Issue 2, Volume 3, December 1978

1978 · Open access

1. Parametric oscillations of dynamical systems with cubic term at the modulation depth under the influence of nonlinear frictions NGUYỄN VĂN ĐẠO PDF

   ▸ Abstract

   This paper deals with the influence of nonlinear frictions to the parametric oscillations of dynamical systems described by the equation with the cubic term at the modulation depth \begin{equation} x+\omega^2x+\varepsilon(cx+dx^3)\cos \gamma t+\varepsilon\alpha x^3+\varepsilon R(x,\dot{x}),\tag{0.1} \end{equation} where $\omega, c, d,\alpha$ are constants, $\varepsilon$ is a small positive parameter, $R(x,\dot{x})$ is a nonlinear function of $x,\dot{x}$ characterized the frictions considered. Three forms of nonlinear frictions will be investigated here [1, 2]: the Coulomb friction, the turbulent one and their combination. As will be seen later in the analysis, the sign and value of parameter $d$ sharply change the motion picture and the stable regions. It must be emphasized that the equation (0.1) describes the real physical systems more precisely than the one in which $d=0$ [4, 5, 6]. The system of type (0.1) with linear friction was studied qualitatively by Minorsky [3] but no attempt has yet been made to investigate it with the Coulomb friction, turbulent one and their combination.

   3-16
2. Varietes riemanniemmes admettant une fonction u telle que $ abla^2 u+fug=0$ ĐẶNG-VŨ-HUYẾN PDF

   ▸ Abstract

   On montre qu'une variété riemannienne $M$ complète, simplement connexe, de dimension $n\ge 2$, munie d'une métrique $g$, admettant une fonction réelle $u$ solution du système $\nabla^2 u +fug=0$, $f$ étant une fonction réelle non nulle sur $M$, est homéomorphe à une sphère $S^n$ ou à un espace euclidien $R^n$.

   17-21
3. Connexions induites et classes caracteristiques TỐNG VĂN ĐỨC PDF

   ▸ Abstract

   Abstract

   23-27
4. Sur certaines relations entre les coefficients binômiaux LÊ VĂN THIÊM, HỒ VĂN HÒA PDF

   ▸ Abstract

   Abstract

   29-34
5. Banach space valued Brownian motions NGUYỄN VĂN THU PDF

   ▸ Abstract

   It is known ([1], [3]) that every real Brownian motion $B(t)$, $t\in [0, 1]$, can be represented as $$B(t)=\sum\limits_nZ_n\int_0^tg_n(s)ds$$ where $\{Z_n\}$ is a sequence of i.i.d. symmetric Gaussian random variables, $\{g_n\}$ a CONS in $L^2[0,1]$ and the series is convergent with probability one uniformly over $[0, 1]$. The aim of the present paper is to prove some complete analogues if this fact for Banach space valued Brownian motions.

   35-46
6. $Gr$ — catégories strictes HOÀNG XUÂN SÍNH PDF

   ▸ Abstract

   On se propose dans cet article de démontrer que toute $Gr$ - catégorie est équivalente à une $Gr$ - catégorie stricte.

   47-60
7. Commutative subalgebras and representations of the envelopping algebra of a solvable lie algebra NGHIÊM-XUÂN-HẢI PDF

   ▸ Abstract

   Abstract

   61-74
8. Classification of unimodular algebraic groups with square integrable representations NGUYỄN HỮU ANH PDF

   ▸ Abstract

   Abstract

   75-82
9. Sur le feuilletage defini par une equation de Pfaff algébrique sur $P_nC$ TRẦN HUY HOÀNG PDF

   ▸ Abstract

   Abstract

   83-97
10. Version parametrique du théorèmes de densité pour les applications multivoques mesurables PHAN VĂN CHƯƠNG PDF

    ▸ Abstract

    Abstract

    99-112
11. Sur une methode d'integration des equations aux derivees partielles ĐỖ TẤN SĨ PDF

    ▸ Abstract

    Une formule d'inversion d'opérateurs différentiels est mise en valeur, permettant la résolution des équations aux dérivées partielles par le calcul hyperdifférentiel. Quelques applications aux équations de la chaleur et de Poisson sont données.

    113-121
12. Comportement asymptotiqe des valeurs propres d'une classe d'operateur de type ``schrödinger'' PHẠM THẾ LẠI PDF

    ▸ Abstract

    Abstract

    123-137