Manage Pension Deficit with Heterogeneous Insurance

This paper considers a positive and increasing pension deficit of a certain pay-as-you-go (PAYG) pension system, and tries to make up for this deficit by using heterogeneous insurance. The positive pension deficit is formulated as a mathematical function in continuous time. The surplus of an appropriate heterogeneous insurance is described by diffusion approximation of a Cramér-Lundberg process. The system of extended Hamilton-Jacobi-Bellman equations under mean-variance criterion is established. The closed-form solution and optimal surplus-multiplier of heterogenous insurance are obtained. Some interpretations further explain the theoretical values of the results.

     

Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Enhanced Power Density of Alcohol Biofuel Cell by Polymer-assisted Crosslinks of 3D Graphene on Carbon Paper as the Bioanode

Herein, we successfully construct the 3D biocompatible graphene through crosslinking 2D graphene nanosheet onto carbon fiber paper with poly(diallyldimethylammonium chloride) (PDDA) as anode of the alcohol biofuel cell. Compared with the bioanode without 3D graphene, the current density and output power of PDDA-graphene-ADH bioanode is increased by 23 % and 41 % at a high concentration of ethanol at pH 8.9, suggesting the stabilization role of graphene in enzyme loading. The study provides us a deep analysis on structures and performances of the bioanode incl. electrochemistry, X-ray photoelectron spectra, and atomic force microscopy images, which is significant to develop the new methods to construct 3D porous electrodes in energy conversion device.     

Isolated resonances and nonlinear damping

We analyze isolated resonance curves (IRCs) in single-degree-of-freedom systems possessing nonlinear damping. Through the combination of singularity theory and the averaging method, the onset and merging of IRCs, which coincide to isola and simple bifurcation singularities, respectively, can be analytically predicted. Numerical simulations confirm the accuracy of the analytical developments. Another important finding of this paper is that we unveil a geometrical connection between the topology of the damping force and IRCs. Specifically, we demonstrate that extremas and zeros of the damping force correspond to the appearance and merging of IRCs. Considering a damping force possessing several minima and maxima confirms the general validity of the analytical result. It also evidences a very complex scenario for which different IRCs are created, co-exist and then merge together to form a super IRC which eventually merges with the main resonance peak.     

Synthesis and Crystal Structure of New Indium Iodate (K<Subscript>0.6</Subscript>Na<Subscript>0.4</Subscript>Ba)In[IO<Subscript>3</Subscript>]<Subscript>6</Subscript>

Crystals of new indium iodate (K_0.6Na_0.4Ba)In[IO₃]₆ were prepared by the hydrothermal synthesis. The unit-cell parameters are a = 11.3984(3) Å, с = 11.3817(3) Å, sp. gr. R3?. The chemical formula of the compound was derived from the structure determination and refinement with anisotropic displacement parameters to R = 0.0284. In the structure the InO₆ octahedra share vertices with six umbrella-like [IO₃]–groups typical of iodates and form isolated 3?-symmetric charged \(\rm{In[IO_{3}]_6^{3-}}\) clusters. Large Ba, K, and Na cations occupy a common site on a threefold axis due to the isomorphous substitution and compensate the charge of the clusters. The new structure extends the family of the recently discovered alkali-metal and barium iodates containing Ti and Zr atoms in octahedral sites. The iodate K₂Ge[IO₃]₆ containing Ge atoms in the centers of octahedra is the parent compound of this structural family.     

Σ-Definability in Hereditarily Finite Superstructures and Computable Analysis

We construct a computable real function not Σ-definable in hereditarily finite superstructures over the extensions with decidable theory of the reals.