in this paper, we study rst order linear fuzzy dierential equations with fuzzy coecient and initial value. we use the generalized dierentiability concept and apply the exponent matrix to present the general form of their solutions. finally, one example is given to illustrate our results.

this paper proposes a new method for parameter estimation of distorted single phase signals, through an improved demodulation-based phase tracking incorporated with a frequency adaptation mechanism. the simulation results demonstrate the superiority of the proposed method compared to the conventional sogi (second-order generalized integrator)-based approach, in spite of the dc-offset and harmon...

suppose $t$ and $s$ are moore-penrose invertible operators betweenhilbert c*-module. some necessary and sufficient conditions are given for thereverse order law $(ts)^{ dag} =s^{ dag} t^{ dag}$ to hold.in particular, we show that the equality holds if and only if $ran(t^{*}ts) subseteq ran(s)$ and $ran(ss^{*}t^{*}) subseteq ran(t^{*}),$ which was studied first by greville [{it siam rev. 8 (1966...

Archibald, Beal, Birkhoff, Blichfeldt, B. H. Camp, Cole, Crum, Dantzig, Dodd, Douglas, Fine, Fiske, Fite, M. C. Foster, Philip Franklin, Fry, Gafafer, Gill, Gronwall, Hazlett, Hebbert, E. R. Hedrick, Hille, Huntington, Joffe, Kellogg, Kircher, Kuhn, Lamson, MacDuffee, Mathewson, Meder, Mirick, Molina, Mullins, Northcott, Oglesby, Osgood, Pell, Pfeiffer, Raynor, Reddick, R. G. D. Richardson, Rit...

This paper focuses on effectivity aspects of the Lüroth’s theorem in differential fields. Let F be a differential field of characteristic 0 and F〈u〉 be the field of differential rational functions generated by a single indeterminate u. Let be given non constant rational functions v1, . . . , vn ∈ F〈u〉 generating a subfield G ⊆ F〈u〉. The differential Lüroth’s theorem proved by Ritt in 1932 state...

We study the following questions: (1) What are all solutions to f ◦f̂ = g◦ĝ with f, g, f̂ , ĝ ∈ C(X) being complex rational functions? (2) For which rational functions f(X) and g(X) with rational coefficients does the equation f(a) = g(b) have infinitely many solutions with a, b ∈ Q? We utilize various algebraic, geometric and analytic results in order to resolve both (1) and a variant of (2) in ...

In the absolutely continuous case, order statistics, record values and several other models of ordered random variables can be viewed as special cases of generalized order statistics, which enables a unified treatment of their theory. This paper deals with discontinuous generalized order statistics, continuing on the recent work of Tran (2006). Specifically, we show that in general neither re...