Let $\mu _{M,D}$ be the self-similar measure generated by $M=RN^q$ and the product-form digit set $D=\{0,1,\ldots ,N-1\}\oplus N^{p_1}\{0,1,\ldots ,N-1\}\oplus \cdots \oplus N^{p_s}\{0,1,\ldots ,N-1\}$, where $R\geq 2$, $N\geq 2$, q, $p_i(1\leq i\leq s)$ are integers with $\gcd (R,N)=1$ and $1\leq p_1<p_2<\cdots <p_s<q$. In this paper, we first show that $\mu _{M,D}$ is a spectral measure with a model spectrum $\Lambda $. Then, we completely settle two types of spectral eigenvalue problems for $\mu _{M,D}$. In the first case, for a real t, we give a necessary and sufficient condition under which $t\Lambda $ is also a spectrum of $\mu _{M,D}$. In the second case, we characterize all possible real numbers t such that $\Lambda '\subset \mathbb {R}$ and $t\Lambda '$ are both spectra of $\mu _{M,D}$.

Tuberculosis (TB) remains a significant public health concern in China. Using data from the Global Burden of Disease (GBD) study 2021, we analyzed trends in age-standardized incidence rate (ASIR), prevalence rate (ASPR), mortality rate (ASMR), and disability-adjusted life years (DALYs) for TB from 1990 to 2021. Over this period, HIV-negative TB showed a marked decline in ASIR (AAPC = −2.34%, 95% CI: −2.39, −2.28) and ASMR (AAPC = −0.56%, 95% CI: −0.62, −0.59). Specifically, drug-susceptible TB (DS-TB) showed reductions in both ASIR and ASMR, while multidrug-resistant TB (MDR-TB) showed slight decreases. Conversely, extensively drug-resistant TB (XDR-TB) exhibited upward trends in both ASIR and ASMR. TB co-infected with HIV (HIV-DS-TB, HIV-MDR-TB, HIV-XDR-TB) showed increasing trends in recent years. The analysis also found an inverse correlation between ASIRs and ASMRs for HIV-negative TB and the Socio-Demographic Index (SDI). Projections from 2022 to 2035 suggest continued increases in ASIR and ASMR for XDR-TB, HIV-DS-TB, HIV-MDR-TB, and HIV-XDR-TB. The rising burden of XDR-TB and HIV-TB co-infections presents ongoing challenges for TB control in China. Targeted prevention and control strategies are urgently needed to mitigate this burden and further reduce TB-related morbidity and mortality.

Multi-loop coupling mechanisms (MCMs) are extensively utilized in the aerospace and aviation industries. This paper analyzes the mobility, singularity, and optimal actuation selection of a 3RR-3RRR MCM on the basis of geometric algebra (GA), where R denotes revolute joint. First, the principle of the shortest path is employed to identify the basic limbs and ascertain the type of coupling limbs. The analytical expression for the twist space and mobility characteristics of the mechanism is obtained by calculating the intersection of the limb’s twist space. The blade of limb constraint is subsequently employed to construct the singular polynomials of the mechanism. The singular configurations of the 3RR-3RRR MCM are analyzed in accordance with the properties of the outer product, resulting in the identification of two distinct types of boundary singularities. Next, the local transmission index is employed to evaluate the motion/force transmission performance of the two actuation schemes and finalize the selection of the superior actuation scheme for the mechanism. Finally, a prototype is developed to evaluate the energy loss resulting from the two actuation schemes, which verifies the correctness of the actuation selection scheme.

This essay argues that modes of conceptualizing global-local entanglements provide a useful lens for looking at the different ways Belt and Road Initiative (BRI) projects localize in BRI-host countries. The essay draws on recent work on George Ritzer to examine examples of BRI projects where global norms and practices are locally conceived and controlled, in contrast to other cases where the projects barely reflect local culture. Examples of Serbia and Hungary are provided to illuminate these points.

Despite being almost 4000m above sea level, cereal crops have been grown in the Ngari Prefecture on the Tibetan Plateau for thousands of years. Where and when domestic crop species adapted to high-altitude growing conditions is a matter of ongoing debate. Here, the authors present a new radiocarbon date from the Gepa serul cemetery, providing the earliest evidence of naked six-rowed barley in Tibet (c. 3500 BP). Evaluating the available evidence for barley cultivation and interregional connections in central Asia at this time, two hypotheses are considered—a generational advance with farmers migrating up river valleys or rapid, long-distance trade through mountain corridors.

Introduction: Late-life depression (LLD) is associated with cognitive deficit with risk of future dementia. By examining the entropy of the spontaneous brain activity, we aimed to understand the neural mechanism pertaining to cognitive decline in LLD.

Methods: We collected MRI scans in older adults with LLD (n = 32), mild cognitive impairment [MCI (n = 25)] and normal cognitive function [NC, (n = 47)]. Multiscale entropy analysis (MSE) was applied to resting-state fMRI data. Under the scale factor (tau) 1 and 2, reliable separation of fMRI data and noise was achieved. We calculated the brain entropy in 90 brain regions based on automated anatomical atlas (AAL). Due to exploratory nature of this study, we presented data of group-wise comparison in brain entropy between LLD vs. NC, MCI vs. NC, and LLD and MCD with a p-value below 0.001.

Results: The mean Mini-Mental State Examination (MMSE) score of LLD and MCI was 27.9 and 25.6. Under tau 2, we found higher brain entropy of LLD in left globus pallidus than MCI (p = 0.002) and NC (p = 0,009). Higher brain entropy of LLD than NC was also found in left frontal superior gyrus, left middle superior gyrus, left amygdala and left inferior parietal gyrus. The only brain region with higher brain entropy in MCI than control was left posterior cingulum (p-value = 0.015). Under tau 1, higher brain entropy was also found in LLD than in MCI in right orbital part of medial frontal gyrus and left globus pallidus (p-value = 0.007 and 0.005).

Conclusions: Our result is consistent with prior hypothesis where higher brain entropy was found during early aging process as compensation. We found such phenomenon particular in left globus pallidus in LLD, which could be served as a discriminative brain region. Being a key region in reward system, we hypothesis such region may be associated with apathy and with unique pathway of cognitive decline in LLD. We will undertake subsequent analysis longitudinally in this cohort

Key words: resting-state fMRI, Late-life depression, Brain entropy, globus pallidus, cognitive decline

In this work, the Riemann–Hilbert (RH) problem is employed to study the multiple high-order pole solutions of the cubic Camassa–Holm (cCH) equation with the term characterizing the effect of linear dispersion under zero boundary conditions and nonzero boundary conditions. Under the reflectionless situation, we generalize the residue theorem and obtain the multiple high-order pole solutions of cCH equation by solving an algebraic system. During the process of establishing the solution of RH problem, to simplify the calculations involving the implicitly expressed of variables (x, t) in the solution, we introduce a new scale (y, t) to ensure the solution of RH problem is explicitly expressed with respect to it. Finally, the exact solutions are obtained for cases involving one high-order pole and N high-order poles.

Although the People’s Republic of China (PRC) and the Republic of China (ROC, also known as Taiwan) and their ruling parties have altered over time, there are quite a few similarities between their models of nation-building, more than is commonly acknowledged. The guofu (father) of the modern Chinese state, Sun Yat-sen, one of the few political leaders who is still honored on both sides of the Taiwan Straits, claimed all the peoples and territories of the former Qing empire comprised a single national community, the so-called Zhonghua minzu. Yet a Han super-majority has long sat at the center of this national imaginary. In this article, we ask what has happened to Sun’s imagined community across the last century, and how it has evolved in the two competing Chinese states the PRC and the ROC. We seek to demonstrate the enduring challenge of Han-centrism for multiethnic nation-building in both countries, while illustrating how shifts in domestic and international politics are altering this national imaginary and the place of ethnocultural diversity within it.

The associations between obesity and liver diseases are complex and diverse. To explore the causal relationships between obesity and liver diseases, we applied two-sample Mendelian randomisation (MR) and multivariable MR analysis. The data of exposures (BMI and WHRadjBMI) and outcomes (liver diseases and liver function biomarker) were obtained from the open genome-wide association study database. A two-sample MR study revealed that the genetically predicted BMI and WHRadjBMI were associated with non-alcoholic fatty liver disease, liver fibrosis and autoimmune hepatitis. Obesity was not associated with primary biliary cholangitis, liver failure, liver cell carcinoma, viral hepatitis and secondary malignant neoplasm of liver. A higher WHRadjBMI was associated with higher levels of biomarkers of lipid accumulation and metabolic disorders. These findings indicated independent causal roles of obesity in non-alcoholic fatty liver disease, liver fibrosis and impaired liver metabolic function rather than in viral or autoimmune liver disease.

Purple nutsedge (Cyperus rotundus L.) is one of the world’s resilient upland weeds, primarily spreading through its tubers. Its emergence in rice (Oryza sativa L.) fields has been increasing, likely due to changing paddy-farming practices. This study aimed to investigate how C. rotundus, an upland weed, can withstand soil flooding and become a problematic weed in rice fields. The first comparative analysis focused on the survival and recovery characteristics of growing and mature tubers of C. rotundus exposed to soil-flooding conditions. Notably, mature tubers exhibited significant survival and recovery abilities in these environments. Based on this observation, further investigation was carried out to explore the morphological structure, nonstructural carbohydrates, and respiratory mechanisms of mature tubers in response to prolonged soil flooding. Over time, the mature tubers did not form aerenchyma but instead gradually accumulated lignified sclerenchymal fibers, with lignin content also increasing. After 90 d, the lignified sclerenchymal fibers and lignin contents were 4.0 and 1.1 times higher than those in the no soil-flooding treatment. Concurrently, soluble sugar content decreased while starch content increased, providing energy storage, and alcohol dehydrogenase activity rose to support anaerobic respiration via alcohol fermentation. These results indicated that mature tubers survived in soil-flooding conditions by adopting a low-oxygen quiescence strategy, which involves morphological adaptations through the development of lignified sclerenchymal fibers, increased starch reserves for energy storage, and enhanced anaerobic respiration. This mechanism likely underpins the flooding tolerance of mature C. rotundus tubers, allowing them to endure unfavorable conditions and subsequently germinate and grow once flooding subsides. This study provides a preliminary explanation of the mechanism by which mature tubers of C. rotundus from the upland areas confer flooding tolerance, shedding light on the reasons behind this weed’s increasing presence in rice fields.

We closely replicated Nurmukhamedov and Sharakhimov (2021), which was the first study to examine the lexical profile of general-audience English podcasts. Nurmukhamedov and Sharakhimov (2021) found that podcast listeners should have a knowledge of the most frequent 3,000 word families and 5,000 word families, respectively, plus proper nouns, marginal words, transparent compounds, and acronyms in order to achieve good and high-level listening comprehension. We followed the methods and procedures of the initial study with a much larger corpus. Specifically, a total of 8,862 podcast transcripts sampled from 12 general-audience podcast programs were used to compile the 14-million-word corpus. Results of the study confirmed Nurmukhamedov and Sharakhimov's (2021) findings in the vocabulary size required to understand general-audience English podcasts. However, some minor differences pertaining to individual podcast programs were revealed, indicating that the sampling of data had an effect on the lexical demand. These findings provide solid evidence to support the validity and generalizability of the initial study's findings. Implications for second language teaching and learning are also discussed.

In the contemporary maritime industry, characterised by intense competition, reduced visibility due to heavy fog is a primary cause of accidents, significantly impairing maritime operational efficiency. Consequently, investigating foggy weather navigation safety holds crucial practical significance. This paper, through an analysis and synthesis of various aspects of foggy navigation technology, including foggy navigation regulations at different ports, fog warnings, foggy vessel environmental perception and foggy auxiliary navigation systems, explores the key issues concerning vessel navigation during foggy conditions from a scientific perspective. This discussion encompasses the aspects of regulatory frameworks, standardisation, and the development of intelligent and responsive onboard equipment. Finally, the paper offers a glimpse into potential strategies for fog navigation.