The Hamiltonian of a conventional quantum system is Hermitian, which ensures real spectra of the Hamiltonian and unitary evolution of the system. However, real spectra are just the necessary conditions for a Hamiltonian to be Hermitian. In this paper, we discuss the metric operators for pseudo-Hermitian Hamiltonian which is similar to its adjoint. We first present some properties of the metric operators for pseudo-Hermitian Hamiltonians and obtain a sufficient and necessary condition for an invertible operator to be a metric operator for a given pseudo-Hermitian Hamiltonian. When the pseudo-Hermitian Hamiltonian has real spectra, we provide a new method such that any given metric operator can be transformed into the same positive-definite one and the new inner product with respect to the positive-definite metric operator is well defined. Finally, we illustrate the results obtained with an example.

For a group G and $m\ge 1$, let $G^m$ denote the subgroup generated by the elements $g^m$, where g runs through G. The subgroups not of the form $G^m$ are the nonpower subgroups of G. We classify the groups with at most nine nonpower subgroups.

We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their relationship with weak random periodic solutions. In particular, we establish the existence of invariant measures of random dynamical systems by virtue of their weak random periodic solutions. We use concrete examples to illustrate the weak random periodic phenomena of dynamical systems induced by random and stochastic differential equations.

Folate, also known as vitamin B9, is a water-soluble vitamin. Previous studies on dietary folate intake in severe headache patients were equivocal. Therefore, we conducted a cross-sectional study to elucidate the relationship between folate intake and severe headache. This cross-sectional study used data from participants over 20 years old who participated in the National Health and Nutrition Examination Survey (NHANES) from 1999 to 2004. The diagnosis of severe headache was made through participants’ self-report in the NHANES questionnaire section. We performed multivariate logistic regression and restricted cubic spline (RCS) regression to explore the relationship between folate intake and severe headache. A total of 9859 participants took part in the study, 1965 of whom were severe headache patients and the rest were non-severe headache. We found that dietary folate intake was significantly and inversely associated with severe headache. Compared with participants with lower folate intake Q1 (≤ 229·97 ug/d), the adjusted OR values for dietary folate intake and severe headache in Q2 (229·98–337 ug/d), Q3 (337·01–485 ug/d) and Q4 (≥ 485·01 ug/d) were 0·81 (95 % CI: 0·67, 0·98, P = 0·03), 0·93 (95 % CI: 0·77, 1·12, P = 0·41) and 0·63 (95 % CI: 0·49, 0·80, P < 0·001), respectively. For women aged 20–50 years, there was a non-linear association between folate intake and severe headache in the RCS. Women aged 20–50 years should have higher awareness of dietary folate and increase their dietary intake of folate, which may aid in preventing severe headache.

Currently there is lack of knowledge on how new types of alternative fuels and their storage conditions change the droplet evaporation characteristics. Liquid fuel is commonly stored in wide varieties of containers, where fuel characteristics may change because of the exposure to the material of the container. This study evaluates the impact of different storage containers on droplet evaporation characteristics of different fuels. It was found that there is a distinct phase transition between high volatility to low volatility phase in each fuel stored in steel drums verses fuel that is stored in plastic drums. The type of fuel contaminated by polymer additive has a high impact on fuel droplet burn rates. Polymer additives also have an impact on nucleate boiling, sub-droplets and soot particles. The burning rate constant, K, of selected pure aromatics, various fuel mixtures and Jet A with different cetane numbers have been evaluated. Research has shown that in the low volatility combustion phase a trend reduction of lowest boiling point pure aromatic burning rate to the highest boiling point pure aromatic burning rate is obvious. Irregular change in droplet diameter between the high volatility phase and low volatility phase during the combustion of aromatics blend was observed. This work has also evaluated the relationship between burning rates and cetane numbers.

OBJECTIVES/GOALS: Biliary tract cancer is an uncommon, aggressive malignancy. Incidence varies geographically and is highest in East Asia and South America and lowest in Western countries. Previous dietary risk evaluations have primarily been case-control studies. We evaluated associations of dietary intakes with BTC risk in three cohort studies in two countries. METHODS/STUDY POPULATION: We evaluated 638,860 adults in China and the United Kingdom enrolled in the Shanghai Women’s Health Study (SWHS), Shanghai Men’s Health Study (SMHS), or UK Biobank (UKB). Dietary intake information was obtained from study participants at baseline using food frequency questionnaires previously validated for these studies. Dietary intakes of major food groups and macronutrients were divided into low, middle, and high intake tertiles. Cox regression was used to estimate hazard ratios and 95% CIs for biliary tract cancer risk associated with major food groups in all three cohorts and macronutrients in the SWHS and SMHS. Participants were excluded if, at enrollment, they had a history of cancer, CHD, stroke, a total daily Kcal count below 500 or exceeding 3500, or developed cancer or died within one year after enrollment. RESULTS/ANTICIPATED RESULTS: The analyzed cohort includes 558,372 participants: 66,945 SWHS, 55,750 SMHS, and 435,677 UKB participants with median enrollment ages of 49, 52, and 57 years old and median follow-up times of 18.1, 12.3, and 10.3 years, respectively. The SWHS observed 205 eligible BTC cases, SMHS 97, and UKB 366. SWHS and SMHS participants were combined for dietary evaluation and the highest tertile of fruit intake showed an inverse association with biliary tract cancer risk when compared to the lowest tertile: HR 0.74 (95% CI, 0.55-0.99); p-trend 0.044. In UKB, the highest tertile of fish intake was associated with a reduced risk when compared to the lowest tertile: HR 0.76 (95% CI, 0.59-0.98); p-trend 0.034. DISCUSSION/SIGNIFICANCE: High dietary fruit intake was associated with a reduced risk of biliary tract cancer only in SWHS and SMHS. High fish intake was associated with a reduced risk of biliary tract cancer only in UKB. Our findings reflect geographic-based BTC risk variation which we will further explore in our next model accounting for population-specific risk factors.

This paper extends the standard double-exponential jump-diffusion (DEJD) model to allow for successive jumps to bring about different effects on the asset price process. The double-exponentially distributed jump sizes are no longer assumed to have the same parameters; instead, we assume that these parameters may take a series of different values to reflect growing or diminishing effects from these jumps. The mathematical analysis of the stock price requires an introduction of a number of distributions that are extended from the hypoexponential (HE) distribution. Under such a generalized setting, the European option price is derived in closed-form which ensures its computational convenience. Through our numerical examples, we examine the effects on the return distributions from the growing and diminishing severity of the upcoming jumps expected in the near future, and investigate how the option prices and the shapes of the implied volatility smiles are influenced by the varying severity of jumps. These results demonstrate the benefits of the modeling flexibility provided by our extension.

Because of the high photon flux, the Crab nebula pulsar is widely used as the observation target for X-ray pulsar-based navigation. The built profile of the Crab pulsar will change over time, however, which means that the pre-calibrated template cannot be used for the long term. In this paper, a novel pulsar-based template-independent navigation method is proposed. The detected phase propagation model is given as a term of position of the vehicle, taking the orbital motion into account. A different method of time-of-arrival process between the recovered profiles is introduced. With the aid of orbital transition matrix, a measurement model is derived to be a term of velocity error of the vehicle varying with time. The state errors of the vehicle are transformed into velocity errors by performing multi-segment observations to achieve the navigation system observability. The navigation equations of the system are then established and can be solved directly. Some simulations are performed to verify the method and suggest that the proposed method is feasible, effective and easy to implement. The precise orbit information of the vehicle can be determined. The state estimation accuracy is basically consistent with the traditional filtering algorithms, and the computational cost is still very low.

The role of dietary factors in osteoporotic fractures (OFs) in women is not fully elucidated. We investigated the associations between incidence of OF and dietary calcium, magnesium and soy isoflavone intake in a longitudinal study of 48 584 postmenopausal women. Multivariable Cox regression was applied to derive hazard ratios (HRs) and 95 % confidence intervals (CIs) to evaluate associations between dietary intake, based on the averages of two assessments that took place with a median interval of 2⋅4 years, and fracture risk. The average age of study participants is 61⋅4 years (range 43⋅3–76⋅7 years) at study entry. During a median follow-up of 10⋅1 years, 4⋅3 % participants experienced OF. Compared with daily calcium intake ≤400 mg/d, higher calcium intake (>400 mg/d) was significantly associated with about a 40–50 % reduction of OF risk among women with a calcium/magnesium (Ca/Mg) intake ratio ≥1⋅7. Among women with prior fracture history, high soy isoflavone intake was associated with reduced OF risk; the HR was 0⋅72 (95 % CI 0⋅55, 0⋅93) for the highest (>42⋅0 mg/d) v. lowest (<18⋅7 mg/d) quartile intake. This inverse association was more evident among recently menopausal women (<10 years). No significant association between magnesium intake and OF risk was observed. Our findings provide novel information suggesting that the association of OF risk with dietary calcium intake was modified by Ca/Mg ratio, and soy isoflavone intake was modified by history of fractures and time since menopause. Our findings, if confirmed, can help to guide further dietary intervention strategies for OF prevention.

This study evaluated the association between inflammatory diets as measured by the Dietary Inflammatory index (DII), inflammation biomarkers and the development of preeclampsia among the Chinese population. We followed the reporting guidelines of the Strengthening the Reporting of Observational Studies in Epidemiology statement for observational studies. A total of 466 preeclampsia cases aged over 18 years were recruited between March 2016 and June 2019, and 466 healthy controls were 1:1 ratio matched by age (±3 years), week of gestation (±1 week) and gestational diabetes mellitus. The energy-adjusted DII (E-DII) was computed based on dietary intake assessed using a seventy-nine item semiquantitative FFQ. Inflammatory biomarkers were analysed by ELISA kits. The mean E-DII scores were −0·65 ± 1·58 for cases and −1·19 ± 1·47 for controls (P value < 0·001). E-DII scores positively correlated with interferon-γ (r s = 0·194, P value = 0·001) and IL-4 (r s = 0·135, P value = 0·021). After multivariable adjustment, E-DII scores were positively related to preeclampsia risk (P trend < 0·001). The highest tertile of E-DII was 2·18 times the lowest tertiles (95 % CI = 1·52, 3·13). The odds of preeclampsia increased by 30 % (95 % CI = 18 %, 43 %, P value < 0·001) for each E-DII score increase. The preeclampsia risk was positively associated with IL-2 (OR = 1·07, 95 % CI = 1·03, 1·11), IL-4 (OR = 1·26, 95 % CI = 1·03, 1·54) and transforming growth factor beta (TGF-β) (OR = 1·17, 95 % CI = 1·06, 1·29). Therefore, proinflammatory diets, corresponding to higher IL-2, IL-4 and TGF-β levels, were associated with increased preeclampsia risk.

Nosema bombycis is a destructive and specific intracellular parasite of silkworm, which is extremely harmful to the silkworm industry. N. bombycis is considered as a quarantine pathogen of sericulture because of its long incubation period and horizontal and vertical transmission. Herein, two single-chain antibodies targeting N. bombycis hexokinase (NbHK) were cloned and expressed in fusion with the N-terminal of Slmb (a Drosophila melanogaster FBP), which contains the F-box domain. Western blotting demonstrated that Sf9-III cells expressed NSlmb–scFv-7A and NSlmb–scFv-6H, which recognized native NbHK. Subsequently, the NbHK was degraded by host ubiquitination system. When challenged with N. bombycis, the transfected Sf9-III cells exhibited better resistance relative to the controls, demonstrating that NbHK is a prospective target for parasite controls and this approach represents a potential solution for constructing N. bombycis-resistant Bombyx mori.

We investigated the drug resistance of Mycobacterium tuberculosis isolates from patients with tuberculosis (TB) and HIV, and those diagnosed with only TB in Sichuan, China. TB isolates were obtained from January 2018 to December 2020 and subjected to drug susceptibility testing (DST) to 11 anti-TB drugs and to GeneXpert MTB/RIF testing. The overall proportion of drug-resistant TB (DR-TB) isolates was 32.1% (n = 10 946). HIV testing was not universally available for outpatient TB cases, only 29.5% (3227/10 946) cases had HIV testing results. The observed proportion of multidrug-resistant TB (MDR-TB) isolates was almost double than that of the national level, with approximately 1.5% and 0.1% of the isolates being extensively drug resistant and universally drug resistant, respectively. The proportions of resistant isolates were generally higher in 2018 and 2019 than in 2020. Furthermore, the sensitivities of GeneXpert during 2018–2020 demonstrated a downward trend (80.9, 95% confidence intervals (CI) 76.8–85.0; 80.2, 95% CI 76.4–84.1 and 75.4, 95% CI 70.7–80.2, respectively). Approximately 69.0% (7557/10 946) of the TB cases with DST results were subjected to GeneXpert detection. Overall, the DR-TB status and the use of GeneXpert in Sichuan have improved, but DR-TB challenges remain. HIV testing for all TB cases is recommended.

Coronavirus disease-2019 (COVID-19) elicits a range of different responses in patients and can manifest into mild to very severe cases in different individuals, depending on many factors. We aimed to establish a prediction model of severe risk in COVID-19 patients, to help clinicians achieve early prevention, intervention and aid them in choosing effective therapeutic strategy. We selected confirmed COVID-19 patients who were admitted to First Hospital of Changsha city between 29 January and 15 February 2020 and collected their clinical data. Multivariate logical regression was used to identify the factors associated with severe risk. These factors were incorporated into the nomogram to establish the model. The ROC curve, calibration plot and decision curve were used to assess the performance of the model. A total of 228 patients were enrolled and 33 (14.47%) patients developed severe pneumonia. Univariate and multivariate analysis showed that shortness of breath, fatigue, creatine kinase, lymphocytes and h CRP were independent factors for severe risk in COVID-19 patients. Incorporating age, chronic obstructive pulmonary disease (COPD) and these factors, the nomogram achieved good concordance indexes of 0.89 [95% confidence interval (CI) 0.832–0.949] and well-fitted calibration plot curves (Hosmer–Lemeshow test: P = 0.97). The model provided superior net benefit when clinical decision thresholds were between 15% and 85% predicted risk. Using the model, clinicians can intervene early, improve therapeutic effects and reduce the severity of COVID-19, thus ensuring more targeted and efficient use of medical resources.