Generic Singularities for 2D Pressureless Flow

In this paper, we consider the Cauchy problem for pressureless gases in two space dimensions with generic smooth initial data (density and velocity). These equations give rise to singular curves, where the mass has positive density w.r.t.~1-dimensional Hausdorff measure. We observe that the system of equations describing these singular curves is not hyperbolic. For analytic data, local solutions are constructed using a version of the Cauchy-Kovalevskaya theorem. We then study the interaction of two singular curves, in generic position. Finally, for a generic initial velocity field, we investigate the asymptotic structure of the smooth solution up to the first time when a singularity is formed.Comment: The manuscript contains 4 figure

Effects of different application ratios of biochar-organic compound fertilizers and chemical fertilizers on soil nutrition content and yield of maize

Overuse of traditional chemical fertilizers may result in environmental pollution and a decrease in the quality of farm produce. By contrast, applying biochar-organic compound fertilizers can enhance soil structure, increase soil fertility, and mitigate pollution levels. This study explores the intricate mechanisms of the combined application of biochar-organic compound fertilizers and chemical fertilizers on soil chemical properties and corn growth. The aim is to elucidate the theoretical foundations supporting the widespread adoption of biochar-organic compound fertilizers. A total of 6 treatments were set up, among which the CK treatment did not apply fertilizer, the CF treatment used bovine excrement organic fertilizer combined with chemical fertilizer, the T1 to T4 treatments used biochar-organic compound fertilizers and replaced 40%, 60%, 80%, and 100% bovine excrement organic fertilizer combined with chemical fertilizer. The results showed that applying biochar-organic compound fertilizers enhanced the slow-release properties of soil available nutrients, increased corn yield, and improved grain quality. Notably, when biochar-organic compound fertilizers were employed instead of 100% bovine excrement organic fertilizer, the yield surpassed that of other treatments, exhibiting a remarkable 9.30% increase compared to the CF treatment. Through comprehensive analysis, it was determined that using biochar-organic compound fertilizer to replace 60% of bovine excrement organic fertilizer is a scheme that can balance both fertilizer efficacy and cost and is recommended to farmers. This research can contribute to promoting the green transformation of agriculture and help achieve the goal of "carbon neutrality"

Sensing danger in the islet: the roles of pattern recognition receptors in β cells and type 1 diabetes

Type 1 diabetes (T1D) is an organ-specific autoimmune disease characterized by the immune-mediated destruction of pancreatic β cells, leading to absolute insulin deficiency and chronic hyperglycemia. Traditionally, the onset of T1D has been attributed to the interplay of genetic predisposition and environmental factors that disrupt immune tolerance. However, growing evidence suggests that β cells are not merely passive targets of immune attack. Instead, under conditions of inflammatory and metabolic stress, β cells actively participate in immune modulation by upregulating various immunologically relevant molecules, particularly pattern recognition receptors (PRRs). These innate immune sensors enable β cells to detect danger-associated signals and modulate local immune responses, thereby influencing their survival and immunogenicity. In this review, we summarize current knowledge about the expression profiles and immunoregulatory roles of PRRs in pancreatic β cells and explore their potential contributions to T1D pathogenesis. A deeper understanding of PRR-mediated signaling in β cells may provide novel insights into the immunopathology of T1D and reveal promising targets for therapeutic intervention

Mass resection as a candidate treatment for uterine PEComas of uncertain malignant potential: a case report and literature review

BackgroundPerivascular epithelioid cell tumours (PEComas) occurring in the uterus are rare, with surgery being the most recommended primary treatment for malignant cases. This study aims to provide clinical guidance on the clinicopathological features and appropriate treatment options for patients with uterine PEComas of uncertain malignant potential.CasesThis case series summarises the clinical courses of 13 patients diagnosed with uterine PEComas of uncertain malignant potential, including clinical and pathological data as well as their outcomes. We identified one case at our hospital, and data for the other 12 cases were extracted from the PubMed database. The 13 patients were aged 9–75 years, with tumour sizes ranging from 1 to 21 cm, and follow-up times ranging from 2 to 71 months. The most common signs and symptoms included abnormal uterine bleeding (AUB) and abdominal pain. Most of the patients (11/13) were managed surgically without any chemotherapy or radiation therapy. Except for the patients who were lost to follow-up, 11 patients were free of any recurrence or metastasis at their last follow-up. Patients with group A tumours (abundant HMB45 expression) had a longer disease-free survival than those with group B tumours.ConclusionsSurgery alone may be appropriate for uterine PEComas of uncertain malignant potential. Surgical treatment plans should consider the patient’s age, fertility requirements, and personal preferences. Mass resection is a viable treatment option for fertility preservation in reproductive-age patients

Systematic identification and characterization of chicken (Gallus gallus) ncRNAs

Recent studies have demonstrated that non-coding RNAs (ncRNAs) play important roles during development and evolution. Chicken, the first genome-sequenced non-mammalian amniote, possesses unique features for developmental and evolutionary studies. However, apart from microRNAs, information on chicken ncRNAs has mainly been obtained from computational predictions without experimental validation. In the present study, we performed a systematic identification of intermediate size ncRNAs (50–500 nt) by ncRNA library construction and identified 125 chicken ncRNAs. Importantly, through the bioinformatics and expression analysis, we found the chicken ncRNAs has several novel features: (i) comparative genomic analysis against 18 sequenced vertebrate genomes revealed that the majority of the newly identified ncRNA candidates is not conserved and most are potentially bird/chicken specific, suggesting that ncRNAs play roles in lineage/species specification during evolution. (ii) The expression pattern analysis of intronic snoRNAs and their host genes suggested the coordinated expression between snoRNAs and their host genes. (iii) Several spatio-temporal specific expression patterns suggest involvement of ncRNAs in tissue development. Together, these findings provide new clues for future functional study of ncRNAs during development and evolution