Image quality in positron emission tomography(PET)is affected by random and scattered coincidences and reconstruction protocols.In this study,we investigated the effects of scattered and random coincidences from outsi...Image quality in positron emission tomography(PET)is affected by random and scattered coincidences and reconstruction protocols.In this study,we investigated the effects of scattered and random coincidences from outside the field of view(FOV)on PET image quality for different reconstruction protocols.Imaging was performed on the Discovery 690 PET/CT scanner,using experimental configurations including the NEMA phantom(a body phantom,with six spheres of different sizes)with a signal background ratio of 4:1.The NEMA phantom(phantom I)was scanned separately in a one-bed position.To simulate the effect of random and scatter coincidences from outside the FOV,six cylindrical phantoms with various diameters were added to the NEMA phantom(phantom II).The 18 emission datasets with mean intervals of 15 min were acquired(3 min/scan).The emission data were reconstructed using different techniques.The image quality parameters were evaluated by both phantoms.Variations in the signal-to-noise ratio(SNR)in a 28-mm(10-mm)sphere of phantom II were 37.9%(86.5%)for ordered-subset expectation maximization(OSEM-only),36.8%(81.5%)for point spread function(PSF),32.7%(80.7%)for time of flight(TOF),and 31.5%(77.8%)for OSEM+PSF+TOF,respectively,indicating that OSEM+PSF+TOF reconstruction had the lowest noise levels and lowest coefficient of variation(COV)values.Random and scatter coincidences from outside the FOV induced lower SNR,lower contrast,and higher COV values,indicating image deterioration and significantly impacting smaller sphere sizes.Amongst reconstruction protocols,OSEM+PSF+TOF and OSEM+PSF showed higher contrast values for sphere sizes of 22,28,and 37 mm and higher contrast recovery coefficient values for smaller sphere sizes of 10 and 13 mm.展开更多
A method for super high resolution comparison measurement is proposed in this paper with a comparison between the frequency standards of different nominal frequencies, which is based on phase coincidence detection of ...A method for super high resolution comparison measurement is proposed in this paper with a comparison between the frequency standards of different nominal frequencies, which is based on phase coincidence detection of the two compared signals. It utilizes the regular phase shift characteristics between the signals. The resolution of the measurement approach can reach 10^-13/s at 5 MHz, and the self-calibration resolution can achieve 10^-14/s in the comparison between 10 MHz and 100 MHz, or even can reach 10^-15/s in the comparison between 10 MHz and 190 MHz. This method implies significant progress in the development of the high precision frequency standard comparison technology.展开更多
Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex: spaces. As applications, some new fixe...Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex: spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.展开更多
The LaBr3(Ce)detector has attracted much attention in recent years because of its superior characteristics compared with other scintillating materials in terms of resolution and efficiency.However,it has a relatively ...The LaBr3(Ce)detector has attracted much attention in recent years because of its superior characteristics compared with other scintillating materials in terms of resolution and efficiency.However,it has a relatively high intrinsic background radiation because of the naturally occurring radioisotopes in lanthanum,actinium,and their daughter nuclei.This limits its applications in low-counting rate experiments.In this study,we identified the radioactive isotopes in theφ3"x 3"Saint-Gobain B380 detector by a coincidence measurement using a Clover detector in a low-background shielding system.Moreover,we carried out a Geant4 simulation of the experimental spectra to evaluate the activities of the main internal radiation components.The total activity of the background radiation of B380 is determined to be 1.523(34)Bq/cm^3.The main sources include 138La at 1.428(34)Bq/cm^3,207Tl at 0.0135(13)Bq/cm^3,211Bi at 0.0136(15)Bq/cm^3,215Po at 0.0135(3)Bq/cm^3,219Rn at 0.0125(12)Bq/cm^3,223Fr at 0.0019(11)Bq/cm^3,223Ra at 0.0127(10)Bq/cm^3,227Th at 0.0158(22)Bq/cm^3,and 227Ac at 0.0135(13)Bq/cm^3.Of these,the activities of 207Tl,211Po,215Po,223Fr,and 227Ac are deduced for the first time from the secular equilibrium established in the decay chain of 227Ac.展开更多
Some new coincidence theorems involving a new class of set-valued mappingscontaining composites of acyclic mappings defined on a contractible space are proved.As applications, some existence theorems of maximal elemen...Some new coincidence theorems involving a new class of set-valued mappingscontaining composites of acyclic mappings defined on a contractible space are proved.As applications, some existence theorems of maximal elements and solutions of abstract variational inequalities, and best approximation theorems are proved. These theorems improve and generalize a number of known results in recent literature.展开更多
In this study, a novel phoswich detector for beta–gamma coincidence detection is designed. Unlike the triple crystal phoswich detector designed by researchers at the University of Missouri, Columbia, this phoswich de...In this study, a novel phoswich detector for beta–gamma coincidence detection is designed. Unlike the triple crystal phoswich detector designed by researchers at the University of Missouri, Columbia, this phoswich detector is of the semi-well type, so it has a higher detection efficiency. The detector consists of BC-400 and NaI:Tl with decay time constants of 2.4 and 230 ns, respectively.The BC-400 scintillator detects beta particles, and the Na I:Tl cell is used for gamma detection. Geant4 simulations of this phoswich detector find that a 2-mm-thick BC-400 scintillator can absorb nearly all of the beta particles whose energies are below 700 keV. Further, for a 2.00-cmthick NaI:Tl crystal, the gamma source peak efficiency for photons ranges from a maximum of nearly 90% at 30 keV to 10% at 1 MeV. The self-absorption effect is also discussed in this paper in order to determine the carrier gas' s influence.展开更多
By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems...By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.展开更多
The results of coincidence experiment which was carried out in the whole month of April,1985 by two gravitational wave detectors in stanford and in Guangzhou are presented.It is found that up to sensitivity of h 10^(-...The results of coincidence experiment which was carried out in the whole month of April,1985 by two gravitational wave detectors in stanford and in Guangzhou are presented.It is found that up to sensitivity of h 10^(-16)the number of coincident events did not excess the number expected statistically.展开更多
The paper describes a method of selenium determination by neutron activation analysis using gamma-gamma coincidence spectrometer with Compton suppression. The analysis results of some standard reference material from ...The paper describes a method of selenium determination by neutron activation analysis using gamma-gamma coincidence spectrometer with Compton suppression. The analysis results of some standard reference material from NBS or IAEA are reported. The differences between our data and reported values are discussed.展开更多
Atrial fibrillation(AF)is the most common form of cardiac arrhythmia,affecting 3 to 6 million people in the US,with an increased incidence in women and elderly,with its prevalence estimated to increase from 5.1 millio...Atrial fibrillation(AF)is the most common form of cardiac arrhythmia,affecting 3 to 6 million people in the US,with an increased incidence in women and elderly,with its prevalence estimated to increase from 5.1 million in 2000 to 15.9 million in 2050 in the US population.[1]Age,hypertension,heart failure,myocardial infarction(MI),genetic factors,and associated systemic inflammatory states are well-established risk factors for the development of AF.[2–6]Lifestyle factors including alcohol consumption,smoking,obesity,sedentary lifestyle,and vigorous physical activity have also been implicated to contribute to the development of AF.[2,7–9]Studies suggest that AF drives up medical expenditure.[10]The European Society of Cardiology,based on the duration,responsiveness to treatment,and therapeutic attitude of the patient and physician,classifies AF into 4 types;when AF occurs and terminates by itself or by intervention within 7 days of onset,it is called paroxysmal AF;if sustained for more than a week,with or without intervention.展开更多
Coincidence Doppler broadening measurements of positron annihilation for multi- walled carbon nanotubes, double-walled carbon nanotubes, single-walled carbon nanotubes and graphite were performed. The ratio curves of ...Coincidence Doppler broadening measurements of positron annihilation for multi- walled carbon nanotubes, double-walled carbon nanotubes, single-walled carbon nanotubes and graphite were performed. The ratio curves of the Doppler broadening for these samples to silicon were obtained. It is shown that there are distinct peaks at the position of 10xl0-arn0c for both carbon nanotubes and graphite, however the amplitudes of the peaks are not the same. We have the opinion that these peaks arise from the annihilation of positron with the 2s and 2p electron of carbon element.展开更多
In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assump...In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.展开更多
The two greatest writers in their respective languages-Willim Shakespeareand Miguel de Cervantes-died on the very same day in the very same yearApril 23, 1616. They probably did not know of each other. Two men who kne...The two greatest writers in their respective languages-Willim Shakespeareand Miguel de Cervantes-died on the very same day in the very same yearApril 23, 1616. They probably did not know of each other. Two men who knewcach other well-the second and the third Prisidents of the U. S., John展开更多
The ^(12)C+^(12)C fusion is one of the most important reactions in modern nuclear astrophysics.The trend and magnitude of the reaction rate within the Gamow window strongly influence various astrophysical processes.Ho...The ^(12)C+^(12)C fusion is one of the most important reactions in modern nuclear astrophysics.The trend and magnitude of the reaction rate within the Gamow window strongly influence various astrophysical processes.However,direct measurement of this reaction is extremely difficult,which makes it necessary to develop indirect methods.In this study,the ^(23)Na+p reaction system was used to study the compound nucleus ^(24)Mg.We employed a thick-target inverse kinematics method combined with theγ-charged-particle coincidence technique to measure the proton andα exit channels of ^(24)Mg.Technical details of the ^(23)Na+p thick-target inverse kinematics experiment and analysis are presented herein.展开更多
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ...The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.展开更多
This paper applies the singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, which are established in [1], to give a un...This paper applies the singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, which are established in [1], to give a unified framework for various collocation methods of numerical solutions of singular integral equations with Cauchy kernels. Under the framework, the coincidence of the direct quadrature method and the indirect quadrature method is very simple and obvious.展开更多
In this paper, the high order delay Duffing equation ax^（2n） ＋bx＋g（x（t-r）） = p（t） are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic s...In this paper, the high order delay Duffing equation ax^（2n） ＋bx＋g（x（t-r）） = p（t） are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic solution is obtained.展开更多
A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0,...A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, 1]×R^3, e（t）∈L^1[0, 1],a≥0, is considered, all theβj＇s have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.展开更多
With the background of China's fast growing economy, Internet has become a key factor to keep the economy go steadily. It is important to quantitatively analyze the whole Internet industry and hence master its dev...With the background of China's fast growing economy, Internet has become a key factor to keep the economy go steadily. It is important to quantitatively analyze the whole Internet industry and hence master its development direction clearly, which will provide regulators with reference for industry analysis, policy formulation, and policy evaluation. This article re-constructs the calculation method of traditional Prosperity Indexes, and builds up a new indicators portfolio for Internet Industry Prosperity Indexes. By calculation, the Internet Industry Coincidence Index value is 105.9. And the Leading Index and Coincidence Index are all within the up-going range, which suggests that China's Internet Industry is likely to remain in its usual fast growing state.展开更多
This article deals with the following second-order multi-point boundary value problem x″（t）=r（t,x（t）,x′（t））＋e（t）,t∈（0,1）x′（0）=m∑i=1aix′（ξi）,x（1）=n∑j=1βjx（ηj）, Under the resonance conditi...This article deals with the following second-order multi-point boundary value problem x″（t）=r（t,x（t）,x′（t））＋e（t）,t∈（0,1）x′（0）=m∑i=1aix′（ξi）,x（1）=n∑j=1βjx（ηj）, Under the resonance conditions m∑i=1ai=1,n∑j=1βj=1,n∑j=1βjηj=1 , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references.展开更多
基金supported by the Tehran University of Medical Sciences under Grant No.36291PET/CT and Cyclotron Center of Masih Daneshvari Hospital at Shahid Beheshti University of Medical Sciences。
文摘Image quality in positron emission tomography(PET)is affected by random and scattered coincidences and reconstruction protocols.In this study,we investigated the effects of scattered and random coincidences from outside the field of view(FOV)on PET image quality for different reconstruction protocols.Imaging was performed on the Discovery 690 PET/CT scanner,using experimental configurations including the NEMA phantom(a body phantom,with six spheres of different sizes)with a signal background ratio of 4:1.The NEMA phantom(phantom I)was scanned separately in a one-bed position.To simulate the effect of random and scatter coincidences from outside the FOV,six cylindrical phantoms with various diameters were added to the NEMA phantom(phantom II).The 18 emission datasets with mean intervals of 15 min were acquired(3 min/scan).The emission data were reconstructed using different techniques.The image quality parameters were evaluated by both phantoms.Variations in the signal-to-noise ratio(SNR)in a 28-mm(10-mm)sphere of phantom II were 37.9%(86.5%)for ordered-subset expectation maximization(OSEM-only),36.8%(81.5%)for point spread function(PSF),32.7%(80.7%)for time of flight(TOF),and 31.5%(77.8%)for OSEM+PSF+TOF,respectively,indicating that OSEM+PSF+TOF reconstruction had the lowest noise levels and lowest coefficient of variation(COV)values.Random and scatter coincidences from outside the FOV induced lower SNR,lower contrast,and higher COV values,indicating image deterioration and significantly impacting smaller sphere sizes.Amongst reconstruction protocols,OSEM+PSF+TOF and OSEM+PSF showed higher contrast values for sphere sizes of 22,28,and 37 mm and higher contrast recovery coefficient values for smaller sphere sizes of 10 and 13 mm.
基金supported by the National Natural Science Foundation of China (Grant Nos.60772135 and 10978017)the Open Fund of Key Laboratory of Precision Navigation and Technology,National Time Service Center,Chinese Academy of Sciences (Grant No.2009PNTT10)the Fundamental Research Funds for the Central Universities,China (Grant No.JY10000905015)
文摘A method for super high resolution comparison measurement is proposed in this paper with a comparison between the frequency standards of different nominal frequencies, which is based on phase coincidence detection of the two compared signals. It utilizes the regular phase shift characteristics between the signals. The resolution of the measurement approach can reach 10^-13/s at 5 MHz, and the self-calibration resolution can achieve 10^-14/s in the comparison between 10 MHz and 100 MHz, or even can reach 10^-15/s in the comparison between 10 MHz and 190 MHz. This method implies significant progress in the development of the high precision frequency standard comparison technology.
基金the NNSF of China(19871059)and the NSF of Education Department of Sichuan Province([2000]25)
文摘Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex: spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature.
基金This work was supported by the National Key R&D program of China(No.2016YFA0400504)by the National Natural Science Foundation of China(Nos.U1832211,U1867210,11922501,11961141004,11575018,11790322,and U1932209).
文摘The LaBr3(Ce)detector has attracted much attention in recent years because of its superior characteristics compared with other scintillating materials in terms of resolution and efficiency.However,it has a relatively high intrinsic background radiation because of the naturally occurring radioisotopes in lanthanum,actinium,and their daughter nuclei.This limits its applications in low-counting rate experiments.In this study,we identified the radioactive isotopes in theφ3"x 3"Saint-Gobain B380 detector by a coincidence measurement using a Clover detector in a low-background shielding system.Moreover,we carried out a Geant4 simulation of the experimental spectra to evaluate the activities of the main internal radiation components.The total activity of the background radiation of B380 is determined to be 1.523(34)Bq/cm^3.The main sources include 138La at 1.428(34)Bq/cm^3,207Tl at 0.0135(13)Bq/cm^3,211Bi at 0.0136(15)Bq/cm^3,215Po at 0.0135(3)Bq/cm^3,219Rn at 0.0125(12)Bq/cm^3,223Fr at 0.0019(11)Bq/cm^3,223Ra at 0.0127(10)Bq/cm^3,227Th at 0.0158(22)Bq/cm^3,and 227Ac at 0.0135(13)Bq/cm^3.Of these,the activities of 207Tl,211Po,215Po,223Fr,and 227Ac are deduced for the first time from the secular equilibrium established in the decay chain of 227Ac.
文摘Some new coincidence theorems involving a new class of set-valued mappingscontaining composites of acyclic mappings defined on a contractible space are proved.As applications, some existence theorems of maximal elements and solutions of abstract variational inequalities, and best approximation theorems are proved. These theorems improve and generalize a number of known results in recent literature.
基金supported by the National Natural Science Foundation of China(Nos.11205108,11475121,and 11575145)the Excellent Youth Fund of Sichuan University(No.2016SCU04A13)
文摘In this study, a novel phoswich detector for beta–gamma coincidence detection is designed. Unlike the triple crystal phoswich detector designed by researchers at the University of Missouri, Columbia, this phoswich detector is of the semi-well type, so it has a higher detection efficiency. The detector consists of BC-400 and NaI:Tl with decay time constants of 2.4 and 230 ns, respectively.The BC-400 scintillator detects beta particles, and the Na I:Tl cell is used for gamma detection. Geant4 simulations of this phoswich detector find that a 2-mm-thick BC-400 scintillator can absorb nearly all of the beta particles whose energies are below 700 keV. Further, for a 2.00-cmthick NaI:Tl crystal, the gamma source peak efficiency for photons ranges from a maximum of nearly 90% at 30 keV to 10% at 1 MeV. The self-absorption effect is also discussed in this paper in order to determine the carrier gas' s influence.
基金This project is supported by the NNSF of China (19871059) and the Natural Science Foundation of Sichuan Education Department (2003A081).
文摘By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.
基金the Science Fund of the Chinese Academy of Sciences and United States National Science Foundation。
文摘The results of coincidence experiment which was carried out in the whole month of April,1985 by two gravitational wave detectors in stanford and in Guangzhou are presented.It is found that up to sensitivity of h 10^(-16)the number of coincident events did not excess the number expected statistically.
文摘The paper describes a method of selenium determination by neutron activation analysis using gamma-gamma coincidence spectrometer with Compton suppression. The analysis results of some standard reference material from NBS or IAEA are reported. The differences between our data and reported values are discussed.
文摘Atrial fibrillation(AF)is the most common form of cardiac arrhythmia,affecting 3 to 6 million people in the US,with an increased incidence in women and elderly,with its prevalence estimated to increase from 5.1 million in 2000 to 15.9 million in 2050 in the US population.[1]Age,hypertension,heart failure,myocardial infarction(MI),genetic factors,and associated systemic inflammatory states are well-established risk factors for the development of AF.[2–6]Lifestyle factors including alcohol consumption,smoking,obesity,sedentary lifestyle,and vigorous physical activity have also been implicated to contribute to the development of AF.[2,7–9]Studies suggest that AF drives up medical expenditure.[10]The European Society of Cardiology,based on the duration,responsiveness to treatment,and therapeutic attitude of the patient and physician,classifies AF into 4 types;when AF occurs and terminates by itself or by intervention within 7 days of onset,it is called paroxysmal AF;if sustained for more than a week,with or without intervention.
基金supported by National Natural Science Foundation of China (No.10835006)
文摘Coincidence Doppler broadening measurements of positron annihilation for multi- walled carbon nanotubes, double-walled carbon nanotubes, single-walled carbon nanotubes and graphite were performed. The ratio curves of the Doppler broadening for these samples to silicon were obtained. It is shown that there are distinct peaks at the position of 10xl0-arn0c for both carbon nanotubes and graphite, however the amplitudes of the peaks are not the same. We have the opinion that these peaks arise from the annihilation of positron with the 2s and 2p electron of carbon element.
基金supported by the Foundation of Education Ministry,Hubei Province,China(Q20122203)
文摘In this paper,we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in such spaces.We consider the obtained assertions without the assumption of normality of cones.The presented results generalize some coupled common fixed point theorems in the existing literature.
文摘The two greatest writers in their respective languages-Willim Shakespeareand Miguel de Cervantes-died on the very same day in the very same yearApril 23, 1616. They probably did not know of each other. Two men who knewcach other well-the second and the third Prisidents of the U. S., John
基金supported by the National Key Research and Development Project (No. 2022YFA1602301)the National Natural Science Foundation of China (Nos. U2267205, 12275361, 12125509, 12222514, 11961141003, and 12005304)+2 种基金the CAST Young Talent Support Planthe CNNC Science Fund for Talented Young Scholarsthe Continuous-Support Basic Scientific Research Project
文摘The ^(12)C+^(12)C fusion is one of the most important reactions in modern nuclear astrophysics.The trend and magnitude of the reaction rate within the Gamow window strongly influence various astrophysical processes.However,direct measurement of this reaction is extremely difficult,which makes it necessary to develop indirect methods.In this study,the ^(23)Na+p reaction system was used to study the compound nucleus ^(24)Mg.We employed a thick-target inverse kinematics method combined with theγ-charged-particle coincidence technique to measure the proton andα exit channels of ^(24)Mg.Technical details of the ^(23)Na+p thick-target inverse kinematics experiment and analysis are presented herein.
文摘The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.
基金NNSF of China, SF of SEC of China and SF of Wuhan University.
文摘This paper applies the singular integral operators, singular quadrature operators and discretization matrices associated with singular integral equations with Cauchy kernels, which are established in [1], to give a unified framework for various collocation methods of numerical solutions of singular integral equations with Cauchy kernels. Under the framework, the coincidence of the direct quadrature method and the indirect quadrature method is very simple and obvious.
文摘In this paper, the high order delay Duffing equation ax^（2n） ＋bx＋g（x（t-r）） = p（t） are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic solution is obtained.
文摘A kind of third order multi-point boundary value problems, x＇＇＇（ ι） = f（ t, x （ t ）, x＂ （ t ）, x＇＇＇ （ t ） ） ＋ m 2 e（t）,t∈（0, 1）,x（0）=ax（ξ）,x＇（0）-0,x（l）= ^m2∑j=1 βjx（ηj）, fεC[0, 1]×R^3, e（t）∈L^1[0, 1],a≥0, is considered, all theβj＇s have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained.
文摘With the background of China's fast growing economy, Internet has become a key factor to keep the economy go steadily. It is important to quantitatively analyze the whole Internet industry and hence master its development direction clearly, which will provide regulators with reference for industry analysis, policy formulation, and policy evaluation. This article re-constructs the calculation method of traditional Prosperity Indexes, and builds up a new indicators portfolio for Internet Industry Prosperity Indexes. By calculation, the Internet Industry Coincidence Index value is 105.9. And the Leading Index and Coincidence Index are all within the up-going range, which suggests that China's Internet Industry is likely to remain in its usual fast growing state.
基金Supported by the NSF of Jiangsu Province(BK2008119)the NSF of the Education Department of Jiangsu Province (08KJB110011)+1 种基金Innovation Project of Jiangsu Province Postgraduate Training Project(CX07S 015z)the Qinglan Program of Jiangsu Province (QL200613)
文摘This article deals with the following second-order multi-point boundary value problem x″（t）=r（t,x（t）,x′（t））＋e（t）,t∈（0,1）x′（0）=m∑i=1aix′（ξi）,x（1）=n∑j=1βjx（ηj）, Under the resonance conditions m∑i=1ai=1,n∑j=1βj=1,n∑j=1βjηj=1 , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references.
