Waring-Goldbach problem for fourth powers in short intervals

2013 ◽  
Vol 8 (6) ◽  
pp. 1407-1423 ◽  
Author(s):  
Hengcai Tang ◽  
Feng Zhao
Keyword(s):  
Short Intervals ◽  
Goldbach Problem

scholarly journals Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem

2017 ◽  
Vol 15 (1) ◽  
pp. 1517-1529
Author(s):  
Zhao Feng
Keyword(s):  
Short Intervals ◽  
Exceptional Sets ◽  
Goldbach Problem ◽  
Almost All

Abstract In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., $\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with $\begin{array}{} |p_i-(N/j)^{1/3}|\leq N^{1/3- \delta +\varepsilon} (1\leq i\leq j), \end{array} $ for some $\begin{array}{} 0 \lt \delta\leq\frac{1}{90}. \end{array} $ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.

scholarly journals Discorrelation Between Primes in Short Intervals and Polynomial Phases

2019 ◽  
Author(s):  
Kaisa Matomäki ◽  
Xuancheng Shao
Keyword(s):  
Short Interval ◽  
Exponential Sum ◽  
Short Intervals ◽  
Goldbach Problem ◽  
Special Case

Abstract Let $H = N^{\theta }, \theta> 2/3$ and $k \geq 1$. We obtain estimates for the following exponential sum over primes in short intervals: \begin{equation*} \sum_{N < n \leq N+H} \Lambda(n) \mathrm e(g(n)), \end{equation*}where $g$ is a polynomial of degree $k$. As a consequence of this in the special case $g(n) = \alpha n^k$, we deduce a short interval version of the Waring–Goldbach problem.

scholarly journals Waring–Goldbach Problem of Even Powers in Short Intervals

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Liqun Hu ◽  
Tanhui Zhang
Keyword(s):  
Prime Numbers ◽  
Short Intervals ◽  
Goldbach Problem ◽  
Average Behaviour

In this paper, we study the average behaviour of the representations of n = p 1 2 + p 2 4 + p 3 4 + p 4 k over short intervals for k ≥ 4 , where p 1 , p 2 , p 3 , p 4 are prime numbers. This improves the previous results.

Artificial satellite orbit computations

1966 ◽  
Vol 25 ◽  
pp. 363-371
Author(s):  
P. Sconzo
Keyword(s):  
Artificial Satellite ◽  
Satellite Orbit ◽  
Artificial Satellites ◽  
Orbital Elements ◽  
Differential Correction ◽  
Gravitational Effects ◽  
Short Intervals ◽  
The Subject ◽  
Introductory Discussion ◽  
Orbit Computation

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.

The Influence of Ascorbic Acid on Platelet Structure and Function

1975 ◽  
Vol 34 (01) ◽  
pp. 050-062
Author(s):  
Dale H Cowan ◽  
Richard C Graham ◽  
Patricia Shook ◽  
Ronda Griffin
Keyword(s):  
Ascorbic Acid ◽  
Open Channel ◽  
Channel System ◽  
Short Intervals ◽  
Platelet Survival ◽  
Artifactual Changes ◽  
Survival Studies ◽  
And Function ◽  
Induced Aggregation ◽  
Platelet Structure

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.

Management of Haemophilia A with Antibodies - The Effect of Combined Treatment with Factor VIII, Hydrocortisone and Cyclophosphamide

1985 ◽  
Vol 54 (04) ◽  
pp. 776-779 ◽  
Author(s):  
U Hedner ◽  
L Tengborn
Keyword(s):  
Factor Viii ◽  
Combined Treatment ◽  
Factor Ix ◽  
Treatment Schedule ◽  
High Antibody ◽  
Anamnestic Response ◽  
Short Intervals ◽  
Low Responders ◽  
Antibody Levels ◽  
High Responders

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.

Mit Initialfemeln zum Plenterwald (Essay) | The creation of selection forest using initial femel cut (essay)

2009 ◽  
Vol 160 (6) ◽  
pp. 137-143
Author(s):  
Rudi Kynast
Keyword(s):  
Mixed Forest ◽  
Point Of View ◽  
Age Group ◽  
Black Forest ◽  
Crown Height ◽  
Short Intervals ◽  
Total Growth ◽  
Cost Calculations ◽  
Selection Forest ◽  
Individual Trees

Although selection forests have clear advantages over age-group forests in view of their total growth performance, their net product and their stability, not to mention the sustainability of their beneficial effect, the proportion of this type of forest is insignificantly small in Germany and also in mixed forest in the mountains. It is therefore all the more surprising that scarcely any discernable efforts have been made to increase the proportion of selection forests. For a conversion, an alternative model for the treatment of the stands is adopted, whereby it is no longer the encouragement of the growth to maturity of individual trees in the stand which is aimed for, but rather the transformation of the whole stand to a selection forest using available stand elements and elements created by an early initiation of regeneration. Based on his experience in the forestry district of Kirchzarten in the Black Forest, Germany, the author describes the procedure for a successful conversion. This is to be started as soon as possible, that is to say when the crown height of the trees is about 18 metres and with corresponding usable dimensions, using small group shelter-wood cuts, a so-called initial femel cut. To get the conversion started it is advisable to remove whole groups of predominantly badly situated and overgrown trees. The stand will be additionally structured later through further interventions at short intervals. In the process, here and there really well situated trees will actually be left to stand solitar y, in other places w hol e self-cont aine d groups will b e created and else where valuabl e mixed s tand elements will be selected for permanent preservation, this in order to create a situation in which there are about 35 overstorey trees per hectare. On the basis of his own cost calculations, the author comes to the conclusion that the conversion is, from a financial point of view, superior compared with the age-group forest in that it brings higher proceeds more quickly and more often.

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