Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are sim...Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.展开更多
While the Bushen Yizhi Formula can treat Alzheimer’s disease(AD),the yet to be ascertained specific mechanism of action was explored in this work.Methods:Different concentrations of the Bushen Yizhi Formula and amylo...While the Bushen Yizhi Formula can treat Alzheimer’s disease(AD),the yet to be ascertained specific mechanism of action was explored in this work.Methods:Different concentrations of the Bushen Yizhi Formula and amyloid-beta peptide(Aβ)were used to treat rat pheochromocytoma cells(P12)and human neuroblastoma cells(SH-SY5Y).Cell morphological changes were observed to determine the in vitro cell damage.Cell Counting Kit(CCK)-8 assay and flow cytometry were employed to identify cell viability and apoptosis/cell cycle,respectively.Western blotting and immunohistochemistry were employed to measure the expressions of endoplasmic reticulum stress(ERS)-related proteins(GRP78 and CHOP),p-IRE1α,IRE1α,ASK1,p-JNK,JNK,Bax,Bcl-2,XBP-1,and Bim.Fura 2-acetoxymethyl ester(Fura-2/AM)was used to determine the intracellular calcium(Ca^(2+))concentration.Also,an AD model was constructed by injecting Aβinto the CA1 area of the hippocampus in Sprague Dawley rats.AD model rats were gavaged with different concentrations of Bushen Yizhi Formula for 14 consecutive days.The Morris water maze experiment was conducted to test the learning and memory of rats.Hematoxylin&Eosin(H&E)and Terminal-deoxynucleotidyl Transferase(TdT)-mediated dUTP Nick-End Labeling(TUNEL)staining were done to determine histopathological changes in the brain.Results:Bushen Yizhi Formula relieved the Aβ-induced effects including cell injury,decreased viability,increased apoptosis,G0/G1 phase cell cycle arrest,upregulation of GRP78,CHOP,p-IRE1α,p-JNK,Bax,XBP-1 and Bim,as well as down-regulation of Bcl-2.These results were also seen with IRE1αsilencing.While Aβsuppressed the learning and memory abilities of rats,the Bushen Yizhi Formula alleviated these effects of Aβ.Brain nerve cell injury induced by Aβcould also be treated with Bushen Yizhi Formula.Conclusion:Bushen Yizhi Formula could influence ERS through the IRE1αsignaling pathway to achieve its therapeutic effects on AD.展开更多
In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
To deduce a new color difference formula based on CIE 1997 Color Appearance Model(CIECAM97s), a color space J a 1 b 1 is first constructed with color appearance descriptors J,a,b in CIECAM97s. The new f...To deduce a new color difference formula based on CIE 1997 Color Appearance Model(CIECAM97s), a color space J a 1 b 1 is first constructed with color appearance descriptors J,a,b in CIECAM97s. The new formula is then deduced in the space and named CDF CIECAM97s. The factors for lightness, chroma and hue correction in the formula are derived by linear regression according to BFD? CP data sets. It is found by statistical analysis that CDF CIECAM97s is in closer accordance with the visual assessments when compared with CMC(1∶1), CIE94 and CIE L *a *b * color difference formulae. Based on color appearance model, the new color difference formula can be used to predict color difference perception in a varity of different viewing conditions.展开更多
Objective:Parkinson’s disease(PD)is the second largest neurodegenerative disease following Alzheimer’s disease(AD),which associated with aging.There are many similarities in pathology and pathogenesis,even in the TC...Objective:Parkinson’s disease(PD)is the second largest neurodegenerative disease following Alzheimer’s disease(AD),which associated with aging.There are many similarities in pathology and pathogenesis,even in the TCM theory understanding,so we can learn from each other in the process of drug discovery.The clinical results showed that Bushen-Yizhi formula(BSYZ)could effectively improve the neurological function score of senile dementia patients and had a better anti-dementia effect.Further pharmacological studies showed that BSYZ had neuroprotective effects,such as anti-inflammatory,anti-oxidation,anti-apoptosis and neurotrophic effects.In this study,the therapeutic effect of BSYZ on PD was evaluated in vivo and in vivo,and its molecular mechanism was discussed in order to expand the scope of application of BSYZ and to provide strategies for drug discovery of related neurodegenerative diseases.Methods:C57 BL/6 mice were injected intraperitoneally with MPTP to construct a PD mouse model.BSYZ(1.46,2.92,5.84 mg·kg-1)was administered for two weeks,and the positive control group was given a NSAID,piroxicam(12.5 mg·kg-1).After 1 week of pretreatment,MPTP was used to construct a PD mouse model.The mice were subjected to Rotation test on days 1,3 and 5,6th day.and the movement coordination and exercise ability of the drug on PD mice were observed on theThe number of TH-positive cells,Iba1 and CD68-labeled microglial cells in SNpc region were observed by immunofluorescence to observe the proliferation and activation of microglial cells and GFAP-labeled astrocytes.Western blotting was used to detect the nuclear transfer of NLRP3,Caspase-1,ASC,pro-IL-1β,IL-1βand NF-κB in the midbrain.Results:1.BSYZ could significantly improve the expression of MPTP model mice in the experiment of fatigue and Y-maze,increase the number of neurons in SNpc region and the positive expression of TH protein.2.BSYZ significantly inhibited the number of Iba1/CD68-positive microglial cells in MPTP-model mice and decreased the number of GFAP-positive astrocytes.3.BSYZ significantly inhibited the expression of NLRP3-associated protein in BV2 microglial cells induced by LPS+ATP and inhibited the nuclear transfer of NF-κB.Conclusion:BSYZ can effectively relieve the motor dysfunction of PD model mice,improve the damage of dopaminergic neurons,inhibit the proliferation and activation of microglial cells and astrocytes,and have good anti-MPTPinduced neuroinflammation and neuroinflammation mediated by nuclear transfer of NF-κB.The results show that BSYZ has a good prospect of anti-Parkinson’s disease and provides valuable drug discovery strategies for the related neurodegenerative diseases.展开更多
Compound Formula Rehmannia has been shown to be clinically effective in treating Parkinson＇s disease and levodopa-induced dyskinesia; however, the mechanisms remain unclear. In this study, we established a model of P...Compound Formula Rehmannia has been shown to be clinically effective in treating Parkinson＇s disease and levodopa-induced dyskinesia; however, the mechanisms remain unclear. In this study, we established a model of Parkinson＇s disease dyskinesia in rats, and treated these animals with Compound Formula Rehmannia. Compound Formula Rehmannia inhibited the increase in mRNA expression of N-methyl-D-aspartate receptor subunits 1 and 2 and excitatory amino acid neurotransmitter genes, and it inhibited the reduction in expression of γ-aminobutyric acid receptor B1, an inhibitory amino acid neurotransmitter gene, in the corpus striatum. In addition, Compound Formula Rehmannia alleviated dyskinesia symptoms in the Parkinson＇s disease rats. These experimental findings indicate that Compound Formula Rehmannia alleviates levodopa-induced dyskinesia in Parkinson＇s disease by modulating neurotransmitter signaling in the corpus striatum.展开更多
Long-term application of levodopa （L-3, 4-dihydroxyphenylalanine, L-DOPA） for Parkinson＇s disease can lead to adverse effects and reduce the amount of dopamine transporter （DAT） in the corpus striatum. The presen...Long-term application of levodopa （L-3, 4-dihydroxyphenylalanine, L-DOPA） for Parkinson＇s disease can lead to adverse effects and reduce the amount of dopamine transporter （DAT） in the corpus striatum. The present study attempted to vedfy whether increasing the amount of DAT can reduce the adverse effects of L-DOPA. The specific radioactive uptake value of DAT in the corpus striatum of the lesioned hemisphere was significantly decreased, but was significantly increased following administration of compound rehmannia formula [Radix rehmanniae preparata （prepared rehmannia root）, Concha margantifera usta （nacre）, Radix paeoniae alba （white peony alba）, Radix salviae miltiotThizae （Danshen root）, Scorpio （scorpion）, green tea] for 4 weeks. The changes in DAT 1251-beta-carbomethoxy-3 beta-（4-iodophenyl） tropane autoradiography were consistent with those in radioactivity. The results revealed that the compound rehmannia formula can reduce the adverse effects of L-DOPA in treating Parkinson＇s disease, possibly by increasing the amount of DAT.展开更多
In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green fun...In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.展开更多
Generalizations of the geometric construction that repeatedly attaches rectangles to a square, originally given by Myerson, are presented. The initial square is replaced with a rectangle, and also the dimensionality o...Generalizations of the geometric construction that repeatedly attaches rectangles to a square, originally given by Myerson, are presented. The initial square is replaced with a rectangle, and also the dimensionality of the construction is increased. By selecting values for the various parameters, such as the lengths of the sides of the original rectangle or rectangular box in dimensions more than two and their relationships to the size of the attached rectangles or rectangular boxes, some interesting formulas are found. Examples are Wallis-type infinite-product formulas for the areas of p-circles with p > 1.展开更多
We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algo...We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.展开更多
By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antino...By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.展开更多
In a recent paper, we <a href="#ref1">[1]</a> discussed that Suto<a href="#ref2" target="_blank"> [2] </a>has pointed out an interesting relativistic extension of ...In a recent paper, we <a href="#ref1">[1]</a> discussed that Suto<a href="#ref2" target="_blank"> [2] </a>has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.展开更多
When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and st...When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot＇s equation and Betti＇s theorem （the reciprocal theorem）. According to the basic solution to Biot＇s equation, Green＇s function Gij and three terms of Green＇s function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe＇s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.展开更多
A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetrie...A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetries and solutions to Riemann-Hilbert problems in soltion theory.展开更多
As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the fi...As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.展开更多
A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the ...In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.展开更多
文摘Implementing machine learning algorithms in the non-conducive environment of the vehicular network requires some adaptations due to the high computational complexity of these algorithms.K-clustering algorithms are simplistic,with fast performance and relative accuracy.However,their implementation depends on the initial selection of clusters number(K),the initial clusters’centers,and the clustering metric.This paper investigated using Scott’s histogram formula to estimate the K number and the Link Expiration Time(LET)as a clustering metric.Realistic traffic flows were considered for three maps,namely Highway,Traffic Light junction,and Roundabout junction,to study the effect of road layout on estimating the K number.A fast version of the PAM algorithm was used for clustering with a modification to reduce time complexity.The Affinity propagation algorithm sets the baseline for the estimated K number,and the Medoid Silhouette method is used to quantify the clustering.OMNET++,Veins,and SUMO were used to simulate the traffic,while the related algorithms were implemented in Python.The Scott’s formula estimation of the K number only matched the baseline when the road layout was simple.Moreover,the clustering algorithm required one iteration on average to converge when used with LET.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
基金supported by the National Natural Science Foundation of China[81904266,82004309].
文摘While the Bushen Yizhi Formula can treat Alzheimer’s disease(AD),the yet to be ascertained specific mechanism of action was explored in this work.Methods:Different concentrations of the Bushen Yizhi Formula and amyloid-beta peptide(Aβ)were used to treat rat pheochromocytoma cells(P12)and human neuroblastoma cells(SH-SY5Y).Cell morphological changes were observed to determine the in vitro cell damage.Cell Counting Kit(CCK)-8 assay and flow cytometry were employed to identify cell viability and apoptosis/cell cycle,respectively.Western blotting and immunohistochemistry were employed to measure the expressions of endoplasmic reticulum stress(ERS)-related proteins(GRP78 and CHOP),p-IRE1α,IRE1α,ASK1,p-JNK,JNK,Bax,Bcl-2,XBP-1,and Bim.Fura 2-acetoxymethyl ester(Fura-2/AM)was used to determine the intracellular calcium(Ca^(2+))concentration.Also,an AD model was constructed by injecting Aβinto the CA1 area of the hippocampus in Sprague Dawley rats.AD model rats were gavaged with different concentrations of Bushen Yizhi Formula for 14 consecutive days.The Morris water maze experiment was conducted to test the learning and memory of rats.Hematoxylin&Eosin(H&E)and Terminal-deoxynucleotidyl Transferase(TdT)-mediated dUTP Nick-End Labeling(TUNEL)staining were done to determine histopathological changes in the brain.Results:Bushen Yizhi Formula relieved the Aβ-induced effects including cell injury,decreased viability,increased apoptosis,G0/G1 phase cell cycle arrest,upregulation of GRP78,CHOP,p-IRE1α,p-JNK,Bax,XBP-1 and Bim,as well as down-regulation of Bcl-2.These results were also seen with IRE1αsilencing.While Aβsuppressed the learning and memory abilities of rats,the Bushen Yizhi Formula alleviated these effects of Aβ.Brain nerve cell injury induced by Aβcould also be treated with Bushen Yizhi Formula.Conclusion:Bushen Yizhi Formula could influence ERS through the IRE1αsignaling pathway to achieve its therapeutic effects on AD.
基金Supported by National Natural Science Foundation of China(Grant Nos.11801006 and 12071489).
文摘In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
文摘To deduce a new color difference formula based on CIE 1997 Color Appearance Model(CIECAM97s), a color space J a 1 b 1 is first constructed with color appearance descriptors J,a,b in CIECAM97s. The new formula is then deduced in the space and named CDF CIECAM97s. The factors for lightness, chroma and hue correction in the formula are derived by linear regression according to BFD? CP data sets. It is found by statistical analysis that CDF CIECAM97s is in closer accordance with the visual assessments when compared with CMC(1∶1), CIE94 and CIE L *a *b * color difference formulae. Based on color appearance model, the new color difference formula can be used to predict color difference perception in a varity of different viewing conditions.
文摘Objective:Parkinson’s disease(PD)is the second largest neurodegenerative disease following Alzheimer’s disease(AD),which associated with aging.There are many similarities in pathology and pathogenesis,even in the TCM theory understanding,so we can learn from each other in the process of drug discovery.The clinical results showed that Bushen-Yizhi formula(BSYZ)could effectively improve the neurological function score of senile dementia patients and had a better anti-dementia effect.Further pharmacological studies showed that BSYZ had neuroprotective effects,such as anti-inflammatory,anti-oxidation,anti-apoptosis and neurotrophic effects.In this study,the therapeutic effect of BSYZ on PD was evaluated in vivo and in vivo,and its molecular mechanism was discussed in order to expand the scope of application of BSYZ and to provide strategies for drug discovery of related neurodegenerative diseases.Methods:C57 BL/6 mice were injected intraperitoneally with MPTP to construct a PD mouse model.BSYZ(1.46,2.92,5.84 mg·kg-1)was administered for two weeks,and the positive control group was given a NSAID,piroxicam(12.5 mg·kg-1).After 1 week of pretreatment,MPTP was used to construct a PD mouse model.The mice were subjected to Rotation test on days 1,3 and 5,6th day.and the movement coordination and exercise ability of the drug on PD mice were observed on theThe number of TH-positive cells,Iba1 and CD68-labeled microglial cells in SNpc region were observed by immunofluorescence to observe the proliferation and activation of microglial cells and GFAP-labeled astrocytes.Western blotting was used to detect the nuclear transfer of NLRP3,Caspase-1,ASC,pro-IL-1β,IL-1βand NF-κB in the midbrain.Results:1.BSYZ could significantly improve the expression of MPTP model mice in the experiment of fatigue and Y-maze,increase the number of neurons in SNpc region and the positive expression of TH protein.2.BSYZ significantly inhibited the number of Iba1/CD68-positive microglial cells in MPTP-model mice and decreased the number of GFAP-positive astrocytes.3.BSYZ significantly inhibited the expression of NLRP3-associated protein in BV2 microglial cells induced by LPS+ATP and inhibited the nuclear transfer of NF-κB.Conclusion:BSYZ can effectively relieve the motor dysfunction of PD model mice,improve the damage of dopaminergic neurons,inhibit the proliferation and activation of microglial cells and astrocytes,and have good anti-MPTPinduced neuroinflammation and neuroinflammation mediated by nuclear transfer of NF-κB.The results show that BSYZ has a good prospect of anti-Parkinson’s disease and provides valuable drug discovery strategies for the related neurodegenerative diseases.
基金supported by the National Natural Science Foundation of China,No.30672684,30973722Science and Technology Support Traditional Chinese Drug Research and Development Project of Shanghai,No.F50102+1 种基金Traditional Chinese Medicine Research Fund of Shanghai Municipal Health Bureau,No.2012J009AAnnual Research Budget of Shanghai University of Traditional Chinese Medicine in 2013,No.2013JW25
文摘Compound Formula Rehmannia has been shown to be clinically effective in treating Parkinson＇s disease and levodopa-induced dyskinesia; however, the mechanisms remain unclear. In this study, we established a model of Parkinson＇s disease dyskinesia in rats, and treated these animals with Compound Formula Rehmannia. Compound Formula Rehmannia inhibited the increase in mRNA expression of N-methyl-D-aspartate receptor subunits 1 and 2 and excitatory amino acid neurotransmitter genes, and it inhibited the reduction in expression of γ-aminobutyric acid receptor B1, an inhibitory amino acid neurotransmitter gene, in the corpus striatum. In addition, Compound Formula Rehmannia alleviated dyskinesia symptoms in the Parkinson＇s disease rats. These experimental findings indicate that Compound Formula Rehmannia alleviates levodopa-induced dyskinesia in Parkinson＇s disease by modulating neurotransmitter signaling in the corpus striatum.
基金the National Natural Science Foundation of China,No.30672684, 30973722the Third Intention Key Disciplinary Areas of Shanghai,No.S30302
文摘Long-term application of levodopa （L-3, 4-dihydroxyphenylalanine, L-DOPA） for Parkinson＇s disease can lead to adverse effects and reduce the amount of dopamine transporter （DAT） in the corpus striatum. The present study attempted to vedfy whether increasing the amount of DAT can reduce the adverse effects of L-DOPA. The specific radioactive uptake value of DAT in the corpus striatum of the lesioned hemisphere was significantly decreased, but was significantly increased following administration of compound rehmannia formula [Radix rehmanniae preparata （prepared rehmannia root）, Concha margantifera usta （nacre）, Radix paeoniae alba （white peony alba）, Radix salviae miltiotThizae （Danshen root）, Scorpio （scorpion）, green tea] for 4 weeks. The changes in DAT 1251-beta-carbomethoxy-3 beta-（4-iodophenyl） tropane autoradiography were consistent with those in radioactivity. The results revealed that the compound rehmannia formula can reduce the adverse effects of L-DOPA in treating Parkinson＇s disease, possibly by increasing the amount of DAT.
文摘In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.
文摘Generalizations of the geometric construction that repeatedly attaches rectangles to a square, originally given by Myerson, are presented. The initial square is replaced with a rectangle, and also the dimensionality of the construction is increased. By selecting values for the various parameters, such as the lengths of the sides of the original rectangle or rectangular box in dimensions more than two and their relationships to the size of the attached rectangles or rectangular boxes, some interesting formulas are found. Examples are Wallis-type infinite-product formulas for the areas of p-circles with p > 1.
基金This paper is a talk on the held in Nanjing, P. R. China, July, 2004.
文摘We present a constructive generalization of Abel-Gontscharoff＇s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for constructing the basis functions of the interpolants are given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)
文摘By introducing the s-parameterized generalized Wigner operator into phase-space quantum mechanics we invent the technique of integration within s-ordered product of operators （which considers normally ordered, antinormally ordered and Weyl ordered product of operators as its special cases）. The s-ordered operator expansion （denoted by s…s ） formula of density operators is derived, which isρ=2/1-s∫d^2β/π〈-β｜ρ｜β〉sexp{2/s-1（s｜β｜^2-β＊α＋βa-αα）}s The s-parameterized quantization scheme is thus completely established.
文摘In a recent paper, we <a href="#ref1">[1]</a> discussed that Suto<a href="#ref2" target="_blank"> [2] </a>has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.
基金Project supported by the National Natural Science Foundation of China(No.10572129)
文摘When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot＇s equation and Betti＇s theorem （the reciprocal theorem）. According to the basic solution to Biot＇s equation, Green＇s function Gij and three terms of Green＇s function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe＇s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.
基金Supported by the National Natural Science Foundation of China(11975145,11972291)The National Science Foundation(DMS-1664561)。
文摘A generalized Liouville’s formula is established for linear matrix differential equations involving left and right multiplications.Its special cases are used to determine the localness of characteristics of symmetries and solutions to Riemann-Hilbert problems in soltion theory.
基金Supported by the National Natural Science Foundation Fujian province of China(2016J01032).
文摘As is well known,the definitions of fractional sum and fractional difference of f(z)on non-uniform lattices x(z)=c1z^(2)+c2z+c3 or x(z)=c1q^(z)+c2q^(-z)+c3 are more difficult and complicated.In this article,for the first time we propose the definitions of the fractional sum and fractional difference on non-uniform lattices by two different ways.The analogue of Euler’s Beta formula,Cauchy’Beta formula on non-uniform lattices are established,and some fundamental theorems of fractional calculas,the solution of the generalized Abel equation on non-uniform lattices are obtained etc.
基金Supported by the Natural Science Foundation of Hubei Province!(992P0 30 7) the National Natural Science Foun-dation of Chi
文摘A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
文摘In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the three formulas lead to the extension of Newton-Raphson’s method and Horner’s method at the same time. This shows originality of Japanese native mathematics (Wasan) in the Edo era (1600- 1867). Suzuki (Ref.[2]) estimates Murase to be a rare mathematician in not only the history of Wasan but also the history of mathematics in the world. Section 1 introduces Murase’s three solutions of the cubic equation of the hearth. Section 2 explains the Horner’s method. We give the generalization of three formulas and the relation between these formulas and Horner’s method. Section 3 gives definitions of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), general recurrence formula of Murase-Newton’s method (Tsuchikura-Horiguchi’s method), and general recurrence formula of the extension of Murase-Newton’s method (the extension of Tsuchikura-Horiguchi’s method) concerning n-degree polynomial equation. Section 4 is contents of the title of this paper.
