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关键词： 11D09   11Y50   Simultaneous Pell equations   Diophantine equations  

摘要： We consider the simultaneous Pell equations$x^2-a{y}^2=1,z^2-b{x}^2=1,$ where $a\ge b\ge 2$ are positive integers. We describe a procedure which, for any fixed b, either confirms that the simultaneous Pell equations have at most one solution in positive integers, or finds all exceptions for which we have two solutions.

关键词： Simultaneous Pell equations   Diophantine equations  

摘要： We consider the simultaneous Pell equations x(2)-ay(2) = 1, z(2)-bx(2) = 1, where a >= b >= 2 are positive integers. We describe a procedure which, for any fixed b, either confirms that the simultaneous Pell equations have at most one solution in positive integers, or finds all exceptions for which we have two solutions.

摘要： 1,3-Dioxolane (C₃H₆O₂) is an emerging oxygenated biofuel with promising carbon neutrality potential. However, existing experiments and models have not demonstrated its negative temperature coefficient (NTC) phenomenon. The ozone-addition methods, which can enhance the low-temperature oxidation activity, were adopted to explore the low-temperature oxidation kinetics of 1,3-dioxolane. In this work, the experiment of ozone-assisted low-temperature oxidation of 1,3-dioxolane was carried out in atmospheric jet-stirred reactor using the synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) method. The temperature range was 410 − 800 K, the equivalence ratio was 0.4, the fuel concentration was 0.5%, and the ozone concentration was 0.1%. Extensive species quantification was achieved, including reactants, main products, active peroxides and other C₀ – C₃ oxidation intermediates. The experiment observed a distinct two-stage oxidation trend of 1,3-dioxolane, including two fuel-decomposition processes and one NTC process. A new detailed mechanism of 1,3-dioxolane includes both low-temperature and high-temperature mechanisms was developed, which can reasonably reproduce the measured species concentration profiles. The model was validated against literature data. The rate of production and sensitivity analyses reveal the decisive role of the ȮH production mechanism in the two-stage oxidation trend of the fuel. The low-temperature activity of 1,3-dioxolane activated by ozone mainly occurs through O₃ (+M) <=> O₂ + Ö (+M) and RH + Ö <=> Ṙ + ȮH. This study provides new experimental data on the NTC behavior observed during the low-temperature oxidation of 1,3-dioxolane in a jet-stirred reactor. The detailed model elucidates the low-temperature oxidation mechanism, providing key insights into the combustion characteristics of this promising biofuel.

关键词： HIV   Molecular surveillance   Molecular epidemiology   Molecular transmission network   Community detection   Exponential random graph model  

摘要： Large clusters in HIV-1 molecular networks contain a substantial proportion of people living with HIV and dominate local epidemics; however, their large size and complex structure pose a challenge for effective public health interventions. We developed an analytical framework to partition the large cluster into small groups for precise intervention. In the HIV-1 CRF07_BC molecular transmission network in Guangzhou, China (2008-2020), a giant component (681 members) was partitioned into 34 communities with dense internal and sparse external links. All 378 inter-community links involved high-centrality members from Community 1 (P < 0.001) and phylogenetic analysis identified Community 1 as the most likely ancestral source of the giant component (marginal probability = 0.989). Exponential random graph models (ERGMs) revealed significant homophily effect among members with specific characteristics in the giant component and its large communities, highlighting potential outbreaks within specific subgroups. Partitioning giant components into communities may be a promising approach to help develop community-level interventions and could improve the effectiveness of interventions targeted at large clusters.

关键词： Heterogeneoushydroformylation   Cobalt   Nitrogen-doped carbon   Acid etching   ZIF-67  

摘要： The hydroformylation of olefins is an important industrial process for aldehyde production; however, heterogeneous cobalt catalysts commonly suffer from metal leaching and nanoparticle sintering under reaction conditions. Herein, we fabricate a series of nitrogen-doped carbon encapsulated cobalt catalysts (Co/NC-X) via controlled acid etching and secondary pyrolysis of ZIF-67 derived Co/NC. By adjusting the etching time, the surface composition and pore structure of the catalysts can be systematically tuned. Among the series, Co/NC-6 (etched for 6 h) exhibits the best catalytic performance, achieving 70.5 % aldehyde selectivity with near-complete conversion, and maintaining stable performance over six consecutive recycling runs with only 0.9 % cumulative Co leaching, outperforming the pristine unetched Co/NC. Structural characterizations show that moderate etching selectively removes unstable surface cobalt species, enriches Co-N_x sites, and optimizes the porous structure. The carbon layer confinement effect serves as the physical basis for the excellent recycling stability of the catalyst, while the enrichment of Co-N_x sites correlates well with the improved aldehyde selectivity. Switching the solvent to isopropanol further improves the aldehyde selectivity to 79.5 %, which may be related to the different wettability of the catalyst surface in different solvents. This work offers a simple and effective strategy for the design of stable and recyclable cobalt-based hydroformylation catalysts.

关键词： 1,6-Hexanediol   Escherichia coli   Transcriptomic analysis   Genome-wide screening   Combinatorial optimization  

摘要： 1,6-Hexanediol (1,6-HDO) is an important chemical platform widely used in polymer and pharmaceutical industries, while its toxicity remains a major bottleneck limiting efficient microbial production. This study demonstrates that 1,6-HDO exhibited strong inhibitory effects on Escherichia coli, reducing the maximum OD₆₀₀ to approximately 50% of the control level under 10 g/L stress. Transcriptomic analysis was performed under 1,6-HDO stress, identifying 779 differentially expressed genes enriched in pathways related to energy metabolism, sulfur metabolism and amino acid metabolism. To systematically identify functional targets associated with tolerance, genome-wide screening using the ASKA overexpression library identified 93 tolerance-related genes that improved E. coli growth under 1,6-HDO stress by 0.06- to 3.17-fold. Notably, multiple targets were functionally associated with energy and amino acid metabolism, consistent with the transcriptomic analysis. Furthermore, co-expression of rumA and yhbO showed the greatest improvement in growth, reaching a biomass of 9.43 under 1,6-HDO stress, which was 2.61-fold higher than that of the control strain. Collectively, this study systematically elucidates the global stress response and identifies key determinants contributing to tolerance, providing valuable targets for developing robust microbial cell factories for efficient 1,6-HDO bioproduction.

关键词： primary   14G12   14G05   secondary   11G35   14H25   14G25   Hasse principle   Brauer–Manin obstruction   del Pezzo surface of degree 4   Hyperelliptic curve  

摘要： Let g be a positive integer congruent to 1 modulo 4 and K be an arbitrary number field. We construct infinitely many explicit one-parameter algebraic families of degree 4 del Pezzo surfaces and genus g hyperelliptic curves such that each K-member of the families violates the Hasse principle. In particular, we obtain algebraic families of non-trivial 2-torsion elements in the Tate–Shafarevich group of algebraic families of elliptic curves over K. These Hasse principle violations are explained by the Brauer–Manin obstruction.

关键词： Well-posedness   lump solution   stripe soliton   bilinear method   inelastic interaction  

摘要： . This paper investigates the global well-posedness, lump solutions, and stripe-soliton interactions for a (2+1)-dimensional nonlinear evolution equation. First, we establish the local well-posedness of the Cauchy problem in Sobolev spaces Hs(R2) with s >= 4 via energy estimates and parabolic regularization, and prove global existence for sufficiently small initial data. Second, using the Hirota bilinear method and a quadratic polynomial ansatz, we prove the existence of a family of nontrivial, real-valued, globally non-singular lump solutions with algebraic decay. Explicit sufficient conditions on the parameters guarantee the positivity of the associated quadratic function, ensuring analyticity and localization. Third, we construct mixed exponential-rational solutions describing a completely inelastic interaction between a lump and a stripe soliton, where the lump is gradually engulfed by the stripe. Numerical plots illustrate the dynamic characteristics of these solutions. The existence theorem and constructive method provide a solid foundation for understanding localized wave phenomena in higher-dimensional integrable systems.

关键词： NGAL   KIM   Acute kidney injury   Chronic kidney disease   Electrochemical immunosensor  

摘要：

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  Electrochemical immunosensors enable highly sensitive detection of AKI biomarkers KIM-1 and NGAL.
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  Nanomaterial-based designs significantly enhance signal amplification and analytical performance.
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  Current studies demonstrate strong potential for early and minimally invasive diagnosis of acute kidney injury.

关键词： Neurofibromatosis type 1   Pheochromocytomas   Paragangliomas   Genetic testing  

摘要： Neurofibromatosis type 1 (NF1) is a genetic multisystem disorder characterized by café-au-lait macules, neurofibromas, and other clinical features. Patients with NF1 have an increased risk of developing various tumours, including pheochromocytomas and paragangliomas (PPGLs), rare neuroendocrine tumours that secrete catecholamines. The prevalence of PPGL in NF1 patients varies, with some studies reporting rates up to 7.7%. Diagnosis relies on clinical symptoms such as hypertension, headaches, and palpitations, alongside biochemical and imaging studies.