Food safety problems caused by excessive nitrite addition have been frequently reported and the detection of nitrite in food is particularly important. The standing time during the pretreatment of primary sample has a...Food safety problems caused by excessive nitrite addition have been frequently reported and the detection of nitrite in food is particularly important. The standing time during the pretreatment of primary sample has a great influence on the concentration of nitrite tested by spectrophotometric method. In this context, three kinds of food samples are prepared, including canned mustard, canned fish and home-made pickled water. A series of standing times are placed during the sample pretreatments and the corresponding nitrite contents in these samples are detected by spectrophotometric method based on N-ethylenediamine dihydrochloride. This study aims to find out a reasonable standing time during the pretreatment of food sample, providing influence factor for precise detection of nitrite.展开更多
Twenty-seven specimens were tested to investigate the uniaxial compression behaviour of an innovative standing support for underground space applications.The innovative standing support consisted of an external fibre ...Twenty-seven specimens were tested to investigate the uniaxial compression behaviour of an innovative standing support for underground space applications.The innovative standing support consisted of an external fibre reinforced polymer(FRP)jacket and the infill column made of cementitious grout,tailings and coal wash rejects.Effects of the FRP layers number and water to the cementitious grout(w/g)ratio were evaluated.Test results indicated that lower w/g ratios produced stronger infill columns.With FRP confinement,the standing support demonstrated strain-hardening loading characteristics with a significant improvement in both strength and ductility.The highest strength and strain of the specimens achieved was 58.4 MPa and 11.8%respectively.Compared with the unconfined specimens,the confinement with four FRP layers increased the specimen strength and associated strain up to 3.6 and 27.0 times respectively.A correlation between the compressive strength of the infill material and the ultrasonic pulse velocity was also investigated.Furthermore,a simple design-oriented model was proposed to predict the peak strength and the corresponding strain of the innovative standing support.展开更多
The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment,in cases when the...The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment,in cases when there were neither external background magnetic field or other factors that destroyed the poloidal symmetry of the tube.The formation mechanism and chirality of helical streamers are discussed according to the surface electromagnetic standing wave theory.The shape of the helical streamers and the characteristics of helical branches are quantitatively analyzed to further expand the application of plasma and streamer theory in the helix problem and chiral catalytic synthesis.展开更多
正At the invitation of the Ministry of Foreign Affairs of Israel, Grand National Assembly of Turkey (TBMM) and Delhi Study Group of India, a delegation of the Chinese Association for International Understanding (CAFIU...正At the invitation of the Ministry of Foreign Affairs of Israel, Grand National Assembly of Turkey (TBMM) and Delhi Study Group of India, a delegation of the Chinese Association for International Understanding (CAFIU) headed展开更多
正The Understanding and Cooperation Dialogue, Sponsored by the Chinese Association for International Understanding (CAFIU) and the China Foundation for Peace and Development (CFPD), and Co-organized by the Chinese Peo...正The Understanding and Cooperation Dialogue, Sponsored by the Chinese Association for International Understanding (CAFIU) and the China Foundation for Peace and Development (CFPD), and Co-organized by the Chinese People' s Association for Peace and展开更多
Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which ca...Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate thewave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/λ0, ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, .and the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.展开更多
Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstan...Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge code. The mode transitions, also known as density jumps, of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude standing helicon waves(SHWs) are responsible for the mode transitions, similar to those of a resonant cavity for laser generation.This paper intends to give a complete and quantitative SHW resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.展开更多
The standing stock of phytoplankton (phy. ) and primary productivity (pp) in the Xiangshan Bay were observed in 1992. The results showed higher biological parameters in the bay. The average chlorophyll a (chl a) conce...The standing stock of phytoplankton (phy. ) and primary productivity (pp) in the Xiangshan Bay were observed in 1992. The results showed higher biological parameters in the bay. The average chlorophyll a (chl a) concentration was (3. 50 5. 93 ) mg/m3 and the primary productivity (444. 5 871. 0) mg/(m2 d). The distribution of chl a and productivity showed distinct spatial and temporal patterns in the bay. The continent influence was Obvious at the top of the bay, lower seawater exchange and higher stability led to higher standing stock of phytoplankton and productivity. At the bay mouth, seawater exchanged continuously with adjacent waters by rapid currents, resulting in fast and unstable exchange and lower standing stock of phytoplankton and primary productivity. The seasonal characters of those parameters were pronounced, in the sequence of spring, summer, autumn and winter. The results of size--fractionated showed that the average contribution of the nano--and picoplankton (< 20pm) to total chl a and productivity were 75 % and 87%, respectively, indicating their importance in phytoplankton community biomass and productivity of the Xiangshan Bay.展开更多
Background: Although the standing long jump (SLJ) is a popular physical fitness assessment, it lacks an updated criterion-reference standard. This study generated the first normative SLJ test data for Chinese aged 8 -...Background: Although the standing long jump (SLJ) is a popular physical fitness assessment, it lacks an updated criterion-reference standard. This study generated the first normative SLJ test data for Chinese aged 8 - 18. Methods: From September 2005 to December 2011, comprehensive physical fitness assessments were conducted on 12,712 school students. The SLJ performances were significantly different between boys and girls (all age groups, p < 0.01). Results: The boys performed better than the girls in each age group. The mean difference increased as the age increased, depicting a prominent variance in muscular strength between boys and girls at age 12, and the variances became larger at age 18. Girls in the 70th percenttile performed similarly to boys performing in the 10th percentile. The onset of muscle strength for boys found in this study corresponded to the onset age of testosterone maturation of Chinese boys investigated in previous studies. Linear regression found age and BMI predicting SLJ significantly for boys and girls, explaining better SLJ results in older boy and the effect of their heavy body size. Conclusions: This study indicated a muscular strength difference between genders during growth and added supporting evidence to the hormonal influence of muscle growth during puberty.展开更多
This paper presents the development of an innovative standing support for underground mines.The main feature of this standing support is its exterior container,a combination of polyvinyl chloride(PVC)with large ruptur...This paper presents the development of an innovative standing support for underground mines.The main feature of this standing support is its exterior container,a combination of polyvinyl chloride(PVC)with large rupture strain and fibre-reinforced polymer(FRP)with high strength-to-weight ratio.To demonstrate the advantages of this cementitious grout filled PVC-FRP tubular(PFT)standing support,a series of compression tests were conducted.Test variables included the strength of cementitious grout infill material and the thickness of FRP jacket.Compression tests were also conducted on cementitious grout-filled PVC tubular(PT)support and cementitious grout-filled FRP tubular(FT)support.These tests showed that PFT support presents a typical strain-hardening behaviour together with an outstanding axial deformation ability(>20%of the overall height of the support).In addition,the maximum compressive strength of PFT support is much higher than that of the corresponding PT support and FT support.Furthermore,using thicker FRP jacket or high strength cementitious grout material can enhance the load carrying capacity of PFT support.These comparative results indicated that the high performance of PFT support is mainly attributed to the combination of confining constituents(i.e.PVC and FRP)and infill material.展开更多
A 2856-MHz,π-mode,seven-cell standingwave deflecting cavity was designed and fabricated for bunch length measurement in Tsinghua Thomson scattering X-ray source(TTX)facility.This cavity was installed in the TTX and p...A 2856-MHz,π-mode,seven-cell standingwave deflecting cavity was designed and fabricated for bunch length measurement in Tsinghua Thomson scattering X-ray source(TTX)facility.This cavity was installed in the TTX and provided a deflecting voltage of 4.2 MV with an input power of 2.5 MW.Bunch length diagnoses of electron beams with energies up to 39 MeV have been performed.In this article,the RF design of the cavity using HFSS,fabrication,and RF test processes are reviewed.High-power operation with accelerated beams and calibration of the deflecting voltage are also presented.展开更多
We report a universal transfer methodology for producing artificial heterostructures of large-area freestanding single-crystalline WTe_(2) membranes on diverse target substrates.The transferred WTe_(2) membranes exhib...We report a universal transfer methodology for producing artificial heterostructures of large-area freestanding single-crystalline WTe_(2) membranes on diverse target substrates.The transferred WTe_(2) membranes exhibit a nondestructive structure with a carrier mobility comparable to that of as-grown films(∼179–1055 cm^(2)·V^(−1)·s^(−1)).Furthermore,the transferred membranes show distinct Shubnikov–de Haas quantum oscillations as well as weak localization/weak anti-localization.These results provide a new approach to the development of atom manufacturing and devices based on atomic-level,large-area topological quantum films.展开更多
In Earth's high-latitude ionosphere, the poleward motion of east–west elongated auroral arcs has been attributed to standing hydromagnetic waves, especially when the auroral arcs appear quasi-periodically with a ...In Earth's high-latitude ionosphere, the poleward motion of east–west elongated auroral arcs has been attributed to standing hydromagnetic waves, especially when the auroral arcs appear quasi-periodically with a recurrence time of a few minutes. The validation of this scenario requires spacecraft observations of ultra-low-frequency hydromagnetic waves in the magnetosphere and simultaneous observations of poleward-moving auroral arcs near the spacecraft footprints. Here we present the first observational evidence from the multi-spacecraft THEMIS (Time History of Events and Macroscale Interactions during Substorms) mission and the conjugated all-sky imager to support the scenario that standing hydromagnetic waves can generate the quasi-periodic appearance of poleward-moving auroral arcs. In this specific event, the observed waves were toroidal branches of the standing hydromagnetic waves, which were excited by a pulse in the solar wind dynamic pressure. Multi-spacecraft measurements from THEMIS also suggest higher wave frequencies at lower L shells (consistent with the distribution of magnetic field line eigenfrequencies), which indicates that the phase difference across latitudes would increase with time. As time proceeds, the enlarged phase difference corresponds to a lower propagation speed of the auroral arcs, which agrees very well with the ground-based optical data.展开更多
Dear Editor,Premacular hemorrhage is a common cause of sudden profound visual loss in otherwise healthy eye.One of the commonest causes of premacular hemorrhage in clinical practice is Valsalva retinopathy,which was f...Dear Editor,Premacular hemorrhage is a common cause of sudden profound visual loss in otherwise healthy eye.One of the commonest causes of premacular hemorrhage in clinical practice is Valsalva retinopathy,which was first described by Thomas Duane in 1972[1].In the setting of Valsalva retinopathy these hemorrhages are a result of ruptured展开更多
In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" ...In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.展开更多
We consider a time independent one dimensional finite range and repulsive constant potential barrier between two impenetrable walls. For a nonrelativistic massive particle projected towards the potential with energies...We consider a time independent one dimensional finite range and repulsive constant potential barrier between two impenetrable walls. For a nonrelativistic massive particle projected towards the potential with energies less than the barrier and irrespective of the spatial positioning of the potential allowing for quantum tunneling, analytically we solve the corresponding Schrodinger equation. For a set of suitable parameters utilizing Mathematica we display the wave functions along with their associated probabilities for the entire region. We investigate the sensitivity of the probability distributions as a function of the potential range and display a gallery of our analysis. We extend our analysis for bound state particles confined within constant attractive potentials.展开更多
Xinjiang is a good place, with pastureland to the north and south of the Tianshan MountainThe Gobi Desert has been changed into fertile fields, irrigated by melting snows.
文摘Food safety problems caused by excessive nitrite addition have been frequently reported and the detection of nitrite in food is particularly important. The standing time during the pretreatment of primary sample has a great influence on the concentration of nitrite tested by spectrophotometric method. In this context, three kinds of food samples are prepared, including canned mustard, canned fish and home-made pickled water. A series of standing times are placed during the sample pretreatments and the corresponding nitrite contents in these samples are detected by spectrophotometric method based on N-ethylenediamine dihydrochloride. This study aims to find out a reasonable standing time during the pretreatment of food sample, providing influence factor for precise detection of nitrite.
文摘Twenty-seven specimens were tested to investigate the uniaxial compression behaviour of an innovative standing support for underground space applications.The innovative standing support consisted of an external fibre reinforced polymer(FRP)jacket and the infill column made of cementitious grout,tailings and coal wash rejects.Effects of the FRP layers number and water to the cementitious grout(w/g)ratio were evaluated.Test results indicated that lower w/g ratios produced stronger infill columns.With FRP confinement,the standing support demonstrated strain-hardening loading characteristics with a significant improvement in both strength and ductility.The highest strength and strain of the specimens achieved was 58.4 MPa and 11.8%respectively.Compared with the unconfined specimens,the confinement with four FRP layers increased the specimen strength and associated strain up to 3.6 and 27.0 times respectively.A correlation between the compressive strength of the infill material and the ultrasonic pulse velocity was also investigated.Furthermore,a simple design-oriented model was proposed to predict the peak strength and the corresponding strain of the innovative standing support.
基金This work was supported by National Natural Science Foundation of China(Nos.12005061,12065019)the Natural Science Foundation of Jiangxi Province(No.20202 BABL214036).
文摘The streamer that is driven by the specific pulse DC discharge parameters can stably form a three-dimensional helical plasma channel in a long dielectric tube in the low-temperature plasma experiment,in cases when there were neither external background magnetic field or other factors that destroyed the poloidal symmetry of the tube.The formation mechanism and chirality of helical streamers are discussed according to the surface electromagnetic standing wave theory.The shape of the helical streamers and the characteristics of helical branches are quantitatively analyzed to further expand the application of plasma and streamer theory in the helix problem and chiral catalytic synthesis.
文摘正At the invitation of the Ministry of Foreign Affairs of Israel, Grand National Assembly of Turkey (TBMM) and Delhi Study Group of India, a delegation of the Chinese Association for International Understanding (CAFIU) headed
文摘正The Understanding and Cooperation Dialogue, Sponsored by the Chinese Association for International Understanding (CAFIU) and the China Foundation for Peace and Development (CFPD), and Co-organized by the Chinese People' s Association for Peace and
基金This subject was partly supported by the National Excellent Youth Foundation of China (Grant No. 49825161)
文摘Based on the theoretical high-order model with a dissipative term for non-linear and dispersive wave in water of varying depth, a 3-D mathematical model of non-linear wave propagation is presented. The model, which can be used to calculate thewave particle velocity and wave pressure, is suitable to the complicated topography whose relative depth (d/λ0, ratio of the characteristic water depth to the characteristic wavelength in deep-water) is equal to or smaller than one. The governing equations are discretized with the improved 2-D Crank-Nicolson method in which the first-order derivatives are corrected by Taylor series expansion, .and the general boundary conditions with an arbitrary reflection coefficient and phase shift are adopted in the model. The surface elevation, horizontal and vertical velocity components and wave pressure of standing waves are numerically calculated. The results show that the numerical model can effectively simulate the complicated standing waves, and the general boundary conditions possess good adaptability.
基金supported by the National Key R&D Program of China(No.2017YFE0301201)National Natural Science Foundation of China(No.11975038)the funding support from the State Key Laboratory of Nuclear Physics and Technology,Peking University(No.NPT2021ZZ03)。
文摘Helicon wave plasma sources have the well-known advantages of high efficiency and high plasma density, with broad applications in many areas. The crucial mechanism lies with mode transitions, which has been an outstanding issue for years. We have built a fluid simulation model and further developed the Peking University Helicon Discharge code. The mode transitions, also known as density jumps, of a single-loop antenna discharge are reproduced in simulations for the first time. It is found that large-amplitude standing helicon waves(SHWs) are responsible for the mode transitions, similar to those of a resonant cavity for laser generation.This paper intends to give a complete and quantitative SHW resonance theory to explain the relationship of the mode transitions and the SHWs. The SHW resonance theory reasonably explains several key questions in helicon plasmas, such as mode transition and efficient power absorption, and helps to improve future plasma generation methods.
基金Zhejiang Natural Scientific Foundation of China under contract! No. 394014.
文摘The standing stock of phytoplankton (phy. ) and primary productivity (pp) in the Xiangshan Bay were observed in 1992. The results showed higher biological parameters in the bay. The average chlorophyll a (chl a) concentration was (3. 50 5. 93 ) mg/m3 and the primary productivity (444. 5 871. 0) mg/(m2 d). The distribution of chl a and productivity showed distinct spatial and temporal patterns in the bay. The continent influence was Obvious at the top of the bay, lower seawater exchange and higher stability led to higher standing stock of phytoplankton and productivity. At the bay mouth, seawater exchanged continuously with adjacent waters by rapid currents, resulting in fast and unstable exchange and lower standing stock of phytoplankton and primary productivity. The seasonal characters of those parameters were pronounced, in the sequence of spring, summer, autumn and winter. The results of size--fractionated showed that the average contribution of the nano--and picoplankton (< 20pm) to total chl a and productivity were 75 % and 87%, respectively, indicating their importance in phytoplankton community biomass and productivity of the Xiangshan Bay.
文摘Background: Although the standing long jump (SLJ) is a popular physical fitness assessment, it lacks an updated criterion-reference standard. This study generated the first normative SLJ test data for Chinese aged 8 - 18. Methods: From September 2005 to December 2011, comprehensive physical fitness assessments were conducted on 12,712 school students. The SLJ performances were significantly different between boys and girls (all age groups, p < 0.01). Results: The boys performed better than the girls in each age group. The mean difference increased as the age increased, depicting a prominent variance in muscular strength between boys and girls at age 12, and the variances became larger at age 18. Girls in the 70th percenttile performed similarly to boys performing in the 10th percentile. The onset of muscle strength for boys found in this study corresponded to the onset age of testosterone maturation of Chinese boys investigated in previous studies. Linear regression found age and BMI predicting SLJ significantly for boys and girls, explaining better SLJ results in older boy and the effect of their heavy body size. Conclusions: This study indicated a muscular strength difference between genders during growth and added supporting evidence to the hormonal influence of muscle growth during puberty.
基金supported by the Australia government through the Australian Research Council’s Industrial Transformation Research Hub for nanoscience based construction material manufacturing(IH150100006)the Australia Coal Industry’s Research Program(C28068)。
文摘This paper presents the development of an innovative standing support for underground mines.The main feature of this standing support is its exterior container,a combination of polyvinyl chloride(PVC)with large rupture strain and fibre-reinforced polymer(FRP)with high strength-to-weight ratio.To demonstrate the advantages of this cementitious grout filled PVC-FRP tubular(PFT)standing support,a series of compression tests were conducted.Test variables included the strength of cementitious grout infill material and the thickness of FRP jacket.Compression tests were also conducted on cementitious grout-filled PVC tubular(PT)support and cementitious grout-filled FRP tubular(FT)support.These tests showed that PFT support presents a typical strain-hardening behaviour together with an outstanding axial deformation ability(>20%of the overall height of the support).In addition,the maximum compressive strength of PFT support is much higher than that of the corresponding PT support and FT support.Furthermore,using thicker FRP jacket or high strength cementitious grout material can enhance the load carrying capacity of PFT support.These comparative results indicated that the high performance of PFT support is mainly attributed to the combination of confining constituents(i.e.PVC and FRP)and infill material.
基金This work was supported by the National Natural Science Foundation of China(No.11922504).
文摘A 2856-MHz,π-mode,seven-cell standingwave deflecting cavity was designed and fabricated for bunch length measurement in Tsinghua Thomson scattering X-ray source(TTX)facility.This cavity was installed in the TTX and provided a deflecting voltage of 4.2 MV with an input power of 2.5 MW.Bunch length diagnoses of electron beams with energies up to 39 MeV have been performed.In this article,the RF design of the cavity using HFSS,fabrication,and RF test processes are reviewed.High-power operation with accelerated beams and calibration of the deflecting voltage are also presented.
基金Supported by the National Key R&D Program of China(Grant No.2017YFA0206304)the National Natural Science Foundation of China(Grant Nos.11874203,61822403,U1732159,11774160,and 61427812)the Fundamental Research Funds for the Central Universities(Grant No.021014380080)。
文摘We report a universal transfer methodology for producing artificial heterostructures of large-area freestanding single-crystalline WTe_(2) membranes on diverse target substrates.The transferred WTe_(2) membranes exhibit a nondestructive structure with a carrier mobility comparable to that of as-grown films(∼179–1055 cm^(2)·V^(−1)·s^(−1)).Furthermore,the transferred membranes show distinct Shubnikov–de Haas quantum oscillations as well as weak localization/weak anti-localization.These results provide a new approach to the development of atom manufacturing and devices based on atomic-level,large-area topological quantum films.
基金supported by the National Natural Science Foundation of China (grant numbers 41774168 and 41421003)
文摘In Earth's high-latitude ionosphere, the poleward motion of east–west elongated auroral arcs has been attributed to standing hydromagnetic waves, especially when the auroral arcs appear quasi-periodically with a recurrence time of a few minutes. The validation of this scenario requires spacecraft observations of ultra-low-frequency hydromagnetic waves in the magnetosphere and simultaneous observations of poleward-moving auroral arcs near the spacecraft footprints. Here we present the first observational evidence from the multi-spacecraft THEMIS (Time History of Events and Macroscale Interactions during Substorms) mission and the conjugated all-sky imager to support the scenario that standing hydromagnetic waves can generate the quasi-periodic appearance of poleward-moving auroral arcs. In this specific event, the observed waves were toroidal branches of the standing hydromagnetic waves, which were excited by a pulse in the solar wind dynamic pressure. Multi-spacecraft measurements from THEMIS also suggest higher wave frequencies at lower L shells (consistent with the distribution of magnetic field line eigenfrequencies), which indicates that the phase difference across latitudes would increase with time. As time proceeds, the enlarged phase difference corresponds to a lower propagation speed of the auroral arcs, which agrees very well with the ground-based optical data.
文摘Dear Editor,Premacular hemorrhage is a common cause of sudden profound visual loss in otherwise healthy eye.One of the commonest causes of premacular hemorrhage in clinical practice is Valsalva retinopathy,which was first described by Thomas Duane in 1972[1].In the setting of Valsalva retinopathy these hemorrhages are a result of ruptured
文摘In this article, we consider quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations of the form <img src="Edit_4d91f4a8-f399-4895-9edd-b0d77ec07654.bmp" alt="" /> Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear <span style="white-space:nowrap;">Schrödinger</span> equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.
文摘We consider a time independent one dimensional finite range and repulsive constant potential barrier between two impenetrable walls. For a nonrelativistic massive particle projected towards the potential with energies less than the barrier and irrespective of the spatial positioning of the potential allowing for quantum tunneling, analytically we solve the corresponding Schrodinger equation. For a set of suitable parameters utilizing Mathematica we display the wave functions along with their associated probabilities for the entire region. We investigate the sensitivity of the probability distributions as a function of the potential range and display a gallery of our analysis. We extend our analysis for bound state particles confined within constant attractive potentials.
文摘Xinjiang is a good place, with pastureland to the north and south of the Tianshan MountainThe Gobi Desert has been changed into fertile fields, irrigated by melting snows.
