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neighborhood
Like the truncations of the Taylor expansion, the truncations of a chromatic expansion at t = t0 of an analytic function f(t) approximate f(t) locally, in a neighborhood of t0.
      
It is available for the case that the sign of f(x) changes frequently or the derivative f'(x) does not exist in the neighborhood of the root, while the Newton method is hard to work.
      
One allows the appearance of eight limit cycles in the neighborhood of infinity, which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.
      
Neighborhood union of independent sets and hamiltonicity of claw-free graphs
      
Let G be a graph, for any u∈V(G), let N(u) denote the neighborhood of u and d(u)=|N(u)| be the degree of u.
      
CAPFM uses the three-dimensional cellular automata as a growth space, and a Moore-type neighborhood as the cellular neighborhood.
      
Conditions for the generation of cycles in the neighborhood of the equilibrium position and at infinity are formulated.
      
Nonlinearities with a principle quadratic part and with a principle homogeneous part of the general (nonpolynomial) type in the neighborhood of the equilibrium position are separately studied.
      
It was assumed that the origin O was the stationary point of the original system of equations, the line M passed through O, F(O) = O, and the discontinuous system was structurally stable within some neighborhood of the point O.
      
Under these assumptions, efficient necessary and sufficient conditions for asymptotic stability of the point O both relative to its full neighborhood and some sectors with centers at O were obtained.
      
These conditions admit considerable variations for the estimates of the control effectiveness matrix in the neighborhood of their exact values, thereby corroborating the possibility of using the adaptation scheme for a wide class of objects.
      
The adjacency matrix defines the point of local minimum, and all arrangements (coordinates) of the Steiner points that are admissible for it define the minimum neighborhood.
      
The spacecraft center of mass was assumed to move in a thin spherical layer in the neighborhood of a certain reference orbit with a limited mass flow rate and constant jet-pipe gas velocity.
      
Formulas for estimating the time of sojourn of the network in the neighborhood of a stable state are derived.
      
According to the numerical investigations, "the ensemble average coincides with the time average" in the neighborhood of the limiting set, i.e., it is sufficient to track only one path in solving optimization problems in such a system.
      
Is constructed a general solution to the integro-differential equation of the Volterra type in partial derivatives in the neighborhood of the equilibrium position.
      
Synthesis of the desired law of motion control in the neighborhood of a specified set
      
Methods and corresponding algorithms for improving a discrete control basing on the approximation in mean of Krotov-Bellman equations in the neighborhood of current approximation trajectory are proposed.
      
We consider the problem of motion of a spherically symmetric balloon satellite along an orbit with a moderate inclination in the neighborhood of a resonance caused by the joint influence of the Earth's oblateness and the pressure of light.
      
Long-period evolution of the orbital elements of geosynchronous objects moving in the neighborhood of separatrices of the region of libration resonance is studied.
      
 

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