Abstract
There are two ways to find the distribution of two-dimensional random variable function: distribution function method and convolution formula method, the distribution function method is too ...large; calculation is easy to make mistakes, the convolution formula method has limitations must be independent, Now let’s introduce the generalized convolution formula, The generalized convolution formula does not require independent constraints and can simplify the operation.
The calculation of double integrals Jiang, Yinshan
Journal of physics. Conference series,
09/2020, Letnik:
1634, Številka:
1
Journal Article
Recenzirano
Odprti dostop
The calculation method of double integral is as follows; (1) Define the method; (2) The double integral is calculated using rectangular coordinates; (3) Double integrals are calculated using polar ...coordinates; (4) The double integral is calculated by using the symmetry of the integral region and the parity of the integrand function.; (5) The double integral is calculated by block integral method; (6) The double integral is calculated using the translation of the coordinate axes; (7) Double integral is calculated by centroid formula.
•Phosphorus-doped TiO2 calcined under different atmosphere were as catalysts for methyl orange photodegradation.•P-doped TiO2 calcined under carbothermic atmosphere (R-TiO2) can decrease the ...concentration of surface O and improve the effect of P species in TiO2 to some extent.•The outstanding photocatalytic activity of P-doped TiO2 is ascribed to the generation of Ti3+ defect sites at the surface or interface of TiO2 caused by P doping.•The activity of recycled P-doped TiO2 was found to retain even after third photodegradation experiment.
Titanium dioxide doped with phosphorus was synthesized by the sol–gel method with H3PO4 addition. The samples were calcined at different temperatures under different atmospheres, in order to affect the TiO combination behavior in P-doped TiO2. The physicochemical properties of the prepared samples were investigated using TG-DTA, XRD, FTIR, XPS, TEM and UV–vis. The photocatalytic activity was evaluated by degradation of methyl orange (MO) dye under UV and visible-light irradiation. The results show that P-doped TiO2 calcined in different thermal atmosphere reveals entirely different performances. The XRD and UV–vis analysis reveal that the effect of P species in TiO2 is increased by calcining in reducing atmosphere. Further photocatalytic experiments also display that P-doped TiO2 calcined under carbothermal reduction atmosphere (R-PT) exhibits higher photocatalytic activity than that calcined in air (A-PT). The XPS results confirms that the calcining atmosphere changes the distribution concentration of surface and interface species in P-doped TiO2, such as surface oxygen and Ti3+ sites, resulting in the improved photocatalytic activity and enhanced reutilization performance of R-PT. Further mechanism study illustrates that the promoting photocatalytic activity of P-doped TiO2 are ascribed to the formation of Ti3+ sites rather than exceeding oxygen on the surface. And the carbothermal process helps to reserve these Ti3+ sites during high temperature calcination, resulting in the increased photocatalytic activity of P-doped TiO2, especially when the doping level of P species is relative low.
TiO2-diatomite photocatalysts were prepared by sol-gel process with various pre-modified diatomite. In order to obtain diatomite with different surface characteristics, two modification approaches ...including calcination and phosphoric acid treatment on the micro-structure of diatomite are introduced. The photocatalysts were characterized by XRD, XPS, nitrogen adsorption-desorption isotherms and micromorphology analysis. The results indicate that, compared with pure TiO2, the anatase-to-rutile phase transition temperature of TiO2 loaded on diatomite carrier is significantly increased to nearly 900 degree C, depending on the different pretreatment method of diatomite. The photocatalytic activities of different samples were evaluated by their degradation rate of methyl orange (MO) dye under UV and visible-light irradiation. The samples prepared by phosphoric acid pretreatment method exhibit the highest photocatalytic activity. After 90min of UV irradiation, about 90% of MO is decomposed by the best effective photocatalyst. And after 8h visible-light irradiation, nearly 60% of MO is decomposed by the same sample. Further mechanism investigation reveals that the H3PO4 pretreatment process can obviously change the surface features of diatomite carrier, cause the formation of Si-O-Ti bond, increase the binding strength between TiO2 and diatomite, restrain crystal growth of loaded TiO2, and thus form thermal-stable mesoporous structure at the granular spaces. It helps to build micro-, meso- and macro-porous hierarchical porous structure in TiO2-diatomite, and improves the charge and mass transfer efficiency during catalyzing process, resulting in the significantly increased photocatalytic activity of TiO2-diatomite pretreated by phosphoric acid.
In this study, a composite separator was prepared by coating a diatomite/polyvinylidene fluoride (PVDF) mixed slurry on the polyethylene terephthalate (PET) nonwoven in order to apply to lithium-ion ...batteries. The effect of the mass ratio of diatomite/PVDF on the physical and electrochemical performance of the composite separators was investigated. SEM observation showed that the unique pores on the diatomite disk gradually became the main pores of the diatomite/PET composite separator with the increasing content of diatomite in the coating. As the content of diatomite in the diatomite/PET composite separator coating increased from 60 to 80 wt%, the porosity, liquid electrolyte absorption rate, and ionic conductivity gradually increased and reached a maximum (63.8%, 0.866 g cm
−3
, 1.43 mS cm
−1
, respectively) at the content of 80 wt%. The contact angle of the composite separators to the electrolyte gradually decreased as the content of diatomite increased and reached a minimum of 13.00° at 80 wt%. After heat treatment at 160 °C for 0.5 h, the composite separator with a diatomite content of 80 wt% shrank merely 1.17% that showed the outstanding thermal stability than the PP separator (39.60%). Furthermore the cells assembled with diatomite composite separators showed better cycle stability and C-rate performance at room temperature, which was related to the reduced interfacial resistance and decreased polarization voltage of the cells. Among them, the composite separator with diatomite/PVDF = 80/20 (
w
/
w
) showed the most excellent cell performance due to the unique pore structure of diatomite.
Abstract
The eigenvalue and eigenvector of matrix is one of the key contents of linear algebra, and it is also the hot topic of postgraduate entrance examination. First of all, we must understand the ...concept of eigenvalue and eigenvector and master the method of solving eigenvalue and eigenvector of matrix.
Hierarchical Co3O4 porous nanowires （NWs） have been synthesized using a hydrothermal method followed by calcination. When employed as a cathode catalyst in non-aqueous Li-oxygen batteries, the Co3O4 ...NWs effectively improve both the round-trip efficiency and cycling stability, which can be attributed to the high catalytic activities of Co3O4 NWs for the oxygen reduction reaction and the oxygen evolution reaction during discharge and charge processes, respectively.
The extraction of alumina from coal fly ash (CFA) is a good way to enhance its value-added utilization. The presence of inert matter with a high degree of polymerization, such as mullite and other ...aluminosilicates, greatly restricts the reactivity of CFA. Thus, the CFA needs to be activated before use. Thermal activation by calcination with added sodium hydrogen sulfate (NaHSO
4
) was carried out in this study. The calcination products were characterized by means of X-ray diffraction, thermal gravimetric and differential scanning calorimetric analysis, and scanning electron microscopy to assess the effects of the additive, calcining temperature, and calcining time on the products. The results indicated that NaHSO
4
facilitated the decomposition of the polymeric phases and significantly improved the alumina extraction. Alumina in CFA was transformed into soluble Na
3
Al(SO
4
)
3
. When CFA was mixed with sodium hydrogen sulfate at a NaHSO
4
/Al
2
O
3
molar ratio of 6, the alumina extraction reached 90 % at 500 °C after 2 h.
Abstract
Advanced algebra is a required course of undergraduate mathematics, which plays a fundamental role in completing the study of other professional courses for students. Matrix theory is an ...important branch of mathematics, it is not only a basic subject, but also themost practical value. Widely used in mathematical theory, matrix is an important basic concept in matrix theory, is a major study of algebra, Positive definite matrix is a kind of important matrix, occupies an important position in “higher algebra”, its theory has rich content, positive definite quadratic form and Euclidean space, physics, probability and optimization control theory are related to it.
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