitz dependence of ε-solutions upon the initial states.     

Temperature transients in flowing boreholes

We consider the problem of temperature transients in a borehole which has been drilled into an isothermal homogeneous solid and which is flowing at a constant rate. At a fixed time, the temperature of the fluid entering the borehole at the bottom is raised by a given amount. We derive the theoretical expression for the temperature response of the borehole and give a few numerical data of practical value.     

Free convection flow through a porous medium bounded by two horizontal walls

Steady free convection flow through a porous medium bounded by two horizontal walls with a uniform axial temperature variation along the walls is considered. We give an analytical solution of the velocity field and discuss the effects of the permeability parameter K and Grashof number G on the velocity.     

Characterizations of hamiltonian geodesics in sub-riemannian geometry

Let (M, ε, g) be a sub-Riemannian manifold. The geodesics of (M, ε, g) are either Hamiltonian or srictly abnormal. In this paper we give necessary and sufficient conditions for a geodesic curve to be Hamiltonian, and we apply this to the study of totally geodesic submanifolds of Lie groups. We also give an example of a foliation by totally geodesic submanifolds, each leaf containing a one parameter family of geodesics which are Hamiltonian in the leaf but stricly abnormal in the ambient space.     

On Expansion of a Solution of General Nonautonomous Polynomial Differential Equation

We give a recursive formula for an expansion of a solution of a general nonautonomous polynomial differential equation. The formula is given on the algebraic level with the use of a shuffle product. This approach minimizes the number of integrations on each order of expansion. Using combinatorics of trees, we estimate the radius of convergence of the expansion.     

液体燃料射流破碎机理研究中的时间模式与空间模式

利用线性不稳定性理论分析了液体燃料射流在分别采用时间模式与空间模式两种方法下液体表面扰动波的波数、频率及最大扰动增长率之间的关系,讨论了两种模式下液体射流结构特征的差别。应用基于粘性液体射流射入气体介质中的物理模型,计算分析了 Ｒｅ 数、 Ｗｅ 数和密度比 Ｑ对时间模式与空间模式差值的影响,结果发现采用时间模式或空间模式并不改变液体射流各阶模式之间的相互关系, Ｗｅ 数和 Ｑ是影响时间模式与空间模式差值的主要因素,而 Ｒｅ 数影响不大。在一定条件下,时间模式与空间模式具有等效性。     

Regional Observability for Semilinear Distributed Parabolic Systems

The purpose of this paper is to explore the concept of regional observability for a class of semilinear distributed parabolic systems. Then we give an approach for the reconstruction of the state on a subregion of the evolution domain. We also study the variation of the estimated state error with respect to measurements errors. At last we present an approach based on fixed point techniques leading to a numerical approach which is successfully tested through an example.     

Markal,a linear-programming model for energy systems analysis: Technical description of the bnl version

As part of a project to assess the value of new energy technologies, an international group of researchers created a linear-programming model of national energy systems. This model, MARKAL, is driven by useful energy demands, optimizes over several time periods collectively, and allows multiobjective analyses to be performed quite easily. We describe here the technical structure of the model, defining the functions determined when satisfying the model's relations and the parameters that must be supplied to give the model content.     

On a Holonomy Flag of Non-holonomic Distributions

We give definition of a holonomy flag in subRiemannian geometry, a generalization of the Riemannian holonomy algebra, and calculate it for the 3D subRiemannian Lie groups for different connections. We rewrite and give new interpretation for the Codazzi equations for the (2,3)-distributions on SU(2) and the Heisenberg group. We calculate holonomy flag for Tanaka-Webster, Tanno, and Wagner connections.     

Negotiating energy futures The politics of energy forecasting

Over the last decade it has become increasingly clear that energy forecasts have been used for partisan purposes. Through energy models and forecasts, industrial, political and administrative interests compete for cognitive and methodological hegemony. We have termed this integration of modelling and politics the ‘scientific negotiation of energy futures’. This article presents core elements of a sociopolitical and institutional perspective with which to analyse the generation of assumptions that underlie energy models and forecasts. We focus on the factors that shape the choice of data, functional forms and modelling methodologies. We point to the filters of professional orientation and organizational structures that give every forecast an inherent cognitive bias. We stress the legitimation function of forecasts in political decision making. These factors are illustrated with a comparative analysis of energy modelling and forecasting over the last 20 years in the UK, Canada, Denmark, France, the Netherlands, Norway, the USA, and FR Germany, and a discussion of the IIASA world energy model.     

Extending the bidding format to promote demand response

We propose an extended bidding structure to allow more realistic demand characteristics and behaviors to be expressed via flexible bids. In today's ISO-run energy markets, demand bid formats are all separable over time. However, a significant and growing segment of demand can be shifted across time and therefore has no way to bid its true valuation of consumption. We propose additional bid types that allow deferrable, adjustable and storage-type loads to better express their value, and thus elicit demand response in the most natural way – via direct participation in the market. We show that the additional bid types are easily incorporated into the existing market with no technological barrier and that they preserve the market's efficiency and incentive-compatibility properties. Using real market data, we give a numerical demonstration that the extended bid format could substantially increase social welfare, and also present additional insight on storage expansion scenarios.     

Generation Theorem for the Streaming Operator in Slab Geometry

We study the one-dimensional streaming operator in slab domain with general boundary conditions described by a linear operator K. We prove that the streaming operator generates a strongly continuous semigroup and determine its upper bound. We also give the expression of the generated semigroup, which we use to describe its asymptotic behavior in the next article in this issue.     

On Zermelo-Like Problems: Gauss–Bonnet Inequality and E. Hopf Theorem

The aim of this paper is to describe the Zermelo navigation problem on Riemannian manifolds as a time-optimal control problem and give an efficient method of evaluating its control curvature. We will show that, up to the change of the Riemannian metric on the manifold, the control curvature of the Zermelo problem has a simple to handle expression which naturally leads to a generalization of the classical Gauss–Bonnet formula in the form of an inequality. This Gauss–Bonnet inequality allows one to generalize the Zermelo problems and obtain a theorem of E. Hopf that establishes the flatness of Riemannian tori without conjugate points.      

The Nusselt condensation and nonisothermality

We extend Nusselts theory of condensation accounting for subcooling of condensate at a variable wall temperature. Neglecting vapour shear, we derive an equation for heat transfer of a saturated pure vapour condensing on a surface of arbitrary shape. Using this equation, we examine the interaction between heat transfer and nonisothermality specifying the conditions that give the mean heat transfer coefficient independent of the temperature profiles. Applying these conditions to the condensation on a horizontal circular tube and on a sphere, we analytically confirm some numerical results from the literature.     

Regional Gradient-Constrained Control Problem. Approaches and Simulations

In this paper, we study an optimal control problem with gradient constraints for linear parabolic systems. Our analysis is based on subdifferential techniques and on Lagrangian multiplier method to characterize the optimal control. We also give numerical scheme for the computation of such a control. The simulations illustrate successfully the obtained results and lead to some conjectures.     

The power grabbers

In this article, we give a broad overview of the problem of energy inefficiency in data centers (DCs), and we introduced the measures that are being taken and can be taken to improve their energy efficiency. We believe it is very unlikely that we will see an overall decrease in the energy consumed in DCs in the near future, given the strong increase in demand, despite the rigorous energy efficiency measures now being introduced. Only a decrease in the rate of increase of energy usage in DCs can reasonably be expected in the foreseeable future.