On the Existence of a Normal Trimagic Square of Order 16n

The study of magic squares has a long history, and magic squares have been applied to many mathematical fields. In this paper, we give a complete solution to the existence of normal trimagic squares of all orders 16n. In particular, we obtain a unified solution for the normal trimagic square of order 16n for n>3 by means of set partitions, semibimagic squares, Latin squares, and new product construction. Since there exist normal trimagic squares of orders 16, 32, and 48, we prove that there exists a normal trimagic square of order 16n for every positive integer n

A TiSe₂-Graphite Dual Ion Battery:Fast Na-Ion Insertion and Excellent Stability

The sodium dual ion battery (Na-DIB) technology is proposed as highly promising alternative over lithium-ion batteries for the stationary electrochemical energy-storage devices. However, the sluggish reaction kinetics of anode materials seriously impedes their practical implementation. Herein, a Na-DIB based on TiSe2-graphite is reported. The high diffusion coefficient of Na-ions (3.21×10−11–1.20×10−9 cm2 s−1) and the very low Na-ion diffusion barrier (0.50 eV) lead to very fast electrode kinetics, alike in conventional surface capacitive storage systems. In-situ investigations reveal that the fast Na-ion diffusion involves four insertion stage compositions. A prototype cell shows a reversible capacity of 81.8 mAh g−1 at current density of 100 mA g−1, excellent stability with 83.52 % capacity retention over 200 cycles and excellent rate performance, suggesting its potential for next-generation large scale high-performance stationary energy storage systems

A Novel TiSe2‐Graphite Dual Ion Battery: Fast Na‐Ion Insertion and Excellent Stability

The sodium dual ion battery (Na-DIB) technology is proposed as highly promising alternative over lithium-ion batteries for the stationary electrochemical energy-storage devices. However, the sluggish reaction kinetics of anode materials seriously impedes their practical implementation. Herein, a Na-DIB based on TiSe2-graphite is reported. The high diffusion coefficient of Na-ions (3.21×10−11–1.20×10−9 cm2 s−1) and the very low Na-ion diffusion barrier (0.50 eV) lead to very fast electrode kinetics, alike in conventional surface capacitive storage systems. In-situ investigations reveal that the fast Na-ion diffusion involves four insertion stage compositions. A prototype cell shows a reversible capacity of 81.8 mAh g−1 at current density of 100 mA g−1, excellent stability with 83.52 % capacity retention over 200 cycles and excellent rate performance, suggesting its potential for next-generation large scale high-performance stationary energy storage systems