A Free Boundary Problem for Some Modified Predator-Prey Model in a Higher Dimensional Environment

Applications of Mathematics - We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated...     

Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

Springer basic sets and modular Springer correspondence for classical types

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic $p$, and with coefficients in a field of odd characteristic $?\ne p$): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols.     

Three-weight linear codes from Weil sums

Journal of Algebraic Combinatorics - By appropriately choosing a defining set, we define a class of linear codes and establish their complete weight enumerators and weight enumerators using Weil...     

Proton conductivity study on three CS/IL@fle-MOF membranes

The low-cost, high specific surface area and porosity, controlled pore size, and chemical properties of metal–organic framework (MOF) materials have attracted much attention in the exploration of proton conduction. The method of chemically modifying MOF structures or introducing conductive medium into the holes can effectively improve the proton conductivities of the materials. Here, the structural tunability of ionic liquid (IL) and flexible MOF (fle-MOF) materials are matched to give full play to the conductivity of IL, the framework support, and the microporous effect of MOFs, which achieves the synergistic effect of performance and expands the temperature range of proton transfer. Three kinds of CS/IL@fle-MOF membranes were prepared by combining three fle-MOFs with 1-carboxymethyl-3-methylimidazole (CMMIM) in different proportions to obtain 15 pieces of membranes. The comparative analyses show that CS/IL@fle-MOF membranes have excellent proton conduction performance at a wider temperature range (263–353 K) and lower relative humidity (75% RH). Among them, the proton conductivities of CS/CMMIM@MIL-88A-25% and CS/CMMIM@MIL-88B-125% are up to 1.33 and 1.42 S cm⁻¹ at 75% RH and 353 K, respectively; whereas those of CS/CMMIM@MIL-53(Fe)-75% and CS/CMMIM@MIL-88B-125% reach up to 2.1 × 10⁻³ and 1.28 × 10⁻³ S cm⁻¹ at 75% RH and 263 K, respectively. The E_a of CS/CMMIM@fle-MOFs is in the range of 0.1–0.5 eV, suggesting that the proton transport follows predominantly the typical Grotthuss transfer mechanism. The results of this study indicate that the CS/CMMIM@fle-MOF membranes combinations offer great potential for the design of composite porous proton-conducting materials.     

Optomechanical-organized multipulse dynamics in ultrafast fiber laser

A novel organized multipulse pattern and its birth dynamics under strong optomechanical effect in microfiber-assisted ultrafast fiber laser are investigated in this work. The background pulses are observed to obviously exhibit selectively amplifying self-organized process of evolving into quasi-stable equidistant clusters. The radio frequency spectrum of the multipulse pattern displays a harmonic mode-locking-like behavior with a repetition rate of 2.0138 GHz, corresponding to the frequency of torsional-radial (TR_2m) acoustic mode in microfiber. The results show the evidence of optomechanical effect in dominating the birth dynamics and pattern of multipulse.     

Construction of long MDS self-dual codes from short codes

In this paper, we propose a mechanism on how to construct long MDS self-dual codes from short ones. These codes are special types of generalized Reed-Solomon (GRS) codes or extended generalized Reed-Solomon codes. The main tool is utilizing additive structure or multiplicative structure on finite fields. By applying this method, more MDS self-dual codes can be constructed.