THE COMPOSITE FORMULAS ON A CONVEXDOMAIN IN C^n

Using the Plemelj formulas for a function and a (n,n-1)-form on a convex domain in Cn, the author obtains their composite formulas and inverse formulas. As an application, the author proves that the singular integral equation with Aizenberg kernel is equivalent to a Fredholm equation.

Exploring the clinical significance of Yinqiao powder based on the compatibility of Chinese herbal formulas

Yinqiao powder comes from the book"Wenbing Tiaobian"(Detailed Analysis of Epidemic Warm Diseases)written by Wu Jutong in the Qing Dynasty(1636-1912),in which it is mentioned that"pungent-cool diaphoretic agent Yinqiao power is used to treat patients with fever,not aversion to cold but thirsty"Yinqiao powder is often used to treat Wind-warm syndrome,warm-heat syndrome and miscellaneous diseases caused by some pathogenic factors in Wei-fen syndrome(Wei-fen syndrome is the syndrome name of the disease and is often used to indicate the initial stage of exogenous febrile disease,which is the syndrome of the body's guard surface.)and upper energizer.With the further research and application of Yinqiao powder,it is more and more widely used in clinic.This article summarizes the clinical application of Yinqiao powder through the analysis of the prescription meaning,compatible prescriptions,decoction methods and other aspects of Yinqiao powder in order to provide more evidence for clinical treatment of febrile disease.At the same time,through the prescription thinking of Yinqiao powder,we can learn Wu Jutong's treatment principle and academic thought of"Shangjiao(Shangjiao is one of the three and is the upper part of the Sanjiao.Generally refers to the chest above the diaphragm,including the heart,lungs and throat.)is like a feather,not lightly".Wu Jutong's flexible use of Chinese medicine and the thought of syndrome differentiation and treatment are also worthy of our study and reference.

THE DIFFERENTIAL INTEGRAL EQUATIONS ONSMOOTH CLOSED ORIENTABLE MANIFOLDS

Using integration by parts and Stokes' formula, the authors give a new definition of Hadamard principal value of higher order singular integrals with Bochner-Martinelli kernel on smooth closed orientable manifolds in C-n. The Plemelj formula and composite formula of higher order singular integral are obtained. Differential integral equations on smooth closed orientable manifolds are treated by using the composite formula.

Singular integral on bounded strictly pseudoconvex domain

Kytmanov and Myslivets gave a special Cauchy principal value of the singular integral on the bounded strictly pseudoconvex domain with smooth boundary. By means of this Cauchy integral principal value, the corresponding singular integral and a composition formula are obtained. This composition formula is quite different from usual ones in form. As an application, the corresponding singular integral equation and the system of singular integral equations are discussed as well.

Prescription analysis of traditional chinese medicine for COVID-19treatment

Background:Coronavirus disease 2019 is still spreading all over the world and without any specific medicine.Traditional Chinese medicine has played an important role in the control of epidemics in China and accumulated many experiences.The aim of this study is to summarize the law of traditional Chinese medicine and provide reference for coronavirus disease 2019 traditional Chinese medicine treatment.Methods:We collected the treatment plans of traditional Chinese medicine for coronavirus disease 2019 in 24 provinces of China to evaluate the basic Chinese medicine formulas,and the efficacy types,frequency,“Four Characters”,“Five Tastes”,“Channel Tropism”of herbal medicines.Combination rules between medicines were calculated by Apriori algorithm and Clementine12.0.Results:The formulas for“Relieving Exterior Syndrome”,“Expelling Dampness”,“Clearing Heat”and“Supplementing”have highest proportion.In prevention period and medical observation period,the medicines mainly have effect for“Clearing Heat”,“Relieving Exterior Syndrome”and“Supplementing”.In treatment period,medicines for“Clearing Heat”,“Relieving Superficies”and“Relieving Dampness”had higher frequency.The“Four Characters”of Chinese medicines in all treatment plans were mainly“Cold”and“Warm”.Medicines in the treatment plans always belong to“Pungent Taste”,“Bitter Taste”and“Sweet Taste”.For“Channel Tropism”,most medicines turned over to the“Lung”,“Stoma”and“Spleen”.The common medicine combinations in the recommended formulas during the prevention period and medical observation period were medicines for“Qi-Supplementing”and“Relieving Superficies”.In treatment period(mild,moderate,severe/critical),medicines for“Dampness Expelling”,“Relieving Superficies”and“Qi-Supplementing”were combined in a high frequency.In recovery period,the medicines for“Dispelling Dampness”combined the medicines for“Promoting Blood Circulation”with highest frequency.Conclusions:We found the characteristics of medicine and prescription rules of traditional Chinese medicine for the treatment of coronavirus disease 2019 and provided scientificity and effectiveness of it.More importantly,it provides reference for the development of new clinical prescriptions for coronavirus disease 2019.

High-Temperature Structural Stabilities of Ni-Based SingleCrystal Superalloys Ni–Co–Cr–Mo–W–Al–Ti–Ta with Varying Co Contents

It has been recently pointed out that the compositions of industrial alloys are originated from cluster-plus-glueatom structure units in solid solutions. Specifically for Ni-based superalloys, after properly grouping the alloying elements into Al, Ni-like（Ni^-）, γ＇-forming Cr-like（Cr^-γ＇） and γ-forming Cr-like（Cr^-γ＇）, the optimal formula for single-crystal superalloys is established [Al–Ni^-12]（AlCr^-γ0：5Cr^-γ1：5）. The Co substitutions for Ni at the shell sites are conducted on the basis of the first-generation single-crystal superalloy AM3, formulated as [Al-Ni2-xCox]（Al1Ti0.25Ta0.25Cr1W0.25Mo0.25）, with x = 1.5, 1.75, 2 and 2.5（the corresponding weight percents of Co are 9.43, 11.0, 12.57 and 15.71, respectively）. The900 ℃ long-term aging follows the Lifshitz–Slyozov–Wagner theory（LSW theory）, and the Co content does not have noticeable influence on the coarsening rate of c0. The microstructure and creep behavior of the four（001） single-crystal alloys are investigated. The creep rupture lifetime is reduced as Co increases. The alloy with the lowest Co（9.43 Co） shows the longest lifetime of about 350 h at 1050 ℃/120 MPa, and all the samples show N-type rafting after creep tests.