We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the IF rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.
The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring tr...The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring transition in Rb-87. The multi-peak fitting approach is used to eliminate the frequency shift affected by the neighboring transition. With locking the carrier envelope offset frequency at 1/4 repetition frequency, the transition frequency is measured to be 770569132739.9 +/- 5.8 kHz, which agrees well with the previous result recommended by Comite International des Poids et Mesures.展开更多
In this paper, we first discuss the methods of comparing two special absolutely convergentsine series, sinnx and sinnx. We state the theorem in.one dimensional case as follows; Theorem. Let be convergent series with n...In this paper, we first discuss the methods of comparing two special absolutely convergentsine series, sinnx and sinnx. We state the theorem in.one dimensional case as follows; Theorem. Let be convergent series with nonnegative terms. SupposeThen for all x∈[0,π]If, in addition, then展开更多
The Absolutely True Diary of a Part-Time Indian is a 2007 National Book Award novel for young adults by Sherman Alexie. Inspired by his own experiences of growing up, award-winning author Sherman Alexie chronicles the...The Absolutely True Diary of a Part-Time Indian is a 2007 National Book Award novel for young adults by Sherman Alexie. Inspired by his own experiences of growing up, award-winning author Sherman Alexie chronicles the contemporary adolescence of one unlucky boy trying to rise above the life everyone expects him to live. As a bildungsroman, the novel honestly depicts the real life in reservation as well as protagonist Arnold's personal development in misfortune. The novel addresses various themes. Through close reading of the novel and with the help of some theories from postcolonial criticism, the present paper tries to analyze the bleak reality of reservation life and protagonist Arnold's struggle for social success, thus interpreting the themes of othering, alienation, unhomeliness, double consciousness, and hope presented in the novel展开更多
It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb...It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).展开更多
We develop a rapid and convenient experimental method of absolutely calibrating the transmission of an x-ray flatresponse filter. The calibration experiment is performed on a small laser-target facility, and a set of ...We develop a rapid and convenient experimental method of absolutely calibrating the transmission of an x-ray flatresponse filter. The calibration experiment is performed on a small laser-target facility, and a set of high resolution holographic flat-field grating spectrometers is used as a discrimination system of the laser-produced x-ray source. Given that the holographic flat-field grating has a relatively large width, the grating is divided into two regions for use in that direction,where one region has the filter added and the other region does not. The filter transmission is determined by dividing the x-ray signal counts detected when the filter is in the line of sight by those detected when the filter is out of the line of sight.We find that the calibration results of this experiment agree with the calibration results using a synchrotron radiation source,as well as simulation results. Our method is not only highly reliable but also rapid and convenient.展开更多
Entanglement-breaking(EB)subspaces determine the additivity of entanglement of formation(EOF),which is a long-standing issue in quantum information.We explicitly construct the twodimensional EB subspaces of any bipart...Entanglement-breaking(EB)subspaces determine the additivity of entanglement of formation(EOF),which is a long-standing issue in quantum information.We explicitly construct the twodimensional EB subspaces of any bipartite system,when system dimensions are equal,and we apply the subspaces to construct EB spaces of arbitrary dimensions.We also present partial construction when system dimensions are different.Then,we present the notion and properties of EB subspaces for some systems,and in particular the absolute EB subspaces.We construct some examples of absolute EB subspaces,as well as EB subspaces for some systems by using multiqubit Dicke states.展开更多
Hi, I’m Jason, an 11-yearold primary school student. I pride myself on being polite and friendly. My favorite subject is English because it’s absolutely fascinating. I thoroughly enjoy my school life.
BACKGROUND As a well-known fact to the public,gestational diabetes mellitus(GDM)could bring serious risks for both pregnant women and infants.During this important investigation into the linkage between GDM patients a...BACKGROUND As a well-known fact to the public,gestational diabetes mellitus(GDM)could bring serious risks for both pregnant women and infants.During this important investigation into the linkage between GDM patients and their altered expression in the serum,proteomics techniques were deployed to detect the differentially expressed proteins(DEPs)of in the serum of GDM patients to further explore its pathogenesis,and find out possible biomarkers to forecast GDM occurrence.METHODS Subjects were divided into GDM and normal control groups according to the IADPSG diagnostic criteria.Serum samples were randomly selected from four cases in each group at 24-28 wk of gestation,and the blood samples were identified by applying iTRAQ technology combined with liquid chromatography-tandem mass spectrometry.Key proteins and signaling pathways associated with GDM were identified by bioinformatics analysis,and the expression of key proteins in serum from 12 wk to 16 wk of gestation was further verified using enzyme-linked immunosorbent assay (ELISA).RESULTS Forty-seven proteins were significantly differentially expressed by analyzing the serum samples between the GDMgravidas as well as the healthy ones. Among them, 31 proteins were found to be upregulated notably and the rest16 proteins were downregulated remarkably. Bioinformatic data report revealed abnormal expression of proteinsassociated with lipid metabolism, coagulation cascade activation, complement system and inflammatory responsein the GDM group. ELISA results showed that the contents of RBP4, as well as ANGPTL8, increased in the serumof GDM gravidas compared with the healthy ones, and this change was found to initiate from 12 wk to 16 wk ofgestation.CONCLUSION GDM symptoms may involve abnormalities in lipid metabolism, coagulation cascade activation, complementsystem and inflammatory response. RBP4 and ANGPTL8 are expected to be early predictors of GDM.展开更多
The exit measures of super-Brownian motions with branching mechanism $\psi (z) = z^\alpha ,1< \alpha \leqslant 2$ from a bounded smooth domain D in ?d+1 are known to be absolutely continuous with respect to the sur...The exit measures of super-Brownian motions with branching mechanism $\psi (z) = z^\alpha ,1< \alpha \leqslant 2$ from a bounded smooth domain D in ?d+1 are known to be absolutely continuous with respect to the surface area on ?D if $d< \frac{2}{{a - 1}}$ whereas in the case $d > 1 + \frac{2}{{a - 1}}$ they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely continuous states for alld≥1.展开更多
Spinal muscular atrophy(SMA)is a genetic condition that results in selective lower motor neuron loss with concomitant muscle weakness and atrophy.The genetic cause of SMA was understood in 1995 when loss or impairment...Spinal muscular atrophy(SMA)is a genetic condition that results in selective lower motor neuron loss with concomitant muscle weakness and atrophy.The genetic cause of SMA was understood in 1995 when loss or impairment of the survival motor neuron 1(SMN1)gene was identified as the main contributing factor(Lefebvre et al.,1995).This,in combination with the discovery that humans have a“back-up”gene,SMN2,which can produce low levels(approximately 10%)of the full-length functional SMN protein,has led to the generation of SMA-specific gene therapies.SMA was traditionally classified according to age of symptom onset and developmental milestones achieved,with life expectancy and severity varying between individuals.Now,SMN2 copy number is used as a proxy for the prediction of disease severity,with higher SMN2 copy number typically being associated with reduced severity of SMA,although this relationship is not absolute:some individuals with low SMN2 copy number have less severe SMA phenotypes and vice versa.Additionally,the etiology of SMA is further complicated by other factors,such as non-typical nucleotide variants and SMN2-independent modifiers of disease severity.展开更多
Systematically determining the discriminatory power of various rainfall properties and their combinations in identifying debris flow occurrence is crucial for early warning systems.In this study,we evaluated the discr...Systematically determining the discriminatory power of various rainfall properties and their combinations in identifying debris flow occurrence is crucial for early warning systems.In this study,we evaluated the discriminatory power of different univariate and multivariate rainfall threshold models in identifying triggering conditions of debris flow in the Jiangjia Gully,Yunnan Province,China.The univariate models used single rainfall properties as indicators,including total rainfall(R_(tot)),rainfall duration(D),mean intensity(I_(mean)),absolute energy(Eabs),storm kinetic energy(E_(s)),antecedent rainfall(R_(a)),and maximum rainfall intensity over various durations(I_(max_dur)).The evaluation reveals that the I_(max_dur)and Eabs models have the best performance,followed by the E_(s),R_(tot),and I_(mean)models,while the D and R_(a)models have poor performances.Specifically,the I_(max_dur)model has the highest performance metrics at a 40-min duration.We used logistic regression to combine at least two rainfall properties to establish multivariate threshold models.The results show that adding D or R_(a)to the models dominated by Eabs,E_(s),R_(tot),or I_(mean)generally improve their performances,specifically when D is combined with I_(mean)or when R_(a)is combined with Eabs or E_(s).Including R_(a)in the I_(max_dur)model,it performs better than the univariate I_(max_dur)model.A power-law relationship between I_(max_dur)and R_(a)or between Eabs and R_(a)has better performance than the traditional I_(mean)–D model,while the performance of the E_(s)–R_(a)model is moderate.Our evaluation reemphasizes the important role of the maximum intensity over short durations in debris flow occurrence.It also highlights the importance of systematically investigating the role of R_(a)in establishing rainfall thresholds for triggering debris flow.Given the regional variations in rainfall patterns worldwide,it is necessary to evaluate the findings of this study across diverse watersheds.展开更多
Background:Hepatocellular carcinoma(HCC)has a poor long-term prognosis.The competition of circular RNAs(circRNAs)with endogenous RNA is a novel tool for predicting HCC prognosis.Based on the alterations of circRNA reg...Background:Hepatocellular carcinoma(HCC)has a poor long-term prognosis.The competition of circular RNAs(circRNAs)with endogenous RNA is a novel tool for predicting HCC prognosis.Based on the alterations of circRNA regulatory networks,the analysis of gene modules related to HCC is feasible.Methods:Multiple expression datasets and RNA element targeting prediction tools were used to construct a circRNA-microRNA-mRNA network in HCC.Gene function,pathway,and protein interaction analyses were performed for the differentially expressed genes(DEGs)in this regulatory network.In the proteinprotein interaction network,hub genes were identified and subjected to regression analysis,producing an optimized four-gene signature for prognostic risk stratification in HCC patients.Anti-HCC drugs were excavated by assessing the DEGs between the low-and high-risk groups.A circRNA-microRNA-hub gene subnetwork was constructed,in which three hallmark genes,KIF4A,CCNA2,and PBK,were subjected to functional enrichment analysis.Results:A four-gene signature(KIF4A,CCNA2,PBK,and ZWINT)that effectively estimated the overall survival and aided in prognostic risk assessment in the The Cancer Genome Atlas(TCGA)cohort and International Cancer Genome Consortium(ICGC)cohort was developed.CDK inhibitors,PI3K inhibitors,HDAC inhibitors,and EGFR inhibitors were predicted as four potential mechanisms of drug action(MOA)in high-risk HCC patients.Subsequent analysis has revealed that PBK,CCNA2,and KIF4A play a crucial role in regulating the tumor microenvironment by promoting immune cell invasion,regulating microsatellite instability(MSI),and exerting an impact on HCC progression.Conclusions:The present study highlights the role of the circRNA-related regulatory network,identifies a four-gene prognostic signature and biomarkers,and further identifies novel therapy for HCC.展开更多
It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the hea...It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy,temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultralow temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.展开更多
The single-valued representation of measurable and continuous set-valued map-pings have been discussed in many papers. In this paper we discuss absolutely continuous single-valued representation of absolutely continuo...The single-valued representation of measurable and continuous set-valued map-pings have been discussed in many papers. In this paper we discuss absolutely continuous single-valued representation of absolutely continuous set-valued mappings using the method of constructing polygonal lines.展开更多
In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a se...In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.展开更多
文摘We first introduce the concepts of absolutely E-pure modules and E-pure split modules. Then, we characterize the IF rings in terms of absolutely E-pure modules. The E-pure split modules are also characterized.
基金Supported by the National Natural Science Foundation of China under Grant Nos 91336103,10934010 and 61078026
文摘The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring transition in Rb-87. The multi-peak fitting approach is used to eliminate the frequency shift affected by the neighboring transition. With locking the carrier envelope offset frequency at 1/4 repetition frequency, the transition frequency is measured to be 770569132739.9 +/- 5.8 kHz, which agrees well with the previous result recommended by Comite International des Poids et Mesures.
文摘In this paper, we first discuss the methods of comparing two special absolutely convergentsine series, sinnx and sinnx. We state the theorem in.one dimensional case as follows; Theorem. Let be convergent series with nonnegative terms. SupposeThen for all x∈[0,π]If, in addition, then
文摘The Absolutely True Diary of a Part-Time Indian is a 2007 National Book Award novel for young adults by Sherman Alexie. Inspired by his own experiences of growing up, award-winning author Sherman Alexie chronicles the contemporary adolescence of one unlucky boy trying to rise above the life everyone expects him to live. As a bildungsroman, the novel honestly depicts the real life in reservation as well as protagonist Arnold's personal development in misfortune. The novel addresses various themes. Through close reading of the novel and with the help of some theories from postcolonial criticism, the present paper tries to analyze the bleak reality of reservation life and protagonist Arnold's struggle for social success, thus interpreting the themes of othering, alienation, unhomeliness, double consciousness, and hope presented in the novel
基金Supported by the Special Science Foundation of the Education Committee of Shaanxi Province(03jk066)
文摘It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11405158 and 11775203)the Presidential Foundation of China Academy of Engineering Physics(Grant No.YZJJLX 2016007)
文摘We develop a rapid and convenient experimental method of absolutely calibrating the transmission of an x-ray flatresponse filter. The calibration experiment is performed on a small laser-target facility, and a set of high resolution holographic flat-field grating spectrometers is used as a discrimination system of the laser-produced x-ray source. Given that the holographic flat-field grating has a relatively large width, the grating is divided into two regions for use in that direction,where one region has the filter added and the other region does not. The filter transmission is determined by dividing the x-ray signal counts detected when the filter is in the line of sight by those detected when the filter is out of the line of sight.We find that the calibration results of this experiment agree with the calibration results using a synchrotron radiation source,as well as simulation results. Our method is not only highly reliable but also rapid and convenient.
文摘Entanglement-breaking(EB)subspaces determine the additivity of entanglement of formation(EOF),which is a long-standing issue in quantum information.We explicitly construct the twodimensional EB subspaces of any bipartite system,when system dimensions are equal,and we apply the subspaces to construct EB spaces of arbitrary dimensions.We also present partial construction when system dimensions are different.Then,we present the notion and properties of EB subspaces for some systems,and in particular the absolute EB subspaces.We construct some examples of absolute EB subspaces,as well as EB subspaces for some systems by using multiqubit Dicke states.
文摘Hi, I’m Jason, an 11-yearold primary school student. I pride myself on being polite and friendly. My favorite subject is English because it’s absolutely fascinating. I thoroughly enjoy my school life.
基金This study was reviewed and approved by the Maternal and child health hospital of Hubei Province(Approval No.20201025).
文摘BACKGROUND As a well-known fact to the public,gestational diabetes mellitus(GDM)could bring serious risks for both pregnant women and infants.During this important investigation into the linkage between GDM patients and their altered expression in the serum,proteomics techniques were deployed to detect the differentially expressed proteins(DEPs)of in the serum of GDM patients to further explore its pathogenesis,and find out possible biomarkers to forecast GDM occurrence.METHODS Subjects were divided into GDM and normal control groups according to the IADPSG diagnostic criteria.Serum samples were randomly selected from four cases in each group at 24-28 wk of gestation,and the blood samples were identified by applying iTRAQ technology combined with liquid chromatography-tandem mass spectrometry.Key proteins and signaling pathways associated with GDM were identified by bioinformatics analysis,and the expression of key proteins in serum from 12 wk to 16 wk of gestation was further verified using enzyme-linked immunosorbent assay (ELISA).RESULTS Forty-seven proteins were significantly differentially expressed by analyzing the serum samples between the GDMgravidas as well as the healthy ones. Among them, 31 proteins were found to be upregulated notably and the rest16 proteins were downregulated remarkably. Bioinformatic data report revealed abnormal expression of proteinsassociated with lipid metabolism, coagulation cascade activation, complement system and inflammatory responsein the GDM group. ELISA results showed that the contents of RBP4, as well as ANGPTL8, increased in the serumof GDM gravidas compared with the healthy ones, and this change was found to initiate from 12 wk to 16 wk ofgestation.CONCLUSION GDM symptoms may involve abnormalities in lipid metabolism, coagulation cascade activation, complementsystem and inflammatory response. RBP4 and ANGPTL8 are expected to be early predictors of GDM.
文摘The exit measures of super-Brownian motions with branching mechanism $\psi (z) = z^\alpha ,1< \alpha \leqslant 2$ from a bounded smooth domain D in ?d+1 are known to be absolutely continuous with respect to the surface area on ?D if $d< \frac{2}{{a - 1}}$ whereas in the case $d > 1 + \frac{2}{{a - 1}}$ they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely continuous states for alld≥1.
基金supported by the Faculty Research Fund(Faculty of Medicine&Health Science,Keele University)Career Development Award–(April 2022)(to SJB)。
文摘Spinal muscular atrophy(SMA)is a genetic condition that results in selective lower motor neuron loss with concomitant muscle weakness and atrophy.The genetic cause of SMA was understood in 1995 when loss or impairment of the survival motor neuron 1(SMN1)gene was identified as the main contributing factor(Lefebvre et al.,1995).This,in combination with the discovery that humans have a“back-up”gene,SMN2,which can produce low levels(approximately 10%)of the full-length functional SMN protein,has led to the generation of SMA-specific gene therapies.SMA was traditionally classified according to age of symptom onset and developmental milestones achieved,with life expectancy and severity varying between individuals.Now,SMN2 copy number is used as a proxy for the prediction of disease severity,with higher SMN2 copy number typically being associated with reduced severity of SMA,although this relationship is not absolute:some individuals with low SMN2 copy number have less severe SMA phenotypes and vice versa.Additionally,the etiology of SMA is further complicated by other factors,such as non-typical nucleotide variants and SMN2-independent modifiers of disease severity.
基金supported by the National Key R&D Program of China(No.2023YFC3007205)the National Natural Science Foundation of China(Nos.42271013,42077440)Project of the Department of Science and Technology of Sichuan Province(No.2023ZHCG0012).
文摘Systematically determining the discriminatory power of various rainfall properties and their combinations in identifying debris flow occurrence is crucial for early warning systems.In this study,we evaluated the discriminatory power of different univariate and multivariate rainfall threshold models in identifying triggering conditions of debris flow in the Jiangjia Gully,Yunnan Province,China.The univariate models used single rainfall properties as indicators,including total rainfall(R_(tot)),rainfall duration(D),mean intensity(I_(mean)),absolute energy(Eabs),storm kinetic energy(E_(s)),antecedent rainfall(R_(a)),and maximum rainfall intensity over various durations(I_(max_dur)).The evaluation reveals that the I_(max_dur)and Eabs models have the best performance,followed by the E_(s),R_(tot),and I_(mean)models,while the D and R_(a)models have poor performances.Specifically,the I_(max_dur)model has the highest performance metrics at a 40-min duration.We used logistic regression to combine at least two rainfall properties to establish multivariate threshold models.The results show that adding D or R_(a)to the models dominated by Eabs,E_(s),R_(tot),or I_(mean)generally improve their performances,specifically when D is combined with I_(mean)or when R_(a)is combined with Eabs or E_(s).Including R_(a)in the I_(max_dur)model,it performs better than the univariate I_(max_dur)model.A power-law relationship between I_(max_dur)and R_(a)or between Eabs and R_(a)has better performance than the traditional I_(mean)–D model,while the performance of the E_(s)–R_(a)model is moderate.Our evaluation reemphasizes the important role of the maximum intensity over short durations in debris flow occurrence.It also highlights the importance of systematically investigating the role of R_(a)in establishing rainfall thresholds for triggering debris flow.Given the regional variations in rainfall patterns worldwide,it is necessary to evaluate the findings of this study across diverse watersheds.
基金This study was supported by grants from the High-level Preresearch Program of Zhejiang Shuren University 2019(KXJ121860)Zhejiang Provincial Natural Science Foundation of China(LQ20H190004)。
文摘Background:Hepatocellular carcinoma(HCC)has a poor long-term prognosis.The competition of circular RNAs(circRNAs)with endogenous RNA is a novel tool for predicting HCC prognosis.Based on the alterations of circRNA regulatory networks,the analysis of gene modules related to HCC is feasible.Methods:Multiple expression datasets and RNA element targeting prediction tools were used to construct a circRNA-microRNA-mRNA network in HCC.Gene function,pathway,and protein interaction analyses were performed for the differentially expressed genes(DEGs)in this regulatory network.In the proteinprotein interaction network,hub genes were identified and subjected to regression analysis,producing an optimized four-gene signature for prognostic risk stratification in HCC patients.Anti-HCC drugs were excavated by assessing the DEGs between the low-and high-risk groups.A circRNA-microRNA-hub gene subnetwork was constructed,in which three hallmark genes,KIF4A,CCNA2,and PBK,were subjected to functional enrichment analysis.Results:A four-gene signature(KIF4A,CCNA2,PBK,and ZWINT)that effectively estimated the overall survival and aided in prognostic risk assessment in the The Cancer Genome Atlas(TCGA)cohort and International Cancer Genome Consortium(ICGC)cohort was developed.CDK inhibitors,PI3K inhibitors,HDAC inhibitors,and EGFR inhibitors were predicted as four potential mechanisms of drug action(MOA)in high-risk HCC patients.Subsequent analysis has revealed that PBK,CCNA2,and KIF4A play a crucial role in regulating the tumor microenvironment by promoting immune cell invasion,regulating microsatellite instability(MSI),and exerting an impact on HCC progression.Conclusions:The present study highlights the role of the circRNA-related regulatory network,identifies a four-gene prognostic signature and biomarkers,and further identifies novel therapy for HCC.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12075197)the Fundamental Research Fund for the Central Universities of China (Grant No. 20720210020)。
文摘It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy,temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultralow temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.
文摘The single-valued representation of measurable and continuous set-valued map-pings have been discussed in many papers. In this paper we discuss absolutely continuous single-valued representation of absolutely continuous set-valued mappings using the method of constructing polygonal lines.
文摘In this paper, we calculate the absolute tensor square of the Dirichlet L-functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet L-functions. This study is a generalization of Akatsuka’s theorem on the Riemann zeta function, and gives a proof of Kurokawa’s prediction proposed in 1992.