Results 221 to 230 of about 1,233,249 (248)

Reflection Function and the Small Parameter Method

Differential Equations, 2004
The paper deals with periodic solutions of multi-dimensional differential systems. By combining symmetry properties expressed by the notion of reflection function with the small parameter method, sufficient conditions for the existence of periodic solutions are derived.
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Parameters of photomultipliers with small photocathodes

Journal of Applied Spectroscopy, 1967
A description is given of FEU-64 tubes, cathode area 0.2 cm2, for Sb-Cs and multialkali cathodes. The latter can measure fluxes of 2 × 10−15 W in the range 4000–6000 a with a signal-to-noise ratio of 10 in a passband of 1 Hz.
B. M. Glukhovskoi, A. L. Osherovich
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Diffusion Processes Depending on a Small Parameter

Theory of Probability & Its Applications, 1962
In this paper we consider a random disturbance of a system of ordinary differential equations which can be written in vector form as follows: \[ x( t ) = a ( {t,x} ), x( 0 ) = x_0 ,\quad t \in [ {0,t_0 } ],t < \infty .\]
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New small RG parameter

Physics Letters A, 1990
Abstract The exact functional renormalization group (RG) equation is used to construct a new version of the perturbation theory whose small parameter is the Fisher exponent η.
Yu.M. Ivanchenko, A.A. Lisyanskii, A.E. Filippov   +2 more
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An Optimal Control Problem with a Small Parameter

Cybernetics and Systems Analysis, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On parabolic equations with a small parameter

Computational Mathematics and Mathematical Physics, 2006
A singularly perturbed parabolic equation with a nonlinear right-hand side of a special form is examined. A numerical analytical study of such equations is performed.
A. B. Vasil’eva, A. A. Plotnikov
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An Optimal Control Problem with the Small Parameter

Journal of Mathematical Sciences, 2004
The plant is of the form \[ \dot x = Ax + Bu + \varepsilon f(x,u) \] and its optimal control is considered. Sufficient conditions are obtained for the continuity of the optimal value function at \(\varepsilon = 0\).
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Attractor of a nonautonomous hyperbolic equation with small parameter

Mathematical Notes, 2000
In a bounded domain \(\Omega\subset \mathbb{R}^n\), the author considers the equation \[ \varepsilon\partial^2_t u+\gamma(t)\partial_tu- \Delta u+f(u,t)+ \varphi(x,t)=0 \tag{1} \] with the Dirichlet boundary condition \(u |_{\partial \Omega}=0\). Here \(\varepsilon\in (0,\varepsilon_0]\) is a small parameter; the functions \(\gamma(t)\), \(f(u,t)\), \(\
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Non linear eigenvalues problems with a small parameter

Integral Equations and Operator Theory, 1984
In this work we study nonlinear eigenvalues problems like \([-\sigma^ 2d^ 2/dt^ 2+(t^ 2-\mu)^ 2+1]u=0\) where \(\mu \in {\mathbb{C}}\), \(\sigma >0\), \(u\in {\mathcal S}({\mathbb{R}}^ n)\). More precisely we study the spectrum of the operator \(Q(\sigma;\mu)=-\sigma^ 2d^ 2/dt^ 2+(t^ 2-\mu)^ 2+1\) when \(\sigma \to 0\), \(\sigma >0\).
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On a modification of the small parameter method

Differential Equations, 2006
There is an extensive class of the differential equations, where a classical method to study analytical properties of their solutions -- the method of small parameter -- is not effective. For example, the equations of so-called barrier type \[ \begin{aligned} w'''&=ww''-2w^{\prime 2},\\ w^{(4)}&=w'''w-3w''w'+c(w^{\prime 2} w-2w''w), \quad c\in\mathbb{C}
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