In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harm...With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.展开更多
The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses.Based on numerically solving the time-dependent Schrodinger equation,the generation ...The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses.Based on numerically solving the time-dependent Schrodinger equation,the generation process of highorder harmonic from the He atom under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields is studied.In this paper,we propose to achieve quasi-chirp-free isolated attosecond pulses by superimposing a higher second-harmonic field on the orthogonal direction of the fundamental frequency field.It is found that the high-energy part of its harmonic emission exhibits small chirp characteristics,which can be used to synthesize isolated attosecond pulses.Through the analysis of the wave packets evolution and the classical motion trajectories of the electron,it is demonstrated that the quasi-chirp-free harmonic can be attributed to the simultaneous return of electrons ionized at different times to the parent particle.The influence of the relative phase of the two pulses on the harmonics is further analyzed,and it is observed that this phenomenon is sensitive to the relative phase,but it can still generate isolated attosecond pulses within a certain phase.展开更多
The intensive care unit(ICU)is a complex setting by nature,and some have described it as bizarre due to its numerous sirens that sound when anything is dangerous,constant activity,equipment,bright lights,and high fata...The intensive care unit(ICU)is a complex setting by nature,and some have described it as bizarre due to its numerous sirens that sound when anything is dangerous,constant activity,equipment,bright lights,and high fatality rate.The demands placed on nurses to care for critically ill patients in this environment frequently prevent nurses and other health‑care professionals from acknowledging the feelings of patient’s relatives or family caregivers,resulting in a hostile environment from the patient’s relative’s perspective.When a patient’s family enters the ICU,they feel that hospital administrators do little to nothing to alleviate their discomfort and fear.Despite research demonstrating the importance of providing a homely environment for patients’families,In Nigeria ICU is still far behind how a conventional ICU environment should be structured to accommodate patient’s relations in the unit.The goal of this study was to look at the patient’s relative’s perspective on providing care for a critically ill patient in an ICU,with a focus on the unit’s complexity and overall experience.Based on the findings of this study,we recommend that hospital administrators ensure that the environment of the upcoming ICU is designed to meet the needs of patient’s relatives by addressing identified environmental concerns,like caring neglect,by providing a friendly and stress‑free environment.展开更多
The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the fi...The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately （n - 1） π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.展开更多
The difference-ratio relations are introduced to separate tidal constituents that are aliaseddue to the sampling interval and sampling span of the TOPEX/POSEIDON altimeter. It is found that some tidal constituents suc...The difference-ratio relations are introduced to separate tidal constituents that are aliaseddue to the sampling interval and sampling span of the TOPEX/POSEIDON altimeter. It is found that some tidal constituents such as K_1 and SSA, though aliased at along track points, are not aliased at crossover points beeause the data at crossover points are double those at along track points. So the harmonic analysis method can be employed directly for the analysis of time series at crossover points. Then the difference-ratio relations from crossover points are introduced to analyze the time series at along track points. The TOPEX/POSEIDON data in the Northwest Pacific are analyzed with this method. The results from this method agree well with tidal constants from tidal gauges.展开更多
The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize th...The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.展开更多
Due to global climate warming and natural and man-made land subsidence etc., relative sea level rise in the coastal plains of China will exceed 2-3 times over the golbal mean value during the first half part of the 21...Due to global climate warming and natural and man-made land subsidence etc., relative sea level rise in the coastal plains of China will exceed 2-3 times over the golbal mean value during the first half part of the 21st century. It will result in a series of adverse impacts on evolution of natural environment and socioeconomic development of the coastal area. This paper analyses environmental and resource effects induced by relative sea level rise in China's coastal areas on the basis of rough estimate of future relative sea level rise. These effects include inundating tidal flat and wetlands and increase in inundated risk of coastal habitable land,exacerbating storm surge. coastal erosion, flooding and salt water intrusion hazards.as well as endangering land. water. tourism and living resources and their utilization.展开更多
Zhao （2003a） first established a congruence for any odd prime p〉3, S（1,1,1 ;p）=-2Bp-3 （mod p）, which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S（α,β, γ,ρ） （modp） is...Zhao （2003a） first established a congruence for any odd prime p〉3, S（1,1,1 ;p）=-2Bp-3 （mod p）, which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S（α,β, γ,ρ） （modp） is considered for all positive integers α,β, γ. We refer to w=α＋β＋ γ as the weight of the sum, and show that if w is even, S（α,β, γ,ρ）=0 （mod p） for p≥w＋3; if w is odd, S（α,β, γ,ρ）=-rBp-w （mod p） for p≥w, here r is an explicit rational number independent ofp. A congruence of Catalan number is obtained as a special case.展开更多
The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Ni...The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.展开更多
Silica glasses doped with Bi2S3 microcystallite was prepared by the sol-gel process. Photoinduced second harmonic generation (SHG) was observed in the glass when it was irradiated with intense 1.06 mum and frequency d...Silica glasses doped with Bi2S3 microcystallite was prepared by the sol-gel process. Photoinduced second harmonic generation (SHG) was observed in the glass when it was irradiated with intense 1.06 mum and frequency doubled laser beams from a mode-locked Nd: YAG laser. It was found that the signal intensity increased with the irradiating time and approached a saturation gradually. The effect may be explained reasonably by the DC field model.展开更多
In terms of single-atom induced dipole moment by Lewenstein model, we present the macroscopic high-order harmonic generation from mixed He and Ne gases with different mixture ratios by solving three-dimensional Maxwel...In terms of single-atom induced dipole moment by Lewenstein model, we present the macroscopic high-order harmonic generation from mixed He and Ne gases with different mixture ratios by solving three-dimensional Maxwell＇s equation of harmonic field. And then we show the validity of mixture formulation by Wagner et al. [Phys. Rev. A 76 （2007） 061403（R）] in macroscopic response level. Finally, using/east squares fitting we retrieve the electron return time of short trajectory by formulation in Kanai et al. [Phys. Rev. Lett. 98 （2007） 153904] when the gas jet is put after the laser focus.展开更多
The most commonly used method for assessing the hydraulic erodibility of rock is Annandale's method.This method is based on a correlation between the erosive force of flowing water and the capacity of rock resista...The most commonly used method for assessing the hydraulic erodibility of rock is Annandale's method.This method is based on a correlation between the erosive force of flowing water and the capacity of rock resistance. This capacity is evaluated using Kirsten's index, which was initially developed to evaluate the excavatability of earth materials. For rocky material, this index is determined according to certain geomechanical factors related to intact rock and rock mass, such as compressive strength of intact rock, rock block size, discontinuity shear strength and relative block structure. To quantify the relative block structure, Kirsten(1982) developed a mathematical expression that accounts for the shape and orientation of the blocks relative to the direction of flow. Kirsten's initial concept for assessing the relative block structure considers that the geological formation is mainly fractured by two joint sets forming an orthogonally fractured system. An adjusted concept is proposed to determine the relative block structure when the fractured system is non-orthogonal where the angle between the planes of the two joint sets is greater or less than 90°. An analysis of the proposed relative block structure rating shows that considering a non-orthogonally fractured system has a significant effect on Kirsten's index and, as a consequence, on the assessment of the hydraulic erodibility of rock.展开更多
In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Final...In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.展开更多
In order to extend the rail life and improve the firing accuracy,the electromagnetic launcher's rail can be modeled as a beam on elastic foundation with simply supported beam with moving load.Euler beam theory is ...In order to extend the rail life and improve the firing accuracy,the electromagnetic launcher's rail can be modeled as a beam on elastic foundation with simply supported beam with moving load.Euler beam theory is applied to build the mechanical model and the analytical solution of the equation subjected to harmonic magnetic pressure is derived in details,which has successfully avoided the errors caused by using the uniform pressure to approximately replace the variable force.Numerical analysis of the dynamic response on rail by using the MATLAB software shows that the peak values of maximal deflection and vibration velocity increase gradually as the exciting frequency increases.Taking the same speed of load into account,the dynamic response of rail is obviously smaller than that under constant force.Therefore the reliable theory basis is provided for the design and control of rail to promote the practical application of electromagnetic launcher.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11801006 and 12071489).
文摘In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
文摘With the help of the classical Abel’s lemma on summation by parts and algorithm of q-hypergeometric summations, we deal with the summation, which can be written as multiplication of a q-hypergeometric term and q-harmonic numbers. This enables us to construct and prove identities on q-harmonic numbers. Several examples are also given.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
基金Project supported by the National Key Research and Development Program of China(Grant No.2019YFA0307700)the National Natural Science Foundation of China(Grant Nos.12074145,11627807,and 11975012)+2 种基金the Research Foundation for Basic Research of Jilin Province,China(Grant No.20220101003JC)the Fundamental Research Funds for the Central Universities of China(Grant No.30916011207)the Outstanding Youth Project of Taizhou University(Grant No.2019JQ002)。
文摘The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses.Based on numerically solving the time-dependent Schrodinger equation,the generation process of highorder harmonic from the He atom under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields is studied.In this paper,we propose to achieve quasi-chirp-free isolated attosecond pulses by superimposing a higher second-harmonic field on the orthogonal direction of the fundamental frequency field.It is found that the high-energy part of its harmonic emission exhibits small chirp characteristics,which can be used to synthesize isolated attosecond pulses.Through the analysis of the wave packets evolution and the classical motion trajectories of the electron,it is demonstrated that the quasi-chirp-free harmonic can be attributed to the simultaneous return of electrons ionized at different times to the parent particle.The influence of the relative phase of the two pulses on the harmonics is further analyzed,and it is observed that this phenomenon is sensitive to the relative phase,but it can still generate isolated attosecond pulses within a certain phase.
文摘The intensive care unit(ICU)is a complex setting by nature,and some have described it as bizarre due to its numerous sirens that sound when anything is dangerous,constant activity,equipment,bright lights,and high fatality rate.The demands placed on nurses to care for critically ill patients in this environment frequently prevent nurses and other health‑care professionals from acknowledging the feelings of patient’s relatives or family caregivers,resulting in a hostile environment from the patient’s relative’s perspective.When a patient’s family enters the ICU,they feel that hospital administrators do little to nothing to alleviate their discomfort and fear.Despite research demonstrating the importance of providing a homely environment for patients’families,In Nigeria ICU is still far behind how a conventional ICU environment should be structured to accommodate patient’s relations in the unit.The goal of this study was to look at the patient’s relative’s perspective on providing care for a critically ill patient in an ICU,with a focus on the unit’s complexity and overall experience.Based on the findings of this study,we recommend that hospital administrators ensure that the environment of the upcoming ICU is designed to meet the needs of patient’s relatives by addressing identified environmental concerns,like caring neglect,by providing a friendly and stress‑free environment.
基金Supported by the National Natural Science Foundation of China under Grant Nos 41274134 and 81527901the '12th Five-Year Plan' Period for Informatization Project in Supercomputing Key Demonstration of Chinese Academy of Sciences under Grant No XXH12503-02-02-2(07)
文摘The phase relation of harmonics in high-intensity focused ultrasound is investigated numerically and experimen- tally. The nonlinear Westervelt equation is solved to model nonlinear focused sound field by using the finite difference time domain method. Experimental waveforms are measured by a robust needle hydrophone. Then the relative phase quantity is introduced and obtained by using the zero-phase filter. The results show that the nth harmonic relative phase quantity is approximately （n - 1） π/3 at geometric center and increases along the axial direction. Moreover, the relative phase quantity decreases with the increase of source amplitude. This phase relation gives an explanation of some nonlinear phenomena such as the discrepancy of positive and negative pressure.
基金his study was supported by the National Natural Science Foundation of China under contract No.40006001.
文摘The difference-ratio relations are introduced to separate tidal constituents that are aliaseddue to the sampling interval and sampling span of the TOPEX/POSEIDON altimeter. It is found that some tidal constituents such as K_1 and SSA, though aliased at along track points, are not aliased at crossover points beeause the data at crossover points are double those at along track points. So the harmonic analysis method can be employed directly for the analysis of time series at crossover points. Then the difference-ratio relations from crossover points are introduced to analyze the time series at along track points. The TOPEX/POSEIDON data in the Northwest Pacific are analyzed with this method. The results from this method agree well with tidal constants from tidal gauges.
基金Project supported by the Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB201008257)Scientific Research Common Program of Beijing Municipal Commission of Education (KM200810011005)+1 种基金PHR (IHLB 201102)research grant of University of Macao MYRG142(Y1-L2)-FST111-KKI
文摘The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.
文摘Due to global climate warming and natural and man-made land subsidence etc., relative sea level rise in the coastal plains of China will exceed 2-3 times over the golbal mean value during the first half part of the 21st century. It will result in a series of adverse impacts on evolution of natural environment and socioeconomic development of the coastal area. This paper analyses environmental and resource effects induced by relative sea level rise in China's coastal areas on the basis of rough estimate of future relative sea level rise. These effects include inundating tidal flat and wetlands and increase in inundated risk of coastal habitable land,exacerbating storm surge. coastal erosion, flooding and salt water intrusion hazards.as well as endangering land. water. tourism and living resources and their utilization.
基金Project (No. 10371107) supported by the National Natural Science Foundation of China
文摘Zhao （2003a） first established a congruence for any odd prime p〉3, S（1,1,1 ;p）=-2Bp-3 （mod p）, which holds when p=3 evidently. In this paper, we consider finite triple harmonic sum S（α,β, γ,ρ） （modp） is considered for all positive integers α,β, γ. We refer to w=α＋β＋ γ as the weight of the sum, and show that if w is even, S（α,β, γ,ρ）=0 （mod p） for p≥w＋3; if w is odd, S（α,β, γ,ρ）=-rBp-w （mod p） for p≥w, here r is an explicit rational number independent ofp. A congruence of Catalan number is obtained as a special case.
文摘The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.
文摘Silica glasses doped with Bi2S3 microcystallite was prepared by the sol-gel process. Photoinduced second harmonic generation (SHG) was observed in the glass when it was irradiated with intense 1.06 mum and frequency doubled laser beams from a mode-locked Nd: YAG laser. It was found that the signal intensity increased with the irradiating time and approached a saturation gradually. The effect may be explained reasonably by the DC field model.
基金Supported by the National Natural Science Foundation of China under Grant No. 10674112the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20096203110001+1 种基金the Foundation of Center of Theoretical Nuclear Physics of National Laboratory of Heavy Ion Accelerator of LanzhouFoundation of Northwest Normal University under Grant No. NWNUKJCXGC-03-62
文摘In terms of single-atom induced dipole moment by Lewenstein model, we present the macroscopic high-order harmonic generation from mixed He and Ne gases with different mixture ratios by solving three-dimensional Maxwell＇s equation of harmonic field. And then we show the validity of mixture formulation by Wagner et al. [Phys. Rev. A 76 （2007） 061403（R）] in macroscopic response level. Finally, using/east squares fitting we retrieve the electron return time of short trajectory by formulation in Kanai et al. [Phys. Rev. Lett. 98 （2007） 153904] when the gas jet is put after the laser focus.
基金the organizations that have funded this project:the Natural Sciences and Engineering Research Council of Canada(Grant No.498020-16)Hydro-Quebec(NC-525700)Mitacs Accelerate Program(Grant Ref.IT10008)
文摘The most commonly used method for assessing the hydraulic erodibility of rock is Annandale's method.This method is based on a correlation between the erosive force of flowing water and the capacity of rock resistance. This capacity is evaluated using Kirsten's index, which was initially developed to evaluate the excavatability of earth materials. For rocky material, this index is determined according to certain geomechanical factors related to intact rock and rock mass, such as compressive strength of intact rock, rock block size, discontinuity shear strength and relative block structure. To quantify the relative block structure, Kirsten(1982) developed a mathematical expression that accounts for the shape and orientation of the blocks relative to the direction of flow. Kirsten's initial concept for assessing the relative block structure considers that the geological formation is mainly fractured by two joint sets forming an orthogonally fractured system. An adjusted concept is proposed to determine the relative block structure when the fractured system is non-orthogonal where the angle between the planes of the two joint sets is greater or less than 90°. An analysis of the proposed relative block structure rating shows that considering a non-orthogonally fractured system has a significant effect on Kirsten's index and, as a consequence, on the assessment of the hydraulic erodibility of rock.
基金The Doctoral Programs Foundation(20113401110009)of Education Ministry of ChinaNatural Science Research Project(2012kj11)of Hefei Normal University+1 种基金Universities Natural Science Foundation(KJ2013A220)of Anhui ProvinceResearch Project of Graduates Innovation Fund(2014yjs02)
文摘In this paper, we first introduce the concept ＂harmonically convex functions＂ in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown.
基金Sponsored by the National Natural Science Foundation of China(Grant No.50875230)
文摘In order to extend the rail life and improve the firing accuracy,the electromagnetic launcher's rail can be modeled as a beam on elastic foundation with simply supported beam with moving load.Euler beam theory is applied to build the mechanical model and the analytical solution of the equation subjected to harmonic magnetic pressure is derived in details,which has successfully avoided the errors caused by using the uniform pressure to approximately replace the variable force.Numerical analysis of the dynamic response on rail by using the MATLAB software shows that the peak values of maximal deflection and vibration velocity increase gradually as the exciting frequency increases.Taking the same speed of load into account,the dynamic response of rail is obviously smaller than that under constant force.Therefore the reliable theory basis is provided for the design and control of rail to promote the practical application of electromagnetic launcher.
