This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we ex...This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 10<sup>30</sup> bits/m<sup>3</sup>), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.展开更多
LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F(p, q, s) on Ω. Characterizing functions in the F(p, q, s) space is a work of consi...LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F(p, q, s) on Ω. Characterizing functions in the F(p, q, s) space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F(p, q, s) space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F(p, q, s) space and Bloch type space on Ω too.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
This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical mode...This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.展开更多
In order to determine the influence of shearer's cutting and neighboring shields' advance on the support resistance variation, leg pressure data of all 235 shields in the panel LW61 of Cumberland coal mine wer...In order to determine the influence of shearer's cutting and neighboring shields' advance on the support resistance variation, leg pressure data of all 235 shields in the panel LW61 of Cumberland coal mine were analyzed. The results show that the relationship between the leg pressure increment and the distance from shield to front drum of shearer is a quadratic function and that the higher leg pressure increment before shield advance tends to be related to adverse roof conditions. In addition, the three proposed leg pressure increment-related parameters and the three traditional parameters(time-weighted average pressure, setting pressure, and final pressure) of approximately 32000 shield supporting cycles were calculated by a self-developed software package to analyze the correlation between them. The results show that there is a powerful connection between them, and that the three proposed leg pressure increment-related parameters could be used as the indexes to evaluate the interaction between shields and the roof, and to identify the periodic weighting.展开更多
In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant ...In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.展开更多
We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>...We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>×<i>n</i> Fiedler companion matrix <i>C</i>, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix <i>L<sub>r</sub></i>, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of <i>L<sub>r</sub></i>, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.展开更多
Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we ...Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition (OSC), and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds.展开更多
Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive an...Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua's circuit.展开更多
We present a new six-dimensional potential energy surface for He-H2S including the intramolecular Q1,Q2,and Q3 normal modes for theν1 symmetric stretching,ν2 bending andν3 asymmetric stretching of H2S.The potential...We present a new six-dimensional potential energy surface for He-H2S including the intramolecular Q1,Q2,and Q3 normal modes for theν1 symmetric stretching,ν2 bending andν3 asymmetric stretching of H2S.The potential was calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triples[CCSD(T)]-F12a level with augmented correlation-consistent polarized-valence triple-zeta(aug-cc-p VTZ)basis set plus the midpoint bond function(3s3p2d1f1g).Three vibrationally averaged potentials with H2S at the vibrational ground stateν1 as well as the excited statesν2 andν3 were generated from the integration of the six-dimensional potential over the Q1,Q2 and Q3 coordinates.Each potential has a planar T-shaped global minimum,a planar local minimum,two inplane saddle points as well as an out-plane saddle point.The global minimum is located at R=3.46A,θ=109.9° andφ=0.0° with a well depth of 35.301 cm^-1.The radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels.The calculated band origins are blue-shifted(0.025 cm^-1 and 0.031 cm^-1)and(0.041 cm^-1 and 0.060 cm^-1)for He-(paraH2S)and He-(ortho-H2S)in theν2 andν3 region of the H2S molecule,respectively.展开更多
The spin transport properties are theoretically investigated when a quantum dot(QD)is side-coupled to Majorana bound states(MBSs)driven by a symmetric dipolar spin battery.It is found that MBSs have a great effect on ...The spin transport properties are theoretically investigated when a quantum dot(QD)is side-coupled to Majorana bound states(MBSs)driven by a symmetric dipolar spin battery.It is found that MBSs have a great effect on spin transport properties.The peak-to-valley ratio of the spin current decreases as the coupling strength between the MBS and the QD increases.Moreover,a non-zero charge current with two resonance peaks appears in the system.In the extreme case where the dot-MBS coupling strength is strong enough,the spin current and the charge current are both constants in the non-resonance peak range.When considering the effect of the Zeeman energy,it is interesting that the resonance peak at the higher energy appears one shoulder.And the shoulder turns into a peak when the Zeeman energy is big enough.In addition,the coupling strength between the two MBSs weakens their effects on the currents of the system.These results are helpful for understanding the MBSs signature in the transport spectra.展开更多
The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is sti...The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is still debatable. When it is at rest, the space-like separation between the constituent particles is the primary variable. When the bound state moves, this space-like separation picks up the time-like separation. The time-separation is not a measurable variable in the present form of quantum mechanics. The only way to deal with this un-observable variable is to treat it statistically. This leads to rise of the statistical variables such entropy and temperature. Paul A. M. Dirac made efforts to construct bound-state wave functions in Einstein’s Lorentz-covariant world. In 1927, he noted that the c-number time-energy relation should be incorporated in the relativistic world. In 1945, he constructed four-dimensional oscillator wave functions with one time coordinate in addition to the three-dimensional space. In 1949, Dirac introduced the light-cone coordinate system for Lorentz transformations. It is then possible to integrate these contributions made by Dirac to construct the Lorentz-covariant harmonic oscillator wave functions. This oscillator system can explain the proton as a bound state of the quarks when it is at rest, and explain the Feynman’s parton picture when it moves with a speed close to that of light. While the un-measurable time-like separation becomes equal to the space-like separation at this speed, the statistical variables become prominent. The entropy and the temperature of this covariant harmonic oscillator are calculated. It is shown that they rise rapidly as the proton speed approaches that of light.展开更多
Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson's quadrature rule involving n-time(1 ≤ n ≤ 4) differentiable mappings and ...Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson's quadrature rule involving n-time(1 ≤ n ≤ 4) differentiable mappings and then to the estimations of error bounds for the adaptive Simpson's quadrature rule.展开更多
The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with sma...The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.展开更多
In this paper, the glycoconjugated volatile compounds of four Croatian Satureja species (Satureja montana L., S. cuneifolia Ten., S. subspicata Vis. and endemic S. visianii Silic) were investigated. Content and compos...In this paper, the glycoconjugated volatile compounds of four Croatian Satureja species (Satureja montana L., S. cuneifolia Ten., S. subspicata Vis. and endemic S. visianii Silic) were investigated. Content and composition of these compounds were examined depending on the stage of plant development. GC and GC–MS analysis of volatile aglycones revealed twenty-one compounds. Thymoquinone, geraniol and carvacrol were detected in all vegetative phases of the investigated plants. Other quantitatively important aglycones were eugenol and thymol of S. montana, phenyl ethyl alcohol, benzene acetaldehyde, borneol, α-terpineol, thymol and eugenol of S. cuneifolia, phenyl ethyl alcohol, benzene acet-aldehyde, terpinen-4-ol, α-terpineol and β-ionone of S. subspicata and camphor, thymol and 8a-acetoxylemolol of S. visianii. Moderate similarity in the chemical composition of essential oils and volatile aglycones of investigated plant species indicate that many biologically active compounds are glycosylated and accumulate as non-volatile glycosides.展开更多
文摘This research aims to integrate Bekenstein’s bound and Landauer’s principle, providing a unified framework to understand the limits of information and energy in physical systems. By combining these principles, we explore the implications for black hole thermodynamics, astrophysics, astronomy, information theory, and the search for new laws of nature. The result includes an estimation of the number of bits stored in a black hole (less than 1.4 × 10<sup>30</sup> bits/m<sup>3</sup>), enhancing our understanding of information storage in extreme gravitational environments. This integration offers valuable insights into the fundamental nature of information and energy, impacting scientific advancements in multiple disciplines.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘LetΩ be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F(p, q, s) on Ω. Characterizing functions in the F(p, q, s) space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F(p, q, s) space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F(p, q, s) space and Bloch type space on Ω too.
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.
基金supported by the National Natural Science Foundation of China (Grant Numbers41807197, 2017YFC0405900, and 51469002)the Natural Science Foundation of Guangxi (Grant Numbers 2017GXNSFBA198087, 2018GXNSFAA138042, and GuiKeAB17195073)Hebei Highlevel Talent Funding Project (B2018003016)。
文摘This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.
基金provided by the National High Technology Research and Development Program of China(No.2012AA062100)the Program for New Century Excellent Talents in University of China(No.NCET-10-0770)
文摘In order to determine the influence of shearer's cutting and neighboring shields' advance on the support resistance variation, leg pressure data of all 235 shields in the panel LW61 of Cumberland coal mine were analyzed. The results show that the relationship between the leg pressure increment and the distance from shield to front drum of shearer is a quadratic function and that the higher leg pressure increment before shield advance tends to be related to adverse roof conditions. In addition, the three proposed leg pressure increment-related parameters and the three traditional parameters(time-weighted average pressure, setting pressure, and final pressure) of approximately 32000 shield supporting cycles were calculated by a self-developed software package to analyze the correlation between them. The results show that there is a powerful connection between them, and that the three proposed leg pressure increment-related parameters could be used as the indexes to evaluate the interaction between shields and the roof, and to identify the periodic weighting.
文摘In this paper, we combine Graeffe matrices with the classical numerical method of Dandelin-Graeffe to estimate bounds for the moduli of the zeros of polynomials. Furthermore, we give some examples showing significant gain for the convergence towards the polynomials dominant zeros moduli.
文摘We use submultiplicative companion matrix norms to provide new bounds for roots for a given polynomial <i>P</i>(<i>X</i>) over the field C[<i>X</i>]. From a <i>n</i>×<i>n</i> Fiedler companion matrix <i>C</i>, sparse companion matrices and triangular Hessenberg matrices are introduced. Then, we identify a special triangular Hessenberg matrix <i>L<sub>r</sub></i>, supposed to provide a good estimation of the roots. By application of Gershgorin’s theorems to this special matrix in case of submultiplicative matrix norms, some estimations of bounds for roots are made. The obtained bounds have been compared to known ones from the literature precisely Cauchy’s bounds, Montel’s bounds and Carmichel-Mason’s bounds. According to the starting formel of <i>L<sub>r</sub></i>, we see that the more we have coefficients closed to zero with a norm less than 1, the more the Sparse method is useful.
基金part by the Foundations of the Jiangxi Natural Science Committee(No:0611005),China.
文摘Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H S-almost all points of the sets. In this paper, following Falconer[1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition (OSC), and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds.
基金Project supported by the Major State Basic Research Development Program of China(Grant No.2012CB215202)the National Natural Science Foundation of China(Grant Nos.61104080 and 61134001)the Fundamental Research Funds for the Central Universities(Grant No.CDJZR13 175501)
文摘Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua's circuit.
基金supported by the National Natural Science Foundation of China(No.21973065)Sichuan Science and Technology Program(No.2018JY0172)。
文摘We present a new six-dimensional potential energy surface for He-H2S including the intramolecular Q1,Q2,and Q3 normal modes for theν1 symmetric stretching,ν2 bending andν3 asymmetric stretching of H2S.The potential was calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triples[CCSD(T)]-F12a level with augmented correlation-consistent polarized-valence triple-zeta(aug-cc-p VTZ)basis set plus the midpoint bond function(3s3p2d1f1g).Three vibrationally averaged potentials with H2S at the vibrational ground stateν1 as well as the excited statesν2 andν3 were generated from the integration of the six-dimensional potential over the Q1,Q2 and Q3 coordinates.Each potential has a planar T-shaped global minimum,a planar local minimum,two inplane saddle points as well as an out-plane saddle point.The global minimum is located at R=3.46A,θ=109.9° andφ=0.0° with a well depth of 35.301 cm^-1.The radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels.The calculated band origins are blue-shifted(0.025 cm^-1 and 0.031 cm^-1)and(0.041 cm^-1 and 0.060 cm^-1)for He-(paraH2S)and He-(ortho-H2S)in theν2 andν3 region of the H2S molecule,respectively.
基金supported by Natural Science Fund for Colleges and Universities in Hebei Province,China(Grant No.ZD2017031)the Doctoral Initial Funding of Hebei University of Science and Technology(Grant No.1181291)。
文摘The spin transport properties are theoretically investigated when a quantum dot(QD)is side-coupled to Majorana bound states(MBSs)driven by a symmetric dipolar spin battery.It is found that MBSs have a great effect on spin transport properties.The peak-to-valley ratio of the spin current decreases as the coupling strength between the MBS and the QD increases.Moreover,a non-zero charge current with two resonance peaks appears in the system.In the extreme case where the dot-MBS coupling strength is strong enough,the spin current and the charge current are both constants in the non-resonance peak range.When considering the effect of the Zeeman energy,it is interesting that the resonance peak at the higher energy appears one shoulder.And the shoulder turns into a peak when the Zeeman energy is big enough.In addition,the coupling strength between the two MBSs weakens their effects on the currents of the system.These results are helpful for understanding the MBSs signature in the transport spectra.
文摘The quantum mechanics of bound states with discrete energy levels is well understood. The quantum mechanics of scattering processes is also well understood. However, the quantum mechanics of moving bound states is still debatable. When it is at rest, the space-like separation between the constituent particles is the primary variable. When the bound state moves, this space-like separation picks up the time-like separation. The time-separation is not a measurable variable in the present form of quantum mechanics. The only way to deal with this un-observable variable is to treat it statistically. This leads to rise of the statistical variables such entropy and temperature. Paul A. M. Dirac made efforts to construct bound-state wave functions in Einstein’s Lorentz-covariant world. In 1927, he noted that the c-number time-energy relation should be incorporated in the relativistic world. In 1945, he constructed four-dimensional oscillator wave functions with one time coordinate in addition to the three-dimensional space. In 1949, Dirac introduced the light-cone coordinate system for Lorentz transformations. It is then possible to integrate these contributions made by Dirac to construct the Lorentz-covariant harmonic oscillator wave functions. This oscillator system can explain the proton as a bound state of the quarks when it is at rest, and explain the Feynman’s parton picture when it moves with a speed close to that of light. While the un-measurable time-like separation becomes equal to the space-like separation at this speed, the statistical variables become prominent. The entropy and the temperature of this covariant harmonic oscillator are calculated. It is shown that they rise rapidly as the proton speed approaches that of light.
基金Supported by the Natural Science Foundation of Zhejiang Province(Y6090361)
文摘Similar to having done for the mid-point and trapezoid quadrature rules,we obtain alternative estimations of error bounds for the Simpson's quadrature rule involving n-time(1 ≤ n ≤ 4) differentiable mappings and then to the estimations of error bounds for the adaptive Simpson's quadrature rule.
基金Project supported by National Natural Science Foundation of China.
文摘The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.
文摘In this paper, the glycoconjugated volatile compounds of four Croatian Satureja species (Satureja montana L., S. cuneifolia Ten., S. subspicata Vis. and endemic S. visianii Silic) were investigated. Content and composition of these compounds were examined depending on the stage of plant development. GC and GC–MS analysis of volatile aglycones revealed twenty-one compounds. Thymoquinone, geraniol and carvacrol were detected in all vegetative phases of the investigated plants. Other quantitatively important aglycones were eugenol and thymol of S. montana, phenyl ethyl alcohol, benzene acetaldehyde, borneol, α-terpineol, thymol and eugenol of S. cuneifolia, phenyl ethyl alcohol, benzene acet-aldehyde, terpinen-4-ol, α-terpineol and β-ionone of S. subspicata and camphor, thymol and 8a-acetoxylemolol of S. visianii. Moderate similarity in the chemical composition of essential oils and volatile aglycones of investigated plant species indicate that many biologically active compounds are glycosylated and accumulate as non-volatile glycosides.
基金Supported by the National Natural Science Foundation of China (31600299)the Youth Science and Technology Nova Program of Shaanxi Province,China (2022KJXX-01)the Scientific Research Program Funded by Yunnan Provincial Education Department,China (2022J0949)。