The Yanchang Formation Chang 7 oil-bearing layer of the Ordos Basin is important in China for producing shale oil.The present-day in situ stress state is of practical implications for the exploration and development o...The Yanchang Formation Chang 7 oil-bearing layer of the Ordos Basin is important in China for producing shale oil.The present-day in situ stress state is of practical implications for the exploration and development of shale oil;however,few studies are focused on stress distributions within the Chang 7 reservoir.In this study,the present-day in situ stress distribution within the Chang 7 reservoir was predicted using the combined spring model based on well logs and measured stress data.The results indicate that stress magnitudes increase with burial depth within the Chang 7 reservoir.Overall,the horizontal maximum principal stress(SHmax),horizontal minimum principal stress(Shmin) and vertical stress(Sv) follow the relationship of Sv≥SHmax>Shmin,indicating a dominant normal faulting stress regime within the Chang 7 reservoir of Ordos Basin.Laterally,high stress values are mainly distributed in the northwestern parts of the studied region,while low stress values are found in the southeastern parts.Factors influencing stress distributions are also analyzed.Stress magnitudes within the Chang 7 reservoir show a positive linear relationship with burial depth.A larger value of Young's modulus results in higher stress magnitudes,and the differential horizontal stress becomes higher when the rock Young's modulus grows larger.展开更多
The objective of this study was to develop once-daily metformin hydrochloride sustained-release tablets (MHSRT) and evaluate their in vitro release behavior. MHSRT were prepared by the film coating method. The in vitr...The objective of this study was to develop once-daily metformin hydrochloride sustained-release tablets (MHSRT) and evaluate their in vitro release behavior. MHSRT were prepared by the film coating method. The in vitro drug release rate of MHSRT and the commercial tablets Fortamet? made in the United States of America in water was fitted with zero order kinetic equation, and Ritger-Peppas kinetic equation in 0.1 M HCl and pH 6.8-phosphate buffer, respectively. The similarity factor f2 values of MHSRT in three different dissolution medium were 82, 80 and 74, respectively in comparison with imported Fortamet?, which were all greater than 50. The results of storage-stability showed that MHSRT were stable for at least 6 months under stress condition (40℃ ± 2℃, RH 75% ± 5%). Therefore, in this study, MHSRT were successfully prepared using optimized formulation technologies that meet mass produce. The in vitro release behavior of MHSRT was almost similar to that of imported Fortamet?.展开更多
Behaviors of C or O in bcc Fe and interactions of C-O and oxygen-carbon-vacancy(O-C-□) are investigated by first principles calculations. Octahedral interstitial site is the most stable position for an O atom in bcc ...Behaviors of C or O in bcc Fe and interactions of C-O and oxygen-carbon-vacancy(O-C-□) are investigated by first principles calculations. Octahedral interstitial site is the most stable position for an O atom in bcc Fe. The migration energy of an O atom in bcc Fe is 0.46 eV. The strength of O-Fe(1 nn) bond(0.32) is slightly greater than that of Fe-Fe metallic bond(0.26). Repulsive interactions of C-C, O-O, and C-O exist in bcc Fe. When the concentration of FIA(FIA refers to C or O) is relatively high, a vacancy can attract four FIAs and form stable FIAs-□ complex.展开更多
We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation in...We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.展开更多
We present the observational results from a detailed timing analysis of the black hole candidate EXO 1846-031 during its outburst in 2019 with the observations of Insight-HXMT,NICER and MAXI.This outburst can be class...We present the observational results from a detailed timing analysis of the black hole candidate EXO 1846-031 during its outburst in 2019 with the observations of Insight-HXMT,NICER and MAXI.This outburst can be classified roughly into four different states.Type-C quasi-periodic oscillations(QPOs)observed by NICER(about 0.1-6 Hz)and Insight-HXMT(about 0.7-8 Hz)are also reported in this work.Meanwhile,we study various physical quantities related to QPO frequency.The QPO rms-frequency relationship in the energy band 1-10 keV indicates that there is a turning pointing in frequency around2 Hz,which is similar to that of GRS 1915+105.A possible hypothesis for the relationship above may be related to the inclination of the source,which may require a high inclination to explain it.The relationships between QPO frequency and QPO rms,hardness,total fractional rms and count rate have also been found in other transient sources,which can indicate that the origin of type-C QPOs is non-thermal.展开更多
Dental caries is one of the most prevalent human diseases resulting from tooth demineralization caused by acid production of bacteria plaque.It remains challenges for current practice to specifically identify,interven...Dental caries is one of the most prevalent human diseases resulting from tooth demineralization caused by acid production of bacteria plaque.It remains challenges for current practice to specifically identify,intervene and interrupt the development of caries while restoring defects.In this study,inspired by natural dental plaque,a stimuli-responsive multidrug delivery system(PMs@NaF-SAP)has been developed to prevent tooth decay and promote enamel restoration.Classic spherical core-shell structures of micelles dual-loaded with antibacterial and restorative agents are self-assembled into bacteria-responsive multidrug delivery system based on the pH-cleavable boronate ester bond,followed by conjugation with salivary-acquired peptide(SAP)to endow the nanoparticle with strong adhesion to tooth enamel.The constructed PMs@NaF-SAP specifically adheres to tooth,identifies cariogenic conditions and intelligently releases drugs at acidic pH,thereby providing antibacterial adhesion and cariogenic biofilm resistance,and restoring the microarchitecture and mechanical properties of demineralized teeth.Topical treatment with PMs@NaF-SAP effectively diminishes the onset and severity of caries without impacting oral microbiota diversity or surrounding mucosal tissues.These findings demonstrate this novel nanotherapy has potential as a promising biomedical application for caries prevention and tooth defect restoration while resisting biofilm-associated diseases in a controlled manner activated by pathological bacteria.展开更多
Purpose We present the five-year in-orbit background evolution of Insight-HXMT since the launch,as well as the effects of the background model in data analysis.Methods The backgrounds of the three main payloads,i.e.,l...Purpose We present the five-year in-orbit background evolution of Insight-HXMT since the launch,as well as the effects of the background model in data analysis.Methods The backgrounds of the three main payloads,i.e.,low-energy telescope,medium-energy telescope,and high-energy telescope,are described.The evolution of the background over time is obtained by simply comparing the background in every year during the in-orbit operation of Insight-HXMT.Results The major observational characteristics of the Insight-HXMT in-orbit background are presented,including the light curve,spectrum,geographical distribution,and long-term evolution.The systematic error in background estimation is investigated for every year.Conclusion The observational characteristics of the five-year in-orbit background are consistent with our knowledge of the satellite design and the space environment,and the background model is still valid for the latest observations of Insight-HXMT.展开更多
A phase field model is developed to simulate the grain evolution of 17-4PH steel during cyclic heat treatment (CHT). Our simulations successfully reproduce the grain morphologies of every CHT. In the process of ever...A phase field model is developed to simulate the grain evolution of 17-4PH steel during cyclic heat treatment (CHT). Our simulations successfully reproduce the grain morphologies of every CHT. In the process of every CHT, phase transformation recrystallization happens. The recrystallized grains appear mainly on the original grain boundaries. The average grain size of 13.2 μm obtained by 1040 ℃×1 h solution treatment for this experimental steel can be refined to 2.2 μm after five CHT's. Furthermore, the effects of phenomenological parameters in our model are discussed.展开更多
Pregnancy is a unique immunologic and microbial condition that requires an adequate level of awareness to provide a fast and protective response against pathogens as well as to maintain a state of tolerance to paterna...Pregnancy is a unique immunologic and microbial condition that requires an adequate level of awareness to provide a fast and protective response against pathogens as well as to maintain a state of tolerance to paternal antigens.Dysregulation of inflammatory pathways in the placenta triggered by pathogens is one of the main factors responsible for pregnancy complications.Type I IFNs are key molecules modulating immune responses at the level of the placenta and are crucial for protection of the pregnancy via their antiviral and immune modulatory properties.In this study,we elucidate the mechanisms controlling the basal expression of IFNβand its negative feedback.Using in vitro and in vivo animal models,we found that TLR signaling maintains basal IFNβlevels through the TLR4-MyD88-independent TBK/IRF3 signaling pathway.We describe the role of the TAM receptor Axl in the regulation of IFNβfunction in human and mouse trophoblast cells.The absence of TAM receptors in vivo is associated with fetal demise due to dysregulation of IFNβexpression and its pro-apoptotic downstream effectors.Collectively,our data describe a feedback signaling pathway controlling the expression and function of IFNβin the trophoblast that is essential for an effective response during viral and microbial infections.展开更多
Investigation into natural fractures is extremely important for the exploration and development of low-permeability reservoirs.Previous studies have proven that abundant oil resources are present in the Upper Triassic...Investigation into natural fractures is extremely important for the exploration and development of low-permeability reservoirs.Previous studies have proven that abundant oil resources are present in the Upper Triassic Yanchang Formation Chang 7 oil-bearing layer of the Ordos Basin,which are accumulated in typical low-permeability shale reservoirs.Natural fractures are important storage spaces and flow pathways for shale oil.In this study,characteristics of natural fractures in the Chang 7 oil-bearing layer are first analyzed.The results indicate that most fractures are shear fractures in the Heshui region,which are characterized by high-angle,unfilled,and ENE-WSW-trending strike.Subsequently,natural fracture distributions in the Yanchang Formation Chang 7 oil-bearing layer of the study area are predicted based on the R/S analysis approach.Logs of AC,CAL,ILD,LL8,and DEN are selected and used for fracture prediction in this study,and the R(n)/S(n)curves of each log are calculated.The quadratic derivatives are calculated to identify the concave points in the R(n)/S(n)curve,indicating the location where natural fracture develops.Considering the difference in sensitivity of each log to natural fracture,gray prediction analysis is used to construct a new parameter,fracture prediction indicator K,to quantitatively predict fracture development.In addition,fracture development among different wells is compared.The results show that parameter K responds well to fracture development.Some minor errors may probably be caused by the heterogeneity of the reservoir,limitation of core range and fracture size,dip angle,filling minerals,etc.展开更多
The crystallographic texture of γ′-Fe4N in compound layer and its influences on the tribological properties of nitrided steel 38CrMoA1 are investigated in the study.The preferred orientation of(200)γ′is produced...The crystallographic texture of γ′-Fe4N in compound layer and its influences on the tribological properties of nitrided steel 38CrMoA1 are investigated in the study.The preferred orientation of(200)γ′is produced by low-temperature nitriding in atmosphere with low nitrogen-hydrogen ratio and increases with the nitriding time.The preferred orientation of(220)γ′appears after 72 h cyclic nitriding.The orientation relationships(0001)ε,/(101)α′,and[ll0]J/[111]γ′(Ill)γ′/(0001)α′ and[011]γ′//[1210]ε,(200)γ′//(l10)α′,and[011]γ′//[111]α′,as well as(1T03)J(220)γ′,and[0100]J/[110]γ′,are established by first-principles method.The misfit of interatornic distance(δ),determining the phase transition resistance,is calculated.Accordingly,two reaction pathways during nitriding,and α′→γ′and α′→ε→γ′,are assumed,which determines the preferred orientations of γ′-Fe4N.Results of wear tests demonstrate that the specimen with preferred orientation of(200)γ′ exhibits lower frictional coefficient and lower wear rate in comparison with the specimen with(220)γ′ preferred orien-tation.(111)γ′ texture usually relates to the lower frictional coefficient but higher wear rate due to the main slip system parallel to the sliding plane.Therefore,the(200)γ′ preferred orientation has a positive significance in improving the wear properties of steels.展开更多
The associated Legendre polynomials play an important role in the central fields,but in the case of′the non-central field we have to introduce the universal associated Legendre polynomials P^m'l_′(x) when studyi...The associated Legendre polynomials play an important role in the central fields,but in the case of′the non-central field we have to introduce the universal associated Legendre polynomials P^m'l_′(x) when studying the modified Pschl-Teller potential and the single ring-shaped potential.We present the evaluations of the integrals involving the universal associated Legendre polynomials and the factor(1-x^2)^(-p-1) as well as some important byproducts of this integral which are useful in deriving the matrix elements in spin-orbit interaction.The calculations are obtained systematically using some properties of the generalized hypergeometric series.展开更多
基金financial supports are from the National Natural Science Foundation of China (41702130 and 41971335)China Postdoctoral Science Foundation (2017T100419 and 2019M660269)Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)。
文摘The Yanchang Formation Chang 7 oil-bearing layer of the Ordos Basin is important in China for producing shale oil.The present-day in situ stress state is of practical implications for the exploration and development of shale oil;however,few studies are focused on stress distributions within the Chang 7 reservoir.In this study,the present-day in situ stress distribution within the Chang 7 reservoir was predicted using the combined spring model based on well logs and measured stress data.The results indicate that stress magnitudes increase with burial depth within the Chang 7 reservoir.Overall,the horizontal maximum principal stress(SHmax),horizontal minimum principal stress(Shmin) and vertical stress(Sv) follow the relationship of Sv≥SHmax>Shmin,indicating a dominant normal faulting stress regime within the Chang 7 reservoir of Ordos Basin.Laterally,high stress values are mainly distributed in the northwestern parts of the studied region,while low stress values are found in the southeastern parts.Factors influencing stress distributions are also analyzed.Stress magnitudes within the Chang 7 reservoir show a positive linear relationship with burial depth.A larger value of Young's modulus results in higher stress magnitudes,and the differential horizontal stress becomes higher when the rock Young's modulus grows larger.
文摘The objective of this study was to develop once-daily metformin hydrochloride sustained-release tablets (MHSRT) and evaluate their in vitro release behavior. MHSRT were prepared by the film coating method. The in vitro drug release rate of MHSRT and the commercial tablets Fortamet? made in the United States of America in water was fitted with zero order kinetic equation, and Ritger-Peppas kinetic equation in 0.1 M HCl and pH 6.8-phosphate buffer, respectively. The similarity factor f2 values of MHSRT in three different dissolution medium were 82, 80 and 74, respectively in comparison with imported Fortamet?, which were all greater than 50. The results of storage-stability showed that MHSRT were stable for at least 6 months under stress condition (40℃ ± 2℃, RH 75% ± 5%). Therefore, in this study, MHSRT were successfully prepared using optimized formulation technologies that meet mass produce. The in vitro release behavior of MHSRT was almost similar to that of imported Fortamet?.
基金Project supported by the Fundamental Research Funds in Heilongjiang Provincial Universities,China(Grant No.135209204)
文摘Behaviors of C or O in bcc Fe and interactions of C-O and oxygen-carbon-vacancy(O-C-□) are investigated by first principles calculations. Octahedral interstitial site is the most stable position for an O atom in bcc Fe. The migration energy of an O atom in bcc Fe is 0.46 eV. The strength of O-Fe(1 nn) bond(0.32) is slightly greater than that of Fe-Fe metallic bond(0.26). Repulsive interactions of C-C, O-O, and C-O exist in bcc Fe. When the concentration of FIA(FIA refers to C or O) is relatively high, a vacancy can attract four FIAs and form stable FIAs-□ complex.
基金Project supported by the National Natural Science Foundation of China(Grant No.11975196)partially by SIP,Instituto Politecnico Nacional(IPN),Mexico(Grant No.20210414)。
文摘We propose a new scheme to study the exact solutions of a class of hyperbolic potential well.We first apply different forms of function transformation and variable substitution to transform the Schrodinger equation into a confluent Heun differential equation and then construct a Wronskian determinant by finding two linearly dependent solutions for the same eigenstate.And then in terms of the energy spectrum equation which is obtained from the Wronskian determinant,we are able to graphically decide the quantum number with respect to each eigenstate and the total number of bound states for a given potential well.Such a procedure allows us to calculate the eigenvalues for different quantum states via Maple and then substitute them into the wave function to obtain the expected analytical eigenfunction expressed by the confluent Heun function.The linearly dependent relation between two eigenfunctions is also studied.
基金the HXMT mission,a project funded by China National Space Administration(CNSA)and the Chinese Academy of Sciences(CAS)supported by the National Key R&D Program of China(2016YFA0400800)the National Natural Science Foundation of China(Grant Nos.11673023,U1838201,U1838115,U1838111,U1838202,11733009 and U1838108)。
文摘We present the observational results from a detailed timing analysis of the black hole candidate EXO 1846-031 during its outburst in 2019 with the observations of Insight-HXMT,NICER and MAXI.This outburst can be classified roughly into four different states.Type-C quasi-periodic oscillations(QPOs)observed by NICER(about 0.1-6 Hz)and Insight-HXMT(about 0.7-8 Hz)are also reported in this work.Meanwhile,we study various physical quantities related to QPO frequency.The QPO rms-frequency relationship in the energy band 1-10 keV indicates that there is a turning pointing in frequency around2 Hz,which is similar to that of GRS 1915+105.A possible hypothesis for the relationship above may be related to the inclination of the source,which may require a high inclination to explain it.The relationships between QPO frequency and QPO rms,hardness,total fractional rms and count rate have also been found in other transient sources,which can indicate that the origin of type-C QPOs is non-thermal.
基金supported by the National Natural Science Foundation of China(No.82001106,81970918,81901043).
文摘Dental caries is one of the most prevalent human diseases resulting from tooth demineralization caused by acid production of bacteria plaque.It remains challenges for current practice to specifically identify,intervene and interrupt the development of caries while restoring defects.In this study,inspired by natural dental plaque,a stimuli-responsive multidrug delivery system(PMs@NaF-SAP)has been developed to prevent tooth decay and promote enamel restoration.Classic spherical core-shell structures of micelles dual-loaded with antibacterial and restorative agents are self-assembled into bacteria-responsive multidrug delivery system based on the pH-cleavable boronate ester bond,followed by conjugation with salivary-acquired peptide(SAP)to endow the nanoparticle with strong adhesion to tooth enamel.The constructed PMs@NaF-SAP specifically adheres to tooth,identifies cariogenic conditions and intelligently releases drugs at acidic pH,thereby providing antibacterial adhesion and cariogenic biofilm resistance,and restoring the microarchitecture and mechanical properties of demineralized teeth.Topical treatment with PMs@NaF-SAP effectively diminishes the onset and severity of caries without impacting oral microbiota diversity or surrounding mucosal tissues.These findings demonstrate this novel nanotherapy has potential as a promising biomedical application for caries prevention and tooth defect restoration while resisting biofilm-associated diseases in a controlled manner activated by pathological bacteria.
基金supports from the National Key R&D Program of China(2021YFA0718500)the National Natural Science Foundation of China under Grants Nos.U1838202 and U1838201This work was partially supported by International Partnership Program of Chinese Academy of Sciences(Grant No.113111KYSB20190020).
文摘Purpose We present the five-year in-orbit background evolution of Insight-HXMT since the launch,as well as the effects of the background model in data analysis.Methods The backgrounds of the three main payloads,i.e.,low-energy telescope,medium-energy telescope,and high-energy telescope,are described.The evolution of the background over time is obtained by simply comparing the background in every year during the in-orbit operation of Insight-HXMT.Results The major observational characteristics of the Insight-HXMT in-orbit background are presented,including the light curve,spectrum,geographical distribution,and long-term evolution.The systematic error in background estimation is investigated for every year.Conclusion The observational characteristics of the five-year in-orbit background are consistent with our knowledge of the satellite design and the space environment,and the background model is still valid for the latest observations of Insight-HXMT.
基金supported by National Natural Science Foundation of China(No.51071061)NSAF(No.11176011)
文摘A phase field model is developed to simulate the grain evolution of 17-4PH steel during cyclic heat treatment (CHT). Our simulations successfully reproduce the grain morphologies of every CHT. In the process of every CHT, phase transformation recrystallization happens. The recrystallized grains appear mainly on the original grain boundaries. The average grain size of 13.2 μm obtained by 1040 ℃×1 h solution treatment for this experimental steel can be refined to 2.2 μm after five CHT's. Furthermore, the effects of phenomenological parameters in our model are discussed.
基金This study is in part funded by grants P01HD054713,R56AI124356,and 3N01 HD23342 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development,National Institutes of Health,Department of Health and Human Services.
文摘Pregnancy is a unique immunologic and microbial condition that requires an adequate level of awareness to provide a fast and protective response against pathogens as well as to maintain a state of tolerance to paternal antigens.Dysregulation of inflammatory pathways in the placenta triggered by pathogens is one of the main factors responsible for pregnancy complications.Type I IFNs are key molecules modulating immune responses at the level of the placenta and are crucial for protection of the pregnancy via their antiviral and immune modulatory properties.In this study,we elucidate the mechanisms controlling the basal expression of IFNβand its negative feedback.Using in vitro and in vivo animal models,we found that TLR signaling maintains basal IFNβlevels through the TLR4-MyD88-independent TBK/IRF3 signaling pathway.We describe the role of the TAM receptor Axl in the regulation of IFNβfunction in human and mouse trophoblast cells.The absence of TAM receptors in vivo is associated with fetal demise due to dysregulation of IFNβexpression and its pro-apoptotic downstream effectors.Collectively,our data describe a feedback signaling pathway controlling the expression and function of IFNβin the trophoblast that is essential for an effective response during viral and microbial infections.
基金supports are from the National Natural Science Foundation of China(Grant Nos.41702130,41971335)Natural Science Foundation of Jiangsu Province,China(BK20201349)Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD).
文摘Investigation into natural fractures is extremely important for the exploration and development of low-permeability reservoirs.Previous studies have proven that abundant oil resources are present in the Upper Triassic Yanchang Formation Chang 7 oil-bearing layer of the Ordos Basin,which are accumulated in typical low-permeability shale reservoirs.Natural fractures are important storage spaces and flow pathways for shale oil.In this study,characteristics of natural fractures in the Chang 7 oil-bearing layer are first analyzed.The results indicate that most fractures are shear fractures in the Heshui region,which are characterized by high-angle,unfilled,and ENE-WSW-trending strike.Subsequently,natural fracture distributions in the Yanchang Formation Chang 7 oil-bearing layer of the study area are predicted based on the R/S analysis approach.Logs of AC,CAL,ILD,LL8,and DEN are selected and used for fracture prediction in this study,and the R(n)/S(n)curves of each log are calculated.The quadratic derivatives are calculated to identify the concave points in the R(n)/S(n)curve,indicating the location where natural fracture develops.Considering the difference in sensitivity of each log to natural fracture,gray prediction analysis is used to construct a new parameter,fracture prediction indicator K,to quantitatively predict fracture development.In addition,fracture development among different wells is compared.The results show that parameter K responds well to fracture development.Some minor errors may probably be caused by the heterogeneity of the reservoir,limitation of core range and fracture size,dip angle,filling minerals,etc.
基金supported by the National Natural Science Foundation of China(Grant Nos.51371070and 51601048)
文摘The crystallographic texture of γ′-Fe4N in compound layer and its influences on the tribological properties of nitrided steel 38CrMoA1 are investigated in the study.The preferred orientation of(200)γ′is produced by low-temperature nitriding in atmosphere with low nitrogen-hydrogen ratio and increases with the nitriding time.The preferred orientation of(220)γ′appears after 72 h cyclic nitriding.The orientation relationships(0001)ε,/(101)α′,and[ll0]J/[111]γ′(Ill)γ′/(0001)α′ and[011]γ′//[1210]ε,(200)γ′//(l10)α′,and[011]γ′//[111]α′,as well as(1T03)J(220)γ′,and[0100]J/[110]γ′,are established by first-principles method.The misfit of interatornic distance(δ),determining the phase transition resistance,is calculated.Accordingly,two reaction pathways during nitriding,and α′→γ′and α′→ε→γ′,are assumed,which determines the preferred orientations of γ′-Fe4N.Results of wear tests demonstrate that the specimen with preferred orientation of(200)γ′ exhibits lower frictional coefficient and lower wear rate in comparison with the specimen with(220)γ′ preferred orien-tation.(111)γ′ texture usually relates to the lower frictional coefficient but higher wear rate due to the main slip system parallel to the sliding plane.Therefore,the(200)γ′ preferred orientation has a positive significance in improving the wear properties of steels.
基金Supported by the National Natural Science Foundation of China under Grant No.11275165Partially by 20160978-SIP-IPN,Mexico
文摘The associated Legendre polynomials play an important role in the central fields,but in the case of′the non-central field we have to introduce the universal associated Legendre polynomials P^m'l_′(x) when studying the modified Pschl-Teller potential and the single ring-shaped potential.We present the evaluations of the integrals involving the universal associated Legendre polynomials and the factor(1-x^2)^(-p-1) as well as some important byproducts of this integral which are useful in deriving the matrix elements in spin-orbit interaction.The calculations are obtained systematically using some properties of the generalized hypergeometric series.