On May 1st, China National Nuclear Corporation(CNNC) announced in Beijing that unit 1 and unit 2 ofTianwan Nuclear Power Plant cooperatively constructedby China and Russia have completed in succession thefirst fuel cy...On May 1st, China National Nuclear Corporation(CNNC) announced in Beijing that unit 1 and unit 2 ofTianwan Nuclear Power Plant cooperatively constructedby China and Russia have completed in succession thefirst fuel cycle operation continuously and safely. It is展开更多
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.展开更多
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends ...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.展开更多
To improve the effect of destroying time-sensitive target (TST), a method of operational effectiveness evaluation is presented and some influential factors are analyzed based on the combat flow of system for destroy...To improve the effect of destroying time-sensitive target (TST), a method of operational effectiveness evaluation is presented and some influential factors are analyzed based on the combat flow of system for destroying TST. Considering the possible operation modes of the system, a waved operation mode and a continuous operation mode are put forward at first. At the same time, some relative formulas are modified. In examples, the influential factors and operation modes are analyzed based on the system effectiveness. From simulation results, some design and operation strategies of the system for destroying time sensitive targets are concluded, which benefit to the improvement of the system effectiveness.展开更多
We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free ferm...We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.展开更多
MIL-88A(Fe)@sponge(MS) was synthesized by a dip-coating method, which displayed efficient photocatalytic Cr(Ⅵ) reduction efficiency under both low power LED UV light and real solar light irradiation. It was observed ...MIL-88A(Fe)@sponge(MS) was synthesized by a dip-coating method, which displayed efficient photocatalytic Cr(Ⅵ) reduction efficiency under both low power LED UV light and real solar light irradiation. It was observed that MS(0.2 g/L) could remove 100% Cr(Ⅵ)(10 mg/L) by adding 0.4 mmol/L tartaric acid(TA) without adjusting pH(pH 5.05) within 6.0 min and 3.0 min under UV light and real solar light irradiation, respectively. Besides, the photo-induced e-and radicals(O_(2)^(·-) and CO_(2)^(·-)) were found to play the momentous roles in the MS/TA/UVL/Cr(Ⅵ) system by the scavenger experiments and electron spin resonance(ESR) tests. MS was also filled into a fixed-bed reactor to test the possibility of long-term Cr(Ⅵ)reduction operation in TA/UVL system. As expected, the results revealed that MS could still maintain 100% activity up to 60 h. These results demonstrated that MIL-88A(Fe) might be the potentially efficient catalyst for large-scale wastewater treatment in the near future.展开更多
This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional met...This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional methods, which are flawed due to missing information or distortion in the seismograph records. The epicenter, trigger time and magnitude from the Lushan earthquake are inverted and analyzed based on high-frequency GNSS data. The inversion results achieved a high precision, which are consistent with the data published by the China Earthquake Administration. Moreover, it has been proven that the inversion method has good theoretical value and excellent application prospects.展开更多
The stability and reliability of an ion source and its beam availability are extremely significant for any accelerator,especially for those high current long term CW operation ones like ADS. Although the first high qu...The stability and reliability of an ion source and its beam availability are extremely significant for any accelerator,especially for those high current long term CW operation ones like ADS. Although the first high quality 306-hours continuous wave(CW) operating curve at 50 m A@35 ke V has been successfully obtained with a standard compact 2.45 GHz ECR ion source at Peking University(PKU), but the uncertainties that caused beam trips before are unacceptable during an accelerator real operation and should be eliminated. Meanwhile, no permission will be given when the beam power is upgraded from 50 m A@35 ke V to 50 m A@50 ke V. To improve the PKU CW proton source quality, several upgrades were done recently. After those improvements, a new long term CW proton beam experiment at 50 m A@50 ke V was carried out in June 2016. The total running time is 300.5 hours, including near 6 hours ion source preparation and 294 hours non-disturb continuous operation. Within the continuous 13 days operation, no beam-off happened, no spark was observed,no beam drop appeared, no interrupting action was needed, and only a few beam fluctuations caused by the air conditional failure occurred. Beam availability and reliability within the 294 hours is 100%. The root-mean-square(RMS) emittance of this 50 m A@50 ke V CW proton beam is about 0.186 π.mm.mrad. A careful inspection of the ion source was done after this long term operation and no obvious damage was found. The restart experimental results obtained after the ion source inspection prove the high repeatability of PKU PMECRIS. In addition, a 130-m A H+beam was obtained at 50 k V with duty factor of 10%(100 Hz/1 ms) with this source. Details will be presented in this paper.展开更多
In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spac...In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.展开更多
The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the diff...The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.展开更多
The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Se...The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.展开更多
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem, Petryshyn's theorem, etc.展开更多
A precise background theory of computational mechanics is formed. Saint_Venant's principle is discussed in chain model by means of this precise theory. The classical continued fraction is developed into operator c...A precise background theory of computational mechanics is formed. Saint_Venant's principle is discussed in chain model by means of this precise theory. The classical continued fraction is developed into operator continued fraction to be the constrictive formulation of the chain model. The decay of effect of a self_equilibrated system of forces in chain model is decided by the convergence of operator continued fraction, so the reasonable part of Saint_Venant's principle is described as the convergence of operator continued fraction. In case of divergence the effect of a self_equilibrated system of forces may be non_zero at even infinite distant sections, so Saint_Venant's principle is not a common principle.展开更多
If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a spec...If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.展开更多
In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe th...In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe those spaces which have property (MB) . Also, we show that if a Banach space X has property (MB) and Banach space Y does not contain , then every operator is completely continuous.展开更多
Based on a compulsive mixing-reacting-sepa-rating-recycling small experimental setup,the continuous reaction performances of benzene alkylation with long chain olefins catalyzed by[BMIM]Cl-AlCl 3 ionic liquid were inv...Based on a compulsive mixing-reacting-sepa-rating-recycling small experimental setup,the continuous reaction performances of benzene alkylation with long chain olefins catalyzed by[BMIM]Cl-AlCl 3 ionic liquid were investigated.Three different situations including normal continuous operation mode(reagent materials),sidetrack feeding from different axial positions along the static mixing reactor(reagent materials)and normal con-tinuous alkylation using industrial paraffin and olefins materials were examined.Even under the relatively hype-critical reaction conditions,the single pass conversion of pure 1-dodecene could reach to nearly 100.0%,and the selectivity of 2-phenyl isomer was higher than 37.7%.Although the positions along the reactor for sidetrack feeding were different,the 100.0%single pass conversion of 1-dodecene was also attained before the outlet of the reactor.The refined industrial olefins as raw material could meet with the requirements of continuous alkyla-tion.The influences of impurities such as di-olefins and non-benzene aromatics on the catalytic activity and stability should be studied further.展开更多
A novel method based on the selective pressure of particle size (particle-size cultivation method, PSCM) was developed for the cultivation and operation of aerobic granular sludge in a continuous-flow reactor, and c...A novel method based on the selective pressure of particle size (particle-size cultivation method, PSCM) was developed for the cultivation and operation of aerobic granular sludge in a continuous-flow reactor, and compared with the conventional method based on the selective pressure of settling velocity (settling-velocity cultivation method, SVCM). Results indicated that aerobic granules could be cultivated in continuous operation mode by this developed method within 14 days. Although in the granulation process, under particle-size selective pressure, mixed liquor suspended solids (MLSS) in the reactor fluctuated greatly and filamentous bacteria dominated the sludge system during the initial operation days, no obvious difference in profile was found between the aerobic granules cultivated by PSCM and SVCM. Moreover, aerobic granules cultivated by PSCM presented larger diameter, lower water content and higher specific rates of nitrification, denitrifieation and phosphorus removal, but lower settling velocity. Under long term operation of more than 30 days, aerobic granules in the continuous-flow reactor could remain stable and obtain good chemical oxygen demand (COD), NH4^+-N, total nitrogen (TN) and total phosphorus (TP) removal. The results indicate that PSCM was dependent on the cultivation and maintenance of the stability of aerobic granules in continuous-flow bioreactors.展开更多
The formation and propagation of the popular off-corner subsurface cracks in bloom continuous casting were investigated through thermo-mechanical analysis using three coupled thermo-mechanical models. A two-dimensiona...The formation and propagation of the popular off-corner subsurface cracks in bloom continuous casting were investigated through thermo-mechanical analysis using three coupled thermo-mechanical models. A two-dimensional thermo-elasto-visco-plastic finite element model was developed to predict the mould gap evolution, temperature profiles and deformation behavior of the solidified shell in the mould region. Then, a three-dimensional model was adopted to calculate the shell growth, tempera- ture history and the development of stresses and strains of the shell in the following secondary cooling zones. Finally, another three-dimensional model was used to analyze the stress distributions in the straightening region, The results showed that the off-corner cracks in the shell originated from the mould owing to the tensile strain developed in the crack sensitive regions of the solidification front, and they could be driven deeper by the possible severe surface temperature rebound and the extensive tensile stress in the secondary cooling zone, especially upon the straightening operation of the bloom casting. It is revealed that more homogenous shell temperature and thickness can be obtained through optimization of mould corner radius, casting speed and secondary cooling scheme, which help to decrease stress and strain concentration and therefore prevent the initiation of the cracks.展开更多
IN 1932, Stone [1] gave the first result concerning C<sub>0</sub> semigroups generated by an unbounded operator,which says that a linear operator is the infinitesimal generator of a C<sub>0</sub&g...IN 1932, Stone [1] gave the first result concerning C<sub>0</sub> semigroups generated by an unbounded operator,which says that a linear operator is the infinitesimal generator of a C<sub>0</sub> group of unitary operators on a Hilbert space if and only if it is skew-adjoint. This result has been applied extensively to linear partial differential equations (PDEs) with a law of conservation. Hille [2] then discovered the generation theorem of the Hille-Yosida type for a C<sub>0</sub> group on a Banach space. There are also some conditions under which a C<sub>0</sub> semigroup on a Banach space can be embedded in a C<sub>0</sub> group. We refer the readers to ref. [3] for details of the results mentioned above.展开更多
基于上海市连续运行基准站(continuously operating reference station,CORS)系统中10个基准站2021-09-10—2021-09-14的观测数据,采用实时精密单点定位(precise point positioning,PPP)技术反演大气可降水量(precipitable water vapor,...基于上海市连续运行基准站(continuously operating reference station,CORS)系统中10个基准站2021-09-10—2021-09-14的观测数据,采用实时精密单点定位(precise point positioning,PPP)技术反演大气可降水量(precipitable water vapor,PWV),探究了台风“灿都”期间PWV与实际降雨量的时空交互特征。结果表明,PWV含量与降雨量显著相关,即PWV在降雨发生前激增,降雨期间保持稳定,降雨完成后回落至原水平。此外,PWV的空间演变还可揭示台风影响期间的水汽输送路径。上述特征证明,实时PWV有预警极端降雨的潜力,未来可在CORS系统部署降雨预警模块,进一步拓宽其服务领域。展开更多
文摘On May 1st, China National Nuclear Corporation(CNNC) announced in Beijing that unit 1 and unit 2 ofTianwan Nuclear Power Plant cooperatively constructedby China and Russia have completed in succession thefirst fuel cycle operation continuously and safely. It is
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.
基金supported by the National Natural Science Foundation of China (60774064)the Aerospace Science Foundation (05D53022)the Youth for NPU Teachers Scientific and Technological Innovation Foundation (W016210)
文摘To improve the effect of destroying time-sensitive target (TST), a method of operational effectiveness evaluation is presented and some influential factors are analyzed based on the combat flow of system for destroying TST. Considering the possible operation modes of the system, a waved operation mode and a continuous operation mode are put forward at first. At the same time, some relative formulas are modified. In examples, the influential factors and operation modes are analyzed based on the system effectiveness. From simulation results, some design and operation strategies of the system for destroying time sensitive targets are concluded, which benefit to the improvement of the system effectiveness.
基金supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB30000000)the National Natural Science Foundation of China(Grant Nos.11774398 and T2121001)。
文摘We study the structure of the continuous matrix product operator(cMPO)^([1]) for the transverse field Ising model(TFIM).We prove TFIM’s cMPO is solvable and has the form T=e^(-1/2H_(F)).H_(F) is a non-local free fermionic Hamiltonian on a ring with circumferenceβ,whose ground state is gapped and non-degenerate even at the critical point.The full spectrum of H_(F) is determined analytically.At the critical point,our results verify the state–operator-correspondence^([2]) in the conformal field theory(CFT).We also design a numerical algorithm based on Bloch state ansatz to calculate the lowlying excited states of general(Hermitian)cMPO.Our numerical calculations coincide with the analytic results of TFIM.In the end,we give a short discussion about the entanglement entropy of cMPO’s ground state.
基金supported by National Natural Science Foundation of China (Nos. 22176012, 51878023)Beijing Natural Science Foundation (No. 8202016)+1 种基金Beijing Talent Project (No. 2020A27)BUCEA Doctor Graduate Scientific Research Ability Improvement Project (No. DG2021004)。
文摘MIL-88A(Fe)@sponge(MS) was synthesized by a dip-coating method, which displayed efficient photocatalytic Cr(Ⅵ) reduction efficiency under both low power LED UV light and real solar light irradiation. It was observed that MS(0.2 g/L) could remove 100% Cr(Ⅵ)(10 mg/L) by adding 0.4 mmol/L tartaric acid(TA) without adjusting pH(pH 5.05) within 6.0 min and 3.0 min under UV light and real solar light irradiation, respectively. Besides, the photo-induced e-and radicals(O_(2)^(·-) and CO_(2)^(·-)) were found to play the momentous roles in the MS/TA/UVL/Cr(Ⅵ) system by the scavenger experiments and electron spin resonance(ESR) tests. MS was also filled into a fixed-bed reactor to test the possibility of long-term Cr(Ⅵ)reduction operation in TA/UVL system. As expected, the results revealed that MS could still maintain 100% activity up to 60 h. These results demonstrated that MIL-88A(Fe) might be the potentially efficient catalyst for large-scale wastewater treatment in the near future.
基金National Natural Science Foundation under Grant No.51574201Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection(Chengdu University of Technology)under Grant No.SKLGP2016K017+2 种基金Open Research Fund by Sichuan Engineering Research Center for Emergency Mapping&Disaster Reduction under Grant No.K2015B008The State Administration of Work Safety under Grant No.2014_3335Soft Science Research Projects in Sichuan Province under Grant No.2015zr0049
文摘This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional methods, which are flawed due to missing information or distortion in the seismograph records. The epicenter, trigger time and magnitude from the Lushan earthquake are inverted and analyzed based on high-frequency GNSS data. The inversion results achieved a high precision, which are consistent with the data published by the China Earthquake Administration. Moreover, it has been proven that the inversion method has good theoretical value and excellent application prospects.
基金Project supported by the National Basic Research Program of China(Grant No.2014CB845502)the National Natural Science Foundation of China(Grant No.11575013)
文摘The stability and reliability of an ion source and its beam availability are extremely significant for any accelerator,especially for those high current long term CW operation ones like ADS. Although the first high quality 306-hours continuous wave(CW) operating curve at 50 m A@35 ke V has been successfully obtained with a standard compact 2.45 GHz ECR ion source at Peking University(PKU), but the uncertainties that caused beam trips before are unacceptable during an accelerator real operation and should be eliminated. Meanwhile, no permission will be given when the beam power is upgraded from 50 m A@35 ke V to 50 m A@50 ke V. To improve the PKU CW proton source quality, several upgrades were done recently. After those improvements, a new long term CW proton beam experiment at 50 m A@50 ke V was carried out in June 2016. The total running time is 300.5 hours, including near 6 hours ion source preparation and 294 hours non-disturb continuous operation. Within the continuous 13 days operation, no beam-off happened, no spark was observed,no beam drop appeared, no interrupting action was needed, and only a few beam fluctuations caused by the air conditional failure occurred. Beam availability and reliability within the 294 hours is 100%. The root-mean-square(RMS) emittance of this 50 m A@50 ke V CW proton beam is about 0.186 π.mm.mrad. A careful inspection of the ion source was done after this long term operation and no obvious damage was found. The restart experimental results obtained after the ion source inspection prove the high repeatability of PKU PMECRIS. In addition, a 130-m A H+beam was obtained at 50 k V with duty factor of 10%(100 Hz/1 ms) with this source. Details will be presented in this paper.
文摘In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.
基金Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of Ministry of Education, China (No.0705)the Dawn Program Fund of Shanghai of China (No.BL200404)Shanghai Leading Academic Discipline Project (No.T0401)
文摘The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.
文摘The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem, Petryshyn's theorem, etc.
文摘A precise background theory of computational mechanics is formed. Saint_Venant's principle is discussed in chain model by means of this precise theory. The classical continued fraction is developed into operator continued fraction to be the constrictive formulation of the chain model. The decay of effect of a self_equilibrated system of forces in chain model is decided by the convergence of operator continued fraction, so the reasonable part of Saint_Venant's principle is described as the convergence of operator continued fraction. In case of divergence the effect of a self_equilibrated system of forces may be non_zero at even infinite distant sections, so Saint_Venant's principle is not a common principle.
基金Supported by the Doctoral programme foundation of National Education Ministry of China
文摘If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ (0 ≤δ 〈 ρ≤ 1). In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 (= F 0 , 2 1 ) → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p (= F 0 , 2 p ) → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.
文摘In this paper, a new class of Banach spaces, termed as Banach spaces with property (MB), will be introduced. It is stated that a space X has property (MB) if every V -subset of X* is an L-subset of X* . We describe those spaces which have property (MB) . Also, we show that if a Banach space X has property (MB) and Banach space Y does not contain , then every operator is completely continuous.
基金This work was supported by the National Program on Key Basic Research Project(G2000048006)Research Foundation of Henan University(05YBZR025).
文摘Based on a compulsive mixing-reacting-sepa-rating-recycling small experimental setup,the continuous reaction performances of benzene alkylation with long chain olefins catalyzed by[BMIM]Cl-AlCl 3 ionic liquid were investigated.Three different situations including normal continuous operation mode(reagent materials),sidetrack feeding from different axial positions along the static mixing reactor(reagent materials)and normal con-tinuous alkylation using industrial paraffin and olefins materials were examined.Even under the relatively hype-critical reaction conditions,the single pass conversion of pure 1-dodecene could reach to nearly 100.0%,and the selectivity of 2-phenyl isomer was higher than 37.7%.Although the positions along the reactor for sidetrack feeding were different,the 100.0%single pass conversion of 1-dodecene was also attained before the outlet of the reactor.The refined industrial olefins as raw material could meet with the requirements of continuous alkyla-tion.The influences of impurities such as di-olefins and non-benzene aromatics on the catalytic activity and stability should be studied further.
基金supported by the National Natural Science Foundation of China (No. 51208231)
文摘A novel method based on the selective pressure of particle size (particle-size cultivation method, PSCM) was developed for the cultivation and operation of aerobic granular sludge in a continuous-flow reactor, and compared with the conventional method based on the selective pressure of settling velocity (settling-velocity cultivation method, SVCM). Results indicated that aerobic granules could be cultivated in continuous operation mode by this developed method within 14 days. Although in the granulation process, under particle-size selective pressure, mixed liquor suspended solids (MLSS) in the reactor fluctuated greatly and filamentous bacteria dominated the sludge system during the initial operation days, no obvious difference in profile was found between the aerobic granules cultivated by PSCM and SVCM. Moreover, aerobic granules cultivated by PSCM presented larger diameter, lower water content and higher specific rates of nitrification, denitrifieation and phosphorus removal, but lower settling velocity. Under long term operation of more than 30 days, aerobic granules in the continuous-flow reactor could remain stable and obtain good chemical oxygen demand (COD), NH4^+-N, total nitrogen (TN) and total phosphorus (TP) removal. The results indicate that PSCM was dependent on the cultivation and maintenance of the stability of aerobic granules in continuous-flow bioreactors.
文摘The formation and propagation of the popular off-corner subsurface cracks in bloom continuous casting were investigated through thermo-mechanical analysis using three coupled thermo-mechanical models. A two-dimensional thermo-elasto-visco-plastic finite element model was developed to predict the mould gap evolution, temperature profiles and deformation behavior of the solidified shell in the mould region. Then, a three-dimensional model was adopted to calculate the shell growth, tempera- ture history and the development of stresses and strains of the shell in the following secondary cooling zones. Finally, another three-dimensional model was used to analyze the stress distributions in the straightening region, The results showed that the off-corner cracks in the shell originated from the mould owing to the tensile strain developed in the crack sensitive regions of the solidification front, and they could be driven deeper by the possible severe surface temperature rebound and the extensive tensile stress in the secondary cooling zone, especially upon the straightening operation of the bloom casting. It is revealed that more homogenous shell temperature and thickness can be obtained through optimization of mould corner radius, casting speed and secondary cooling scheme, which help to decrease stress and strain concentration and therefore prevent the initiation of the cracks.
文摘IN 1932, Stone [1] gave the first result concerning C<sub>0</sub> semigroups generated by an unbounded operator,which says that a linear operator is the infinitesimal generator of a C<sub>0</sub> group of unitary operators on a Hilbert space if and only if it is skew-adjoint. This result has been applied extensively to linear partial differential equations (PDEs) with a law of conservation. Hille [2] then discovered the generation theorem of the Hille-Yosida type for a C<sub>0</sub> group on a Banach space. There are also some conditions under which a C<sub>0</sub> semigroup on a Banach space can be embedded in a C<sub>0</sub> group. We refer the readers to ref. [3] for details of the results mentioned above.
文摘基于上海市连续运行基准站(continuously operating reference station,CORS)系统中10个基准站2021-09-10—2021-09-14的观测数据,采用实时精密单点定位(precise point positioning,PPP)技术反演大气可降水量(precipitable water vapor,PWV),探究了台风“灿都”期间PWV与实际降雨量的时空交互特征。结果表明,PWV含量与降雨量显著相关,即PWV在降雨发生前激增,降雨期间保持稳定,降雨完成后回落至原水平。此外,PWV的空间演变还可揭示台风影响期间的水汽输送路径。上述特征证明,实时PWV有预警极端降雨的潜力,未来可在CORS系统部署降雨预警模块,进一步拓宽其服务领域。