Preparation of interactive educational and methodical providing: look from the student, from the teacher and from the developer

There is analysed some experience of chair of Applied mathematics of the Ural state economic university in the area of development and using the interactive educational and methodical providing.В работе проанализирован опыт кафедры Прикладной математики Уральского государственного экономического университета в области разработки и использования интерактивного учебно-методического обеспечения

Quantum Lorentz Gas: Effective Equations and Spectral Analysis

We consider the quantum Lorentz gas (QLG) in the plane. We show that the spectral properties of the quantum Lorentz gas can be obtained from the study of a homogeneous system of one-dimensional integral equations. The qualitative spectral analysis is performed, and the spectrum is shown to have a band structure. The wave functions in the complete configuration space can be constructed in terms of the solutions of the obtained effective equations. We apply the obtained result to a simpler Lorentz gas model including additional symmetryECRussia collaboration Contract ESPRIT P 9282 ACTCS, International Science Foundation and the Russian Foundation for Fundamental Reseaxch

One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities

A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple, continuous, filling the real axis; the eigenfunctions, the resolvent and the spectral measure are constructed explicitly. For this (unperturbed) system the resonance spectrum is shown to be empty. The model considering impurity in a single node is also constructed using the operator extension theory methods. The spectral analysis is performed and the dispersion equation for the resolvent singularities is obtained. The resonance spectrum is shown to contain infinite discrete set of resonances. One-to-one correspondence of the constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure

On a classification of E. coli promoters according to their electrostatic potential

Classiˇcation of promoters and other functionally important genome fragments according to their nucleotide sequences and physicochemical properties is a key factor for understanding gene transcription, replication, recombination and their regulation. The classiˇcation of genome promoters is usually performed on the basis of analysis of their primary structures. However, such an approach does not allow one to obtain a simple answer because it is the physicochemical properties of DNA that control the process of gene transcription and its regulation. Electrostatic interactions comprise an essential component of those processes. This work presents the approach that allows computation of electrostatic potentials of long nucleotide sequences of DNA for both procaryotic and eucaryotic species. The elecrtostatic potentials of E. coli promoters and periodic sequences were calculated. We suppose that the electrostatic characteristics of the genome promoters together with primary structure provide their reliable classiˇcation. Š² ¸¸¨Ë¨± ꬅ ¶·µ³µÉµ·µ¢¨¤·Ê£¨Ì ËÊ´±Í¨µ´ ²Ó´µ ¢ ¦´ÒÌ Ô²¥³¥´Éµ¢ £¥´µ³ ¶µ¨Ì´Ê±²¥µ-ɨ¤´Ò³ ¶µ¸²¥¤µ¢ É¥²Ó´µ¸ÉÖ³¨Ë¨ §¨±µ-̨³¨Î¥¸±¨³¸¢µ°¸É¢ ³ Ö¢²Ö¥É¸Ö ±²ÕÎ¥¢Ò³ Ë ±Éµ·µ³ ¤²Ö ¶µ´¨³ ´¨Ö ¶·µÍ¥¸¸µ¢ É· ´¸±·¨ ¶Í¨¨£¥´µ¢, ·¥¤Ê ¶²¨± ͨ¨, ·¥±µ³¡¨´ ͨ¨¨¨Ì ·¥£Ê²Öͨ¨. ¡Òδµ ±² ¸¸¨Ë¨± ꬅ ¶·µ³µÉµ·µ¢ £¥´µ³ ¶·µ¢µ¤¨É¸Ö´ µ¸´µ¢¥ ´ ²¨ § ¨Ì ¶¥·¢¨Î´Ò̸ɷʱÉÊ·. ¤´ ±µ É ±µ° ¶µ¤Ìµ¤´¥ ¶µ §¢µ²Ö¥É ¶µ²ÊΨÉÓ µ¤´µ §´ δµ£µ µÉ¢¥É , É. ±. § ¶·µÍ¥¸¸É· ´¸±·¨ ¶Í¨¨¨¥¥ ·¥-£Ê²ÖÍ¨Õ ¢ µ¸´µ¢´µ³ µÉ¢¥É¸É¢¥´´Ò ˨ §¨±µ-̨³¨Î¥¸±¨¥¸¢µ°¸É¢ "Š. ‚ ¦´ÊÕ ·µ²Ó ¢ ʱ § ´´ÒÌ ¶·µÍ¥¸¸ ̨£· ÕÉ Ô²¥±É·µ¸É ɨΥ¸±¨¥ ¢ § ¨³µ¤¥°¸É¢¨Ö. ‚´ ¸ÉµÖÐ¥°· ¡µÉ¥ · §¢¨É ¶µ¤Ìµ¤, ¶µ §¢µ-²ÖÕШ°¢ÒΨ¸²ÖÉÓ Ô²¥±É·µ¸É ɨΥ¸±¨¥ ¶µÉ¥´Í¨ ²Ò ¤²¨´´Ò̴ʱ²¥µÉ¨¤´ÒÌ ¶µ¸²¥¤µ¢ É¥²Ó´µ¸É¥°" Š ± ± ¤²Ö ¶·µ± ·¨µÉ, É ±¨¤²Ö Ôʱ ·¨µÉ. ³¨¢ÒΨ¸²¥´Ò Ô²¥±É·µ¸É ɨΥ¸±¨¥ ¶µÉ¥´Í¨ ²Ò ¶·µ³µÉµ·µ¢ E. coli¨ ¶¥·¨µ¤¨Î¥¸±¨Ì ¶µ¸²¥¤µ¢ É¥²Ó´µ¸É¥°. OEÒ ¶µ² £ ¥³, Îɵ Ô²¥±É·µ¸É ɨΥ¸±¨¥ Ì · ±É¥·¨¸É¨±¨ ¶·µ³µÉµ·µ¢ £¥´µ³ ¸µ¢³¥¸É´µ¸ ¶¥·¢¨Î´µ°¸É·Ê±ÉÊ·µ°µ¡¥¸ ¶¥Î ɨ̴ ¤¥¦´ÊÕ ±² ¸¸¨Ë¨± ͨÕ

Multitemporal generalization of the Tangherlini solution

The n-time generalization of the Tangherlini solution [1] is considered. The equations of geodesics for the metric are integrated. For $n = 2$ it is shown that the naked singularity is absent only for two sets of parameters, corresponding to the trivial extensions of the Tangherlini solution. The motion of a relativistic particle in the multitemporal background is considered. This motion is governed by the gravitational mass tensor. Some generalizations of the solution, including the multitemporal analogue of the Myers-Perry charged black hole solution, are obtained.Comment: 14 pages. RGA-CSVR-005/9