Multiplicity of Solutions for Nonlinear Biharmonic Equation Involving Critical Parameter and Critical Exponent

By using variational method, the multiplicity of solutions for nonlinear biharmonic equation involving critical parameter and critical exponent are established.

Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter γ 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

Effects of critical geometric parameters on the optical performance of a conical cavity receiver

The optical performance of a receiver has a great influence on the efficiency and stability of a solar thermal power system.Most of the literature focuses on the optical performance of receivers with different geometric shapes,but less research is conducted on the effects of critical geometric parameters.In this paper,the commercial software TracePro was used to investigate the effects of some factors on a conical cavity receiver,such as the conical angle,the number of loops of the helical tube,and the distance between the focal point of the collector and the aperture.These factors affect the optical efficiency,the maximum heat flux density,and the light distribution in the conical cavity.The optical performance of the conical receiver was studied and analyzed using the Monte Carlo ray tracing method.To make a reliable simulation,the helical tube was attached to the inner wall of the cavity in the proposed model.The results showed that the amount of light rays reaching the helical tube increases with the increasing of the conical angle,while the optical efficiency decreases and the maximum heat flux density increases.The increase in the number of loops contributed to an increase in the optical efficiency and a uniform light distribution.The conical cavity receiver had an optimal optical performance when the focal point of the collector was near the aperture.

The development of Fructus corni quality standard considering the effects of processing

The quality standards for Fructus Comi have been established based on the effects of the manufacturing processes.Three critical process parameters(CPPs)of extraction,filtration,and concentration to prepare Fructus Comi concentrate were identified by Plackett-Burman design with a single batch of Fructus Corni,which were heating medium temperature,extraction time,and water addition.Morroniside yield,loganin yield,and dry matter yield were process critical quality attributes(CQAs).CPPs arranged with a Box-Behnken design were applied to treat different batches of Fructus Comi After constructing a model that included CPPs,material propertie s,and process CQAs,loganin content was found to be the critical material attribute(CMA).The design space was calculated with a probability method.According to the limits of process CQAs,the minimum content of loganin in Fructus Corni was calculated with an error propagation method,which was 6.92 mg·g^(-1).When the content of loganin in Fructus Corni reaches up to 6.92 mg·g^(-1),the material is considered high-quality and is most suitable for the process.High-quality material can be used for production of Fructus Comi concentrate.This method can also be used to set material quality standards for other Chinese medicines.

Experimental verification of parameter m in Hoeke-Brown failure criterion considering the effects of natural fractures

HoekeBrown failure criterion is one of the widely used rock strength criteria in rock mechanics and mining engineering.Based on the theoretical expression of HoekeBrown parameter m of an intact rock,the parameter m has been modified by crack parameters for fractured rocks.In this paper,the theoretical value range and theoretical expression form of the parameter m in HoekeBrown failure criterion were discussed.A critical crack parameter B was defined to describe the influence of the critical crack when the stress was at the peak,while a parameter b was introduced to represent the distribution of the average initial fractures.The parameter m of a fractured rock contained the influences of critical crack(B),confining pressure(s3)and initial fractures(b).Then the triaxial test on naturally fractured limestones was conducted to verify the modification of the parameter m.From the ultrasonic test and loading test results of limestones,the parameter m can be obtained,which indicated that the confining pressure at a high level reduced the differences of m among all the specimens.The confining pressure s3 had an exponential impact on m,while the critical crack parameter B had a negative correlation with m.Then the expression of m for a naturally fractured limestone was also proposed.

Granulation process analysis technologies and potential applications in traditional Chinese medicine

Pharmaceutical production is changing from batch production to continuous production,during which granulation is one of the most important unit operations.The quality of mass-produced products is traditionally guaranteed by conducting off-line testing,which cannot meet the demand of continuous production for real-time monitoring of critical process parameters and critical quality attributes(CQAs)of the pharmaceutical granulation technology.Since the U.S.Food and Drug Administration proposed process analytical technology(PAT)in 2004,many PAT tools have been developed to monitor the granulation process and provide information regarding the granulation operation conditions and endpoint determination.In this article,we review the recent research and application of two PAT modes in the granulation process,namely,single CQA and multi-CQA PAT,with the aim to provide references for comprehensively improving the technological level of the pharmaceutical granulation process.Furthermore,the potential applications in traditional Chinese Medicine are discussed.

Extraction process in Chuantieling(CTL) based on the quality by design(QbD) concept

Objective This study aimed to design and optimize the water extraction process for Chuantieling(喘贴灵,CTL)based on the concept of quality by design(QbD).Methods The single-factor experiments were used to select the best experimental points of CTL water extraction.On this basis,the transfer rate of ephedrine hydrochloride and sin-apine thiocyanate,and the yield of the extract were evaluated as the evaluation indicators.The liquid-solid ratio,extraction time,and pH value were selected as the main factors to carry out the Box-Behnken design(BBD).A mathematical model of the critical process parameters(CPPs)and critical quality attributes(CQAs)was established,the interaction between CQAs and CPPs was examined,and the CTL extraction process design space was established and optimized,which guaranteed the stability of the process.The high performance liquid chro-matography(HPLC)was used to analyze the main active compounds in the CTL extract.Results Through single-factor experiments,the best experimental parameters were found to be a liquid-solid ratio of 8∶1,extraction time of 90 min,pH value of 4,and extraction times of three.The experimental variance analysis results of the BBD showed that the P value of the re-gression model was less than 0.05,and the lack-of-fit value was greater than 0.01,indicating that the constructed model had good predictive ability.The operating space of the CPPs of the CTL water extraction process was combined with the actual production situation.In the pro-duction situation,the best extraction process was nine times of water addition,72 min of ex-traction time,and 4.5 of pH value.The HPLC results showed that the peak areas of ephedrine hydrochloride,sinapine thiocyanate,tetrahydropalmatine,methyl eugenol,cinnamaldehyde,and 6-gingerol in the CTL extract accounted for 0.94%,14.32%,0.78%,31.23%,0.34%,and 0.44%of the total peak area,respectively.Conclusion The water extraction process design space of CTL based on QbD was conducive to actual production operations,ensuring the stability of the process.

Critical process parameter identification of manufacturing processes of Astragali Radix extract with a weighted determination coeffcient method

Objective:Critical process parameters(CPPs)identification is an important step of the implementation of quality by design(Qb D)concept.There are many CPP identification methods,such as risk analysis method,sensitivity analysis method,multiple linear regression method,standard partial regression coefficient(SPRC)method,and so on.The SPRC method can consider multiple process critical quality attributes(CQAs)simultaneously,but the determination of CPP number is subjective.Therefore,new CPP identification method is still required.Methods:The manufacturing process of Astragali Radix extract,which contained water reflux extraction,concentration,and ethanol precipitation,was used as an example.First,the multiple process CQAs were determined to be the yield of pigment,dry matter,sugars,and active ingredients.Second,the potential CPPs were determined by a knowledge organization method.Plackett-Burman designed experiments were then performed.A weighted determination coefficient(R2 w)method was presented to identify CPPs.In this method,the importance of different CQAs was considered.Process parameters were removed one-by-one according to their importance index.The decrease in R2 wwas used to characterize the importance of the removed parameter.If the decrease of R2 wwas less than a preset threshold,the removed parameter was not a CPP.Results:During the manufacturing process of Astragali Radix extract,the potential CPPs determined by the knowledge organization method were water consumption,reflux extraction time,extraction frequency,ethanol content,ethanol consumption,and concentration endpoint.Reflux extraction time,the first ethanol consumption,the second ethanol consumption,and the second ethanol precipitation refrigeration temperature were found to be CPPs using the weighted determination coefficient method with the threshold of 10%.Conclusion:Using the weighted determination coefficient method,CPPs can be determined with all the CQAs considered based on their importance.The determination of CPP number is more objective compared with the SPRC method.

Effect of arc-current and spray distance on elastic modulus and fracture toughness of plasma-sprayed chromium oxide coatings

In this experimental study, chromium oxide powder was sprayed on a low-carbon steel substrate using the atmospheric plasma spray process. The current and standoff distances(SODs) were varied to study their effect on the fracture toughness of the coatings. Theoretically, as the arc current increases, the melting of the ceramic oxide should increase and this in turn should lead to the formation of a dense coating. However,it was observed that if the arc power is too high and because the particle size of the powder is small(approximately 30 μm), the particles tend to fly away from the plasma core. Similarly, an appropriate SOD should provide the particles with more melting time, thus resulting in a dense coating. On the other hand, a larger SOD leads to the solidification of the molten particles before the droplets can reach the substrate. All these effects may lead to substantial variation in the fracture toughness of the coating. The present paper attempts to correlate the plasma spraying parameters and microstructure of the coating with the fracture toughness and other primary coating properties.