A Dynamical Approach to the Perron-Frobenius Theory and Generalized Krein-Rutman Type Theorems

We present a new dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in the literature. As a result, we develop a complex version of the Perron-Frobenius theory and prove a variety of generalized Krein-Rutman type theorems for real operators. In particular, we establish some new Krein-Rutman type theorems for sectorial operators in a formalism that can be directly applied to elliptic operators, which allow us to reduce significantly the technical PDE arguments involved in the study of the principal eigenvalue problems of these operators.Comment: 40 page

LaRC TPI 1500 series polymers

The crystallization behavior and the melt flow properties of two batches of 1500 series LaRC-TPI polymers from Mitsui Toatsu Chemicals (MTC) were investigated. The characterization methods include Differential Scanning Calorimetry, the x ray diffractography and the melt rheology. The as-received materials possess initial crystalline melting peak temperatures of 295 and 305 C, respectively. These materials are less readily recrystallizable at elevated temperatures when compared to other semicrystalline thermoplastics. For the samples annealed at temperatures below 330 C, a semicrystalline polymer can be obtained. On the other hand, a purely amorphous structure is realized in the samples annealed at temperatures above 330 C. Isothermal crystallization kinetics were studied by means of the simple Avrami equation. The viscoelastic properties at elevated temperatures below and above glass transition temperature of the polymers were measured. Information with regard to the molecule sizes and distributions in these polymers were also extracted from melt rheology

Credit Risk and Macroeconomic Stress Tests in China

This paper examines the vulnerability of commercial banks in China to the changes in macroeconomic conditions by employing a macroeconomic stress test. We particularly focus on how the changes in housing market related variables and the scale of shadow banking influence the credit risks of China’s entire banking system. Based on the result of a Vector Autoregression (VAR) model, we proceed with a five-scenario analysis. Our main finding is the ability of shadow banking to absorb the credit risks of commercial banks rather than there being a spill over effect, according to the data from Q1 2005 to Q2 2016.1 Moreover, the mortgage loan is risky to commercial banks during this period. In addition, our scenario analysis suggests that China’s banking system is relatively stable and that the Central Bank of China is capable of monitoring the credit risks of commercial banks using appropriate credit policies

Photoproduction of C-even quarkonia at EIC and EicC

The $\eta_c$ photoproduction in $ep$ collision has long been proposed as an ideal process to probe the existence of odderon. In the current work, we systematically investigate the photoproduction of various $C$-even heavy quarkonia (exemplified by $\eta_{c(b)}$, and $\chi_{c(b)J}$ with $J=0,1,2$) via one-photon exchange channel, at the lowest order in $\alpha_s$ and heavy quark velocity in the context of NRQCD factorization. We find that the photoproduction rates of the $C$-even quarkonia through this mechanism are comparable in magnitude with that through the odderon-initiated mechanism, even in the Regge limit ($s\gg -t$), though the latter types of predictions suffers from considerable theoretical uncertainties. The future measurements of these types of quarkonium photoproduction processes in \texttt{EIC} and \texttt{EicC} are crucial to ascertain which mechanism plays the dominant role.Comment: 16 pages, 9 figure

A micromechanical model on specific damping capacity caused by micro cracks

Dispersed micro cracks are widely found in engineer materials, e.g. concrete, ceramic and composite. Specific damping capacity (SDC) caused by friction on micro crack surfaces (FSDC) was investigated in this study. Firstly, frictional energy dissipation (FED) of individual micro crack was modeled analytically and it was further validated by unit cell FE approach. Then, the model was employed in macro-scale cantilever beams involving regular and random multi micro cracks respectively. FEDs and FSDCs of the beams with different micro crack angles and densities are predicted. The study indicated that FED (and FSDC) depends on crack angle and stress state in structure. FSDC is independent to magnitudes of load and modulus of material in elastic scope. To materials with low viscosity, damping might increase significantly with the presence of multi micro cracks of high density