New results on the positive solutions of nonlinear second-order differential systems

In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form $$\left\{\begin{aligned} &u''=-f(t,v), \ \ 0< t< 1,\\&v''=-g(t,u), \ \ 0< t< 1\\&u(0)=v(0)=0,\varsigma u(\zeta)=u(1),\varsigma v(\zeta)=v(1),\end{aligned}\right.$$ where $f:(0,1)\times [0,+\infty)\to [0,+\infty),g:[0,1]\times [0,+\infty)\to [0,+\infty),00,$ and $\varsigma\zeta< 1,f$ may be singular at $t = 0$ and/or $t = 1.$ Under some rather simple conditions, by means of monotone iterative technique, a necessary and sufficient condition for the existence of positive solutions is established, a result on the existence and uniqueness of the positive solution and the iterative sequence of solution is given

Ga III triarylcorroles with push–pull substitutions

Two A2B type H3corroles and two GaIIItriarylcorroles with carbazole substitutions at 10-positions were synthesized and characterized. An analysis of structure–property relationships of the corroles has been carried out by investigating the optical spectroscopy of the dyes to trends predicted in DFT and TD-DFT calculations. Interestingly, the photodynamic therapy (PDT) and photodynamic antimicrobial chemotherapy (PACT) activity properties of the GaIIItriarylcorroles were determined against the MCF-7 breast cancer line, and Staphyloccocus aureus (S. aureus) and Escherichia coli (E. coli), respectively. The cationic G-2Q species exhibited the most favorable properties with an IC50 value of 7.8 μM against MCF-7 cells, and Log reduction values of 7.78 and 3.26 against planktonic S. aureus and E. coli at 0.5 and 10 μM, respectively

Identification and quantification of viable Lacticaseibacillus rhamnosus in probiotics using validated PMA-qPCR method

The identification and quantification of viable bacteria at the species/strain level in compound probiotic products is challenging now. Molecular biology methods, e.g., propidium monoazide (PMA) combination with qPCR, have gained prominence for targeted viable cell counts. This study endeavors to establish a robust PMA-qPCR method for viable Lacticaseibacillus rhamnosus detection and systematically validated key metrics encompassing relative trueness, accuracy, limit of quantification, linear, and range. The inclusivity and exclusivity notably underscored high specificity of the primers for L. rhamnosus, which allowed accurate identification of the target bacteria. Furthermore, the conditions employed for PMA treatment were fully verified by 24 different L. rhamnosus including type strain, commercial strains, etc., confirming its effective discrimination between live and dead bacteria. A standard curve constructed by type strain could apply to commercial strains to convert qPCR Cq values to viable cell numbers. The established PMA-qPCR method was applied to 46 samples including pure cultures, probiotics as food ingredients, and compound probiotic products. Noteworthy is the congruity observed between measured and theoretical values within a 95% confidence interval of the upper and lower limits of agreement, demonstrating the relative trueness of this method. Moreover, accurate results were obtained when viable L. rhamnosus ranging from 103 to 108 CFU/mL. The comprehensive appraisal of PMA-qPCR performances provides potential industrial applications of this new technology in quality control and supervision of probiotic products

Search for light dark matter from atmosphere in PandaX-4T

We report a search for light dark matter produced through the cascading decay of $\eta$ mesons, which are created as a result of inelastic collisions between cosmic rays and Earth's atmosphere. We introduce a new and general framework, publicly accessible, designed to address boosted dark matter specifically, with which a full and dedicated simulation including both elastic and quasi-elastic processes of Earth attenuation effect on the dark matter particles arriving at the detector is performed. In the PandaX-4T commissioning data of 0.63 tonne$\cdot$year exposure, no significant excess over background is observed. The first constraints on the interaction between light dark matter generated in the atmosphere and nucleus through a light scalar mediator are obtained. The lowest excluded cross-section is set at $5.9 \times 10^{-37}{\rm cm^2}$ for dark matter mass of $0.1$ MeV$/c^2$ and mediator mass of 300 MeV$/c^2$. The lowest upper limit of $\eta$ to dark matter decay branching ratio is $1.6 \times 10^{-7}$

Efficient radical-based light-emitting diodes with doublet emission.

Organic light-emitting diodes (OLEDs)1-5, quantum-dot-based LEDs6-10, perovskite-based LEDs11-13 and micro-LEDs14,15 have been championed to fabricate lightweight and flexible units for next-generation displays and active lighting. Although there are already some high-end commercial products based on OLEDs, costs must decrease whilst maintaining high operational efficiencies for the technology to realise wider impact.  Here we demonstrate efficient action of radical-based OLEDs16, whose emission originates from a spin doublet, rather than a singlet or triplet exciton. While the emission process is still spin-allowed in these OLEDs, the efficiency limitations imposed by triplet excitons are circumvented for doublets. Using a luminescent radical emitter, we demonstrate an OLED with maximum external quantum efficiency of 27 per cent at a wavelength of 710 nanometres-the highest reported value for deep-red and infrared LEDs. For a standard closed-shell organic semiconductor, holes and electrons occupy the highest occupied and lowest unoccupied molecular orbitals (HOMOs and LUMOs), respectively, and recombine to form singlet or triplet excitons. Radical emitters have a singly occupied molecular orbital (SOMO) in the ground state, giving an overall spin-1/2 doublet. If-as expected on energetic grounds-both electrons and holes occupy this SOMO level, recombination returns the system to the ground state, giving no light emission. However, in our very efficient OLEDs, we achieve selective hole injection into the HOMO and electron injection to the SOMO to form the fluorescent doublet excited state with near-unity internal quantum efficiency

Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second-order matrix differential system U′=A(x)U+B(t)V, V′=C(x)U−A∗(t)V, where A(t), B(t), and C(t) are (n×n)-matrices, and B, C are Hermitian. These results are sharper than some previous results