I. Introduction. Stokes' theorem on a manifold is a central theorem of mathematics. Special cases include the integral theorems of vector analysis and the Cauchy-Goursat theorem. My purpose here is to prove this version of Stokes' Theorem. Let ω be a continuous differential (n − 1)-form on a compact oriented n-manifold M with boundary ∂M. Suppose that ω is differen-tiable on M − ∂M and dω is Le...

Изучается $n$-мерная система уравнений с доминирующими частными производными $n$-го порядка. Признаком, отличающим рассматриваемую систему от других систем производными, является наличие первого слагаемого в уравнениях правой части системы, представляющего собой доминирующую производную, при этом все остальные входящие уравнения системы производные получаются из нее отбрасыванием по крайней мер...

For semilinear Gellerstedt equations with Tricomi, Goursat, or Dirichlet boundary conditions, we prove Pohožaev-type identities and derive nonexistence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical-exponent phenomenon of power type in the nonlinearity is exhibited in these mixed elliptic-hyperbolic or degenerate settings where...

In this paper, the method of exterior diflerential systems for analyzing nonlinear systems is presented. Conditions are given for converting Pfafian systems into Goursat normal f o r m , and for converting control systems into Brunovsky form. All of the existing results on feedback linearization for control systems can be restated in the language of Pfafian systems, and in addition, new conditi...

By defining a closure operator on effective equivalence relations in a regular category C, it is possible to establish a bijective correspondence between these closure operators and the regular epireflective subcategories of C, on the model of the closure operators on kernels in homological categories [5]. When C is an exact Goursat category [6], this correspondence restricts to a bijection bet...

Partheite is a zeolite-like mineral of composition Ca2AI4Si401s(OH)2 . 4H20. It crystallizes with monoclinic symmetry, space group C2jc, a=21.555(3), b=8.761(1), c=9.304(2) A, p=91.55(2), Z=4, Dm=2.39 gjcm3, Dx=2.41 gjcm3. Its structure consists of T-centered T04 tetrahedra (T=AI,Si) which are connected via corners to a 3-dimensional framework. Due to the presence of hydroxyl groups the framewo...

The influence of the cations on the condensation of the anions in the salts (A')Zn(II) Br4 and (A)2Zn(II)Br4 is studied by 81 Br NQR and X-ray crystal structure analysis. (A')Zn(II)Br4(A' = [H3N(CH2)3NH3] + ) (1) shows a phase transition at 474 K. The phase II of (1) crystallizes with isolated [ZnBrJ " tetrahedra: monoclinic P2 t/«, Z = 4, a = 1108.4 (5), b = 1096.8 (2), c = 1118.5 (6) pm, and ...