Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization

We deal with the differential conditions for local optimality. The conditions that we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based on only first-order and second-order derivatives. A similar result is proved for equality constrained problems, although the necessary conditions require the regularity of the equality constraints.     

On the properties of solutions to the Goursat-Darboux problem with boundary and distributed controls

We consider a control system described by the Goursat-Darboux equation. The system is controlled by distributed and boundary controls. The controls are subject to the constraints given as multivalued mappings with closed, possibly nonconvex, values depending on the phase variable. Alongside the initial constraints, we consider the convexified constraints and the constraints whose values are the extreme points of the convexified constraints. We study the questions of existence of solutions and establish connections between the solutions under various constraints.     

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.     

一种求解混合多目标规划问题的功效函数法

逻辑生长函数相对于龚珀兹生长函数具有拐点高和对称性的特点,采用逻辑生长函数形式的功效函数法求解混合多目标规划问题具有形式简单、计算量小、符合实际的优点。证明了用这种方法求出的最优解是有效解。讨论了满意值对有效解的影响。逻辑生长函数还可以应用于多维变量评价的功效系数法中。     

Fixed-sign solutions for a system of singular focal boundary value problems

We consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments. Using Schauder fixed point theorem, we establish criteria such that the system of boundary value problems has at least one fixed-sign solution.     

On Nash Equilibria for Noncooperative Games Governed by the Burgers Equation

Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’ equation to be dominant enough with respect to the uniform convexity of the payoffs. This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel M. Ramos are acknowledged.     

Patterns in parabolic problems with nonlinear boundary conditions

We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem.     

Excitation of plant growth in dormant temperature by steady magnetic field

Experimental results of applying a steady magnetic field (20 and 30 mT) on agricultural plants reveal that their growth is more than that of control plants. Considering that these plants have ferritin cells, and each ferritin cell has 4500 Fe atoms, it is obvious that they have an outstanding role in the plants’ growth. As the last spin magnetic moment (SMM) of the Fe atom posed to an external magnetic field (EMF), the composition of SMM and EMF create an oscillator in the system. Then we have a moment of force on ferritin cells. This oscillator exerts its energy, then damps and finally locates in the field direction. The relaxed energy increased the internal temperature (i.e., the effective temperature of the magnetic spin system of plant) so that it is situated in a proper temperature for growing. This phenomenon (temperature increasing) occurs in the initial minutes of applying the magnetic field. So it depends on the number of times of locating the plant in magnetic field in a day (n). If this number (n) passes the critical value, the plant reaches a burning temperature and growth is perturbed. In this paper, the plant growth rate and critical temperature in a steady magnetic field were investigated and formulated theoretically. An innovative result in this research is as follows: if a plant's environment was in the dormant temperature, we could increase the internal temperature of the plant by applying a magnetic field n times in a day (for growth).     

200MW非再热双抽供热机组变工况计算及工况图的绘制

工况图在热电厂的设计和运行中具有广泛的用途。本文根据引进型双抽非再热200MW供热机组的技术特点，通过编程在纯凝汽工况、单抽工业抽汽工况、单抽采暖抽汽工况和双抽供热等典型变工况计算的基础上，完成了当新蒸汽负荷、工业抽汽负荷和采暖抽汽负荷发生改变时的变工况计算，并绘制了该机组的运行工况图．