A robust guaranteed cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, the repetitive controller combined with preview compensator is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed cost preview repetitive control problem is transformed into the guaranteed cost control problem for the augmented dynamic system. For given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) techniques. By incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included to show the effectiveness of the proposed method.

In this paper, a class of semi-linear elliptic equations involving Hardy-Sobolev critical exponents has been investigated. This problem comes from the consideration of standing waves in the anisotropic Schr\"{o}dinger equation, also it is very important in the field of hydrodynamics, glaciology, quantum field theory and statistical mechanics. By a detailed estimation for the extremum function and using Mountain Pass Lemma with $\left( PS\right) _{c}$ conditions, the existence of positive solutions has been obtained. On the other hand, by establishing Pohozaev-type identity and using the properties of Bessel function, the nonexistence of positive solution also has been obtained. These results are extensions of E. Jannelli's research (\cite[Theorem 1.A-1.C]{EJ}).

With the increase of global human activities, a large number of technogenic magnetic particles (TMPs) generated by industrial activities such as coal combustion, traffic and so on enter sediments on continental shelves. However, there is currently a lack of understanding of the spatiotemporal distribution of TMPs on continental shelves, as well as the sedimentary effects they cause. This review work comprehensively analyzes the source, morphology, composition, and spatiotemporal distribution characteristics of TMPs. Then it elucidates their magnetic contribution to sedimentary environments in continental shelf seas, as well as the influence of heavy metals and active iron. At the same time, the existing problems and future development directions of TMPs on continental shelves are summarized.

In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.

Objective: Identify factors associated with excessive day time sleepiness (EDS) in individuals with obstructive sleep apnea (OSA), and analyze the effects that obesity and gender have on excessive daytime sleepiness in such individuals. Methods: A total of 160 people were selected for this study. All the people have completed a clinical evaluation, and whose apnea-hypopnea index (AHI) > 10 events/hour of sleep on polysomnography were included in the study from the Department of otolaryngology. Results: The Mean age was 43.87±11.34 years, mean EDS score was 14.09± 4.91, and mean AHI was 43.88±20.66 events/hour of sleep. Male presented lower mean age, higher EDS scores, and more time in apnoea, whereas females presented with higher mean age, lower EDS scores, and less time in sleep apnea. The EDS score showed best correlation with duration of apnoea (r = 0.448; p < 0.01), peripheral oxygen saturation (SpO₂; r = -0.458; p < 0.01) and AHI (r = 0.484; p < 0.01). The mean body mass index (BMI) was 27.41±3.86 kg/m². Normal, Overweight, obese, and morbidly obese were observed in 20%, 61%, 18%, and 0.6% of cases, respectively. Severity of the disease best correlated with BMI (r = 0.421; p < 0.01). Conclusions: OSA is predominant in males (M/F 5:1), and obese population. Females diagnosed with OSA have higher mean age. However, EDS scores and time spent in sleep apnoea is lower in females. Higher BMI is associated with EDS, irrespective of gender.

For the diagnosis of disease, the ability to quantitatively detect trace amounts of the causal proteins from bacteria/viruses as biomarkers in patient specimens is highly desirable. Here we introduce a simple, rapid, and colorimetric assay as a de novo, ultrasensitive detection method. This ultrasensitive assay consists of sandwich enzyme-linked immunosorbent assay (ELISA) and thionicotinamide-adenine dinucleotide (thio-NAD) cycling, forming an ultrasensitive ELISA, in which the signal substrate (i.e., thio-NADH) accumulates in a triangular manner, and the accumulated thio-NADH is measured at its maximum absorption wavelength of 400 nm. We have successfully achieved a limit of detection of ca. 10–18 moles/assay for a target protein. As an example of infectious disease detection, HIV-1 p24 could be measured at 0.0065 IU/assay (i.e., 10⁻¹⁸ moles/assay), and as a marker for a lifestyle-related disease, adiponectin could be detected at 2.3 × 10⁻¹⁹ moles/assay. In particular, despite the long-held belief that the trace amounts of adiponectin in urine can only be detected using a radioisotope, our ultrasensitive ELISA was able to detect urinary adiponectin. This method is highly versatile, because simply changing the antibody enables the detection of various proteins. This assay system requires only the measurement of absorbance, thus it requires equipment that is easily obtained by medical facilities, which facilitates diagnosis in hospitals and clinics. Moreover, we describe an expansion of our ultrasensitive ELISA to a non-amplification nucleic acid detection method for nucleic acids using hybridization. These de novo methods will enable simple, rapid, and accurate diagnosis.

Terrestrial plant resources are becoming increasingly scarce; moreover, the development of science and technology has facilitated the exploration of marine ecosystems. We isolated and identified six novel (1–6) and six (7–12) known secondary metabolites of Alternaria sp MCCC 3A00467 by chromatographic and spectroscopic techniques and investigated their antitumor activities in human myeloma (U266), liver cancer (HepG2), and lung cancer (A549) cells by the MTT assay. Among these compounds, the new compounds 2, 3 and 4 exhibited excellent anticancer activities with IC₅₀ values of 21.98, 24.99 and 14.78 μg/mL, respectively. These compounds obtained from a marine source have the potential to be developed into novel anticancer drugs.