Fixed point properties of the binomial function are developed. It is shown that for any 1 < L < N, TLNhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability pFAand an initial detection probability pD, then TLN(pFA) < pFAand TLN(pD) > pDif, and only if, pFA < p? < pD. When this condition is satisfied, as N → ∞, TLN(pFA) → 0 and TLN(pD → 1. 相似文献
The present paper sheds some light on a mathematical model for blood flow through stenosed arteries with axially variable peripheral layer thickness and variable slip at the wall. The model consists of a core region of suspension of all the erythrocytes assumed to be a Casson fluid and a peripheral layer of plasma as a Newtonian fluid. For such models, in literature, the peripheral layer thickness and slip velocity are assumed a priori based on experimental observations. In the present analysis, new analytic expressions for the thickness of the peripheral layer, slip velocity and core viscosity have been obtained in terms of measurable quantities (flow rate (Q), centerline velocity (U), pressure gradient (−dp/dz), plasma viscosity (μp) and yield stress (θ)). Using the experimental values of Q, U, (−dp/dz), μp and θ, the values of the peripheral layer thickness, core viscosity, and slip velocity at the wall have been computed. The theoretically obtained peripheral layer thickness has been compared with its experimental value. It is found that the agreement between the two is very good (error<1.4%). Further, a comparison between theoretical and experimental values of core viscosity is made and it is observed that the error between the two becomes 3.7465% in the case of two-layered model (Casson-Newtonian) for tube diameter 40 μm. The analysis developed here could be used to determine the more accurate values of the apparent viscosity of blood, agreeability, rigidity and deformability of red cells. This information of blood could be useful in the development of new diagnosis tools for many diseases. 相似文献
Using data generated by progressive nucleation mechanism on the cumulative fraction of citations of individual papers published successively by a hypothetical author, an expression for the time dependence of the cumulative number Lsum(t) of citations of progressively published papers is proposed. It was found that, for all nonzero values of constant publication rate ΔN, the cumulative citations Lsum(t) of the cumulative N papers published by an author in his/her entire publication career spanning over T years may be represented in distinct regions: (1) in the region 0 < t < Θ0 (where Θ0 ≈ T/3), Lsum(t) slowly increases proportionally to the square of the citation time t, and (2) in the region t > Θ0, Lsum(t) approaches a constant Lsum(max) at T. In the former region, the time dependence of Lsum(t) of an author is associated with three parameters, viz. the citability parameter λ0, the publication rate ΔN and his/her publication career t. Based on the predicted dependence of Lsum(t) on t, a useful scientometric age-independent measure, defined as citation acceleration a = Lsum(t)/t2, is suggested to analyze and compare the scientific activities of different authors. Confrontation of the time dependence of cumulative number Lsum(t) of citations of papers with the theoretical equation reveals one or more citation periods during the publication careers of different authors. 相似文献
If T maps a convex domain DT into itself, and if {ωn} is a real sequence with range in (0, 1] then the recursive averaging process, generates a sequence {x?n}; with range in DT. Under suitable conditions on DT, T and {ωn} the sequence {x?n} will converge in some sense to a fixed point of T. We prove that if DT is a closed convex subset of a complex Hilbert space H, if Tω = (1 ? ω) I + ωT is a strict contraction for some ω ? (0, 1], and if {ωn} satisfies the conditions, and then, for arbitrary ξ ? DT, {x?n} converges strongly to (the unique) fixed point of T. We also prove that if DT and {ωn} satisfy the foregoing conditions, if T has at least one fixed point, and if Tω is non-expansive for some ω ? (0, 1], then for all ξ ? DT, {x?n} converges at least weakly to some fixed point of T. Finally, we apply these results to linear equations involving bounded normal operators and obtain an extension of the classical Neumann operator series. 相似文献
