ON THE ZEROS OF THE FUNCTION $ \zeta(s)$ ON SHORT INTERVALS OF THE CRITICAL LINE

1985 ◽  
Vol 24 (3) ◽  
pp. 523-537 ◽  
Author(s):  
A A Karatsuba
2021 ◽  
Vol 49 (6) ◽  
Author(s):  
Louis-Pierre Arguin ◽  
Frédéric Ouimet ◽  
Maksym Radziwiłł

2019 ◽  
Vol 20 (4) ◽  
pp. 271-293
Author(s):  
Z. Kh. Rakhmonov ◽  
Sh. A. Khavrulloev ◽  
A.S. Aminov

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Giovanni Coppola ◽  
Maurizio Laporta

We give a general link between weighted Selberg integrals of any arithmetic function f and averages of f correlations in short intervals, proved by the elementary dispersion method (our version of Linnik’s method). We formulate conjectural bounds for the so-called modified Selberg integral of the divisor functions dk(n), gauged by the Cesaro weight in the short interval n∈x-H,x+H and improved by these some recent results by Ivić. The same link provides, also, an unconditional improvement. Then, some remarkable conditional implications on the 2kth moments of Riemann zeta function on the critical line are derived. We also give general requirements on f that allow our treatment for f weighted Selberg integrals.


1966 ◽  
Vol 25 ◽  
pp. 363-371
Author(s):  
P. Sconzo

In this paper an orbit computation program for artificial satellites is presented. This program is operational and it has already been used to compute the orbits of several satellites.After an introductory discussion on the subject of artificial satellite orbit computations, the features of this program are thoroughly explained. In order to achieve the representation of the orbital elements over short intervals of time a drag-free perturbation theory coupled with a differential correction procedure is used, while the long range behavior is obtained empirically. The empirical treatment of the non-gravitational effects upon the satellite motion seems to be very satisfactory. Numerical analysis procedures supporting this treatment and experience gained in using our program are also objects of discussion.


1975 ◽  
Vol 34 (01) ◽  
pp. 050-062
Author(s):  
Dale H Cowan ◽  
Richard C Graham ◽  
Patricia Shook ◽  
Ronda Griffin

SummaryTo determine the effect on platelet behavior of transient exposure of platelets to ascorbic acid, studies of platelet function and ultrastructure were done before exposure to ascorbic acid at pH 6.5, during exposure to pH 6.5, and after restoration of pH to pre-acidifìcation levels. The effect of ascorbic acid (A. A.) was compared to that of HCl and citric acid (C. A.). ADP- and collagen-induced aggregation of normal platelets were significantly impaired by both A. A. and C. A. but were less affected by HCl. The release of 14C-serotonin was significantly reduced by each agent. The ultra-structure of normal platelets brought to pH 6.5 by A.A. was normal. After neutralization, there was marked dilatation of the open channel system and loss of the disc shape. When platelets were brought to pH 6.5 by A. A., then neutralized, the aggregates which formed after stimulation by ADP or collagen were smaller than normal, the platelets were less closely approximated, and degranulation was less complete. The data show that exposure of platelets to ascorbic acid for short intervals impairs their function when measured after restoration of pH to levels compatible with maximal responses. Platelet survival studies using autologous platelets labelled with 51Cr in the presence or absence of ascorbic acid showed that the recovery of normal platelets was unaffected by ascorbic acid, whereas recovery of platelets from patients with idiopathic thrombocytopenic purpura, idiopathic thrombocythemia, and alcohol-related thrombocytopenia was markedly reduced. The injury resulting from the use of ascorbic acid in preparing platelets for studies of platelet survival in patients with disorders affecting platelets may impair the recovery of the cells, resulting in artifactual changes in the survival studies.


1985 ◽  
Vol 54 (04) ◽  
pp. 776-779 ◽  
Author(s):  
U Hedner ◽  
L Tengborn

SummaryImmune tolerance has by several methods been induced in haemophiliacs with antibodies. A conversion of “high responders” into “low responders” was previously reported after repeated moderate factor IX doses over periods of 7-10 days in combination with cyclophosphamide and steroids in two patients with haemophilia B and inhibitors. This paper reports similar results in a heamophilia A patient by giving factor VIII, cyclophosphamide, and steroids during relatively short periods of time (7-8 days). The anamnestic response markedly decreased already following the first treatment and never exceeded a level of 1 u/ml (˜ 3 BU/ml) even when boosted with ordinary factor VIII doses for only 3 days. It is concluded that the markedly decreased secondary antibody response is most probably the result of factor VIII given at short intervals (twice a day) for periods of up to about one week when given in combination with cyclophosphamide and steroids. The same effect may be achieved by other methods. The treatment schedule suggested in the present paper is, however, simple and avoids long periods of high antibody levels. Furthermore, the total factor VIII dose used is lower than suggested in most other treatment schedules, which makes the treatment substantially less expensive.


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