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In this paper, we consider universality in short intervals for the zeta-function attached to a normalized Hecke-eigen cusp form with respect to the modular group. For this, we apply a conjecture for the mean square in short interval on the critical strip for that zeta-function. The proof of the obtained universality theorem is based on a probabilistic limit theorem in the space of analytic functions. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is utilizing the analytic methods to study Hybrid mean value including the character, the general trigonometric sums, and the general quadratic Gauss sums, then obtain several mean value asymptotic formulae. [ABSTRACT FROM AUTHOR]

In this paper, we give a detailed proof of an asymptotic formula for averages of coefficients of a class of degree seven L -functions which can be factorized as a product of degree one and degree six L -functions. We can break the 3/4-barrier in the error term and get an explicit exponent 3 4 − 307 85172 + ε. Our proof relies on methods from the theory of exponential sums. [ABSTRACT FROM AUTHOR]

The paper is devoted to methods of solution of binary additive problems with semiprime numbers, which form sufficiently "rare" subsequences of the natural series. Additional conditions are imposed on these numbers; the main condition is belonging to so-called Vinogradov intervals. We solve two problems that are analogs to the Titchmarsh divisor problem; namely, based on the Vinogradov method of trigonometric sums, we obtain asymptotic formulas for the number of solutions to Diophantine equations with semiprime numbers of a specific form. [ABSTRACT FROM AUTHOR]

In this note, we give a detailed proof of an asymptotic for averages of coefficients of a class of degree three L-functions which can be factorized as a product of a degree one and a degree two L-functions. We emphasize that we can break the 1/2-barrier in the error term, and we get an explicit exponent. Our proof relies on methods from the theory of exponential sums. [ABSTRACT FROM AUTHOR]

OBJECTIVES: Short time between consecutive work shifts (quick returns, ie, ≤11 hours between shifts) is associated with sleepiness and fatigue, both of which have been linked to risk of injury. This paper aims to study quick returns between work shifts and risk of injury among Danish hospital workers. METHOD: The study population included 69 200 employees, primarily working at hospitals, corresponding to 167 726 person years at risk between 2008–2015. Information on working hours was obtained from payroll data in the Danish Working Hour Database and linked, at an individual level, with data on 11 834 injury records identified in the National Patient Register and the Danish Register of Causes of Death. Multivariate Poisson regression models were used to calculate incidence rate ratios (IRR) with 95% confidence intervals (CI). RESULTS: Results showed the shorter the time between shifts, the higher the risk of injury. Thus, an elevated risk of injury was observed after quick returns compared with the standard 15–17 hours between shifts (IRR 1.39, 95% CI 1.23–1.58). Furthermore, when assessing the number of days since a quick return, the risk of injury was especially high within the first two days (day 1: IRR 1.39, 95% CI 1.23–1.58; day 2: IRR 1.39, 95% CI 1.21–1.58) following a quick return. CONCLUSIONS: Our results suggest that quick returns increased the risk of injury, in particular within the first two days following a quick return. These findings point towards avoiding or reducing the number of quick returns in order to lower employees’ risk of injury.

Let N be a sufficiently large integer. We prove that almost all sufficiently large even integers n ∈ [N − 6U, N + 6U] can be represented as { n = p 1 2 + p 2 3 + p 3 3 + p 4 3 + p 5 3 + p 6 3 | p 1 2 − N 6 | ≤ U , | p i 3 − N 6 | ≤ U , i = 2 , 3 , 4 , 5 , 6 where U = N1−δ+ε with δ ⩽ 8/225. [ABSTRACT FROM AUTHOR]

Let n > 1 be an integer. Φ(e)(n) is a multiplicative function. The integer d = Пsi=1 pbii is called an exponential divisor of n = Пsi=1 paii, if bi|ai for every i ∊ {1; 2; ...; s}. Let Φ(e)(n) denote the number of divisors d of n such that d and n have no common exponential divisors. The aim of the paper is to establish a short interval for r-th power of the function Φ(e)(n) for any fixed integer r ≥ 1. [ABSTRACT FROM AUTHOR]

If bi|ai for every i ∊ {1; 2; ...; s}, then the integer d = Пsi=1 pbii is called an exponential divisor of n = Пsi=1 paii > 1. The number of exponential divisors of n is denoted by Ƭ(e)(n). Similarly to the generalization of dk(n) from d(n), Ƭ(e)(n) can be extended to Ƭ(e)k (n). In this paper, we shall establish a short interval result for the function (Ƭ(e)3 (n))-r. [ABSTRACT FROM AUTHOR]

Assume that K is Gaussian field, and a K (n) is the number of non-zero integral ideals in Z [ i ] with norm n . We establish an Erdős–Kac type theorem weighted by a K (n 2) l (l ∈ Z +) in short intervals. We also establish an asymptotic formula for the average behavior of a K (n 2) l in short intervals. [ABSTRACT FROM AUTHOR]

The study aimed to (a) typify the cardiorespiratory, metabolic, and performance responses during a single sprint interval training (SIT) session, (b) investigate the interference of 2 subsequent sessions on cardiorespiratory, metabolic, and performance responses, and (c) verify the relationships of SIT total work performed with aerobic fitness indices. Thirty-six untrained men performed 2 SIT sessions (SIT1 and SIT2) separated by 24 hours of recovery. Each session was composed of 4 Wingate bouts interspersed by 4 minutes. Within SIT sessions, bout work, peak power, and mean power of each Wingate bout decreased significantly, while the fatigue index increased over time (p < 0.001). The SIT elicited lower acute responses of oxygen uptake and heart rate than maximal values (≈67 and ≈79%, respectively) (p < 0.05) as well as a short time spent at high cardiorespiratory demand. For SIT outcomes, no interactions were verified between Wingate bout performance, average heart rate, and average oxygen uptake. In addition, the oxygen uptake integral (SIT1:300.5 ± 38.6 ml·kg; SIT2:306.9 ± 41.1 ml·kg) and total work (SIT1:54.6 ± 10.4 kJ; SIT2:54.9 ± 10.6 kJ) did not differ between SIT sessions (p > 0.05). Furthermore, significant moderate to strong correlations were found between SIT1 and SIT2 total work and peak oxygen uptake (r = 0.48; r = 0.52, respectively), maximal aerobic power (r = 0.89; r = 0.89, respectively), and respiratory compensation point (r = 0.80; r = 0.78, respectively). In summary, an SIT session elicited a short time spent at high cardiorespiratory demand, while the SIT total work was significantly correlated with aerobic fitness indices. In addition, 2 consecutive SIT sessions interspaced by 24 hours did not affect performance outcomes, or cardiorespiratory and blood responses. [ABSTRACT FROM AUTHOR]

Let n > 1 be an integer. The integer d ... is called an exponential divisor of ... i, if bijai for every i ∈ 1; 2; ...; s. Let τ(e)(n) denote the exponential divisor function. Similar to the generalization from d(n) to dk(n), τ(e)(n) can be extended to .... In this paper, we investigate the case k = 3 and establish a short interval result for the r -th power of the function τ3(e) 3 (n). [ABSTRACT FROM AUTHOR]

Summary: Intervals between dual-energy X-ray absorptiometry (DXA) scans were evaluated in a large cohort of typical clinical practice. Intensive DXA scanning (intervals < 23 months) decreased substantially, from 16.7% in 2006 to 6.7% in 2015. Introduction: Serial dual-energy X-ray absorptiometry (DXA) measurements are suggested for patients at high risk of fractures. However, little is known about how often DXA testing occurs in clinical practice. Methods: We examined time intervals between DXA testing for monitoring purpose at two academic medical centers in the US between 2004 and 2017. The primary outcome was the presence of testing intervals < 23 months (termed "intensive DXA testing"). A generalized linear mixed model was used to evaluate the association between selected patient-level clinical factors and intensive DXA testing. Results: Forty-nine thousand four hundred ninety-four DXA tests from 20,200 patients were analyzed. The mean time interval between scans was 36 ± 21 months. Only 11.1% of the repeated DXA testing met the criterion for intensive testing. The percentage of intensive DXA testing dropped from 16.7% in 2006 to 6.7% in 2015 (p for trend < 0.001). After adjusting for age, gender, number of outpatient visits, and calendar year, correlates of intensive DXA testing included a baseline T-score < −2.5 at any anatomic site (OR, 4.8; 95%CI, 4.0–5.7), active use of drugs for osteoporosis (OR, 1.6; 95%CI, 1.3–1.9), and active use of glucocorticoids (OR, 1.3; 95%CI, 1.2–1.4). Conclusions: The predictors of intensive DXA testing suggest that this practice is used preferentially in patients with multiple risk factors and to monitor the response to pharmacotherapy. However, intensive DXA testing has become less common in real-world clinical practice over the last decade. Further studies are required to better define the optimal use of bone mineral density testing in this vulnerable population. [ABSTRACT FROM AUTHOR]

Objectives Short time between consecutive work shifts (quick returns, ie, =11 hours between shifts) is associated with sleepiness and fatigue, both of which have been linked to risk of injury. This paper aims to study quick returns between work shifts and risk of injury among Danish hospital workers. Method The study population included 69 200 employees, primarily working at hospitals, corresponding to 167 726 person years at risk between 2008-2015. Information on working hours was obtained from payroll data in the Danish Working Hour Database and linked, at an individual level, with data on 11 834 injury records identified in the National Patient Register and the Danish Register of Causes of Death. Multivariate Poisson regression models were used to calculate incidence rate ratios (IRR) with 95% confidence intervals (CI). Results Results showed the shorter the time between shifts, the higher the risk of injury. Thus, an elevated risk of injury was observed after quick returns compared with the standard 15-17 hours between shifts (IRR 1.39, 95% CI 1.23-1.58). Furthermore, when assessing the number of days since a quick return, the risk of injury was especially high within the first two days (day 1: IRR 1.39, 95% CI 1.23-1.58; day 2: IRR 1.39, 95% CI 1.21-1.58) following a quick return. Conclusions Our results suggest that quick returns increased the risk of injury, in particular within the first two days following a quick return. These findings point towards avoiding or reducing the number of quick returns in order to lower employees' risk of injury. [ABSTRACT FROM AUTHOR]

Let n> 1 be an intrger, κ(e)(n) denote the maximal e-squarefree e-divisor of n. In this paper, we shall establish a short interval result for the function κ(e)(n). [ABSTRACT FROM AUTHOR]

Let $${\mathcal {L}}$$ be the set of integers n which can be written as Using the circle method and sieves, we prove that $${\sum_{N < n \leq N+Y , {n\in \mathcal {L}}} 1\geq \gamma Y}$$ holds for $${Y=N^{17/18}}$$ , where $${\gamma > 0}$$ is an absolute constant. [ABSTRACT FROM AUTHOR]

Treatment strategies for advanced knee osteoarthritis with coexistent joint infection are not well established. While in periprosthetic joint infection the two-stage approach has been studied extensively, only few case reports on two-stage total knee arthroplasty (TKA) for knee osteoarthritis with coexistent joint infection have been published. The purpose of this paper was to report on our method of implementing a two-stage TKA with intervening antibiotic-loaded articulating cement spacers and a short interval between first- and second-stage procedures to treat two patients with Staphylococcus aureus-infected end-stage knee osteoarthritis. Consistent infection eradication was found at a 1-year follow-up with postoperative range of motion and knee scores comparing favourably with those of other case series. Level of evidence V. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Hip joint replacement is 1 of the most successful surgical procedures of the last century and the number of replacements implanted is steadily growing. An infected hip arthroplasty is a disaster, it leads to patient suffering, surgeon's frustration and significant costs to the health system. The treatment of an infected hip replacement is challenging, healing rates can be low, functional results poor with decreased patient satisfaction. However, if a patient-adapted treatment of infected hip joints is used a success rate of above 90% can be obtained. Patient-adapted treatment is based on 5 important concepts: teamwork; understanding the biofilm; diagnostic accuracy; correct definition and classification of PJI; and patient-tailored treatment. This review presents a patient-adapted treatment strategy to prosthetic hip infection. It incorporates the best aspects of the single and staged surgical strategies and promotes the short interval philosophy for the 2-stage approach. [ABSTRACT FROM AUTHOR]

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As the fast economic development and urban expansion, it is difficult for traditional methods to monitor land use changes in short time interval. Moreover, remotely sensed data acquired by optical sensors is often limited by bad weathers and cloud cover. SAR images, such as RADARSAT-1, are an ideal tool for weather-proof observation on ground surface. This paper analyzed the results of land use change detections with time lags of 24, 48 and 72 days according to the period of acquisition dates of RADARSAT-1. The results need a compromise between accuracies and efficiencies related to the time lags. For most of the situation, it is sufficient of using a time lag of 24 days to obtain accuracy of 60% or above. In some cases of months, a time lag of 48 days is needed. For obtaining higher accuracies, longer time lag such as 72 days is needed. [ABSTRACT FROM AUTHOR]

We study the 'symmetry integral', say $$I_f$$, of some arithmetic functions $$f:\mathbb{N }\rightarrow \mathbb{R }$$; we obtain from lower bounds of $$I_f$$ (for a large class of arithmetic functions $$f$$) lower bounds for the 'Selberg integral' of $$f$$, say $$J_f$$ (both these integrals give informations about $$f$$ in almost all the short intervals $$[x-h,x+h]$$, when $$N\le x\le 2N$$). In particular, when $$f=d_k$$, the divisor function (having Dirichlet series $$\zeta ^k$$, with $$\zeta $$ the Riemann zeta function), where $$k\ge 3$$ is integer, we give lower bounds for the Selberg integrals, say $$J_k=J_{d_k}$$, of the $$d_k$$. We apply elementary methods (Cauchy inequality to get Large Sieve type bounds) in order to give $$I_f$$ lower bounds. [ABSTRACT FROM AUTHOR]

We prove that almost all integers N satisfying some necessary congruence conditions are the sum of almost equal fourth prime powers. [ABSTRACT FROM AUTHOR]

Let τ(e) (n) denote the number of exponential divisor of n. Similar to the general- ization from d(n) to dk(n), we extended τ(e) (n) to τke(n)k-1 τ3e (n))². The aim of this paper is to establish a short interval result for the function (¿ (e) 3 (n))2. This enriches the properties of the exponential divisor function. [ABSTRACT FROM AUTHOR]

Let p be a prime, χ denote the Dirichlet character modulo p and $L(p)=\{a\in {\mathbb{Z}}^{+}|(a,p)=1,a\bar{a}\equiv 1(\bmod\ p),|a-\bar{a}|\le H\}$. We study the distribution of elements in the set L( p) in character over the short interval. In this paper, we use the analytic method and show the distribution property of and give a non-trivial estimate. [ABSTRACT FROM AUTHOR]

Let n > 1 be an integer, φ(e)(n) is a multiplicative function. In this paper, we shall establish a short interval result for the function φ(e)(n). [ABSTRACT FROM AUTHOR]

Let a(n) denote the number of nonisomorphic Abelian groups with n elements. In this paper, we shall establish a short internal result of a2(n). [ABSTRACT FROM AUTHOR]

Let t(e)(n) denote the number of e-squarefree e-divisor of n. The aim of this paper is to establish a short interval result for the function (t(e)(n))r. This enriches the properties of the e-squarefree e-divisor function. [ABSTRACT FROM AUTHOR]

let n > 1 be an integer, gcd(a, b) denote the greatest commom divisor of a and b. A(n) denotes the arithmetic mean of gcd(1, n), ..., gcd(n, n). In this paper, we shall establish a short interval result for the function A(n). [ABSTRACT FROM AUTHOR]

In this paper we shall establish a short interval result for the Smarandache ceil function and the Dirichlet divisor function by the convolution method. [ABSTRACT FROM AUTHOR]

Let $\mathcal{H}_{k}$ denote the set { n∣2| n, $n\not\equiv 1\ (\mathrm{mod}\ p)$ ∀ p>2 with p−1| k}. We prove that when $X^{\frac{11}{20}\left(1-\frac{1}{2k}\right) +\varepsilon}\leqq H\leqq X$, almost all integers $n\in\allowbreak {\mathcal{H}_{k} \cap (X, X+H]}$ can be represented as the sum of a prime and a k-th power of prime for k≧3. Moreover, when $X^{\frac{11}{20}\left(1-\frac{1}{k}\right) +\varepsilon}\leqq H\leqq X$, almost all integers n∈( X, X+ H] can be represented as the sum of a prime and a k-th power of integer for k≧3. [ABSTRACT FROM AUTHOR]

Abstract: Imaging biomarkers are useful outcome measures in treatment trials. We compared sample size estimates for future treatment trials performed over 6 or 12-months in progressive supranuclear palsy using both imaging and clinical measures. We recruited 16 probable progressive supranuclear palsy patients that underwent baseline, 6 and 12-month brain scans, and 16 age-matched controls with serial scans. Disease severity was measured at each time-point using the progressive supranuclear palsy rating scale. Rates of ventricular expansion and rates of atrophy of the whole brain, superior frontal lobe, thalamus, caudate and midbrain were calculated. Rates of atrophy and clinical decline were used to calculate sample sizes required to power placebo-controlled treatment trials over 6 and 12-months. Rates of whole brain, thalamus and midbrain atrophy, and ventricular expansion, were increased over 6 and 12-months in progressive supranuclear palsy compared to controls. The progressive supranuclear palsy rating scale increased by 9 points over 6-months, and 18 points over 12-months. The smallest sample size estimates for treatment trials over 6-months were achieved using rate of midbrain atrophy, followed by rate of whole brain atrophy and ventricular expansion. Sample size estimates were further reduced over 12-month intervals. Sample size estimates for the progressive supranuclear palsy rating scale were worse than imaging measures over 6-months, but comparable over 12-months. Atrophy and clinical decline can be detected over 6-months in progressive supranuclear palsy. Sample size estimates suggest that treatment trials could be performed over this interval, with rate of midbrain atrophy providing the best outcome measure. [Copyright &y& Elsevier]

let n > 1 be an integer, log ρ(n) denote the number of regular integers m(mod n) such that1 ≤ m ≤ n. In this paper we shall establish a short interval result for the function log ρ(n). [ABSTRACT FROM AUTHOR]

The integer d = Πs i=1 pbi i is called an exponential divisor of n = Πs i=1 pai i > 1 if bi∣ai for every i ϵ {1, 2, …, s}. The exponential convolution of aithmetic functions is defined by (f ʘ g)(n) = Σb1c1-a1 &#x2026 Σ brcr=ar = f(pb1 1 … pbr r)g(pc1 1 … pcr r), where n = Πs i=1 pai i. The inverse of the constant function with respect to ʘ is called the exponential analogue of the Möbius function, which is denoted by μ(e). The aim of this paper is to establish a short interval result for the function μ(e). [ABSTRACT FROM AUTHOR]