Stability analysis of some integrable Euler equations for SO(n)

A family of special cases of the integrable Euler equations on $so(n)$ introduced by Manakov in 1976 is considered. The equilibrium points are found and their stability is studied. Heteroclinic orbits are constructed that connect unstable equilibria and are given by the orbits of certain 1-parameter subgroups of SO(n). The results are complete in the case $n=4$ and incomplete for $n>4$.Comment: 15 pages, LaTeX, minor stylistic changes in v

Biomedical management of individual training of qualified greco-roman style

In the conditions of increase of requirements to the implementation of medico-biological control of the training process it is necessary in the implementation of all the structural components management training for wrestlers. With the aim of protecting the health of athletes biomedical support appropriate to implement based on the use of simulation modeling taking into account the individual characteristics of athletesВ условиях повышения требований к осуществлению медико-биологического контроля тренировочного процесса необходимо его внедрение во все структурные компоненты управления подготовкой борцов. С целью сохранения здоровья атлетов медико-биологическое сопровождение целесообразно реализовывать на основе использования имитационного моделирования с учетом индивидуальных особенностей спортсмено

Fomenko-Mischenko Theory, Hessenberg Varieties, and Polarizations

The symmetric algebra g (denoted S(\g)) over a Lie algebra \g (frak g) has the structure of a Poisson algebra. Assume \g is complex semi-simple. Then results of Fomenko- Mischenko (translation of invariants) and A.Tarasev construct a polynomial subalgebra \cal H = \bf C[q_1,...,q_b] of S(\g) which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of \g. Let G be the adjoint group of \g and let \ell = rank \g. Identify \g with its dual so that any G-orbit O in \g has the structure (KKS) of a symplectic manifold and S(\g) can be identified with the affine algebra of \g. An element x \in \g is strongly regular if \{(dq_i)_x\}, i=1,...,b, are linearly independent. Then the set \g^{sreg} of all strongly regular elements is Zariski open and dense in \g, and also \g^{sreg \subset \g^{reg} where \g^{reg} is the set of all regular elements in \g. A Hessenberg variety is the b-dimensional affine plane in \g, obtained by translating a Borel subalgebra by a suitable principal nilpotent element. This variety was introduced in [K2]. Defining Hess to be a particular Hessenberg variety, Tarasev has shown that Hess \subset \g^sreg. Let R be the set of all regular G-orbits in \g. Thus if O \in R, then O is a symplectic manifold of dim 2n where n= b-\ell. For any O\in R let O^{sreg} = \g^{sreg}\cap O. We show that O^{sreg} is Zariski open and dense in O so that O^{sreg} is again a symplectic manifold of dim 2n. For any O \in R let Hess (O) = Hess \cap O. We prove that Hess(O) is a Lagrangian submanifold of O^{sreg} and Hess =\sqcup_{O \in R} Hess(O). The main result here shows that there exists, simultaneously over all O \in R, an explicit polarization (i.e., a "fibration" by Lagrangian submanifolds) of O^{sreg} which makes O^{sreg} simulate, in some sense, the cotangent bundle of Hess(O).Comment: 36 pages, plain te

Force dipoles and stable local defects on fluid vesicles

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area and volume preserving conformal transformations, which breaks the symmetry between the two points. The volume constraint fixes the distance $S$, measured along the surface, between the two points; if it is relaxed, a second zero mode appears, reflecting the independence of the energy on $S$; in the absence of this constraint a pathway opens for the membrane to slip out of the defect. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. The magnitude of these forces varies inversely with $S$ and so diverges as the points merge; the corresponding torques vanish in these defects. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and in distant regions as a biharmonic quadrupole. Comparison of the distribution of stress with the quadratic approximation in the height functions points to shortcomings of the latter representation. Radial tension is accompanied by lateral compression, both near the singularities and far away, with a crossover from tension to compression occurring in the region between them.Comment: 26 pages, 10 figure

PROFESSIONAL CONSULTING, PLANNING AND DESIGN OF REGIONAL DEVELOPMENT IN THE FACE OF INCREASING UNCERTAINTIES AND RISKS

The article reveals features of the ongoing transformations in the field of consulting, planning and design in the field of regional development in the face of increasing uncertainties and risks, primarily related to climate change and biodiversity loss. It shows that the very basis of such work is significantly changing, as the world-system becomes more complex, during the transition from the concept of an “empty” world to a “full” world. This change includes increasing emphasis on ensuring the resilience of human-dominated ecosystems, a change in decision-making, using behavioral a “responsible” human model that best meets the needs of inclusive sustainable development.The authors define features of consulting, planning and design of regional development in the face of increasing uncertainties and risks, as a special type of thinking activity, in a situation of approaching radical uncertainty. The article shows the necessity of supplementing natural science approaches with the tools and practices of post-normal science and the narrative theory of beliefs, as well as the ideas of K. Friston, implemented within his dynamic causal model.Such an approach is based on a systematic approach to decision-making in regional development and pays special attention to the adaptation of individuals and communities to high risks and uncertainties, primarily climatic and natural. It helps to better reflect the diversity of geographical conditions, to clarify the range of effective solutions for sustainable development of regions and increase the long-term resilience of business

On the Cartan Model of the Canonical Vector Bundles over Grassmannians

We give a representation of canonical vector bundles over Grassmannian manifolds as non-compact affine symmetric spaces as well as their Cartan model in the group of the Euclidean motions.Comment: 6 page

Plasticizer Effect on Dielectric and Relaxation Parameters of Xanthan

The dielectric and relaxation properties of pure and plasticized (with water, glycerol and PPG-200) xanthan were studied by  broadband dielectric relaxation spectroscopy. Within frequency range 10–107 Hz, a solid xanthan and its gels demonstrated two relaxation processes: the β-relaxation and relaxation of gel fragments formed due to xanthan/plasticizer interaction. The relaxation time decreased in the raw of plasticizers: PPG-200 > water > glycerol; the segmental dynamics of xanthan respectively grow. The ionic conductivity of gel samples increased in the following sequence:  water < PPG-200 < glycerol

Invariant metrics and Hamiltonian Systems

Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of them and finally find commuting functions under the corresponding Lie-Poisson bracketComment: 16 pages corrected typos, changed contents (Prop. 3.4 and Theorem in Section 3

RISK MANAGEMENT ALGORITHM FOR ENSURING THE SANITARY SAFETY OF THE POPULATION IN THE AREA OF THE OIL REFINERY

The article reveals the main features and characteristics of the algorithm of actions to ensure environmental safety of the population in the areas of oil refineries based on the mechanism of health risk assessment at all stages of the life cycle of environmentally hazardous production facilities. Methodologically, the algorithm implements the provisions of existing standards, regulatory documents and recommendations on health risk assessment of the population and is a sequence of procedures for making informed decisions on ensuring that health risk to the population exposed to potential negative environmental impacts meets the regulatory level. Application of the algorithm ensures compliance with the regulatory level of environmental impacts on the border of the sanitary protection zone of oil refineries and adjacent residential areas.A special emphasis is made on the stages of design and operation of environmentally hazardous objects, when the level of created health risks is especially sensitive to the results of decisions made. Timely identification of hazards and assessment of health risks at the design stage helps to choose the location of environmentally hazardous facilities, considering created risks in specific industrial and urban conditions. At the operation stage, the areas with highest risk levels of the sanitary protection zone boundary and the industrial site are identified, as well as priority production facilities and chemical toxicants (in terms of created risks). This gives a reason for adjusting the programs of industrial and environmental control, for specifying the priority of investment programs and plans of environmental protection measures. In practical terms the specific features of actions in conditions of high risks are defined to ensure the health risk meets the regulatory level in functioning of environmentally hazardous oil refining object, avoiding significant financial environmental costs as a result of making ecologically insufficiently justified planning and technological decisions at the design stage. The algorithm is universal, because it can be used for the existing production facilities and new construction projects, regardless of industry specifics

An electrooptical muscle contraction sensor

An electrooptical sensor for the detection of muscle contraction is described. Infrared light is injected into the muscle, the backscattering is observed, and the contraction is detected by measuring the change, that occurs during muscle contraction, between the light scattered in the direction parallel and perpendicular to the muscle cells. With respect to electromyography and to optical absorption-based sensors, our device has the advantage of lower invasiveness, of lower sensitivity to electromagnetic noise and to movement artifacts, and of being able to distinguish between isometric and isotonic contractions