The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner produ...The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.展开更多
This study investigates the width of the secondary eyewall(SE)immediately following its formation in tropical cyclones with surface environmental winds aligned and counter-aligned with environmental vertical wind shea...This study investigates the width of the secondary eyewall(SE)immediately following its formation in tropical cyclones with surface environmental winds aligned and counter-aligned with environmental vertical wind shear(VWS),using idealized numerical experiments.Results reveal that the SE develops greater radial extent when surface winds align with VWS compared to counter-aligned conditions.In alignment configurations,shear-enhanced surface winds on the right flank amplify surface enthalpy fluxes,thereby elevating boundary-layer entropy within the downshear outer-core region.Subsequently,more vigorous outer rainbands develop,inducing marked acceleration of tangential winds in the outer core preceding SE formation.The resultant radial expansion of supergradient winds near the boundary-layer top triggers widespread convective activity immediately beyond the inner core.Progressive axisymmetrization of this convective forcing ultimately generates an expansive SE structure.展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the...This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.展开更多
The surface dielectric barrier discharge （SDBD） plasma actuator has shown great promise as an aerodynamic flow control device. In this paper, the encapsulated electrode width of a SDBD actuator is changed to study t...The surface dielectric barrier discharge （SDBD） plasma actuator has shown great promise as an aerodynamic flow control device. In this paper, the encapsulated electrode width of a SDBD actuator is changed to study the airflow acceleration behavior. The effects of encapsulated electrode width on the actuator performance are experimentally investigated by measuring the dielectric layer surface potential, time-averaged ionic wind velocity and thrust force. Experimental results show that the airflow velocity and thrust force increase with the encapsulated electrode width. The results can be attributed to the distinct plasma distribution at different encapsulated electrode widths.展开更多
Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow...Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow field in slab continuous casting(CC)molds with narrow widths for the production of automobile exposed panels.Reasonable agreement between the calculated results and measured subsurface velocities of liquid steel was obtained under different operating parameters of the CC process.The simulation results reveal that the flow field in the horizontal plane located 50 mm from the meniscus can be used as the characteristic flow field to optimize the flow field of molten steel in the mold.Increases in casting speed can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone.The flow field of liquid steel in a 1040 mm-wide slab CC mold can be improved by an Ar gas flow rate of 7 L·min^−1 and casting speed of 1.7 m·min^−1.Under the present experimental conditions,the double-roll flow pattern is generally stable at a submerged entry nozzle immersion depth of 170 mm.展开更多
Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give ...Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).展开更多
This study was undertaken to examine which factors contributed to the correction of crowding in two patients who underwent nonextraction orthodontic treatment. A study model analysis was conducted to determine the eff...This study was undertaken to examine which factors contributed to the correction of crowding in two patients who underwent nonextraction orthodontic treatment. A study model analysis was conducted to determine the effects of the orthodontic treatment for crowding with high canines on crown angulation and dental arch width in two patients. The results showed that the crown angulation was significantly increased, indicating distal tipping in the maxillary dental arch. This tendency was most commonly observed in the premolars among the lateral teeth. With respect to the dental arch width, the largest change was evident in the first molar and first premolar regions in cases 1 and 2, respectively. On the basis of these results, up-righting of mesially tipped lateral teeth and expansion of narrow dental arches could prove to be the keys to the success of space regaining or correction of high canines and mild crowding.展开更多
To investigate the impact of combustor width on continuous rotating detonation(CRD)fueled by ethylene and air,a series of 3 D simulations are conducted by changing the inner cylinder radius of an annular combustor whi...To investigate the impact of combustor width on continuous rotating detonation(CRD)fueled by ethylene and air,a series of 3 D simulations are conducted by changing the inner cylinder radius of an annular combustor while retaining the same outer cylinder radius.The results show that the CRD wave propagates more steadily and faster as the combustor width increases.The high-temperature zone at the backward-facing step preheats the propellants and contributes to the steady propagation of the CRD wave in 25-and 30-mm wide combustors.The highest and the lowest velocities are obtained in the30-and 15-mm wide combustors at,respectively,1880.27 and 1681.01 m/s.On the other hand,the average thrust decreases as the combustor width increases.The highest thrust is obtained in the 15-mm wide combustor while the lowest is in the 30-mm wide combustor,at 758.06 and 525.93 N,respectively.Nevertheless,the thrust is much more stable in the 25-and 30-mm wide combustors than in the 15-and 20-mm wide combustors.展开更多
We performed systematic laser spectroscopic investigations of La I spectral lines, using optogalvanic detection. Sixteen previously unknown even parity levels, having energies between 40,300 and 44,300 cm<sup>-1...We performed systematic laser spectroscopic investigations of La I spectral lines, using optogalvanic detection. Sixteen previously unknown even parity levels, having energies between 40,300 and 44,300 cm<sup>-1</sup>, are reported. These levels classify altogether 67 lines, not listed in spectral tables. The new levels were found due to the observation of the depopulation of the lower levels of the excited transitions. We found a remarkable variation of the observed widths of single hyperfine structure components dependent on the energy of the upper excited levels. Some levels having energies higher than 43,000 cm<sup>-1</sup> appear to have a very high ionization probability.展开更多
The wavelength-tunable and switchable narrow bandwidth mode-locking operation is demonstrated in an all fiber laser based on semiconductor-saturable absorber mirror （SESAM）. Two narrow-band fiber Bragg gratings cent...The wavelength-tunable and switchable narrow bandwidth mode-locking operation is demonstrated in an all fiber laser based on semiconductor-saturable absorber mirror （SESAM）. Two narrow-band fiber Bragg gratings centered at 1029.9nm and 1032nm respectively with a polarization controller inserted between them are used to realize the wavelength switchable between 1029.9nm and 1032nm. The laser delivers different pulse widths of 7.5ps for 1030nm and 20ps for 1032nm. The maximum output power for both could reach -6.5mW at single pulse operation. The output wavelength couM be tuned to about 0.gnm intervals ranging from 1030.2nm to 1031.1 nm and from 1032.15nm to 1033.7nm with the temperature change of the fiber Bragg grating, respectively.展开更多
Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the...Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.展开更多
基金supported by the National Natural Science Foundation of China(12071444,12201581)the Fundamental Research Program of Shanxi Province of China(202103021223191).
文摘The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.
基金jointly supported by the National Natural Science Foundation of China[grant numbers U2342202,42175005,and 42175016]the Qing Lan Project[grant number R2023Q06]。
文摘This study investigates the width of the secondary eyewall(SE)immediately following its formation in tropical cyclones with surface environmental winds aligned and counter-aligned with environmental vertical wind shear(VWS),using idealized numerical experiments.Results reveal that the SE develops greater radial extent when surface winds align with VWS compared to counter-aligned conditions.In alignment configurations,shear-enhanced surface winds on the right flank amplify surface enthalpy fluxes,thereby elevating boundary-layer entropy within the downshear outer-core region.Subsequently,more vigorous outer rainbands develop,inducing marked acceleration of tangential winds in the outer core preceding SE formation.The resultant radial expansion of supergradient winds near the boundary-layer top triggers widespread convective activity immediately beyond the inner core.Progressive axisymmetrization of this convective forcing ultimately generates an expansive SE structure.
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
基金The project is supported partly by the NationalNatural Science Foundation of China(10071007)and partly by the Foundation for University Key Teachers bythe Ministry of Education of China and partly by the Scientific Research Foundation for Returned Ov
文摘This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.
基金supported by National Natural Science Foundation of China(No.11175037)National Natural Science Foundation for Young Scientists of China(No.11305017)Special Fund for Theoretical Physics(No.11247239)
文摘The surface dielectric barrier discharge （SDBD） plasma actuator has shown great promise as an aerodynamic flow control device. In this paper, the encapsulated electrode width of a SDBD actuator is changed to study the airflow acceleration behavior. The effects of encapsulated electrode width on the actuator performance are experimentally investigated by measuring the dielectric layer surface potential, time-averaged ionic wind velocity and thrust force. Experimental results show that the airflow velocity and thrust force increase with the encapsulated electrode width. The results can be attributed to the distinct plasma distribution at different encapsulated electrode widths.
基金This work was financially supported by the Hunan Valin Lianyuan Iron&Steel Co.,Ltd.,China(No.18H00582).The authors are grateful to Hunan Valin Lianyuan Iron&Steel Co.,Ltd.,China for their assistance with the industrial measurement of velocities near the mold surface.
文摘Computational simulations and high-temperature measurements of velocities near the surface of a mold were carried out by using the rod deflection method to study the effects of various operating parameters on the flow field in slab continuous casting(CC)molds with narrow widths for the production of automobile exposed panels.Reasonable agreement between the calculated results and measured subsurface velocities of liquid steel was obtained under different operating parameters of the CC process.The simulation results reveal that the flow field in the horizontal plane located 50 mm from the meniscus can be used as the characteristic flow field to optimize the flow field of molten steel in the mold.Increases in casting speed can increase the subsurface velocity of molten steel and shift the position of the vortex core downward in the downward circulation zone.The flow field of liquid steel in a 1040 mm-wide slab CC mold can be improved by an Ar gas flow rate of 7 L·min^−1 and casting speed of 1.7 m·min^−1.Under the present experimental conditions,the double-roll flow pattern is generally stable at a submerged entry nozzle immersion depth of 170 mm.
基金Supported by the National Natural Science Foundation of China(11161033)Supported by the Inner Mongolia Normal University Talent Project Foundation(RCPY-2-2012-K-036)+1 种基金Supported by the Inner Mongolia Normal University Graduate Research Innovation Foundation(CXJJS14053)Supported by the Inner Mongolia Autonomous Region Graduate Research Innovation Foundation(S20141013525)
文摘Let M(u) be an N-function, L_r(f, x) and K_r(f, x) are Bak operator and Kantorovich operator, W_M(L_r(f)) and W_M(K_r(f)) are the Sobolev-Orlicz classes defined by L_r(f, x), K_r(f, x) and M(u). In this paper we give the asymptotic estimates of the n-K widths d_n(W_M(L_r(f)), L_2[0, 1]) and d_n(W_M(K_r(f)), L_2[0, 1]).
文摘This study was undertaken to examine which factors contributed to the correction of crowding in two patients who underwent nonextraction orthodontic treatment. A study model analysis was conducted to determine the effects of the orthodontic treatment for crowding with high canines on crown angulation and dental arch width in two patients. The results showed that the crown angulation was significantly increased, indicating distal tipping in the maxillary dental arch. This tendency was most commonly observed in the premolars among the lateral teeth. With respect to the dental arch width, the largest change was evident in the first molar and first premolar regions in cases 1 and 2, respectively. On the basis of these results, up-righting of mesially tipped lateral teeth and expansion of narrow dental arches could prove to be the keys to the success of space regaining or correction of high canines and mild crowding.
基金supported by the National Natural Science Foundation of China(No.51776220)the Postgraduate Scientific Research Innovation Project of Hunan Province,China。
文摘To investigate the impact of combustor width on continuous rotating detonation(CRD)fueled by ethylene and air,a series of 3 D simulations are conducted by changing the inner cylinder radius of an annular combustor while retaining the same outer cylinder radius.The results show that the CRD wave propagates more steadily and faster as the combustor width increases.The high-temperature zone at the backward-facing step preheats the propellants and contributes to the steady propagation of the CRD wave in 25-and 30-mm wide combustors.The highest and the lowest velocities are obtained in the30-and 15-mm wide combustors at,respectively,1880.27 and 1681.01 m/s.On the other hand,the average thrust decreases as the combustor width increases.The highest thrust is obtained in the 15-mm wide combustor while the lowest is in the 30-mm wide combustor,at 758.06 and 525.93 N,respectively.Nevertheless,the thrust is much more stable in the 25-and 30-mm wide combustors than in the 15-and 20-mm wide combustors.
文摘We performed systematic laser spectroscopic investigations of La I spectral lines, using optogalvanic detection. Sixteen previously unknown even parity levels, having energies between 40,300 and 44,300 cm<sup>-1</sup>, are reported. These levels classify altogether 67 lines, not listed in spectral tables. The new levels were found due to the observation of the depopulation of the lower levels of the excited transitions. We found a remarkable variation of the observed widths of single hyperfine structure components dependent on the energy of the upper excited levels. Some levels having energies higher than 43,000 cm<sup>-1</sup> appear to have a very high ionization probability.
基金Supported by the National High Technology Research and Development Program of China under Grant No 2014AA041901NSAF Foundation of the National Natural Science Foundation of China under Grant No U1330134+1 种基金the Opening Project of Shanghai Key Laboratory of All Solid-State Laser and Applied Techniques under Grant No 2012ADL02the National Natural Science Foundation of China under Grant Nos 61308024 and 11174305
文摘The wavelength-tunable and switchable narrow bandwidth mode-locking operation is demonstrated in an all fiber laser based on semiconductor-saturable absorber mirror （SESAM）. Two narrow-band fiber Bragg gratings centered at 1029.9nm and 1032nm respectively with a polarization controller inserted between them are used to realize the wavelength switchable between 1029.9nm and 1032nm. The laser delivers different pulse widths of 7.5ps for 1030nm and 20ps for 1032nm. The maximum output power for both could reach -6.5mW at single pulse operation. The output wavelength couM be tuned to about 0.gnm intervals ranging from 1030.2nm to 1031.1 nm and from 1032.15nm to 1033.7nm with the temperature change of the fiber Bragg grating, respectively.
基金partially supported by National Nature Science Foundation of China(61372187)Sichuan Key Technology Research and Development Program(2012GZ0019,2013GXZ0155)the Fund of Lab of Security Insurance of Cyberspace,Sichuan Province(szjj2014-079)
文摘Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.
