Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Methyl orange degradation enhanced by hydrogen spillover onto platinum nanocatalyst surface

Following a thermal reduction method, platinum nanoparticles were synthesized and stabilized by polyvinylpyrrolidone. The colloidal platinum nanoparticles were stable for more than 3 months. The micrograph analysis unveiled that the colloidal platinum nanoparticles were well dispersed with an average size of 2.53 nm. The sol–gel‐based inverse micelle strategy was applied to synthesize mesoporous iron oxide material. The colloidal platinum nanoparticles were deposited on mesoporous iron oxide through the capillary inclusion method. The small‐angle X‐ray scattering analysis indicated that the dimension of platinum nanoparticles deposited on mesoporous iron oxide (Pt‐Fe₂O₃) was 2.64 nm. X‐ray photoelectron spectroscopy (XPS) data showed that the binding energy on Pt‐Fe₂O₃ surface decreased owing to mesoporous support–nanoparticle interaction. Both colloidal and deposited platinum nanocatalysts improved the degradation of methyl orange under reduction conditions. The activation energy on the deposited platinum nanocatalyst interface (2.66 kJ mol^?1) was significantly lowered compared with the one on the colloidal platinum nanocatalyst interface (40.63 ± 0.53 kJ mol^?1).     

Utilizing the Space‐Charge Region of the FeNi‐LDH/CoP p‐n Junction to Promote Performance in Oxygen Evolution Electrocatalysis

The modulation of electron density is an effective option for efficient alternative electrocatalysts. Here, p‐n junctions are constructed in 3D free‐standing FeNi‐LDH/CoP/carbon cloth (CC) electrode (LDH=layered double hydroxide). The positively charged FeNi‐LDH in the space‐charge region can significantly boost oxygen evolution reaction. Therefore, the j at 1.485 V (vs. RHE) of FeNi‐LDH/CoP/CC achieves ca. 10‐fold and ca. 100‐fold increases compared to those of FeNi‐LDH/CC and CoP/CC, respectively. Density functional theory calculation reveals OH^? has a stronger trend to adsorb on the surface of FeNi‐LDH side in the p‐n junction compared to individual FeNi‐LDH further verifying the synergistic effect in the p‐n junction. Additionally, it represents excellent activity toward water splitting. The utilization of heterojunctions would open up an entirely new possibility to purposefully regulate the electronic structure of active sites and promote their catalytic activities.     

T-x-y diagram of the Ni-Bi-Se system

Some polythermal sections of the Ni-Bi-Se system have been investigated by DTA, X-ray powder diffraction, microstructural analysis, and microhardness measurements. The liquidus surface has been constructed for this system. The compounds NiBi₂Se₄ and Ni₃Bi₂Se₂ are formed by dystectic reactions and melt at 1088 and 980 K, respectively. The regions of primary and joint phase crystallization have been determined. A commutation of Bi₂Se₃-based thermoelements with a metal nickel bus-bar has been proposed.     

A New Two‐Dimensional Coordination Polymer of Mercury(II) with very High Thermal Stability

A 2D Hg^II coordination polymer containing ligands 1,2,4‐triazole (Htrz) and thiocyanate, [Hg(μ₃‐trz)(SCN)]_n ( 1 ) has been synthesized and characterized by elemental analysis and IR spectroscopy. The single‐crystal X‐ray data show the coordination number of Hg atoms is four and the ligand trz^? acts as a three‐fold donor. The thermal stability of compound 1 was studied by thermal gravimetric and differential thermal analyses. The composition and formation of the complex in methanol solution were found to be in support of its solid state structure.     

On the Embedding of Ordered Semigroups into Ordered Group

It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L-maher and R-maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R-maher semigroup can be embedded into an ordered group.