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Daniel FRANCO Gennaro INFANTE Donal O'REGAN 《数学学报(英文版)》2006,22(6):1745-1750
We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation. 相似文献
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Bernardo Lafuerza-Guillén Donal O’regan Reza Saadati 《Proceedings Mathematical Sciences》2007,117(1):61-70
We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness
of a quotient. 相似文献
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Mohamed El-Gebeily Donal O'Regan 《Journal of Mathematical Analysis and Applications》2007,334(1):140-156
Existence theory is developed for the equation ?(u)=F(u), where ? is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ? to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained. 相似文献
7.
Summary Some simple ideas are used here to prove a theorem on generating functions for a certain class of q-polynomials. This general theorem is then applied to derive a fairly large number of known as well as new generating functions for the familiar q-analogues of various polynomial systems including, for example, the classical orthogonal polynomials of Hermite, Jacobi, and Laguerre. A number of other interesting consequences of the theorem are also discussed. 相似文献
8.
R.A. Gunasekaran M. Agarwal A. Singh P. Dubasi P. Coane K. Varahramyan 《Optics and Lasers in Engineering》2005,43(6):1086
A novel small fluid controlled optical lens system that is capable of displaying dynamic variation of its focal length and field-of-view (FOV) is designed and fabricated. In this active lens system, appropriate volume of the optical fluid can be pumped into or out of the lens chamber to provide double-convex (DCX) or double-concave (DCV) lens effect. Simple optical imaging experiments were performed using different sets of glass lenses with fixed focal lengths to determine the optimum lens configuration required for designing a dynamic optical lens system. The experimental results obtained from the glass lenses demonstrate that a combination of a single DCX lens with three DCV lenses provides a wider FOV. The flexible membranes for fluid controlled lenses were fabricated using polydimethylsiloxane polymer material, which has good optical transparency and elasticity. A simple fluid injection system is used to vary the radius of curvature of the lenses, and thereby to change the focal length. A dynamic optical lens system with a combination of one DCX and multiple variable focal length DCV lenses as designed here can image an object with a wide range of focal length and FOV. With this fluid controlled optical system, the FOV and focal length could be continuously varied and a maximum FOV of 118.3° could be achieved. The smallest f-number (f/#) for this fluid controlled single lens system was found to be 1.3, which corresponds to the numerical aperture value of 0.35. 相似文献
9.
Sea nodules were extensively studied over a wide range of temperature ranging from 77K to 1175K using Mossbauer effect and
ESR. The Mossbauer studies of the nodules at 77K and room temperature show a quadrupole doublet whereas at higher temperatures
magnetic spectra were obtained starting at around 875K which ultimately gives a hyperfine field of around 390 KOe at 1175
K. The Mossbauer spectra recorded at 30K did not show any significant change in the room temperature spectra. The analysis
of the spectra upto 775K showed two positions of FeR+, vie., octahedral and tetrahedral which were varified by ESR of the diluted samples. 相似文献
10.
On range searching with semialgebraic sets 总被引:1,自引:0,他引:1