Results 121 to 130 of about 102,915 (146)

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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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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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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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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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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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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Turbulence in systems with small parameters

Czechoslovak Journal of Physics, 1980
Turbulence in systems where small parameters intervene, mainly through the interaction subsystem-environment, is described. The relaxation has typical features which determine experimental results. Fluctuations can be calculated and phase transitions can be predicted.
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Small-signal parameters for transistors

Electrical Engineering, 1954
The commonly used sets of parameters are discussed briefly and it is shown how the performance of the transistor can be determined with equal facility from any of the sets that may be provided.
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