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.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Dose‐dependent exposure profile and metabolic characterization of notoginsenoside R1 in rat plasma by ultra‐fast liquid chromatography–electrospray ionization–tandem mass spectrometry

Notoginsenoside R₁ (NGR₁), a diagnostic protopanaxatriol‐type (ppt‐type) saponin in Panax notoginseng, possesses potent biological activities including antithrombotic, anti‐inflammatory, neuron protection and improvement of microcirculation, yet its pharmacokinetics and metabolic characterization as an individual compound remain unclear. The aim of this study was to investigate the exposure profile of NGR₁ in rats after oral and intravenous administration and to explore the metabolic characterization of NGR₁. A simple and sensitive ultra‐fast liquid chromatographic–tandem mass spectrometric method was developed and validated for the quantitative determination of NGR₁ and its major metabolites, and for characterization of its metabolic profile in rat plasma. The blood samples were precipitated with methanol, quantified in a negative multiple reaction monitoring mode and analyzed within 6.0 min. Validation parameters (linearity, precision and accuracy, recovery and matrix effect, stability) were within acceptable ranges. After oral administration, NGR₁ exhibited dose‐independent exposure behaviors with t_1/2 over 8.0 h and oral bioavailability of 0.25–0.29%. A total of seven metabolites were characterized, including two pairs of epimers, 20(R)‐notoginsenoside R₂/20(S)‐notoginsenoside R₂ and 20(R)‐ginsenoside Rh₁/20(S)‐ginsenoside Rh₁, with the 20(R) form of saponins identified for the first time in rat plasma. Five deglycometabolites were quantitatively determined, among which 20(S)‐notoginsenoside R₂, ginsenoside Rg₁, ginsenoside F₁ and protopanaxatriol displayed relatively high exploration, which may partly explain the pharmacodynamic diversity of ginsenosides after oral dose.     

The quartet theory of human emotions: An integrative and neurofunctional model

Despite an explosion of research in the affective sciences during the last few decades, interdisciplinary theories of human emotions are lacking. Here we present a neurobiological theory of emotions that includes emotions which are uniquely human (such as complex moral emotions), considers the role of language for emotions, advances the understanding of neural correlates of attachment-related emotions, and integrates emotion theories from different disciplines. We propose that four classes of emotions originate from four neuroanatomically distinct cerebral systems. These emotional core systems constitute a quartet of affect systems: the brainstem-, diencephalon-, hippocampus-, and orbitofrontal-centred affect systems. The affect systems were increasingly differentiated during the course of evolution, and each of these systems generates a specific class of affects (e.g., ascending activation, pain/pleasure, attachment-related affects, and moral affects). The affect systems interact with each other, and activity of the affect systems has effects on – and interacts with – biological systems denoted here as emotional effector systems. These effector systems include motor systems (which produce actions, action tendencies, and motoric expression of emotion), peripheral physiological arousal, as well as attentional and memory systems. Activity of affect systems and effector systems is synthesized into an emotion percept (pre-verbal subjective feeling), which can be transformed (or reconfigured) into a symbolic code such as language. Moreover, conscious cognitive appraisal (involving rational thought, logic, and usually language) can regulate, modulate, and partly initiate, activity of affect systems and effector systems. Our emotion theory integrates psychological, neurobiological, sociological, anthropological, and psycholinguistic perspectives on emotions in an interdisciplinary manner, aiming to advance the understanding of human emotions and their neural correlates.     

Mechanism of Insertion Reactions between Silylenoid H2SiLiF and GeH3R (R =F,OH, NH2): a Theoretical Study

Theoretical investigations on the insertion reaction mechanisms of three- membered-ring silylenoid H2 Si Li F with GeH 3R(R = F, OH, NH2) have been systematically carried out by combined density functional theory(DFT) and ab initio quantum chemical calculations. The geometries of all stationary points for these reactions were optimized using the B3 LYP method and then the QCISD method was used to calculate the single-point energies. The calculated results indicate that, there are one precursor complex(Q), one transition state(TS), and one intermediate(IM) which connect the reactants and the products along the potential energy surface. The insertion reactions of three-membered-ring silylenoid with Ge H3 R proceed in a concerted manner, forming H2RSi-Ge H3 and Li F. The calculated potential energy barriers of the three reactions are 29.17, 30.90, and 54.07 k J/mol, and the reaction energies for the three reactions are –127.05, –116.91, and –103.31 k J/mol, respectively. The insertion reactions in solvents are similar to those in vacuum. Under the same situation, the insertion reactions should occur easily in the following order: GeH 3-F GeH 3-OH GeH 3-NH2. The elucidations of the mechanism of these insertion reactions provided a new mode of silicon-germanium bond formation.     

Theoretical investigation into coordination and selectivity of uranyl-unilateral benzotriazole salophens (X = O/S) for R/S-triadimefons

The design of new uranyl-ligands (uranyl-Ls) is of great significance for the separation and utilization of uranium. In this paper, the triazole group was introduced into uranyl-salophen (uranyl-S) to form new asymmetric uranyl-unilateral benzotriazole salophen (uranyl-UBS); we further replaced two oxygen atoms of uranyl-UBS with two sulfur atoms to generate uranyl-unilateral benzotriazole thio-salophen (uranyl-UBTS) as a new receptor. Then, we comprehensively explored coordination models of uranyl-UBS and uranyl-UBTS with R/S-triadimefons (R/S-TDFs) enantiomers as the guests using density functional theory calculations at the B3LYP//RECP/6-311G** level; we then investigated enantioselectivity recognition of the new receptors to the guests R/S-TDFs. The results indicated that the uranium atoms of the receptors uranyl-S, uranyl-UBS and uranyl-UBTS could coordinate with the carbonyl oxygens in guests R/S-TDFs to form complexes of guest-receptors R/S-TDFs-uranyl-Ls that exhibited two stable V-shaped structures with quite different properties. It was found that the coordination ability to the guests R/S-TDFs is uranyl-UBTS > uranyl-UBS > uranyl-S, while the enantioselectivity for the guests is uranyl-UBTS > uranyl-S > uranyl-UBS and, when the receptor is the same, R-TDF has stronger coordination ability than S-TDF. These results provide information and theoretical supports for the experiments of asymmetric uranyl-UBS with R/S-TDFs, and produce a reference for further exploring the coordination characteristics of asymmetric uranyl-salophen with the triazole derivatives.     

Computational design of rasagiline derivatives: Searching for enhanced antioxidant capability

A set of new rasagiline derivatives is presented. They were designed to be antioxidant compounds with the potential to be used for treating neurodegenerative disorders. They are expected to be multifunctional molecules that can help reduce oxidative stress, which is thought to contribute to neurodegenerative disorders. The CADMA-Chem computational protocol was used to produce rasagiline derivatives and to evaluate their likeliness as oral drugs and antioxidants. Three of them were identified as the most promising ones. They are proposed to be better free radical scavengers than rasagiline. In addition, they are expected to keep the parent's molecule neuroprotective capability. Hopefully, the results presented here would promote further experimental and theoretical investigations on these compounds.