The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infini...The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.展开更多
The root is crucial for the physiological function of the tooth, and a healthy root allows an artificial crown to function as required clinically. Tooth crown development has been studied intensively during the last f...The root is crucial for the physiological function of the tooth, and a healthy root allows an artificial crown to function as required clinically. Tooth crown development has been studied intensively during the last few decades, but root development remains not well understood. Here we review the root development processes, including cell fate determination, induction of odontoblast and cementoblast differentiation, interaction of root epithelium and mesenchyme, and other molecular mechanisms. This review summarizes our current understanding of the signaling cascades and mechanisms involved in root development. It also sets the stage for de novo tooth regeneration.展开更多
Objective:To explore the phytochemical constituents from petroleum ether and diehloromethane extracts of Moringa oleifera(M.oleufera)roots using GC/GC—MS.Methods:A total of 5.11 kg fresh and undried crashed root of M...Objective:To explore the phytochemical constituents from petroleum ether and diehloromethane extracts of Moringa oleifera(M.oleufera)roots using GC/GC—MS.Methods:A total of 5.11 kg fresh and undried crashed root of M.oleifera were cut into small pieces and extracted with petroleum ether and diehloromethane(20 L.each) at room temperature for 2 d.The concentrated extracts were subjected to their GC—MS analysis.Results:The GC-MS analysis of the petroleum ether and diehloromethane extracts of M.oleifern roots,which showed promising biological activities,has resulted in the identification 102 compounds.These constituents belong to 15 classes of compounds including hydrocarbons,fatty acids,esters,alcohols,isolhioeyanate.thiocyanale,pyrazine,aromalics.alkamides.cyanides,steroids,halocompounds.urea and N-hydroxyimine derivatives,unsaturated alkenamides.alkyne and indole.GC/GC-MS studies on petroleum ether extraet of the roots revealed that it contained 39 compounds,belonging to nine classes.Cyclooctasulfur S8 has been isolated as a pure compound from the extract.The major compounds identified from petroleum ether extract were trans-13-clocosene(37.9%).nonacosane(32.6%).cycloartenol(28.6%) nonadecanoic acid(13.9%) and cyclooctasulfur S8(13.9%).Dichloromethane extract of the roots was composed of 63 compounds of which nasimizinol(58.8%) along with oleic acid(46.5%),N—benzyl-N-(7—cyanato heptanamide(38.3%),N—benzyl-N—(1—chlorononyl) amide(30.3%),bis[3—benzyl prop-2-ene]-1-one(19.5%) and N.N-dibeuzyl—2-ene pent 1.5—diamide(11.6%) were the main constituents.Conclusions:This study helps to predict the formula and structure of active molecules which can be used as drugs.This result also enhances the traditional usage of M.oleifera which possesses a number of bioactive compounds.展开更多
We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>...We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>×<i>n</i> Fiedler companion matrix <i>C</i>, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix <i>L<sub>r</sub></i>, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of <i>L<sub>r</sub></i>, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.展开更多
Occlusion is commenced by contact of a tooth with an opposing tooth and is the mechanical force working against the periodontal ligament (PDL). Our recent study indicated that occlusion regulated tooth root elongation...Occlusion is commenced by contact of a tooth with an opposing tooth and is the mechanical force working against the periodontal ligament (PDL). Our recent study indicated that occlusion regulated tooth root elongation occurs during root development in rat molars. Using a non-occlusal model established to directly examine the effects of the absence of occlusion in developing first molars of upper jaw, histological analysis was performed to count the number of HERS cells, with Microarray used to analyse gene expression profiles. HERS cell numbers in normal molars decreased significantly more than those in experimental molars. In microarray data, a total of 59 genes showed significant differences (fold change > 2.0). Expressions of 55 genes in the experimental molars, which included PLAP-1/asporin and periostin, were significantly decreased than those in normal molars. These data indicate that occlusion during root development leads to a decrease in the number of HERS cells, and that the aforementioned genes may play an essential role in normal root formation.展开更多
BACKGROUND Ewing’s sarcoma(ES)is a highly aggressive bone malignancy.Extraskeletal ES(EES)originating in the spinal canal is extremely rare.Herein,we report on a rare case of EES with a primary lumbar spinal nerve ro...BACKGROUND Ewing’s sarcoma(ES)is a highly aggressive bone malignancy.Extraskeletal ES(EES)originating in the spinal canal is extremely rare.Herein,we report on a rare case of EES with a primary lumbar spinal nerve root including the complete diagnosis and treatment.CASE SUMMARY A young female patient presented with a complaint of right lower limb pain for 1 mo.Magnetic resonance imaging(MRI)revealed an 11 mm×14 mm×31 mm mass in the lumbar epidural region extending at the fifth lumbar spine(L5)level toward the right L5 neural foramen.Our initial diagnosis was an epidural schwannoma.The patient underwent total laminectomy,tumor resection and pedicle screw internal fixation and the L5 root tumor was found to have been completely removed intraoperatively.Histopathological examination of the lesion showed a typical ES with a large number of small,round cells.Immunohistochemistry analysis indicated positive CD99 and S100.After surgery,the patient received chemotherapy and radiotherapy with a 1 year of follow-up and no recurrent tumors or new lesions were found upon spine MRI and positron emission tomography/computed tomography reexamination.CONCLUSION Clinically,ES outside the bone should be considered when nerve root tumors are encountered inside and outside the spinal canal and the diagnosis should be determined by pathological biopsy.After surgical resection,chemotherapy and radiotherapy should be performed.After treatment,active follow-up and regular review should be completed.展开更多
This paper discusses the problem of the extraction of characteristic roots on Bessel-Neumann's mixed equations. It gives the expressions and the evaluation of the minimum root. The advantage of the method has no u...This paper discusses the problem of the extraction of characteristic roots on Bessel-Neumann's mixed equations. It gives the expressions and the evaluation of the minimum root. The advantage of the method has no use for the table of the multi-figure number Bessel function and it does not need computer but can calculate all the characteristic roots The precision of these roots is still high.展开更多
The P2X7 receptor mRNA and proteins in guinea-pig dorsal root ganglia (DRG) were studied by using RT-PCR and immunohistochemistry. The co-localization of P2X7 receptor with four cytochemical markers, the neurofilame...The P2X7 receptor mRNA and proteins in guinea-pig dorsal root ganglia (DRG) were studied by using RT-PCR and immunohistochemistry. The co-localization of P2X7 receptor with four cytochemical markers, the neurofilament protein NF200, S100, substance P and isolectin t34 (IB4) binding glyco-conjugates, were also examined. It was found that P2X7 receptor immunoreactivity (P2X7 R-IR) was present mostly in large-and medium-sized DRG neurons (62%±9% and 36%±6% respectively in all P2X7 R-IR neurons). All the P2X7 R-IR neurons were also NF200 and S100 immunopositive. However, in a small number of NF200 or S100 immunopositive neurons no P2XTR-IR was detectable. All the IB4-positive or substance P-immunopositive neurons had no P2X7 R-IR. These results demonstrate that P2X7 receptors are expressed in a large subpopulation of DRG neurons and they may play a role in the transduction of specific peripheral sensory signals.展开更多
Root Analogous Municipal Solid Waste System “RA-MSW” is a novel management system that manages waste, biogas, and leachate in bioreactor landfill. Different than conventional disposal at landfills, waste is penetrat...Root Analogous Municipal Solid Waste System “RA-MSW” is a novel management system that manages waste, biogas, and leachate in bioreactor landfill. Different than conventional disposal at landfills, waste is penetrated by synthetic roots that serve dual mission for biogas collection and leachate recirculation. RA-MSW roots are permeable hydropho- bic polymer material that are formed on-place or prefabricated at factory from recyclable material available on the dumping area. Since the material is hydrophobic, it does not contain water in the voids providing more space for gas transport and collection. The roots are also interchangeably used for leachate recirculation where the parameters of wa- ter content, nutrients, pH, and temperature are optimized to enhance biogas production simultaneously with leachate treatment. RA-MSW provides new approach of waste management and control;it has new virtues of landfill operation;new material medium for biogas collection;new biocell design configuration;new manipulation for leachate and biogas. The approach adds new merits for solid waste management, bio-energy utilization, and the concept of 5 R’s cycle for MSW management.展开更多
Culture Street is the place which no visitor to Tianjin will want to miss. There one can find Qing-style mansions stretching for more than six hundred metres, displays of antiques and per-formances of well-preserved c...Culture Street is the place which no visitor to Tianjin will want to miss. There one can find Qing-style mansions stretching for more than six hundred metres, displays of antiques and per-formances of well-preserved cultural activities. The street is located at the northeastern corner of old Tianjin city where the roots of the city’s history and culture lie. Two hundred years ago when Tianjin was a small port, Tianhou (Goddess of the Temple) was already there. Merchants and those who were traveling away from home by sea would all go to the temple to ask for the god-展开更多
Objective: To observe the effects of RRD on serum levels of cytokines interleukin-2 (IL-2), interleukin-10 (IL-10) and thymus and spleen index in S180 mice, and to explore the mechanism of tumor inhibition by RRD. Met...Objective: To observe the effects of RRD on serum levels of cytokines interleukin-2 (IL-2), interleukin-10 (IL-10) and thymus and spleen index in S180 mice, and to explore the mechanism of tumor inhibition by RRD. Methods: Fifty Kunming healthy mice, half male and half female, were randomly divided into five groups: normal control group, model control group, cyclophosphamide group (CTX group), red raspberry group (RRD group) and combined administration of red raspberry and cyclophosphamide group (RRD + CTX group), with 10 mice in each group only. The other 40 mice were injected with 0.2 mLS180 tumor suspension at the right axilla to make the model experiment, except 10 mice in the normal control group. The next day, the normal control group and model control group were given intragastric administration of 0.02 mL/g/d saline, CTX group was given intragastric administration of 0.4 mL/20 g/d saline and 20 mg/kg/d CTX, RRD group was given intragastric administration of 0.4 mL/20 g/d RRD, RRD+CTX group was given intragastric administration of 0.4 mL/20 g/d RRD and 20 mg/kg/d CTX for 10 d, once a day. Serum levels of IL-2 and IL-10 were measured by ELISA, and thymus and spleen indexes were measured. Results: Red raspberry rhizome decoction could increase serum IL-2 level (P < 0.05), decrease IL-10 level (P < 0.05), increase thymus index (P < 0.05) and decrease spleen index (P < 0.05) in S180 mice. Conclusion:The anti-tumor effect of the water decoction of red raspberry rhizome may be related to the regulation of immune suppression and the improvement of immune organ function of the tumor-bearing organism.展开更多
The aortic aneurysm is the 13th leading cause of death in Western countries. The incidence of thoracic aortic aneurysms is estimated at 4.5 cases per 100,000. The diagnosis is often made on a chest x-ray or other imag...The aortic aneurysm is the 13th leading cause of death in Western countries. The incidence of thoracic aortic aneurysms is estimated at 4.5 cases per 100,000. The diagnosis is often made on a chest x-ray or other imaging tests, such as an echocardiogram done for other heart diseases. Echocardiography is the first test to assess the diameter of the ascending aorta and its progression over time. Most patients are first assessed and followed up with spiral thoracic computed tomography with injection of contrast medium, supplemented by 3-dimensional reconstruction of the aneurysm in order to improve the accuracy of measurements, identification of its proximal part and distal. When dilation of the ascending aorta reaches the critical diameter of 50 mm, there is a risk of aortic dissection or rupture. Supravalvular aneurysms are treated by replacing the ectatic portion with a Dacron<span style="white-space:nowrap;">®</span> tube in the supracoronary position. Aortic root aneurysms, including coronary ostia, require tube replacement, reimplantation of coronary ostia, as well as surgery on the aortic valve. In this article, we report a case of aneurysm of the aortic root and the ascending aorta treated by aortic valve replacement and the ascending aorta associated with the Cabrol hemi-mustache technique and we review the literature.展开更多
文摘The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type.
基金supported by grants from the NIDCR, NIH (DE012711 and DE014078) to Yang ChaiNational Natural Science Foundation of China (81170943)+1 种基金Beijing Natural Science Foundation (7122051)Funding for Talents in Beijing (D) (2010D003034000012) to Xiao-Feng Huang
文摘The root is crucial for the physiological function of the tooth, and a healthy root allows an artificial crown to function as required clinically. Tooth crown development has been studied intensively during the last few decades, but root development remains not well understood. Here we review the root development processes, including cell fate determination, induction of odontoblast and cementoblast differentiation, interaction of root epithelium and mesenchyme, and other molecular mechanisms. This review summarizes our current understanding of the signaling cascades and mechanisms involved in root development. It also sets the stage for de novo tooth regeneration.
文摘Objective:To explore the phytochemical constituents from petroleum ether and diehloromethane extracts of Moringa oleifera(M.oleufera)roots using GC/GC—MS.Methods:A total of 5.11 kg fresh and undried crashed root of M.oleifera were cut into small pieces and extracted with petroleum ether and diehloromethane(20 L.each) at room temperature for 2 d.The concentrated extracts were subjected to their GC—MS analysis.Results:The GC-MS analysis of the petroleum ether and diehloromethane extracts of M.oleifern roots,which showed promising biological activities,has resulted in the identification 102 compounds.These constituents belong to 15 classes of compounds including hydrocarbons,fatty acids,esters,alcohols,isolhioeyanate.thiocyanale,pyrazine,aromalics.alkamides.cyanides,steroids,halocompounds.urea and N-hydroxyimine derivatives,unsaturated alkenamides.alkyne and indole.GC/GC-MS studies on petroleum ether extraet of the roots revealed that it contained 39 compounds,belonging to nine classes.Cyclooctasulfur S8 has been isolated as a pure compound from the extract.The major compounds identified from petroleum ether extract were trans-13-clocosene(37.9%).nonacosane(32.6%).cycloartenol(28.6%) nonadecanoic acid(13.9%) and cyclooctasulfur S8(13.9%).Dichloromethane extract of the roots was composed of 63 compounds of which nasimizinol(58.8%) along with oleic acid(46.5%),N—benzyl-N-(7—cyanato heptanamide(38.3%),N—benzyl-N—(1—chlorononyl) amide(30.3%),bis[3—benzyl prop-2-ene]-1-one(19.5%) and N.N-dibeuzyl—2-ene pent 1.5—diamide(11.6%) were the main constituents.Conclusions:This study helps to predict the formula and structure of active molecules which can be used as drugs.This result also enhances the traditional usage of M.oleifera which possesses a number of bioactive compounds.
文摘We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>×<i>n</i> Fiedler companion matrix <i>C</i>, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix <i>L<sub>r</sub></i>, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of <i>L<sub>r</sub></i>, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.
文摘Occlusion is commenced by contact of a tooth with an opposing tooth and is the mechanical force working against the periodontal ligament (PDL). Our recent study indicated that occlusion regulated tooth root elongation occurs during root development in rat molars. Using a non-occlusal model established to directly examine the effects of the absence of occlusion in developing first molars of upper jaw, histological analysis was performed to count the number of HERS cells, with Microarray used to analyse gene expression profiles. HERS cell numbers in normal molars decreased significantly more than those in experimental molars. In microarray data, a total of 59 genes showed significant differences (fold change > 2.0). Expressions of 55 genes in the experimental molars, which included PLAP-1/asporin and periostin, were significantly decreased than those in normal molars. These data indicate that occlusion during root development leads to a decrease in the number of HERS cells, and that the aforementioned genes may play an essential role in normal root formation.
文摘BACKGROUND Ewing’s sarcoma(ES)is a highly aggressive bone malignancy.Extraskeletal ES(EES)originating in the spinal canal is extremely rare.Herein,we report on a rare case of EES with a primary lumbar spinal nerve root including the complete diagnosis and treatment.CASE SUMMARY A young female patient presented with a complaint of right lower limb pain for 1 mo.Magnetic resonance imaging(MRI)revealed an 11 mm×14 mm×31 mm mass in the lumbar epidural region extending at the fifth lumbar spine(L5)level toward the right L5 neural foramen.Our initial diagnosis was an epidural schwannoma.The patient underwent total laminectomy,tumor resection and pedicle screw internal fixation and the L5 root tumor was found to have been completely removed intraoperatively.Histopathological examination of the lesion showed a typical ES with a large number of small,round cells.Immunohistochemistry analysis indicated positive CD99 and S100.After surgery,the patient received chemotherapy and radiotherapy with a 1 year of follow-up and no recurrent tumors or new lesions were found upon spine MRI and positron emission tomography/computed tomography reexamination.CONCLUSION Clinically,ES outside the bone should be considered when nerve root tumors are encountered inside and outside the spinal canal and the diagnosis should be determined by pathological biopsy.After surgical resection,chemotherapy and radiotherapy should be performed.After treatment,active follow-up and regular review should be completed.
文摘This paper discusses the problem of the extraction of characteristic roots on Bessel-Neumann's mixed equations. It gives the expressions and the evaluation of the minimum root. The advantage of the method has no use for the table of the multi-figure number Bessel function and it does not need computer but can calculate all the characteristic roots The precision of these roots is still high.
文摘The P2X7 receptor mRNA and proteins in guinea-pig dorsal root ganglia (DRG) were studied by using RT-PCR and immunohistochemistry. The co-localization of P2X7 receptor with four cytochemical markers, the neurofilament protein NF200, S100, substance P and isolectin t34 (IB4) binding glyco-conjugates, were also examined. It was found that P2X7 receptor immunoreactivity (P2X7 R-IR) was present mostly in large-and medium-sized DRG neurons (62%±9% and 36%±6% respectively in all P2X7 R-IR neurons). All the P2X7 R-IR neurons were also NF200 and S100 immunopositive. However, in a small number of NF200 or S100 immunopositive neurons no P2XTR-IR was detectable. All the IB4-positive or substance P-immunopositive neurons had no P2X7 R-IR. These results demonstrate that P2X7 receptors are expressed in a large subpopulation of DRG neurons and they may play a role in the transduction of specific peripheral sensory signals.
文摘Root Analogous Municipal Solid Waste System “RA-MSW” is a novel management system that manages waste, biogas, and leachate in bioreactor landfill. Different than conventional disposal at landfills, waste is penetrated by synthetic roots that serve dual mission for biogas collection and leachate recirculation. RA-MSW roots are permeable hydropho- bic polymer material that are formed on-place or prefabricated at factory from recyclable material available on the dumping area. Since the material is hydrophobic, it does not contain water in the voids providing more space for gas transport and collection. The roots are also interchangeably used for leachate recirculation where the parameters of wa- ter content, nutrients, pH, and temperature are optimized to enhance biogas production simultaneously with leachate treatment. RA-MSW provides new approach of waste management and control;it has new virtues of landfill operation;new material medium for biogas collection;new biocell design configuration;new manipulation for leachate and biogas. The approach adds new merits for solid waste management, bio-energy utilization, and the concept of 5 R’s cycle for MSW management.
文摘Culture Street is the place which no visitor to Tianjin will want to miss. There one can find Qing-style mansions stretching for more than six hundred metres, displays of antiques and per-formances of well-preserved cultural activities. The street is located at the northeastern corner of old Tianjin city where the roots of the city’s history and culture lie. Two hundred years ago when Tianjin was a small port, Tianhou (Goddess of the Temple) was already there. Merchants and those who were traveling away from home by sea would all go to the temple to ask for the god-
文摘Objective: To observe the effects of RRD on serum levels of cytokines interleukin-2 (IL-2), interleukin-10 (IL-10) and thymus and spleen index in S180 mice, and to explore the mechanism of tumor inhibition by RRD. Methods: Fifty Kunming healthy mice, half male and half female, were randomly divided into five groups: normal control group, model control group, cyclophosphamide group (CTX group), red raspberry group (RRD group) and combined administration of red raspberry and cyclophosphamide group (RRD + CTX group), with 10 mice in each group only. The other 40 mice were injected with 0.2 mLS180 tumor suspension at the right axilla to make the model experiment, except 10 mice in the normal control group. The next day, the normal control group and model control group were given intragastric administration of 0.02 mL/g/d saline, CTX group was given intragastric administration of 0.4 mL/20 g/d saline and 20 mg/kg/d CTX, RRD group was given intragastric administration of 0.4 mL/20 g/d RRD, RRD+CTX group was given intragastric administration of 0.4 mL/20 g/d RRD and 20 mg/kg/d CTX for 10 d, once a day. Serum levels of IL-2 and IL-10 were measured by ELISA, and thymus and spleen indexes were measured. Results: Red raspberry rhizome decoction could increase serum IL-2 level (P < 0.05), decrease IL-10 level (P < 0.05), increase thymus index (P < 0.05) and decrease spleen index (P < 0.05) in S180 mice. Conclusion:The anti-tumor effect of the water decoction of red raspberry rhizome may be related to the regulation of immune suppression and the improvement of immune organ function of the tumor-bearing organism.
文摘The aortic aneurysm is the 13th leading cause of death in Western countries. The incidence of thoracic aortic aneurysms is estimated at 4.5 cases per 100,000. The diagnosis is often made on a chest x-ray or other imaging tests, such as an echocardiogram done for other heart diseases. Echocardiography is the first test to assess the diameter of the ascending aorta and its progression over time. Most patients are first assessed and followed up with spiral thoracic computed tomography with injection of contrast medium, supplemented by 3-dimensional reconstruction of the aneurysm in order to improve the accuracy of measurements, identification of its proximal part and distal. When dilation of the ascending aorta reaches the critical diameter of 50 mm, there is a risk of aortic dissection or rupture. Supravalvular aneurysms are treated by replacing the ectatic portion with a Dacron<span style="white-space:nowrap;">®</span> tube in the supracoronary position. Aortic root aneurysms, including coronary ostia, require tube replacement, reimplantation of coronary ostia, as well as surgery on the aortic valve. In this article, we report a case of aneurysm of the aortic root and the ascending aorta treated by aortic valve replacement and the ascending aorta associated with the Cabrol hemi-mustache technique and we review the literature.