A note on the number of subquantales

In this note, it is proved for n ≤ 5 that if Q is a finite quantale with |Q| ≥ n, then there are at least n subquantales of Q. However, the result does not hold when |Q| ≥ 6. Also, an example is given of a sequence of quantales of cardinality p + 2 for p prime, each of which have exactly 5 subquantales.     

Numerical simulation for the temperature changing rule of the crude oil in a storage tank based on the wavelet finite element method

In order to study the temperature changing rule of the crude oil in the storage tank, the wavelet finite element method, the traditional finite element method and the test were used to carry out the numerical simulation. Firstly, the thermal wavelet finite element was put forward established based on thermal finite element theory and the wavelet theory. And the computational model and three boundary conditions were established. And then the temperature changing rule of the crude oil in the storage tank in 24 h for three boundary conditions was obtained by using three methods, and the results showed that the wavelet finite element method had advantages in the numerical analysis of the temperature changing rule of the crude oil in the storage. And then the temperature distribution rule of the crude oil in the storage tank under different conditions in 5 h was obtained. And the temperature changing mechanism of the crude oil was summarized finally.     

Photoisomerization Mechanism of Ruthenium Sulfoxide Complexes: Role of the Metal‐Centered Excited State in the Bond Rupture and Bond Construction Processes

Phototriggered intramolecular isomerization in a series of ruthenium sulfoxide complexes, [Ru(L)(tpy)(DMSO)]ⁿ⁺ (where tpy=2,2’:6’,2’’‐terpyridine; DMSO=dimethyl sulfoxide; L=2,2’‐bipyridine (bpy), n=2; N,N,N’,N’‐tetramethylethylenediamine (tmen) n=2; picolinate (pic), n=1; acetylacetonate (acac), n=1; oxalate (ox), n=0; malonate (mal), n=0), was investigated theoretically. It is observed that the metal‐centered ligand field (³MC) state plays an important role in the excited state S→O isomerization of the coordinated DMSO ligand. If the population of ³MC_S state is thermally accessible and no ³MC_O can be populated from this state, photoisomerization will be turned off because the ³MC_S excited state is expected to lead to fast radiationless decay back to the original ¹GS_S ground state or photodecomposition along the Ru²⁺?S stretching coordinate. On the contrary, if the population of ³MC_S (or ³MC_O) state is inaccessible, photoinduced S→O isomerization can proceed adiabatically on the potential energy surface of the metal‐to‐ligand charge transfer excited states (³MLCT_S→³MLCT_O). It is hoped that these results can provide valuable information for the excited state isomerization in photochromic d⁶ transition‐metal complexes, which is both experimentally and intellectually challenging as a field of study.     

Flexural contact in MEMS stiction

Adhesive force between two solid surfaces can lead to stiction failure of the micro-electro-mechanical systems (MEMS) device. The competition between the adhesive force and the beam restoring force determines whether the stiction occurs or not. Previous models assume that the stuck beam deforms either as the arc-shape or the S-shape, which causes significant differences in the measurements of adhesion and disputations among researchers. The contact mechanics model presented in this paper shows that the assumptions of the arc-shape and S-shape on the beam deformation over-simplify the problem; both the arc-shaped deformation and S-shaped deformation significantly deviate from the real ones. The previous theories are shown to be incompatible with the recent experimental results. The model presented in this paper attempts to explain those new experimental results and resolve some disputations on the previous models. The instabilities of jump-in during loading process and jump-off during unloading process are also incorporated in this model.