Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.     

Simultaneous quantification of levofloxacin,pefloxacin, ciprofloxacin and moxifloxacin in microvolumes of human plasma using high‐performance liquid chromatography with ultraviolet detection

Levofloxacin, pefloxacin, ciprofloxacin and moxifloxacin are four fluoroquinolones used in the treatment of serious bacterial infections. The antibacterial activity of fluoroquinolones is concentration dependent. Therefore, therapeutic drug monitoring in daily clinical practice is warranted to ensure the therapy's efficacy and prevent bacterial resistance. The purpose of the present study was to develop a method using high‐pressure liquid chromatography with an ultraviolet detector for simultaneous quantification of these four fluoroquinolones in human plasma. A 50 μL aliquot of plasma was precipitated by 200 μL of methanol using gatifloxacin as internal standard. The chromatographic separation was performed on a Kinetex XB‐C₁₈ column using a mobile phase composed of a mixture of orthophosphoric acid 0.4% (v/v), acetonitrile and methanol at a flow rate of 1.2 mL/min. Dual UV wavelength mode was used, with levofloxacin and moxifloxacin monitored at 293 nm, and pefloxacin and ciprofloxacin monitored at 280 nm. The calibration was linear over the ranges of 0.125–25 mg/L for levofloxacin, 0.1–20mg/L for moxifloxacin and 0.05‐10 mg/L for both pefloxacin and ciprofloxacin. Inter‐ and intra‐day trueness and precision were <13% for all the compounds under study. The proposed method was simple, reliable, cost‐effective and suitable for therapeutic drug monitoring or pharmacokinetics studies.     

Synthesis and Structure Determination of SCM-15: A 3D Large Pore Zeolite with Interconnected Straight 12×12×10-Ring Channels

A new germanosilicate zeolite named SCM-15 (Sinopec Composite Material No. 15), the first zeolite containing a 3-dimensional (3D) channel system with interconnected 12-, 12-, and 10-ring channels (pore sizes: 6.1×7.2, 6.1×7.4, and 5.2×5.9 Å), has been synthesized using neutral 4-pyrrolidinopyridine as organic structure-directing agents (OSDAs). Its structure has been determined by combining single-crystal electron diffraction (SCED) and synchrotron powder X-ray diffraction (SPXD) data. The unique open framework structure of SCM-15 is related to that of FOS-5 ( BEC ), ITQ-7 ( ISV ), PKU-16 ( POS ), ITQ-26 ( IWS ), ITQ-21, Beta polymorph B, and SU-78B, since all these framework structures can be constructed from similar chains which are connected through shared 4-ring or double 4-ring (d4r) units. Based on this relation, six topologically reasonable 3D large or extra-large pore hypothetical zeolites are predicted.     

Bis-tridentate IrIII Phosphors Bearing Two Fused Five-Six-Membered Metallacycles: A Strategy to Improved Photostability of Blue Emitters

Iridium complexes bearing chelating cyclometalates are popular choices as dopant emitters in the fabrication of organic light-emitting diodes (OLEDs). In this contribution, we report a series of blue-emitting, bis-tridentate Ir^III complexes bearing chelates with two fused five-six-membered metallacycles, which are in sharp contrast to the traditional designs of tridentate chelates that form the alternative, fused five-five metallacycles. Five Ir^III complexes, Px-21 – 23 , Cz-4 , and Cz-5 , have been synthesized that contain a coordinated dicarbene pincer chelate incorporating a methylene spacer and a dianionic chromophoric chelate possessing either a phenoxy or carbazolyl appendage to tune the coordination arrangement. All these tridentate chelates afford peripheral ligand–metal–ligand bite angles of 166–170°, which are larger than the typical bite angle of 153–155° observed for their five-five-coordinated tridentate counterparts, thereby leading to reduced geometrical distortion in the octahedral frameworks. Photophysical measurements and TD-DFT studies verified the inherent transition characteristics that give rise to high emission efficiency, and photodegradation experiments confirmed the improved stability in comparison with the benchmark fac-[Ir(ppy)₃] in degassed toluene at room temperature. Phosphorescent OLED devices were also fabricated, among which the carbazolyl-functionalized emitter Cz-5 exhibited the best performance among all the studied bis-tridentate phosphors, showing a maximum external quantum efficiency (EQE_max) of 18.7 % and CIE_x,y coordinates of (0.145, 0.218), with a slightly reduced EQE of 13.7 % at 100 cd m⁻² due to efficiency roll-off.     

Liquid crystalline behaviours of some 3-perfluoroalkylbenzoate esters

A series of 3-perfluoroalkylbenzoate esters are synthesised. They tend to exhibit enantiotropic SmA and SmC phases. The clearing points are decreased with increasing the alkoxy chain length and show odd-even effect. With increasing the fluorocarbon chain length, the melting and clearing points increase; however, the SmC phase is suppressed.     

Rational solutions for a combined (3 + 1)-dimensional generalized BKP equation

Nonlinear Dynamics - In this paper, we focus on the rational solutions for a combined (3&nbsp;+&nbsp;1)-dimensional generalized BKP equation. By using the symbolic computation with Maple,...     

Klingen $${\mathfrak {p}}^2$$ p 2 vectors for $$\mathrm{GSp}(4)$$ GSp ( 4 )

The Ramanujan Journal - We calculate the dimensions of the spaces of invariant vectors under the Klingen congruence subgroup of level $${\mathfrak {p}}^2$$ for all irreducible, admissible...     

Scheme to measure the expectation value of a physical quantity in weak coupling regime

In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, ifthe coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointercan not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, whichmakes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurementmethod in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement,our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped40Ca+ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.     

树状大分子接枝型聚合物色谱分离材料研究进展

随着色谱固定相制备技术和材料科学领域的不断发展,目前已经有大量修饰方法和新型材料被用于固相萃取、高效液相色谱以及离子色谱聚合物固定相填料的功能化修饰。其中聚酰胺-胺(PAMAM)树状大分子由于其独特的结构和性质,在色谱分离材料结构完善和性能提升中也发挥了重要的作用。该文主要综述了PAMAM树状大分子在以聚合物为基质的色谱分离材料修饰中的应用,并对其今后的发展进行了展望。     

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.