K. Knopp, "Infinite sequences and series," Dover Publications, 1956. Home/Search Document Not in Database Summary Related Articles Check |
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On the Number of Prime Numbers less than a Given Quantity - Kolev (2000) (Correct)
....2 z 1 3 z 1 4 z . 36) Proof: If #z 1, then (1 2 1 z )#(z) # # n=1 1 n z 2 # # n=1 1 (2n) z = 1 1 2 z 1 3 z 1 4 z . The last series converges for z in #z 0 by Abel Dirichlet Dedekind generalization of the alternating series test (see [18], 5.5) If b n # 0 and b n is sequence of bounded variation, i.e. # # n=1 b n b n 1 #, then # # n=1 ( 1) n b n converges. In our case n z is of bounded variation since # # # # 1 n z 1 (n 1) z # # # # = O # 1 n 1 #z # , 37) so the ....
K. Knopp, Infinite Sequences and Series, Dover, New York, 1956.
An Infeasible Interior Proximal Method for Convex.. - Yamashita.. (2000) (Correct)
....Let oe k : k X j=1 j and b k : oe Gamma1 k k X j=1 j a j . If oe k 1, then (i) lim inf k 1 a k lim inf k 1 b k lim sup k 1 b k lim sup k 1 a k . ii) If lim k 1 a k = a 1, then lim k 1 b k = a. Proof. i) See [19; Lemma 3:5] ii) This result, originally given in [16], follows immediately from (i) 2 3 Algorithm In this section, we propose an infeasible interior proximal method for the solution of problem (P) In order to motivate this method, consider the following iterative scheme with a sequence fffi k g ae m such that ffi k 0: x k ; y k ....
K. Knopp, Infinite Sequences and Series, Dover Publications, Inc., New York, 1956.
Parallel PET Reconstruction by EM Iteration with.. - Olesen, Gregor.. (1994) (1 citation) (Correct)
.... Delta Delta M k b j ; which shows that pixel k 1 b converges to a fixed, positive value b if and only if the multiplier product M 0 b Delta Delta Delta M k b also converges to a fixed, positive value; this in turn requires that the computed multiplier M k b itself converge to 1 [13]. Thomason 6 Materials and Methods Initial Image, Sinograms, and P Matrix In this study, initial image 0 is a uniform image in which each pixel has the same positive value. 512 iterations are carried out for EM ML without employing regularization, filtering, or prior probabilities (cf. 14, ....
K Knopp. Infinite Sequences and Series. Dover, New York, 1956.
Ergodic, Primal Convergence in Dual Subgradient.. - Larsson, Patriksson, .. (Correct)
....ergodic sequence is defined by equal weights. We also present a heuristic projection procedure for the finite attainment of primal optimality. Henceforth, we make repeated use of the following lemma; it is a special case of a result of Silverman and Toeplitz, and a proof can be found in, e.g. Knopp (1956, Theorem 2, p. 35) Lemma 3.1 Assume that the sequence ffi ts g ae fulfils the conditions fi ts 0; s = 0; t Gamma 1; t Gamma1 X s=0 fi ts = 1; t = 1; 2; and lim t 1 fi ts = 0; s = 0; 1; If the sequence fb s g ae r is such that lim s 1 b s = b, then lim ....
Knopp, K. (1956) Infinite Sequences and Series, Dover Publications, New York, NY.
Model Reduction For Control Design - Schelfhout (1996) (5 citations) (Correct)
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K. Knopp, "Infinite sequences and series," Dover Publications, 1956.
Group Formation in Risk-Sharing Arrangements - Genicot, Ray (2002) (Correct)
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Knopp, K. (1956), Infinite Sequences and Series, New York: Dover Publications.
Analytical And Computational Methods For Modelling The Long-Term.. - Pollett (Correct)
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Knopp, K., Infinite Sequences and Series, Dover, New York, 1956.
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