Objective: To elucidate the expression of the bcl-2 gene in association with both biological characteristics of hu- man primary pancreatic carcinoma and patient's prog- nosis. Methods: The s-p immunohistochemistry...Objective: To elucidate the expression of the bcl-2 gene in association with both biological characteristics of hu- man primary pancreatic carcinoma and patient's prog- nosis. Methods: The s-p immunohistochemistry assay was used to detect the expression of the bcl-2 gene on para- ffin-embedded sections from 97 cases of primary pan- creatic carcinoma, 32 cases of pancreatitis, and 21 ca- ses of normal pancreas. Results: Among the 97 cases of pancreatic carcinoma, 70 (72.2%) showed positive staining for the bcl-2 pro- tein. In the 32 cases of pancreatitis, 3 (9.4%) showed positive immunostaining for the bcl-2, and in the nor- mal pancreas cases, 1 (4.8%) showed positive immu- nostaining for the bcl-2. However, the positive staining rates of the bcl-2 protein were lower in tumor tissue from the patients with metastases and tumor-node-me- tastasis (TNM) stages Ⅲ, Ⅳ than in those from those with non-metastases, well differentiation, non-invasion and TNM stages Ⅰ, Ⅱ. The patients with positive im- munostaining of bcl-2 have a longer postoperative sur- vival than those with negative staining. Conclusions: Pancreatic carcinoma expressed a high positivity for bcl-2. Findings suggested that the overex- pression of bcl-2 is related to the carcinogenesis and progression of human pancreatic carcinoma. Bcl-2 might be one of the parameters in terms of biological characteristics and good prognosis in patients with pancreatic carcinoma.展开更多
Objective:To compare effect of immunoprevention or immunotherapy based on denderitic cells (DCs),or supernatants on pancreatic carcinoma and hepatocelluar carcinoma in ritro and in vivo.Methods:DCs and monouclear cell...Objective:To compare effect of immunoprevention or immunotherapy based on denderitic cells (DCs),or supernatants on pancreatic carcinoma and hepatocelluar carcinoma in ritro and in vivo.Methods:DCs and monouclear cells (immunoeffecetor cells) were stimulated with hGM-CSF,hIL-4,hTNF-α,PC3 TA or BEL7402 TA and hIL-2,then DCs and immunoeffector cells were cocultured,and supernatants were harvested.In vitro,the immunoeffector cells were divided into A0 group (without DCs stimulated),A1 group (DCs stimulated,cultured with cytokines cocktail),A2 group (DCs stimulated,cultured with cytokines cocktail and tumor antigen.DCs vaccine).Cytoxicity assay was performed with lactate dehydogenase method,In vivo,the nude mice were allocated in 3 groups:prevention group,receiving immunoeffector cells activated by DCs vaccine 2 days before inoculation with PC3 or BEL7402;treatment group,receiving immunoeffector cells activated by DCs vaccine after development of implanted tumor in all nude mice;control group,receiving equivalents amount of RPMI1640 cultured liquid.On the 45th day,all the nude mice were sacrificed and the tumor was weighed.Results:The maximal inhibition rate of the A0.A1 andA2 were 3.5%.68.1%.81.0% in the BEL7402;4.5%,33.0%.62.4% in the PC3.The differences in tumor weight among three groups were significant,but the difference were not significant between the PC3 and BEL7402.Conclusions:DCs vaccine or supernatants may play an important role in treating and preventing against malignant tumor.展开更多
By throwing a particle with electric charge and angular momentum into the black holes, much evidence shows that the naked singularity of some (3+1)-dimensional black holes might be seen, which is not allowed in the...By throwing a particle with electric charge and angular momentum into the black holes, much evidence shows that the naked singularity of some (3+1)-dimensional black holes might be seen, which is not allowed in the weak cosmic censorship conjecture. In this study, we consider a (2+1)-dimensional Peldan black hole and find that it could be destroyed under certain conditions in both extreme and near-extreme cases.展开更多
Objective:The mechanism of Chinese herbal medicine"Bi xie and Tu fuling"on the treatment of gouty arthritis was explored through network pharmacological methods.Methods:First,the TCMSP Chinese medicine syste...Objective:The mechanism of Chinese herbal medicine"Bi xie and Tu fuling"on the treatment of gouty arthritis was explored through network pharmacological methods.Methods:First,the TCMSP Chinese medicine system pharmacology database and analysis platform were used to define the bioavailability(OB)30%and drug-likeness(DL)0.18.Database to mine genetic targets related to gouty arthritis disease.Finally,the two genes are intersected to construct a Chinese medicine regulatory network of Chinese medicine-components-target genes-disease.The genes in the network are used to construct a protein interaction network to find core genes for analysis of GO and KEGG.Results:There were a total of 84 active ingredients in Chinese medicine Poria and Poria cocos,and 17 effective ingredients and 180 genetic targets were obtained after screening.600 disease targets for gouty arthritis were identified,and 58 were common target genes for both.PPI network analysis revealed that IL1β,VEGFA,MAPK1,IL10,and PTGS2 may be drugs for treating gouty arthritis.Key targets.GO enrichment analysis identified 1,399 entries(P<0.05),of which biological processes mainly include biological stimulation,biological regulation,cell metabolism,etc;KEGG pathway enrichment analysis identified 152 signal pathways,of which signal pathways involved inflammation,metabolism,In terms of aging,mainly including the IL-4,IL-10,IL-13,IL-17signal pathway,etc.Conclusion:"Bi xie and Tu fuling"drugs have anti-inflammatory and immunological effects on gouty arthritis through multiple targets and multiple pathways.The mechanism of lowering uric acid and protecting liver and kidney is not clear.It needs molecular biology research to improve it.The mechanism of the action of the"Bi xie and Tu fuling"medicine pair provides new ideas for the clinical prescriptions.展开更多
Objective:To Find the core targets and drug action mechanism of Si Miao decoction for the treatment of acute gouty arthritis.Methods:Through the TCMSP database,the chemical composition of all the drugs in Si Miao deco...Objective:To Find the core targets and drug action mechanism of Si Miao decoction for the treatment of acute gouty arthritis.Methods:Through the TCMSP database,the chemical composition of all the drugs in Si Miao decoction was obtained.The Perl script was compiled and the UniProt database was searched to determine the corresponding target of the chemical composition.Then,the disease databases such as OMIM,DisGeNET,and GeneCards were searched in order to determine acute gouty arthritis Related targets.Finally,screen common targets for drugs and diseases,use the STRING database and Cytoscape software to build a network control map of drugs-chemical components-targets-disease.Use R language software to screen common targets and find the four best The core targets of San for the treatment of acute gouty arthritis.The GO and KEGG analysis of the core targets were performed to clarify the core targets and mechanism of Si Miao decoction for the treatment of gout.Results:There are 64 effective chemical components in Si Miao decoction,197 genetic targets,600 disease targets,and 58 common targets.It is predicted that IL6,VEGFA,IL1B,JUN,PTGS2,and CCL2 may be treated by Si Miao decoction for gout The core target of arthritis.GO enrichment analysis identified 85 entries,of which biological processes mainly included the regulation of cytokine activity,protease activation,nucleic acid expression,etc.;KEGG pathway enrichment analysis identified 135 signaling pathways,of which signaling pathways involved the IL-17 signaling pathway,TNF signaling pathway,Th17 cell differentiation and other pathways.Conclusion:Si Miao decoction acts on acute gouty arthritis by regulating the occurrence of inflammation,and has significant anti-inflammatory and immune effects.The formula is rigorous and scientific,and it is worthy of clinical application.展开更多
Background The placebo response of sham acupuncture in patients with primary dysmenorrhea is a substantial factor associated with analgesia.However,the magnitude of the placebo response is unclear.Objective This meta-...Background The placebo response of sham acupuncture in patients with primary dysmenorrhea is a substantial factor associated with analgesia.However,the magnitude of the placebo response is unclear.Objective This meta-analysis assessed the effects of sham acupuncture in patients with primary dysmenorrhea and the factors contributing to these effects.Search strategy PubMed,Embase,Web of Science,and Cochrane CENTRAL databases were searched from inception up to August 20,2022.Inclusion criteria Randomized controlled trials(RCTs)using sham acupuncture as a control for female patients of reproductive age with primary dysmenorrhea were included.Data extraction and analysis Pain intensity,retrospective symptom scale,and health-related quality of life were outcome measures used in these trials.Placebo response was defined as the change in the outcome of interest from baseline to endpoint.We used standardized mean difference(SMD)to estimate the effect size of the placebo response.Results Thirteen RCTs were included.The pooled placebo response size for pain intensity was the largest(SMD=−0.99;95%confidence interval[CI],−1.31 to−0.68),followed by the retrospective symptom scale(Total frequency rating score:SMD=−0.20;95%CI,−0.80 to−0.39.Average severity score:SMD=−0.35;95%CI,−0.90 to−0.20)and physical component of SF-36(SMD=0.27;95%CI,−0.17 to 0.72).Studies using blunt-tip needles,single-center trials,studies with a low risk of bias,studies in which patients had a longer disease course,studies in which clinicians had<5 years of experience,and trials conducted outside Asia were more likely to have a lower placebo response.Conclusion Strong placebo response and some relative factors were found in patients with primary dysmenorrhea.PROSPERO registration number:CRD42022304215.展开更多
Successful regeneration of cartilage tissue at a clinical scale has been a tremendous challenge in the past decades. Microcarriers (MCs), usually used for cell and drug delivery, have been studied broadly across a wid...Successful regeneration of cartilage tissue at a clinical scale has been a tremendous challenge in the past decades. Microcarriers (MCs), usually used for cell and drug delivery, have been studied broadly across a wide range of medical fields, especially the cartilage tissue engineering (TE). Notably, microcarrier systems provide an attractive method for regulating cell phenotype and microtissue maturations, they also serve as powerful injectable carriers and are combined with new technologies for cartilage regeneration. In this review, we introduced the typical methods to fabricate various types of microcarriers and discussed the appropriate ma-terials for microcarriers. Furthermore, we highlighted recent progress of applications and general design prin-ciple for microcarriers. Finally, we summarized the current challenges and promising prospects of microcarrier-based systems for medical applications. Overall, this review provides comprehensive and systematic guidelines for the rational design and applications of microcarriers in cartilage TE.展开更多
The thermodynamical quantities are usually considered as the independent ones in the case of the existence of multi-horizons. Comparing the first laws for the event horizon and cosmological horizon of Schwarzschild-de...The thermodynamical quantities are usually considered as the independent ones in the case of the existence of multi-horizons. Comparing the first laws for the event horizon and cosmological horizon of Schwarzschild-de Sitter space-time, we find them share the same values of mass, charge and cosmological constant, which might imply that there exists entanglement between the two horizons. Naturally we attempt to add an extra term, which contributed to the total entropy of the black hole. We recalculate the total entropy and the effective specific heat by taking the globally effective first law and find that they will be emanative when the two horizons approach to each other.展开更多
By adopting a result from generalized uncertainty principles (GUP), we modify the inner bound of the membrane model to a physical fixed value and get the cut-offs naturally rather than by hand, which are both in brick...By adopting a result from generalized uncertainty principles (GUP), we modify the inner bound of the membrane model to a physical fixed value and get the cut-offs naturally rather than by hand, which are both in brickwall model and membrane model, and the semi-classical quantization condition could always be valid as well. We also calculate the entropies of Schwarzschild-de Sitter black hole and find the GUP we choose qualitatively shows that the requirement of mass in this method is the same as the natural requirement of the Schwarzschild-de Sitter black hole,which means the method might be self-consistent.展开更多
If radiative and self-force effects are neglected, we find that feeding a test particle into a near-extremal Kerr- Newman-AdS black hole could lead to destroy their event horizon, giving rise to naked singularities. H...If radiative and self-force effects are neglected, we find that feeding a test particle into a near-extremal Kerr- Newman-AdS black hole could lead to destroy their event horizon, giving rise to naked singularities. Hence radiative and self-force effects must be taken into account to further test cosmic censorship. Moreover, the allowed paxameter range for this test particle is very narrow, this leaves the possibility of radiative and self-force effects considerations to cure the problem of WCC violation in Kerr-Newman-AdS spacetime.展开更多
We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the...We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the surface area at the horizons without cut-off. And reveal the possible value of the minimum length.展开更多
文摘Objective: To elucidate the expression of the bcl-2 gene in association with both biological characteristics of hu- man primary pancreatic carcinoma and patient's prog- nosis. Methods: The s-p immunohistochemistry assay was used to detect the expression of the bcl-2 gene on para- ffin-embedded sections from 97 cases of primary pan- creatic carcinoma, 32 cases of pancreatitis, and 21 ca- ses of normal pancreas. Results: Among the 97 cases of pancreatic carcinoma, 70 (72.2%) showed positive staining for the bcl-2 pro- tein. In the 32 cases of pancreatitis, 3 (9.4%) showed positive immunostaining for the bcl-2, and in the nor- mal pancreas cases, 1 (4.8%) showed positive immu- nostaining for the bcl-2. However, the positive staining rates of the bcl-2 protein were lower in tumor tissue from the patients with metastases and tumor-node-me- tastasis (TNM) stages Ⅲ, Ⅳ than in those from those with non-metastases, well differentiation, non-invasion and TNM stages Ⅰ, Ⅱ. The patients with positive im- munostaining of bcl-2 have a longer postoperative sur- vival than those with negative staining. Conclusions: Pancreatic carcinoma expressed a high positivity for bcl-2. Findings suggested that the overex- pression of bcl-2 is related to the carcinogenesis and progression of human pancreatic carcinoma. Bcl-2 might be one of the parameters in terms of biological characteristics and good prognosis in patients with pancreatic carcinoma.
文摘Objective:To compare effect of immunoprevention or immunotherapy based on denderitic cells (DCs),or supernatants on pancreatic carcinoma and hepatocelluar carcinoma in ritro and in vivo.Methods:DCs and monouclear cells (immunoeffecetor cells) were stimulated with hGM-CSF,hIL-4,hTNF-α,PC3 TA or BEL7402 TA and hIL-2,then DCs and immunoeffector cells were cocultured,and supernatants were harvested.In vitro,the immunoeffector cells were divided into A0 group (without DCs stimulated),A1 group (DCs stimulated,cultured with cytokines cocktail),A2 group (DCs stimulated,cultured with cytokines cocktail and tumor antigen.DCs vaccine).Cytoxicity assay was performed with lactate dehydogenase method,In vivo,the nude mice were allocated in 3 groups:prevention group,receiving immunoeffector cells activated by DCs vaccine 2 days before inoculation with PC3 or BEL7402;treatment group,receiving immunoeffector cells activated by DCs vaccine after development of implanted tumor in all nude mice;control group,receiving equivalents amount of RPMI1640 cultured liquid.On the 45th day,all the nude mice were sacrificed and the tumor was weighed.Results:The maximal inhibition rate of the A0.A1 andA2 were 3.5%.68.1%.81.0% in the BEL7402;4.5%,33.0%.62.4% in the PC3.The differences in tumor weight among three groups were significant,but the difference were not significant between the PC3 and BEL7402.Conclusions:DCs vaccine or supernatants may play an important role in treating and preventing against malignant tumor.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11275099,11435006 and 11405130the Double First-Class University Construction Project of Northwest University
文摘By throwing a particle with electric charge and angular momentum into the black holes, much evidence shows that the naked singularity of some (3+1)-dimensional black holes might be seen, which is not allowed in the weak cosmic censorship conjecture. In this study, we consider a (2+1)-dimensional Peldan black hole and find that it could be destroyed under certain conditions in both extreme and near-extreme cases.
基金National administration of TCM base special fund(No.JDZX2015277)Beijing municipal science and technology commission science and technology star project(No.Z191100001119025)
文摘Objective:The mechanism of Chinese herbal medicine"Bi xie and Tu fuling"on the treatment of gouty arthritis was explored through network pharmacological methods.Methods:First,the TCMSP Chinese medicine system pharmacology database and analysis platform were used to define the bioavailability(OB)30%and drug-likeness(DL)0.18.Database to mine genetic targets related to gouty arthritis disease.Finally,the two genes are intersected to construct a Chinese medicine regulatory network of Chinese medicine-components-target genes-disease.The genes in the network are used to construct a protein interaction network to find core genes for analysis of GO and KEGG.Results:There were a total of 84 active ingredients in Chinese medicine Poria and Poria cocos,and 17 effective ingredients and 180 genetic targets were obtained after screening.600 disease targets for gouty arthritis were identified,and 58 were common target genes for both.PPI network analysis revealed that IL1β,VEGFA,MAPK1,IL10,and PTGS2 may be drugs for treating gouty arthritis.Key targets.GO enrichment analysis identified 1,399 entries(P<0.05),of which biological processes mainly include biological stimulation,biological regulation,cell metabolism,etc;KEGG pathway enrichment analysis identified 152 signal pathways,of which signal pathways involved inflammation,metabolism,In terms of aging,mainly including the IL-4,IL-10,IL-13,IL-17signal pathway,etc.Conclusion:"Bi xie and Tu fuling"drugs have anti-inflammatory and immunological effects on gouty arthritis through multiple targets and multiple pathways.The mechanism of lowering uric acid and protecting liver and kidney is not clear.It needs molecular biology research to improve it.The mechanism of the action of the"Bi xie and Tu fuling"medicine pair provides new ideas for the clinical prescriptions.
基金National Natural Resources Foundation program(No.81373802)Beijing Natural Science Foundation(No.7172244)Beijing Science and Technology Project(No.Z191100006619024)
文摘Objective:To Find the core targets and drug action mechanism of Si Miao decoction for the treatment of acute gouty arthritis.Methods:Through the TCMSP database,the chemical composition of all the drugs in Si Miao decoction was obtained.The Perl script was compiled and the UniProt database was searched to determine the corresponding target of the chemical composition.Then,the disease databases such as OMIM,DisGeNET,and GeneCards were searched in order to determine acute gouty arthritis Related targets.Finally,screen common targets for drugs and diseases,use the STRING database and Cytoscape software to build a network control map of drugs-chemical components-targets-disease.Use R language software to screen common targets and find the four best The core targets of San for the treatment of acute gouty arthritis.The GO and KEGG analysis of the core targets were performed to clarify the core targets and mechanism of Si Miao decoction for the treatment of gout.Results:There are 64 effective chemical components in Si Miao decoction,197 genetic targets,600 disease targets,and 58 common targets.It is predicted that IL6,VEGFA,IL1B,JUN,PTGS2,and CCL2 may be treated by Si Miao decoction for gout The core target of arthritis.GO enrichment analysis identified 85 entries,of which biological processes mainly included the regulation of cytokine activity,protease activation,nucleic acid expression,etc.;KEGG pathway enrichment analysis identified 135 signaling pathways,of which signaling pathways involved the IL-17 signaling pathway,TNF signaling pathway,Th17 cell differentiation and other pathways.Conclusion:Si Miao decoction acts on acute gouty arthritis by regulating the occurrence of inflammation,and has significant anti-inflammatory and immune effects.The formula is rigorous and scientific,and it is worthy of clinical application.
基金This work was supported by the National Natural Science Foundation of China(No.82174234)the National Science Fund for Distinguished Young Scholars(No.81825024)。
文摘Background The placebo response of sham acupuncture in patients with primary dysmenorrhea is a substantial factor associated with analgesia.However,the magnitude of the placebo response is unclear.Objective This meta-analysis assessed the effects of sham acupuncture in patients with primary dysmenorrhea and the factors contributing to these effects.Search strategy PubMed,Embase,Web of Science,and Cochrane CENTRAL databases were searched from inception up to August 20,2022.Inclusion criteria Randomized controlled trials(RCTs)using sham acupuncture as a control for female patients of reproductive age with primary dysmenorrhea were included.Data extraction and analysis Pain intensity,retrospective symptom scale,and health-related quality of life were outcome measures used in these trials.Placebo response was defined as the change in the outcome of interest from baseline to endpoint.We used standardized mean difference(SMD)to estimate the effect size of the placebo response.Results Thirteen RCTs were included.The pooled placebo response size for pain intensity was the largest(SMD=−0.99;95%confidence interval[CI],−1.31 to−0.68),followed by the retrospective symptom scale(Total frequency rating score:SMD=−0.20;95%CI,−0.80 to−0.39.Average severity score:SMD=−0.35;95%CI,−0.90 to−0.20)and physical component of SF-36(SMD=0.27;95%CI,−0.17 to 0.72).Studies using blunt-tip needles,single-center trials,studies with a low risk of bias,studies in which patients had a longer disease course,studies in which clinicians had<5 years of experience,and trials conducted outside Asia were more likely to have a lower placebo response.Conclusion Strong placebo response and some relative factors were found in patients with primary dysmenorrhea.PROSPERO registration number:CRD42022304215.
基金The authors thank Shuo Wang and Shen Ji for helpful discussion.This work was supported by the National Natural Science Foundation of China(Grant No.81773091)the Natural Science Foundation of Beijing Municipality(Grant No.7212020)+4 种基金Science and Technology Planning Project of Beijing Municipal Education Commission(Grant No.KM202110025013)the Beijing Municipal Excellent Talents Project(Grant No.2020A43)Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA16020802)CAS Engineering Laboratory for Intelligent Organ Manufacturing(Grant No.KFJ-PTXM-039)the National Natural Science Foundation of China(Grant No.82001848).
文摘Successful regeneration of cartilage tissue at a clinical scale has been a tremendous challenge in the past decades. Microcarriers (MCs), usually used for cell and drug delivery, have been studied broadly across a wide range of medical fields, especially the cartilage tissue engineering (TE). Notably, microcarrier systems provide an attractive method for regulating cell phenotype and microtissue maturations, they also serve as powerful injectable carriers and are combined with new technologies for cartilage regeneration. In this review, we introduced the typical methods to fabricate various types of microcarriers and discussed the appropriate ma-terials for microcarriers. Furthermore, we highlighted recent progress of applications and general design prin-ciple for microcarriers. Finally, we summarized the current challenges and promising prospects of microcarrier-based systems for medical applications. Overall, this review provides comprehensive and systematic guidelines for the rational design and applications of microcarriers in cartilage TE.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675139,11605137,11435006,11405130the Double First-Class University Construction Project of Northwest University+1 种基金supported by the China Postdoctoral Science Foundation under Grant No.2017M623219Shaanxi Postdoctoral Science Foundation
文摘The thermodynamical quantities are usually considered as the independent ones in the case of the existence of multi-horizons. Comparing the first laws for the event horizon and cosmological horizon of Schwarzschild-de Sitter space-time, we find them share the same values of mass, charge and cosmological constant, which might imply that there exists entanglement between the two horizons. Naturally we attempt to add an extra term, which contributed to the total entropy of the black hole. We recalculate the total entropy and the effective specific heat by taking the globally effective first law and find that they will be emanative when the two horizons approach to each other.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675139,11605137,11435006,11405130the Double First-Class University Construction Project of Northwest University+1 种基金the China Postdoctoral Science Foundation under Grant No.2017M623219Shaanxi Postdoctoral Science Foundation
文摘By adopting a result from generalized uncertainty principles (GUP), we modify the inner bound of the membrane model to a physical fixed value and get the cut-offs naturally rather than by hand, which are both in brickwall model and membrane model, and the semi-classical quantization condition could always be valid as well. We also calculate the entropies of Schwarzschild-de Sitter black hole and find the GUP we choose qualitatively shows that the requirement of mass in this method is the same as the natural requirement of the Schwarzschild-de Sitter black hole,which means the method might be self-consistent.
基金Supported by the National Science Foundation of China under Grant Nos.11675139,11405130,11647050
文摘If radiative and self-force effects are neglected, we find that feeding a test particle into a near-extremal Kerr- Newman-AdS black hole could lead to destroy their event horizon, giving rise to naked singularities. Hence radiative and self-force effects must be taken into account to further test cosmic censorship. Moreover, the allowed paxameter range for this test particle is very narrow, this leaves the possibility of radiative and self-force effects considerations to cure the problem of WCC violation in Kerr-Newman-AdS spacetime.
基金Supported by National Natural Science Foundation of China under Grant Nos.11275099,11435006,11405130the Double FirstClass University Construction Project of Northwest University
文摘We study the entropy of Schwarzschild-de Sitter black holes based on generalized uncertainty principle with brick-wall method by counting degrees of freedom near the horizons and obtain the entropy proportional to the surface area at the horizons without cut-off. And reveal the possible value of the minimum length.