scholarly journals A NOTE ON PRIMES IN SHORT INTERVALS

2006 ◽  
Vol 02 (01) ◽  
pp. 105-110 ◽  
Author(s):  
TSZ HO CHAN
Keyword(s):  
Gaussian Distribution ◽  
Distribution Of Primes ◽  
Short Intervals ◽  
Littlewood Conjecture ◽  
Average Form

Montgomery and Soundararajan obtained evidence for the Gaussian distribution of primes in short intervals assuming a quantitative Hardy–Littlewood conjecture. In this article, we show that their methods may be modified and an average form of the Hardy–Littlewood conjecture suffices.

scholarly journals On the distribution of primes in short intervals

Mathematika ◽  
1976 ◽  
Vol 23 (1) ◽  
pp. 4-9 ◽  
Author(s):  
P. X. Gallagher
Keyword(s):  
Distribution Of Primes ◽  
Short Intervals

scholarly journals The combinatorics of moment calculations

2010 ◽  
Vol Volume 33 ◽  
Author(s):  
hugh L Montgomery
Keyword(s):  
Random Variables ◽  
Distribution Of Primes ◽  
Short Intervals ◽  
International Audience ◽  
Binomial Random Variables

International audience In this paper, we consider the distribution of primes in intervals of length $\asymp\log x$; this leads to insights concerning Poisson random variables. Later, we consider reduced residues $({\rm mod}\,q)$ in short intervals, which similarly motivates us to derive further information concerning moments of binomial random variables. This discussion is extended further, where we consider the distribution of primes in intervals of length $\asymp x^{\theta}$ where $0<\theta<1$. Our analysis gives rise to a family of polynomials.

There is entanglement in the primes

2015 ◽  
Vol 15 (7&8) ◽  
pp. 622-659
Author(s):  
Jose I. Latorre ◽  
German Sierra
Keyword(s):  
Prime Numbers ◽  
Analytical Approximation ◽  
Von Neumann Entropy ◽  
Distribution Of Primes ◽  
Scaling Properties ◽  
Von Neumann ◽  
Quantum Register ◽  
Littlewood Conjecture ◽  
Primality Test ◽  
Quantum Version

Large series of prime numbers can be superposed on a single quantum register and then analyzed in full parallelism. The construction of this Prime state is efficient, as it hinges on the use of a quantum version of any efficient primality test. We show that the Prime state turns out to be very entangled as shown by the scaling properties of purity, Renyi entropy and von Neumann entropy. An analytical approximation to these measures of entanglement can be obtained from the detailed analysis of the entanglement spectrum of the Prime state, which in turn produces new insights in the Hardy-Littlewood conjecture for the pairwise distribution of primes. The extension of these ideas to a Twin Prime state shows that this new state is even more entangled than the Prime state, obeying majorization relations. We further discuss the construction of quantum states that encompass relevant series of numbers and opens the possibility of applying quantum computation to Arithmetics in novel ways.

scholarly journals On the distribution of primes in short intervals

1993 ◽  
Vol 45 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Jerzy KACZOROWSKI ◽  
Alberto PERELLI
Keyword(s):  
Distribution Of Primes ◽  
Short Intervals

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.

Structure images of Si, Ge and Mos2 crystals and some application to radiation damage studies

1978 ◽  
Vol 36 (1) ◽  
pp. 292-293 ◽  
Author(s):  
K. Izui ◽  
T. Nishida ◽  
S. Furuno ◽  
H. Otsu ◽  
S. Kuwabara
Keyword(s):  
Radiation Damage ◽  
Exposure Time ◽  
Gaussian Distribution ◽  
Intensity Distribution ◽  
Chromatic Aberration ◽  
Magnetic Lens

Recently we have observed the structure images of silicon in the (110), (111) and (100) projection respectively, and then examined the optimum defocus and thickness ranges for the formation of such images on the basis of calculations of image contrasts using the n-slice theory. The present paper reports the effects of a chromatic aberration and a slight misorientation on the images, and also presents some applications of structure images of Si, Ge and MoS2 to the radiation damage studies.(1) Effect of a chromatic aberration and slight misorientation: There is an inevitable fluctuation in the amount of defocus due to a chromatic aberration originating from the fluctuations both in the energies of electrons and in the magnetic lens current. The actual image is a results of superposition of those fluctuated images during the exposure time. Assuming the Gaussian distribution for defocus, Δf around the optimum defocus value Δf0, the intensity distribution, I(x,y) in the image formed by this fluctuation is given by

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.

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