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1.
M.K. Aouf 《Journal of The Franklin Institute》2010,347(10):1927-1941
Let denote the class of functions analytic in U={z:|z|<1} which satisfy for fixed M, z=reiθ∈U and
2.
VCO sweep-rate limit for a phase-lock loop 总被引：1，自引：0，他引：1
John Stensby 《Journal of The Franklin Institute》2009,346(3):223-236
Phase-lock loops (PLLs) serve important roles in phase-lock receivers, coherent transponders, and similar applications. For many of these uses, the bandwidth of the loop must be kept small to limit the detrimental influence of noise, and this requirement makes the natural PLL pull-in phenomenon too slow and/or unreliable. For each such case, the phase-lock acquisition process can be aided by the application of an external sweep voltage to the loop voltage controlled oscillators (VCOs). The goal is to have the applied sweep voltage rapidly decrease the closed-loop frequency error to a point where phase lock occurs quickly. For a second-order loop containing a perfect integrator loop filter, there is a maximum VCO sweep-rate magnitude, denoted here as Rm rad/s2, for which phase lock is guaranteed. If the applied VCO sweep rate is less than Rm, the loop cannot sweep past a stable phase-lock point, and it will phase lock. On the other hand, for an applied sweep-rate magnitude that is greater than Rm, the PLL may sweep past a lock point and fail to phase lock. In the existing PLL literature, only a trial-and-error approach has been described for estimating Rm, given values of loop damping factor ζ and natural frequency ωn. Furthermore, no plots exist of computed versus ζ and versus ζ (BL denotes loop-noise bandwidth). These deficiencies are dealt with in this paper. A new iterative numerical technique is given that converges to the maximum sweep-rate magnitude Rm. It is used to generate data for plots of and versus ζ, the likes of which have never appeared before in the PLL literature. 相似文献
3.
In this paper, we consider multipoint boundary value problem for third-order differential equations with p-Laplacian at resonance
4.
M.A. Bokhari 《Journal of The Franklin Institute》2007,344(5):637-645
The n-point Gauss quadrature rule states that
5.
F.B. Gao 《Journal of The Franklin Institute》2011,348(6):1020-1034
We consider an n-dimensional p-Laplacian-like neutral functional differential equation (NFDE) in the form
6.
Differential subordinations and argument inequalities 总被引：1，自引：0，他引：1
The main object of the present paper is to investigate certain properties of multivalent functions associated with a linear operator . 相似文献
7.
Muhammet Kamali 《Journal of The Franklin Institute》2007,344(6):867-872
A certain differential operator Dn+p is introduced for functions of the form
8.
In this paper we stochastically perturb the functional Kolmogorov-type system
9.
Montgomery multiplication over rings 总被引：1，自引：0，他引：1
Montgomery multiplication of two elements a and b of a finite field Fq is defined as abr-1 where r is a fixed field element in . In this paper we define Montgomery multiplication of elements a(x) and b(x) in a polynomial ring modulo the ideal generated by a reducible polynomial f(x). We then show that Montgomery multiplication over a field represented by a polynomial ring modulo an irreducible pentanomial can be performed more efficiently in terms of time delay by embedding the field in a quotient of a polynomial ring modulo a reducible trinomial. The trinomial has a degree that is slightly higher than that of the pentanomial, thereby increasing the number of gates in the multiplier by a small amount. 相似文献
10.
11.
Cemil Tunç 《Journal of The Franklin Institute》2011,348(7):1404-1415
We establish some sufficient conditions which guarantee asymptotic stability of the null solution and boundedness of all the solutions of the following nonlinear differential equation of third order with the variable delay, r(t)
12.
B.A. Frasin 《Journal of The Franklin Institute》2011,348(6):1013-1019
In this paper, we introduce the integral operator of analytic functions. The order of convexity of this integral operator when γ=1 is determined. Furthermore, we derive sufficient conditions for this operator to be analytic and univalent in the open unit disc. 相似文献
14.
The block entropies computed by lumping and gliding are calculated for the binary expansions of the Feigenbaum constants α and δ, and for . Small but significant deviations from randomness are revealed for the binary expansions of the Feigenbaum constants α and δ, supporting the conclusions of the previous relevant work by the authors. 相似文献
15.
In this paper, the second order non-linear differential equation
16.
Salim A. Messaoudi 《Journal of The Franklin Institute》2007,344(5):765-776
In this paper we consider the semilinear viscoelastic equation
17.
In this paper, we investigated the differential equation
18.
D.N. Chalishajar 《Journal of The Franklin Institute》2007,344(1):12-21
Dhakne and Kendre [On abstract nonlinear mixed Volterra-Fredholm integro-differential equations, Presented Paper in the International Conference at IIT-Bombay, 11-13 December, 2004] has proved the existence of the abstract nonlinear mixed Volterra-Fredholm integro-differential system of the type
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