不适定问题的基本定理（Ⅱ）

前[1]已证基本定理关于条件(B)与条件(I—D)的等价性，本给出定理中条件(I)与条件(I-D)的等价性，从而三个条件(B)、(I)、(I—D)是相互等价的。     

一类具有二次自然增长条件的三角形椭圆组弱解的正则性

考虑非线性椭圆组 是有界域 (0.1) 其系数满足下列条件: 当相似文献   

用条件(PW)刻画的幺半群

本文引入了条件(PW),讨论了条件(PW)与条件(P)、条件(PE)之间的关系,刻画了幺半群上S-系的平坦性.     

一类拟线性椭圆方程组非平凡解的存在性

首先证明了一个抽象的紧性定理,然后借此定理证明了对应于一类拟线性椭圆方程组的泛函在比Boccardo和De．Figueiredo(2002)的条件更弱的条件(文中记为弱类(AR)条件)下满足(C)条件,并利用山路引理证明了这类拟线性椭圆方程组非平凡解的存在性,最后举出两个例子验证了文中所给条件(即弱类(AR)条件)的确比Boccardo和De．Figueiredo(2002)的条件弱．     

新题征展(72)

A题组新编1.下列条件对于函数f(x)定义域中的每一个x都成立,其中(a≠0,k≠0,a,b,k∈R):(1)条件1f(x)-f(-x)=0;条件2f(a x)=f(a-x);条件3f(kx b)=f(-kx-b);条件4f(x)=(x-a)0.其中判断函数f(x)是偶函数的条件是.(2)条件1f(a x)=f(a-x);2f(x)=f(2a-x);3f(3a-x)=f(x-a);4f(x)=(x-a)     

关于Lax-Wendroff格式的稳定性条件

是格式(2)稳定的充分条件。条件(11)显然比条件(5)、(7)都更好一些,而且由于(6)和(11)互不包含,从而改变了过去认为Ldx-Wendroff的第二种格式(3)比第一种格式(2)稳定性条件更好的看法。 本文末我们讨论了与格式(2)、(3)类似的一个二阶精度格式,对方程式(8),证明了稳定性的充要条件是,然后推广到方程组。     

三面角的面角性質

立体几何課本已經給出定理1 对于任一三面角,有下列兩性質成立(其中α,β,γ为三面角的三个面角) 因此条件(ⅰ)和条件(ⅱ)是用一組角(α,β,γ)做面角,能構成三面角的必要条件。假如用一組角(100°,10°,15°)做面角,就不能構成三面角,因为它們滿足条件(ⅱ)而不滿足条件(ⅰ)。用一組角(100°,120°,140°)做面角,也不能構成三面角,因为它們滿足条件(ⅰ)而不滿足条件(ⅱ)。但是同时滿足条件(ⅰ)和条件(ⅱ)的三个角,假如(100°,70°,40°),用它們做面角,能否構成三面角?即,条件(ⅰ)和条件(ⅱ)是否为充分的呢?現行立几課本里沒有給出答复。本文目的就在于对此做出結論——建立其充分条件。     

条件Erlang分布的双参数加法定理

X(γ)和Y(k)服从参数(γ,λ)和(k,μ)的Erlang分布且相互独立.本文证明了在X(γ)相似文献   

环的极小条件包含极大条件的充要性

熟知的 C.Hopking 一般定理指出:含有左单元结合环的左理想极小条件必含左理想极大条件.本文给出了结合环(不一定含左单元)的左理想极小条件包含左理想极大条件的一个充要条件.Hopking 定理是我们定理的自然推论.对于交换结合环,Cohen 指出:若此环含有单元,则理想极小条件(记为条件(i))等价于理想极大条件以及每个素理想是极大理想(记为条件(ii)).本文给出了任意交换结合环(不一定含有单元)中条件(i)等价于条件(ii)的一个充要条件.Cohen 的结果自然是我们结果的一种特殊情况.     

“恒成立”与“恒有解”

1　含参数的式子 ｆ(ｘ) =ｇ(ｘ) 在什么条件下“在Ｒ上恒成立”与“在Ｒ上恒有解”是有区别的“ｆ(ｘ) =ｇ(ｘ) 在什么条件下对于任意实数ｘ恒成立”是求此式在Ｒ上成为恒等式的条件 ,即参数的范围 .用函数的观点看 ,命题等价于“在什么条件下 (即参数取什么范围内的值时 ) ,函数 ｙ =ｆ(ｘ)与函数 ｙ =ｇ(ｘ) 在Ｒ上是同一函数” .“ｆ(ｘ) =ｇ(ｘ) 在什么条件下在Ｒ上恒有解”是求关于ｘ的方程有实数解的条件 .用函数的观点看 ,命题等价于“在什么条件下 (即参数的范围 ) ,函数 ｙ =ｆ(ｘ) 与 ｙ =ｇ(ｘ) 的图象总有交点” .显然 ,可以将…     

Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.     

Nonlinear Electromagnetic Delay of Electromagnetic Signals Propagating in the Magnetic Meridian Plane of Pulsars and Magnetars

We analyze the propagation of electromagnetic waves in the magnetic meridian planes of neutron stars with a strong magnetic field in the framework of the parameterized post-Maxwellian electrodynamics of the vacuum. The origin of these electromagnetic waves is the curvature emission of X-rays and gamma rays from high-energy electrons in the vicinity of the magnetic poles of neutron stars. We show that in the case of a slowly varying intensity of X-ray and gamma-ray emission, the delay of the slow normal mode of electromagnetic waves relative to the fast mode results in a shift of the time dependence of the intensity of the detected radiation with one polarization relative to that of the radiation with the orthogonal polarization. In the case of single X-ray or gamma-ray pulses, the delay effect results in the polarization of the detected pulse varying during the pulse length, the leading edge of all pulses being polarized normally to the magnetic equator plane of the neutron star. We note that the modern level of the experimental technique, in principle, allows observing the manifestations of the delay effect for signals of different polarizations.     

Seepage of a gas condensate mixture when using the geoloosening method

The problem of the seepage of a two-phase multicomponent hydrocarbon mixture for evaluating the efficiency of the use of the geoloosening method in gas condensate deposits is considered. The geoloosening method is a technology for increasing the productivity of wells, developed at the Institute of Problems in Mechanics of the Russian Academy of Sciences, and it ensures an increase in the permeability of the critical zone of a well because of directed relief of the stratum. The initiation of the geoloosening process requires the creation of deep depressions at the well bottom and, as a result, there is an accumulation of retrograde condensate in the neighbourhood of the well, which leads to a decrease in the phase permeability with respect to the gas. It is necessary to take account of the existence of these two processes, which are mutually counter directed from the point of view of the change in permeability, when this method is used for gas condensate deposits. Due to the change in the chemical composition of the mixture in the condensation process and the action of capillary forces, the gas content at each point and each instant is not the equilibrium content and, consequently, cannot be directly determined from the phase diagram of the substance. A differential scheme is used to describe the seepage of the mixture, according to which, unlike an integral scheme, the relation for the transition into the liquid phase is specified for increments and not for the pressure and volume values themselves. Numerical calculations of the steady seepage of a hydrocarbon mixture are carried out for the necessary depression levels for the conditions in the Astrakhan gas condensate deposit and the effectiveness of the use of the geoloosening method there is demonstrated.     

Prediction of the deformation properties of a polymeric composite with a granular-fibrous filler

Conclusion A variant of calculation of the characteristics of the deformation properties of a hybrid composite containing a complex disperse filler in the form of granular particles and short fibers was proposed. The effect of aggregation of the granular filler, the statistical distributions of the fibers by lengths and orientation in the material, and the anisotropy of the fibers are taken into consideration in the calculation. The statistical distribution of the orientation of the fibers is given by a function proportional to the distance from the center to the surface of a triaxial ellipsoid in the corresponding direction. The uniform random distribution of the fibers in bulk and in the plane is a special case of this distribution. The results of the analysis of the effect of the parameters of the statistical distributions of the length and orientation of short fibers on the elasticity characteristics of a composite are reported. The dependence of the creep of the composite on the ratio of the concentration of the components of the complex filler was determined, and the efficiency of partial replacement of a granular filler by a short-fiber filler to inhibit creep of the composite was demonstrated. The possibilities of predicting the long-term creep were experimentally confirmed on the example of LDPE filled with ground limestone and short glass fibers.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 898–909, September–October, 1987.     

An investigation on the influence of slot injection/suction on the spreading of a thin film under gravity on a rotating disk

We investigate the influence of slot injection/suction on the axisymmetric spreading of a thin film under the influence of gravity and rotation. The effects of surface tension are ignored. We allow a very thin film to precede the bulk of the fluid to overcome the singularity which arises as a consequence of applying the no-slip boundary condition. We show how the width of the slot and magnitude of the injection/suction influences the height of ridges and depth of cavities on the profile of the free surface of the thin film. Rotation increases the depth of the cavities and the height of the ridges as compared to the effects of gravity alone. The presence of rotation also results in the formation of a breaking wave.     

The thermodynamically consistent equations of a thermoelastic saturated porous medium

A phenomenological model of a porous medium saturated with fluid is considered with in the framework of the hypothesis of interpenetrating continua. Assuming that there are no phase transitions, that the contribution of pulsations to the stress tensor and kinetic energy is small, and the components of the medium are in thermal equilibrium, mass, momentum and energy equations and a law of conservation of compatibility of the deformations and velocities are formulated. Using a representation of the force of interaction of the components in the form of the sum of equilibrium and dissipative components, a new form of inequality is obtained for the rate of entropy production. A definition of a thermoelastic saturated porous medium is given. The symmetry group of such a medium is considered as a set of two groups, corresponding to the symmetry of the skeleton and the fluid. It is shown that, in the class of thermoelastic porous media with an arbitrary type of symmetry of the skeleton, the saturating fluid can only be an ideal fluid, while the thermodynamic potentials and the porosity, stresses and entropies determined by them do not depend on the temperature gradient and the relative fluid velocity. It is found that the condition of incompressibility of only one of the components of the medium leads to the elimination of the porosity from the governing relations, rather than to kinematic limitations. The limitations imposed on the governing relations by the principle of thermodynamic consistency and the requirement of independence of the choice of the frame of reference are investigated. A form of the governing relations, necessary and sufficient to satisfy these principles, is obtained. It is shown that the Biot equations are one of the forms of thermodynamically consistent governing relations. A thermodynamic validation of the effective-stress tensor is given.     

The topology of the zero-level lines of the components of the acceleration vector in subsonic flows

The steady subsonic flow past bodies of finite dimensions, when the stream is unbounded and uniform at infinity is considered. The structure formed by the stationary points (points where both components of the acceleration vector vanishes), by the zero-level of the components of the acceleration vector emerging from them and the body past which the flow occurs is studied. It is shown that each of the above-mentioned lines must reach the surface of the body past which the flow takes place. This fact, in particular, enables one to estimate the overall number of streamlines with zero curvature emerging from the stationary points in terms of the number of zeros of the curvature of the streamlines on the body around which the flow takes place, including the branch points of a dividing streamline. With a view to refining the above mentioned number of zeros, the known solution for the neighbourhoods of the branch points of a streamline is considered and the singularity of the flow in the neighbourhoods of points of discontinuity of the curvature of the wall around which the flow occurs is investigated. In order to illustrate the above, certain properties of the flow past convex bodies are refined and a fairly broad class of so-called convex-concave bodies with zero angle of tapering of the trailing edge is constructed and considered. It is shown that, for this body, there are not more than four zeros of the curvature of the streamline and, as a consequence, there are no branch points of the isobars and isoclines in the flow field, including at infinity, an infinitely distant point is the sole stationary point and, most important of all, in the case of the flow past the given bodies the values of the circulation and the lifting force cannot vanish. The mathematical apparatus employed is based on the equations of gas dynamics constructed earlier for certain combinations of the components of the acceleration vector.     

Identification and orbit determination of a tethered satellite system

Orbital motion of a tethered satellite system, composed of two satellites and an inextensible tether, is considered by using a perturbed two-body model. This approach is adopted so that the determination of the orbit of one of the satellites can be attempted without using observations of the motion of the other satellite in the system. The identification of the tethered condition of the system using observations of only one of the satellites in the tethered satellite system is considered. The characteristics of the `tether perturbed' motion of the observed satellite are investigated. Estimation of the state of the system using near perfect data is also illustrated. Observations of one satellite provide the entire state of the system and a parameter involving the ratio of the masses of satellites and the tether length.