scholarly journals Gaussian Primes in Narrow Sectors

2021 ◽  
Author(s):  
Joshua Stucky
Keyword(s):  
Short Interval ◽  
Short Intervals ◽  
Brown's Method ◽  
Gaussian Primes

Abstract We generalize a Theorem of Ricci and count Gaussian primes $\mathfrak{p}$ with short interval restrictions on both the norm and the argument of $\mathfrak{p}$. We follow Heath-Brown’s method for counting rational primes in short intervals.

scholarly journals Square-full numbers in short intervals

1991 ◽  
Vol 110 (1) ◽  
pp. 1-3 ◽  
Author(s):  
D. R. Heath-Brown
Keyword(s):  
Positive Integer ◽  
Riemann Hypothesis ◽  
Prime Factor ◽  
Short Interval ◽  
Short Intervals ◽  
Image Position

A positive integer n is called square-full if p2|n for every prime factor p of n. Let Q(x) denote the number of square-full integers up to x. It was shown by Bateman and Grosswald [1] thatBateman and Grosswald also remarked that any improvement in the exponent would imply a ‘quasi-Riemann Hypothesis’ of the type for . Thus (1) is essentially as sharp as one can hope for at present. From (1) it follows that, for the number of square-full integers in a short interval, we havewhen and y = o (x½). (It seems more suggestive) to write the interval as (x, x + x½y]) than (x, x + y], since only intervals of length x½ or more can be of relevance here.)

scholarly journals Systematic Variation in Rhythm Production as Tempo Changes

2017 ◽  
Vol 34 (3) ◽  
pp. 303-312 ◽  
Author(s):  
Scott Barton ◽  
Laura Getz ◽  
Michael Kubovy
Keyword(s):  
Short Interval ◽  
Systematic Variation ◽  
Short Intervals ◽  
Context Dependent ◽  
Rhythm Production ◽  
Production Accuracy

We investigated the effect of tempo on the production of the syncopated 3-2 son clave rhythm. We recorded eleven experienced percussionists performing the clave pattern at tempi ranging from 70 bpm to 210 bpm. As tempo increased, percussionists shortened the longest intervals and lengthened the shortest interval towards an intermediate interval that is located in the first and second positions in the pattern. This intermediate interval was stable across tempi. Contrary to prior studies, we found that the complexity of interval ratios had little effect on production accuracy or stability and the “short” interval in the pattern was not particularly stable. These results suggest that as tempo is varied, (1) experienced musicians systematically distort rhythmic intervals, (2) rhythmic configuration, and not just the complexity of interval ratios, affects the production of rhythmic intervals, and (3) the distinction between long and short intervals is context-dependent.

scholarly journals Comparison of Long and Short High-Intensity Interval Exercise Bouts on Running Performance, Physiological and Perceptual Responses

2017 ◽  
Vol 02 (01) ◽  
pp. E20-E27 ◽  
Author(s):  
Sverre Valstad ◽  
Erna von Heimburg ◽  
Boye Welde ◽  
Roland van den Tillaar
Keyword(s):  
High Intensity ◽  
Short Interval ◽  
Total Duration ◽  
Interval Training ◽  
Running Performance ◽  
Interval Exercise ◽  
Short Intervals ◽  
High Intensity Training ◽  
High Intensity Interval ◽  
Intensity Training

AbstractThis study compared the effects of long (4×4 min) and short intervals (4×8×20 s) of high-intensity interval exercise bouts (HIIT) on running performance, physiological and perceptual responses, and excess postexercise oxygen consumption (EPOC). Twelve healthy college students (8 men, 4 women; mean age=22±2 years) performed long (90–95% of peak heart rate) and short intervals (maximal intensity) of high-intensity training (running on a non-motorized treadmill) with the same total duration on separate days. The total volume of consumed oxygen during recovery was the same in both cases (P=0.21), whereas the short intervals of high-intensity training were performed at a faster mean running velocity (3.5±0.18 vs. 2.95±0.07 m/s) and at a lower RPEbreath compared with the long intervals of high-intensity training. The blood lactate concentration also tended to be lower during the short intervals of high-intensity training, indicating that short-interval training was perceived to be easier than long-interval training, even though the cardiovascular and metabolic responses are similar. Furthermore, EPOC lasted significantly longer (83.4±3.2 vs. 61.3±27.9 min, P=0.016) and tended to be higher (8.02±4.22=vs. 5.70±3.75 L O2, P=0.053) after short intervals than after long intervals of training.

The Effect of Knowledge of Results on Learning and Performance IV. The Direction of the Error in Very Simple Skills

1951 ◽  
Vol 3 (1) ◽  
pp. 36-42 ◽  
Author(s):  
Valerie Dees ◽  
G. C. Grindley
Keyword(s):  
Short Interval ◽  
The Other ◽  
Time Interval ◽  
Knowledge Of Results ◽  
Short Intervals ◽  
Visual Knowledge ◽  
Other Hand ◽  
The Subject ◽  
And Performance ◽  
Learning And Performance

Re-examination of the data discussed in previous papers of this series shows a greater tendency toward “overshooting” when the time interval between trials, in some of the experiments, is short than when it is longer. The subject tends to make a bigger movement or exert more pressure with short intervals. This seems to be true with or without visual knowledge of results. On the other hand, with the experiments in which the task was to press a key for a given short interval, the effect was not conclusively shown. A hypothesis is put forward to explain these results in terms of proprioceptive adaptation.

scholarly journals On the asymptotic formulae for some multiplicative functions in short intervals

2015 ◽  
Vol 11 (05) ◽  
pp. 1571-1587 ◽  
Author(s):  
Alisa Sedunova
Keyword(s):  
Short Interval ◽  
Multiplicative Functions ◽  
Density Estimates ◽  
Mean Values ◽  
Short Intervals ◽  
Asymptotic Formulae ◽  
Free Region ◽  
Complex Integration ◽  
The Mean ◽  
Riemann Ζ Function

We are going to study the mean values of some multiplicative functions connected with the divisor function in short interval of summation. The asymptotics for such mean values will be proved. Considering instead of well-known multiplicative functions, their inverses lead to very weak results of application of standard methods of complex integration. In order to get better estimations, we propose another method which uses as its main tools the density estimates and zero-free region for Riemann ζ-function and Dirichlet L-functions.

Influence of short-interval fire occurrence on post-fire recovery of fire-prone shrublands in California, USA

2013 ◽  
Vol 22 (2) ◽  
pp. 184 ◽  
Author(s):  
Caitlin L. Lippitt ◽  
Douglas A. Stow ◽  
John F. O'Leary ◽  
Janet Franklin
Keyword(s):  
Life Histories ◽  
Fire History ◽  
Short Interval ◽  
Fire Regimes ◽  
Fire Frequency ◽  
Natural Occurrence ◽  
Contributing Factors ◽  
Type Conversion ◽  
Short Intervals ◽  
Mean Fire Interval

In recent decades, fire frequency has increased with population growth at the wildland–urban interface in southern California, USA. Short intervals (<5 years) between successive fires can be detrimental to plant species that require longer intervals between fires to reach reproductive maturity. The resilience of vegetation to changes in fire regimes is of particular interest for shrublands in Mediterranean climates, which in general are susceptible to high frequencies of wildfire. Research on how fire has shaped the life histories of shrubs in Mediterranean climates is central to understanding how to protect sensitive habitat while allowing for the natural occurrence of wildfire in these regions. Frequently burned chamise chaparral shrublands in San Diego County, California, were mapped in the field with the aid of satellite imagery and analysed to investigate changes in vegetation condition and composition associated with short intervals between fires. Fire history, terrain and land-cover characteristics of mapped stands were tested to determine the factors associated with disturbed and converted vegetation. Results indicate that number of burns and mean fire interval are contributing factors in post-fire change in chaparral stands. Chamise chaparral is vulnerable to alteration and type conversion when fire return intervals are 4–5 years or less.

scholarly journals Studies on the flexor reflex.—II. The reflex response evoked by two centripetal volleys

1931 ◽  
Vol 107 (754) ◽  
pp. 535-556 ◽  
Keyword(s):  
Refractory Period ◽  
Short Interval ◽  
Afferent Nerve ◽  
Reflex Response ◽  
Flexor Reflex ◽  
Central Effects ◽  
Reflex Pathway ◽  
Short Intervals ◽  
Reflex Arc ◽  
Set Up

When an afferent nerve is stimulated by two similar break-shocks at a sufficiently short interval, it has been found that the ensuing reflex response is no greater than the response to a single break-shock. The shortest interval at which the second stimulus produces an additional response has been called “the least interval for muscular summation” (Adrian and Olmsted, 1922). Different observes have found fairly comparable values for this interval in the mammalian preparation: 0·75 σ to 1·31 σ (Sherrington and Sowton, 1915); 1·2 σ to 2·4 σ (Adrian and olmsted, 1922); 1·0 σ to 2·4 σ (Forbes, Querido, Whitaker and Hurxthal, 1928). It was at first thought that the ineffectiveness of the second stimulus at intervals less that “the least interval” was due to a refractory period of the central part of the reflex arc; consequently the “least interval” was used as a measure of the duration of the absolutely refractory period of the reflex arc. Forbes (1922), however, pointed out that the duration of the “least interval” was similar to the duration of the absolutely refractory period of the afferent nerve ( cf . Sherrington, 1921, p. 257), and concluded that the ineffectiveness of the second stimulus was probably due to its inability to set up centripetal impulses in the afferent nerve, and not to a blocking of such impulses by a refractory period in some part of the central reflex pathway. Later (1928) Forbes and his co-workers suggested that the reflex response added by the second centripetal volley, when it followed the first at very short intervals, might not be due to a second discharge of those motoneourones which had already responded to the first volley. Other motoneurones might be excited by summation of the central effects of the two centripetal volleys. If that were so, “the least interval for muscular summation” would have no relation to the refractory period of the reflex pathway.

scholarly journals Factors Associated with Inadequate Birth Intervals in the BRISA Birth Cohort, Brazil

2020 ◽  
Vol 42 (02) ◽  
pp. 067-073
Author(s):  
Raphael Barbosa ◽  
Maria Teresa Seabra Soares Britto Alves ◽  
Ian Nathasje ◽  
Deysianne Chagas ◽  
Vanda Ferreira Simões ◽  
...  
Keyword(s):  
Gestational Diabetes ◽  
Birth Interval ◽  
Multinomial Logistic Regression ◽  
Short Interval ◽  
Univariate Analysis ◽  
P Value ◽  
Birth Intervals ◽  
Short Intervals ◽  
Factors Associated ◽  
Prenatal Visits

Abstract Objective To determine the prevalence of inadequate birth interval and its associated factors in the BRISA study. Methods Cross-sectional study using data from the BRISA cohort. Birth interval was categorized into “adequate” (≥ 2 years or < 5 years between births), “short interval” (< 2 years) and “long interval” (≥ 5 years). The analysis of the factors associated with short and long birth intervals used multinomial logistic regression. Results The prevalence of adequate birth intervals was 48.3%, of long intervals, 34.6%, and of short intervals, 17.1%. Skin color, age, education level, economic status, type of delivery, number of prenatal visits, parity, blood pressure, diabetes, and anemia (p-value was < 0.2 in the univariate analysis) proceeded to the final model. The variable ≥ 3 births (odds ratio [OR] = 1.29; confidence interval [CI]: 1.01–1.65) was associated with short intervals. Age < 20 years old (OR = 0.48; CI: 0.02–0.12) or ≥ 35 years old (OR = 2.43; CI: 1.82–3.25), ≥ 6 prenatal visits (OR = 0.58; CI: 0.47–0.72), ≥ 3 births (OR = 0.59; CI: 0.49–0.73), and gestational diabetes (OR = 0.38; CI: 0.20–0.75) were associated with long intervals. Conclusion Older mothers were more likely to have long birth intervals, and higher parity increases the chances of short birth intervals. Furthermore, gestational diabetes and adequate prenatal care presented higher chances of having adequate birth intervals, indicating that health assistance during pregnancy is important to encourage an adequate interval between gestations.

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 $H = N^{\theta }, \theta&gt; 2/3$ and $k \geq 1$. We obtain estimates for the following exponential sum over primes in short intervals: \begin{equation*} \sum_{N &lt; 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.

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