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THE FIRST EULERIAN INTEGRALSome of the next articles are maybe not open access.
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Elliptic Integrals of the First Kind
SIAM Journal on Mathematical Analysis, 1977The reciprocal square root of any real polynomial with known zeros and degree not exceeding four is integrated in terms of a standard integral by a new quadratic transformation which preserves symmetry in the zeros. If at least one zero is real, this method, unlike earlier methods, leads to a single standard integral instead of a difference of two ...
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On an integral equation of first kind
Siberian Mathematical Journal, 1991In \(\mathbb{R}^3\) the family \(\Gamma\) of straight lines \(\xi_1 = x_1 + (\xi_3 - x_3) \cos \alpha\), \(\xi_2 = x_2 + (\xi_3 - x_3) \sin \alpha\), \(0 \leq \alpha \leq 2 \pi\), passing through the point \(x = (x_1, x_2, x_3)\), and the equation \[ \int_\Gamma u(\xi)d \ell + \int_{\mathbb{R}^3} \theta (k) \rho (\alpha, x, \xi) u(\xi)d \xi = v(x ...
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Integration of first- and second-order orientation
Journal of the Optical Society of America A, 2003The problem of how visual information such as orientation is combined across space bears on key visual abiities, such as texture perception. Orientation signals can be derived from both luminance and contrast, but it is not well understood how such information is pooled or how these different orientation signals interact in the integration process.
Harriet A, Allen +3 more
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Approximate First Integrals of a Galaxy Model
Nonlinear Dynamics, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ünal, G., Gorali, G.
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Asymptotic Expansion of the First Elliptic Integral
SIAM Journal on Mathematical Analysis, 1985Summary: Asymptotic formulas with error bounds are obtained for the first elliptic integral near its logarithmic singularity. It is convenient to start from the more general problem of expanding the integral over the positive t- axis of \([(t+x)(t+y)(t+z)(t+w)]^{-1/2}\).
Carlson, B. C., Gustafson, John L.
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Stabilization of positive systems with first integrals
Automatica, 2002The paper concerns an affine control system whose drift term defines a positive system with first integrals. Under a suitable hypothesis, the authors construct feedbacks which stabilize a level set of the first integrals. Conditions are provided \(f\) for the same feedback to globally stabilize an equilibrium point.
Patrick De Leenheer, Dirk Aeyels
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Strictly Cooperative Systems with a First Integral
SIAM Journal on Mathematical Analysis, 1987We consider systems of differential equations \(dx_ i/dt=F_ i(x_ 1,...,x_ n)\) in the nonnegative orthant in the n-space satisfying the following hypotheses: i) \(F(0)=0\); ii) if \(x_ ...
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