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.     

XANES/EPR Evidence of the Oxidation of Nickel(II) Quinolinylpropioamide and Its Application in Csp3−H Functionalization

An in situ generated oxidation species of nickel quinolinylpropioamide intermediate was produced. Characterization by X-ray absorption near edge structure (XANES) and EPR provides complementary insights into this oxidized nickel species. With aliphatic amides and isocyanides as substrates, a nickel-catalyzed facile synthesis of structurally diverse five-membered lactams could be achieved.     

Functional Organic Semiconductors Based on Bay‐Annulated Indigo (BAI)

The advancement of organic electronics has been continually pushed by the need for stable and high performance acceptor materials. By utilizing inexpensive and stable indigo dye as a starting material, Bay‐Annulated Indigo (BAI) provides a new motif for the development of semiconducting materials. Modular and straightforward synthesis makes BAI an outstanding platform for molecular design, while excellent stability, strong absorption, and high ambipolar mobility render BAI‐based materials excellent candidates for organic electronics. BAI‐based polymers and small molecules have taken advantage of these properties to show promising results in a variety of applications.     

Integrating photocatalytic reduction of CO_2 with selective oxidation of tetrahydroisoquinoline over InP–In_2O_3 Z-scheme p-n junction

The development of a facile strategy to construct stable hierarchal porous heterogeneous photocatalysts remains a great challenge for efficient CO_2 reduction. Additionally, hole-trapping sacrificial agents(e.g., triethanolamine, triethylamine, and methanol) are mostly necessary, which produce useless chemicals, and thus cause costs/environmental concerns. Therefore,utilizing oxidation ability of holes to develop an alternative photooxidation reaction to produce value-added chemicals, especially coupled with CO_2 photoreduction, is highly desirable. Here, an in situ partial phosphating method of In_2O_3 is reported for synthesizing In P–In_2O_3 p-n junction. A highly selective photooxidation of tetrahydroisoquinoline(THIQ) into value-added dihydroisoquinoline(DHIQ) is to replace the hole driven oxidation of typical sacrificial agents. Meanwhile, the photoelectrons of In P–In_2O_3 p-n junction can induce the efficient photoreduction of CO_2 to CO with high selectivity and stability. The evolution rates of DHIQ and CO are 2 and 3.8 times higher than those of the corresponding In_2O_3 n-type precursor, respectively. In situ irradiated X-ray photoelectron spectroscopy and electron spin resonance are utilized to confirm that the direct Z-scheme mechanism of In P–In_2O_3 p-n junction accelerate the efficient separation of photocarriers.     

Practical algorithm substitution attack on extractable signatures

Designs, Codes and Cryptography - An algorithm substitution attack (ASA) can undermine the security of cryptographic primitives by subverting the original implementation. An ASA succeeds when it...     

Analysis of the human breast milk microbiome and bacterial extracellular vesicles in healthy mothers

The microbiota of human breast milk (HBM) contribute to infant gut colonization; however, whether bacterial extracellular vesicles (EVs) are present in HBM or might contribute to this process remains unknown. In this study, we characterized the HBM microbiota of healthy Korean mothers and measured the key bacteria likely affecting infant gut colonization by analyzing both the microbiota and bacterial EVs. A total of 22 HBM samples were collected from lactating mothers. The DNA of bacteria and bacteria-derived EVs was extracted from each sample. In alpha-diversity analyses, bacterial samples showed higher richness and evenness than bacterial EV samples, and beta-diversity analyses showed significant differences between bacteria and bacterial EVs within identical individual samples. Firmicutes accounted for the largest proportion among the phyla, followed by Proteobacteria, Bacteroidetes, and Actinobacteria, in both bacteria and bacterial EV samples. At the genus level, Streptococcus (25.1%) and Staphylococcus (10.7%) were predominant in bacterial samples, whereas Bacteroides (9.1%), Acinetobacter (6.9%), and Lactobacillaceae(f) (5.5%) were prevalent in bacterial EV samples. Several genera, including Bifidobacterium, were significantly positively correlated between the two samples. This study revealed the diverse bacterial communities in the HBM of healthy lactating mothers, and found that gut-associated genera accounted for a high proportion in bacterial EV samples. Our findings suggest the existence of key bacteria with metabolic activity that are independent of the major bacterial populations that inhabit HBM, and the possibility that EVs derived from these bacteria are involved in the vertical transfer of gut microbiota.Subject terms: Immunogenetics, Immunization     

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.