The complex submanifolds \mbox{$F^l\subset {\bf C}^{l+p}$} with minimal holomorphic curvature of a complex Grassmann manifold along the holomorphic planes tangent to the nondegenerate Grassmann image are investigated. 2000 Mathematics Subject Classification: 53B25. [ Full-text available (PDF) ] Top of the page.
In this paper the comparison between recently propozed notion of compact subdifferential and K.M.Garg median set, F.Clarke, P.Michel -- J.P.Penot subdifferentials, B.N.Pshenichnyi subdifferential and superdifferential, J.P.Aubin contingent derivative is realized. 2000 Mathematics Subject Classification: 46J52. [ Full-text available (PDF) ] Top of the page.
In the article we consider the spectral problem originated by the linearized modified and classical Stefan problems. Using the generalized Green's formulaes problem is reduced to spectral problem for linear self-adjoint operator matrices acting in Hilbert space. It is proved that spectrum consist of normal positive eigenvalues and finite or infinite number of negative eigenvalues. The system of eigenelements is complete and orthogonal. 2000 Mathematics Subject Classification: 35P05, 25P10. [ Full-text available (PDF) ] Top of the page.
Approximate bimodal solutions of the Boltzmann equation with the modes of special kind are built. Correspondent flows in a gas of hard spheres are accelerating-packing screws, besides their densities partially depend on the temperatures. Some sufficient conditions for infinitesimality of the mixed discrepancy between the sides of the equation are obtained. 2000 Mathematics Subject Classification: 76P05, 45K05, 82C40, 35Q55. [ Full-text available (PDF) ] Top of the page.
In this work, using the Controllability Function method created by V.I. Korobov, we give a solution to the synthesis problem for the nonlinear system $\dot{x}_{1}=u,\, \dot{x}_{2}=x_{1}^{3},\,\left\vert u\right\vert \leq1,$ i.e. we find a set of positional bounded controls $u=u(x_1,x_2)$ with $|u|\leq1$ such that the trajectory of the system $\dot{x}_{1}=u(x_1,x_2),\, \dot{x}_{2}=x_{1}^{3}$, starting at the initial position $x_0$ terminates at the origin in finite time $T(x_0)$. 2000 Mathematics Subject Classification: 47A45. [ Full-text available (PDF) ] Top of the page.
Influence of dissipative and permanent moments on stability of even rotation of whipping top Lagrange with an arbitrary axisymmetrical cavity, fully filled ideal liquid, is appraised. On the example of ellipsoid cavity numeral researches of areas of stability are conducted. 2000 Mathematics Subject Classification: 70E06. [ Full-text available (PDF) ] Top of the page.
In the paper Wold's deconposition for polynomial sequences in a Hilbert space $H$, i.e. sequences of a kind $x_n = p_n (A) x_0,\ n\in\Z_+$, where $A$ is a self-adjoint operator in $H$, and $p_n$ are orthogonal polynomials on the real line is obtained. Also a notion of an index of singularity for polynomial sequences is introduced and studied. 2000 Mathematics Subject Classification: 42C05, 33C45, 60G. [ Full-text available (PDF) ] Top of the page.
The main part of the operator of the diffraction problem of the plane wave on the sphere with a circular aperture is found and inverted. The method of regularization is based on the use of the techniques of the Abel integral transformation. As a result, the Fredholm infinite system of algebraic equations of the second kind with a compact operator in Hilbert space $l_2$ is obtained. The system is effectively solvable. The several cases of the problem formulation are considered. 2000 Mathematics Subject Classification: 65N12, 35A25,78A45. [ Full-text available (PDF) ] Top of the page.
The definition of the linear (vector) space only on the basic of 4 axioms is proposed. 2000 Mathematics Subject Classification: 15A03. [ Full-text available (PDF) ] Top of the page.
The properties of mechanical systems with non-integer number degrees of freedom are discussed. The existence of additional resonance frequencies has been established when the damper coefficients approach infinity. It has been also established that such systems display oscillatory properties under all values of damper coefficient. 2000 Mathematics Subject Classification: 92C10. [ Full-text available (PDF) ] Top of the page.
The present paper is devoted to elaboration of the mechanical and mathematical models of the locomotor organelles of living cells. Organelle movements are considered as a special case of the motility. The new approach to the modelling of organelle movements is considered. This approach is based on the solution of the first problem of the dynamics. This problem is solved for normal and mutant cases. The supposition concerned to the dependence of generalized forces on generalized coordinates and velocities has been formulated. As a result of the computer modelling, the different organelle beat patterns are obtained. 2000 Mathematics Subject Classification: 92C37. [ Full-text available (PDF) ] Top of the page.
Following work [Korobov V.I., Pavlichkov S.S. Global properties of the triangular systems in the singular case// J. Math. Anal. Appl. -- 2008. -- {\bf 342}. -- P.~1426-1439], we consider the class of MIMO (multi-input and multi-output) triangular systems of the so-called "generalized triangular form" defined by the same conditions as in [Korobov V.I., Pavlichkov S.S. Global properties of the triangular systems in the singular case // J. Math. Anal. Appl. -- 2008. -- {\bf 342}. -- P.~1426-1439] except the following one: in comparison with the above-mentioned work, we remove the assumption about $C^1$ - smoothness of the dynamics and assume that the dynamics satisfies the local Lipschitz condition w.r.t. states and controls only. In the current work, is proven that such a new class is globally controllable (by means of controls from class $C^{\mu}$ with an arbitrary $\mu \ge 0$ including $C^{\infty}$). The background of the proof is a modification of the construction proposed in [Korobov V.I., Pavlichkov S.S. Global properties of the triangular systems in the singular case // J. Math. Anal. Appl. -- 2008. -- {\bf 342}. -- P.~1426-1439]. Whereas this new class is wider than that from [Korobov V.I., Pavlichkov S.S. Global properties of the triangular systems in the singular case // J. Math. Anal. Appl. -- 2008. -- {\bf 342}. -- P.~1426-1439] to some extent, we prove its global controllability only (while in the above-mentioned work stronger results were obtained for the $C^1$ - case). 2000 Mathematics Subject Classification: 93C10, 93B10, 93B11, 93B05, 93B52. [ Full-text available (PDF) ] Top of the page.