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Full-Text Articles in Mathematics
The Lebesgue Integral As The Almost Sure Limit Of Random Riemann Sums, John C. Keffer, Caslav V. Stanojevic
The Lebesgue Integral As The Almost Sure Limit Of Random Riemann Sums, John C. Keffer, Caslav V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
A method is given for generating random intermediate points for a sequence of partitions. For the corresponding random Riemann sums it is shown that they converge almost surely to the Lebesgue integral. © 1982 American Mathematical Society.
Tauberian Conditions For V-Convergence Of Fourier Series, Caslav V. Stanojevic
Tauberian Conditions For V-Convergence Of Fourier Series, Caslav V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
It is proved that Fourier series with asymptotically even coefficients and satisfying (formula present here), for some 1 < p < 2, converge in L1-norm if and only if (formula present here), where En(t) =Σk=0neiktRecent results of Stanojevic [1], Bojanic and Stanojevic [2], and Goldberg and Stanojevic [3] are special cases of some corollaries to the main theorem. © 1982 American Mathematical Society.
A Note On Fixed-Point Theorems, Troy L. Hicks, M. D. Humphries
A Note On Fixed-Point Theorems, Troy L. Hicks, M. D. Humphries
Mathematics and Statistics Faculty Research & Creative Works
In an earlier note, S. P. Singh gave an extension of a theorem of Brosowski in a normed linear space setting. Variants of this theorem are considered in the context of strictly convex, reflexive, and inner product spaces. © 1982.
Conjugate Type Boundary Value Problems For Functional-Differential Equations, P. W. Eloe, L. J. Grimm
Conjugate Type Boundary Value Problems For Functional-Differential Equations, P. W. Eloe, L. J. Grimm
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
A Class Of L¹-Convergence, R. Bojan1c, C. V. Stanojevic
A Class Of L¹-Convergence, R. Bojan1c, C. V. Stanojevic
Mathematics and Statistics Faculty Research & Creative Works
It is proved that if the Fourier coefficients (an) of /E L!(0, ir) satisfy (*)L" kp\Aan\p = o(l), for some 1
< 2, then \\sn- f\\ = o(l), if and only if a" lg n * o(l). For cosine trigonometric series with coefficients of bounded variation and satisfying (*) it is proved that a necessary and sufficient condition for the series to be a Fourier series is (an) E 6, where G is the Garrett-Stanojevic [4] class. © 1982 American Mathematical Society.
Sequential Probability Ratio Tests For The Shape Parameter Of A Nonhomogeneous Poisson Process, Lee J. Bain, Max Engelhardt
Sequential Probability Ratio Tests For The Shape Parameter Of A Nonhomogeneous Poisson Process, Lee J. Bain, Max Engelhardt
Mathematics and Statistics Faculty Research & Creative Works
Sequential probability ratio tests for the shape parameter of one or more nonhomogeneous Poisson processes, with power intensity functions, are provided. The tests can be performed when the scale parameter is an unknown nuisance parameter; the effective loss of not knowing the scale parameter is one observation per process. The resulting tests can be expressed in terms of the maximum likelihood estimators of the shape parameters for the usual fixed sample procedure. A further advantage of the present approach is that the scale parameters for different processes, in the multiple sample procedures, need not be equal. Approximations for the operating …