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In this paper, we give some extensions for Mortenson’s identities in series with the Bell polynomial using the partial fraction decomposition. As applications, we obtain some combinatorial identities involving the harmonic numbers.

Background: Patients with chronic obstructive pulmonary disease (COPD) are more susceptible to Aspergillus colonization or infection. Several studies have demonstrated that invasive pulmonary Aspergillosis (IPA) and Aspergillus hypersensitivity (AH) have a detrimental effect on COPD. However, it remains to be clarified whether Aspergillus colonization is associated with acute exacerbation of COPD (AECOPD). This study aimed to explore the impact of Aspergillus colonization in the lower respiratory tract on AECOPD. Method: Patients with Aspergillus colonization were identified from a retrospective cohort of hospitalized AECOPD from 2011 to 2016 in eight centers in Shanghai, China. The demographic information, conditions of the stable stage, clinical characteristics during hospitalization, and 1-year follow-up information after discharge were collected and compared to participants without fungi colonization. Result: Twenty-six hospitalized AECOPD patients with Aspergillus colonization and 72 controls were included in the final analysis after excluding patients with other fungi isolation and matching. The rates of recurrence of acute exacerbation within 90 days and 180 days after discharge in the patients with Aspergillus colonization were both significantly higher than that in the fungi negative patients (90 days: 19.2 vs. 4.2%, p = 0.029; 180 days: 23.1 vs. 4.2%, p = 0.010), and the all-cause mortality within 1 year was also higher (11.5 vs. 0.0%, p = 0.017). Multivariate logistic regression analysis showed that Aspergillus colonization was an independent risk factor for the recurrence of acute exacerbation within 90 days and 180 days (90 days: OR = 8.661, 95% CI: 1.496-50.159, p = 0.016; 180 days: OR =10.723, 95% CI: 1.936-59.394, p = 0.007). Conclusion: Aspergillus colonization may predict poor prognosis of AECOPD while leading to an increased risk of recurrent AECOPD in a short period.

Background Acute uncomplicated lower urinary tract infection (UTI) is one of the most common bacterial infections. Patients usually present with dysuria, urinary urgency, urinary frequency, and suprapubic pain or tenderness. Approximately 150 million people are diagnosed with UTI each year worldwide. The high recurrence rate of lower UTI is a common problem of clinical treatment. The misuse of antibiotics has led to the emergence of a number of resistant bacterial strains. Thus, traditional Chinese medicine is considered as an alternative option for treating acute uncomplicated lower UTI. Thus, this study aims to evaluate the efficacy and safety of Sanjin tablets (SJT) for the treatment of acute uncomplicated lower UTI, explore whether SJT can reduce or substitute the use of antibiotics, and reduce the recurrence rate in the treatment of acute uncomplicated lower UTI. Methods/design In this study, a randomized, double-blind, double-dummy, parallel control of positive drug, multicenter clinical study will be established. A total of 252 patients with acute uncomplicated lower UTI (syndrome of dampness-heat in the lower jiao) will be randomly allocated in the ratio of 1:1:1 to three groups: experimental group; control group 1; and control group 2. The experimental group receives Sanjin tablets plus levofloxacin tablets (LT) placebo; the control group 1 receives LT plus SJT placebo; and the control group 2 receives SJT plus LT on the first five days, SJT plus LT placebo on the last two days. Each group will be treated for seven days and followed-up 1–2 times. The primary outcome measures of effective rate and recurrence rate are symptoms. Secondary outcome measures of effective rate and recurrence rate are the urine leukocytes, bacteriology examination, and safety assessment. Outcomes will be assessed at baseline and after treatment. Discussion This study protocol will provide the research data of efficacy and safety of SJT for the treatment of acute uncomplicated lower UTI. The first aim is to determine whether Sanjin tablets can reduce the use of antibiotics; the second aim is to determine whether Sanjin tablets can substitute the use of antibiotics. The recurrence rate will be assessed after cured to determine whether SJT can reduce the recurrence rate. The results of this study will improve the rational use of drugs, especially the rational application of antibiotics. It will also enable safety evaluation from laboratory indices and adverse events, which will provide reliable evidence for clinical treatment. Trial registration ClinicalTrials.gov, NCT03658291 . Registered on 4 September 2018.

To explore impact of on the acute exacerbation of chronic obstructive pulmonary disease (AECOPD) outcome. A retrospective, multi-center, case-control study was performed. Patients hospitalized for AECOPD in 25 centers during Jan 2011-Dec 2016 were enrolled. Data were collected, including demographic information, conditions during the stable phase of COPD, clinical characteristics of AECOPD, and follow-up information within 1 year after discharge. Univariate analysis and binary logistic regression were applied, and < 0.05 was regarded as significant. Totally 1,103 patients were analyzed, with 644 lower respiratory airway (LTR) positive cases and 459 negative controls. Long-term prognosis was significantly different between positive and negative group, including the recurrent AECOPD within 180 days (75.5 vs. 6.6%, < 0.001) and mortality within 1 year (6.9 vs. 0.4%, < 0.001). Univariate logistic analysis showed that LTR isolation was related to higher recurrence rate of AECOPD within 180 days and mortality within 1 year. Binary logistic regression analysis demonstrated that LTR isolation was independently associated with recurrence of AECOPD within 180 days. LTR isolation was associated with worse long-term prognosis of AECOPD and independently related to higher risks of recurrent AECOPD within 180 days.

In 1915, Ramanujan stated the following formula ∫ 0 ∞ t x − 1 ( − a t ; q ) ∞ ( − t ; q ) ∞ d t = π sin π x ( q 1 − x , a ; q ) ∞ ( q , a q − x ; q ) ∞ , where 0 < q < 1 , x > 0 , and 0 < a < q x . The above formula is called Ramanujan’s beta integral. In this paper, by using q-exponential operator, we further extend Ramanujan’s beta integral. As some applications, we obtain some new integral formulas of Ramanujan and also show some new representation with gamma functions and q-gamma functions.

In this paper, by using the Euler-Maclaurin expansion, we establish an inequality of a weight coefficient. Using this inequality, we derive a reverse Hilbert's type inequality. As applications, an equivalent form is obtained.

By observing that the infinite triangle obtained from some generalized harmonic numbers follows a Riordan array, we using connections between the Stirling numbers of both kinds and other inverse generalized harmonic numbers. we proved some combinatorial sums and inverse generalized harmonic number identities.

The purposeof this paper is to establish on a generalization of Hilbert’s inequality and its reinforcement.

Linewidth narrowing and other quantum coherent effects based on three-photon coherent population trapping （CPT） in Ca＋ ions are investigated. If the propagation directions of the three lasers obey the phase matching condition, the dark linewidth resulting from the CPT can be very narrow, and it can be controlled by adjusting the parameters of the lasers.