As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that ...As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that this stratification re-flects the stratified convexity/concavity of the boundary ?with respect to the ?v-flow. We study the behavior of this stratification under deformations of the vector field v. We also investigate the restrictions that the existence of a convex/concave traversing ?v-flow imposes on the topology of X. Let be the orthogonal projection of on the tangent bundle of . We link the dynamics of theon the boundary with the property of in X being convex/concave. This linkage is an instance of more general phenomenon that we call “holography of traversing fields”—a subject of a different paper to follow.展开更多
Image segmentation is an important research area in Computer Vision and the GVF-snake is an effective segmentation algorithm presented in recent years. Traditional GVF-snake algorithm has a large capture range and can...Image segmentation is an important research area in Computer Vision and the GVF-snake is an effective segmentation algorithm presented in recent years. Traditional GVF-snake algorithm has a large capture range and can deal with boundary concavities. However, when interesting object has deep concavities, traditional GVF-snake algorithm can’t converge to true boundaries exactly. In this paper, a novel improved scheme was proposed based on the GVF-snake. The central idea is introduce dynamic balloon force and tangential force to strengthen the static GVF force. Experimental results of synthetic image and real image all demonstrated that the improved algorithm can capture boundary concavities better and detect complex edges more accurately.展开更多
This paper, firstly, establishes the formula of production possibilities set by using axiomatic method, upon which some optimal production functions are based in different senses of optimization. Finally, this paper p...This paper, firstly, establishes the formula of production possibilities set by using axiomatic method, upon which some optimal production functions are based in different senses of optimization. Finally, this paper proves that the optimal production functions possess homogeneity,superadditive, and concavity.展开更多
The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ R × R is still open. In this paper, we prove that S(a, b; x, y) ...The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ R × R is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : a 0, b 0, a + b 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : b 0, b a, a + b 1} ∪ {(a, b) : a 0, a b, a + b 1}.展开更多
Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address th...Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon. .展开更多
In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In...In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler's constant γ.展开更多
The flow visualization work with the aid of PIV and Piezometer deals with flip-flop flow around diamond-shaped cylinder bundle revised with concavities on both bundle walls. It is disclosed that 1) the concavity const...The flow visualization work with the aid of PIV and Piezometer deals with flip-flop flow around diamond-shaped cylinder bundle revised with concavities on both bundle walls. It is disclosed that 1) the concavity constructed on both side-walls of a diamond cylinder induces a substantial change in the flow patterns in the exit jet-stream field and jet- stream dispersion, 2) pressure characteristics are quantitatively measured in a diverging-flow region in diamond cylinder bundles with concavityand in its downstream region, and 3) flip-flop flow occurs in the flow passages and its occurrence condition is obtained.展开更多
In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions ...In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.展开更多
This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of c...This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.展开更多
Plant leaves, insects and geckos are masters of adhesion or anti-adhesion by smartly designed refined surface structures with micro- and nano- 'technologies'. Understanding the basic principles in the design of the ...Plant leaves, insects and geckos are masters of adhesion or anti-adhesion by smartly designed refined surface structures with micro- and nano- 'technologies'. Understanding the basic principles in the design of the unique surface structures is of great importance in the manufacture or synthesis of micro- and nano- devices in MEMS or NEMS. This study is right inspired by this effort, focusing on the mechanics of wet adhesion between fibers having concave tips and a flat substrate via capillary forces. We show that the concave surface can effectively enhance the wet adhesion by reducing the effective contact angle of the fiber, firmly pinning the liquid bridge at its circumferential edge. A critical contact angle is identified below which the adhesion strength can achieve its maximum, being insensitive to the contact angle between the fiber and liquid. The analytical expression for the critical angle is derived. Then a tentative design for the profile of concave surfaces is proposed, considering the effects of chamfering size, deformation and buckling, etc. The effect of liquid volume on the wet adhesion of multiple-fiber system is also discussed.展开更多
Large tanks are extensively used for storing water,petrochemicals and fuels.Since they are often cited in earthquake-prone areas,the safe and continuous operation of these important structures must be ensured even whe...Large tanks are extensively used for storing water,petrochemicals and fuels.Since they are often cited in earthquake-prone areas,the safe and continuous operation of these important structures must be ensured even when severe earthquakes occur,since their failure could have devastating financial and socio-environmental consequences.Base-isolation has been widely adopted for the efficient seismic protection of such critical facilities.However,base-isolated tanks can be located relatively close to active faults that generate strong excitations with special characteristics.Consequently,viscous dampers can be incorporated into the isolation system to reduce excessive displacement demands and to avoid overconservative isolator design.Nonetheless,only a few studies have focused on the investigation of seismic response of base-isolated liquid storage tanks in conjunction with supplemental viscous dampers.Therefore,the impact of the addition of supplemental linear viscous dampers on the seismic performance of tanks isolated by single friction pendulum devices is investigated herein.Four levels of supplemental damping are assessed and compared with respect to isolators′displacement capacity and accelerations that are transferred to the tanks.展开更多
In this paper,we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line.The results are obtained by the Leggett-Williams fixed point theorem.
A new technique is used in Discrete Least Square Meshfree(DLSM) method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced ...A new technique is used in Discrete Least Square Meshfree(DLSM) method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced Discrete Least Squares Meshless method named as VDLSM(Voronoi based Discrete Least Squares Meshless) is developed in order to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks. Existing meshless methods cannot estimate precisely the required unknowns in the vicinity of the above mentioned boundaries. Conducted researches are limited to domains with regular convex boundaries. To this end, the advantages of the Voronoi tessellation algorithm are implemented. The support domains of the sampling points are determined using a Voronoi tessellation algorithm. For the weight functions, a cubic spline polynomial is used based on a normalized distance variable which can provide a high degree of smoothness near those mentioned above discontinuities. Finally, Moving Least Squares(MLS) shape functions are constructed using a varitional method. This straight-forward scheme can properly estimate the unknowns(in this particular study, the temperatures at the nodal points) near and on the crack faces, crack tip or concave boundaries without need to extra backward corrective procedures, i.e. the iterative calculations for modifying the shape functions of the nodes located near or on these types of the complex boundaries. The accuracy and efficiency of the presented method are investigated by analyzing four particular examples. Obtained results from VDLSM are compared with the available analytical results or with the results of the well-known Finite Elements Method(FEM) when an analytical solution is not available. By comparisons, it is revealed that the proposed technique gives high accuracy for the solution of the steady-state heat conduction problems within cracked domains or domains with concave boundaries and at the same time possesses a high convergence rate which its accuracy is not sensitive to the arrangement of the nodal points. The novelty of this paper is the use of Voronoi concept in determining the weight functions used in the formulation of the MLS type shape functions.展开更多
We synthesized octapod Cu-Au bimetallic alloy with a concave structure by employing a replacement reaction between Au PPh3Cl and Cu nanocubes. Using the Cu nanocube as sacrificial templates, we have successfully gener...We synthesized octapod Cu-Au bimetallic alloy with a concave structure by employing a replacement reaction between Au PPh3Cl and Cu nanocubes. Using the Cu nanocube as sacrificial templates, we have successfully generated high-active sites on alloy nanocrystals by carefully tuning the replacement reaction and growth. The key is to afford the proper concentration of Au PPh3Cl-TOP to the reaction solution. When the Au precursor with high concentration is injected into the galvanic replacement reaction, the growth dominated the process and hollowed octapod Cu-Au alloy was obtained. In contrast, when the concentration of the Au precursor is low, the replacement reaction can only take place at the nanocrystals, leading to generate Cu-Au nanocages. This work provides an effective strategy for the preparation of hollow bimetallic nanocrystals with high-active sites.展开更多
It is concluded from the results of testing the frequency characteristics of the sub micron precision machine tool servo control system, that the existence of several oscillating modalities is the main factor that aff...It is concluded from the results of testing the frequency characteristics of the sub micron precision machine tool servo control system, that the existence of several oscillating modalities is the main factor that affects the performance of the control system. To compensate for this effect,several concave filters are utilized in the system to improve the control accuracy. The feasibility of compensating for several oscillating modalities with a single concave filter is also studied. By applying a modified Butterworth concave filter to the practical system, the maximum stable state output error remains under ±10 nm in the closed loop positioning system.展开更多
In this work, we have selected three number of stepped type solar stills of the same overall dimensions 620 mm (W) × 808 mm (L) but with different absorber surface areas due to the variation in the shape of the b...In this work, we have selected three number of stepped type solar stills of the same overall dimensions 620 mm (W) × 808 mm (L) but with different absorber surface areas due to the variation in the shape of the basin surface. The other design parameters like depth of water, thickness of glass cover, insulation thickness, type of condensing cover, absorbing material provided over the basin, and angle of inclination of the still were kept constant to study the effect of shape of the absorber surface over the distillate yield obtained. The shape of the absorber surface provided in the basins of solar stills A, E and F was flat, convex and concave respectively. When the convex and concave type stepped solar stills are used, the average daily water production has been found to be 56.60% and 29.24% higher than that of flat type stepped solar still respectively. Also an economic analysis was made. The payback period of flat type, convex type and concave type stepped solar still is 823 days, 525 days and 637 days respectively. Thus, the convex type solar still gives the returns within the least possible time as compared to other two types of stepped solar stills. The laboratory tests were conducted to test the quality of water after distillation. The tests indicate that the quality of water in terms of pH, electrical conductivity, total hardness, TDS, Alkalinity, Nitrates etc. is well within the desirable limits as prescribed by WHO for Indian specific conditions.展开更多
The differential equations of movement along the concave profile of the grate, consisting of three broken lines, are integrated on Maple 9.5 under initial conditions, using separate functions, and graphs of the depend...The differential equations of movement along the concave profile of the grate, consisting of three broken lines, are integrated on Maple 9.5 under initial conditions, using separate functions, and graphs of the dependence of movement and speed over time are presented. The graphs show the patterns of change in displacement and speed at different angles, friction coefficient of seeds along grate with a broken line of a concave profile.展开更多
Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diamete...Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diameter, is larger than 1, there exists two-dimensional tensile stress in the deformed body, when the ratio is smaller than 1, there exists shear stress in static hydraulic zone. The former breaks through the theory that there is three-dimensional compressive stress irrespective of any ratio of height to diameter. The latter satisfactorily explains the mechanism of layer-like cracks in disk-shaped forgings and the flanges of forged gear axles. The representation of the two models makes the upsetting, theory into correct and perfect stage.展开更多
基金Partially supported by NSF (10801079)Partially supported by RFDP (20080551002)+1 种基金Partially supported by LPMC of MOE of ChinaPartially supported by the 973 Program of MOST, NNSF, MCME, RFDP, LPMC of MOE of China, S. S. Chern Foundation, and Nankai University
文摘In this paper, the concavity of closed geodesics proposed by M. Morse in 1930s is studied.
文摘As has been observed by Morse [1], any generic vector field v on a compact smooth manifold X with boundary gives rise to a stratification of the boundary by compact submanifolds , where . Our main observation is that this stratification re-flects the stratified convexity/concavity of the boundary ?with respect to the ?v-flow. We study the behavior of this stratification under deformations of the vector field v. We also investigate the restrictions that the existence of a convex/concave traversing ?v-flow imposes on the topology of X. Let be the orthogonal projection of on the tangent bundle of . We link the dynamics of theon the boundary with the property of in X being convex/concave. This linkage is an instance of more general phenomenon that we call “holography of traversing fields”—a subject of a different paper to follow.
文摘Image segmentation is an important research area in Computer Vision and the GVF-snake is an effective segmentation algorithm presented in recent years. Traditional GVF-snake algorithm has a large capture range and can deal with boundary concavities. However, when interesting object has deep concavities, traditional GVF-snake algorithm can’t converge to true boundaries exactly. In this paper, a novel improved scheme was proposed based on the GVF-snake. The central idea is introduce dynamic balloon force and tangential force to strengthen the static GVF force. Experimental results of synthetic image and real image all demonstrated that the improved algorithm can capture boundary concavities better and detect complex edges more accurately.
文摘This paper, firstly, establishes the formula of production possibilities set by using axiomatic method, upon which some optimal production functions are based in different senses of optimization. Finally, this paper proves that the optimal production functions possess homogeneity,superadditive, and concavity.
基金supported by National Natural Science Foundation of China (Grant Nos. 60850005, 10771195)the Natural Science Foundation of Zhejiang Province (Grant Nos. D7080080, Y607128, Y7080185)
文摘The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ R × R is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : a 0, b 0, a + b 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b) : b 0, b a, a + b 1} ∪ {(a, b) : a 0, a b, a + b 1}.
文摘Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon. .
基金Supported by the National Natural Science Foundation of China(11171307)
文摘In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler's constant γ.
文摘The flow visualization work with the aid of PIV and Piezometer deals with flip-flop flow around diamond-shaped cylinder bundle revised with concavities on both bundle walls. It is disclosed that 1) the concavity constructed on both side-walls of a diamond cylinder induces a substantial change in the flow patterns in the exit jet-stream field and jet- stream dispersion, 2) pressure characteristics are quantitatively measured in a diverging-flow region in diamond cylinder bundles with concavityand in its downstream region, and 3) flip-flop flow occurs in the flow passages and its occurrence condition is obtained.
文摘In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.
基金the Natural Science Foundation ofFujian Province of China(S0650021,2006J0215)the National Natural Science Foundation of China(10771086)
文摘This article proposes a few tangent cones,which are relative to the constraint qualifications of optimization problems.With the upper and lower directional derivatives of an objective function,the characteristics of cones on the constraint qualifications are presented.The interrelations among the constraint qualifications,a few cones involved, and level sets of upper and lower directional derivatives are derived.
基金supported by the National Natural Science Foundation of China through Grant Nos 10628205,10732050 and10872115National Basic Research Program of China through Grant No 2007CB936803,and SRF-SEM for ROCS
文摘Plant leaves, insects and geckos are masters of adhesion or anti-adhesion by smartly designed refined surface structures with micro- and nano- 'technologies'. Understanding the basic principles in the design of the unique surface structures is of great importance in the manufacture or synthesis of micro- and nano- devices in MEMS or NEMS. This study is right inspired by this effort, focusing on the mechanics of wet adhesion between fibers having concave tips and a flat substrate via capillary forces. We show that the concave surface can effectively enhance the wet adhesion by reducing the effective contact angle of the fiber, firmly pinning the liquid bridge at its circumferential edge. A critical contact angle is identified below which the adhesion strength can achieve its maximum, being insensitive to the contact angle between the fiber and liquid. The analytical expression for the critical angle is derived. Then a tentative design for the profile of concave surfaces is proposed, considering the effects of chamfering size, deformation and buckling, etc. The effect of liquid volume on the wet adhesion of multiple-fiber system is also discussed.
文摘Large tanks are extensively used for storing water,petrochemicals and fuels.Since they are often cited in earthquake-prone areas,the safe and continuous operation of these important structures must be ensured even when severe earthquakes occur,since their failure could have devastating financial and socio-environmental consequences.Base-isolation has been widely adopted for the efficient seismic protection of such critical facilities.However,base-isolated tanks can be located relatively close to active faults that generate strong excitations with special characteristics.Consequently,viscous dampers can be incorporated into the isolation system to reduce excessive displacement demands and to avoid overconservative isolator design.Nonetheless,only a few studies have focused on the investigation of seismic response of base-isolated liquid storage tanks in conjunction with supplemental viscous dampers.Therefore,the impact of the addition of supplemental linear viscous dampers on the seismic performance of tanks isolated by single friction pendulum devices is investigated herein.Four levels of supplemental damping are assessed and compared with respect to isolators′displacement capacity and accelerations that are transferred to the tanks.
基金Supported by the NNSF of China(10871116)Supported by the NSFSP of China(ZR2010AM005)
文摘In this paper,we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line.The results are obtained by the Leggett-Williams fixed point theorem.
文摘A new technique is used in Discrete Least Square Meshfree(DLSM) method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced Discrete Least Squares Meshless method named as VDLSM(Voronoi based Discrete Least Squares Meshless) is developed in order to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks. Existing meshless methods cannot estimate precisely the required unknowns in the vicinity of the above mentioned boundaries. Conducted researches are limited to domains with regular convex boundaries. To this end, the advantages of the Voronoi tessellation algorithm are implemented. The support domains of the sampling points are determined using a Voronoi tessellation algorithm. For the weight functions, a cubic spline polynomial is used based on a normalized distance variable which can provide a high degree of smoothness near those mentioned above discontinuities. Finally, Moving Least Squares(MLS) shape functions are constructed using a varitional method. This straight-forward scheme can properly estimate the unknowns(in this particular study, the temperatures at the nodal points) near and on the crack faces, crack tip or concave boundaries without need to extra backward corrective procedures, i.e. the iterative calculations for modifying the shape functions of the nodes located near or on these types of the complex boundaries. The accuracy and efficiency of the presented method are investigated by analyzing four particular examples. Obtained results from VDLSM are compared with the available analytical results or with the results of the well-known Finite Elements Method(FEM) when an analytical solution is not available. By comparisons, it is revealed that the proposed technique gives high accuracy for the solution of the steady-state heat conduction problems within cracked domains or domains with concave boundaries and at the same time possesses a high convergence rate which its accuracy is not sensitive to the arrangement of the nodal points. The novelty of this paper is the use of Voronoi concept in determining the weight functions used in the formulation of the MLS type shape functions.
基金supported by the Fundamental Research Funds for the Central Universities under Grant No.JB181404。
文摘We synthesized octapod Cu-Au bimetallic alloy with a concave structure by employing a replacement reaction between Au PPh3Cl and Cu nanocubes. Using the Cu nanocube as sacrificial templates, we have successfully generated high-active sites on alloy nanocrystals by carefully tuning the replacement reaction and growth. The key is to afford the proper concentration of Au PPh3Cl-TOP to the reaction solution. When the Au precursor with high concentration is injected into the galvanic replacement reaction, the growth dominated the process and hollowed octapod Cu-Au alloy was obtained. In contrast, when the concentration of the Au precursor is low, the replacement reaction can only take place at the nanocrystals, leading to generate Cu-Au nanocages. This work provides an effective strategy for the preparation of hollow bimetallic nanocrystals with high-active sites.
文摘It is concluded from the results of testing the frequency characteristics of the sub micron precision machine tool servo control system, that the existence of several oscillating modalities is the main factor that affects the performance of the control system. To compensate for this effect,several concave filters are utilized in the system to improve the control accuracy. The feasibility of compensating for several oscillating modalities with a single concave filter is also studied. By applying a modified Butterworth concave filter to the practical system, the maximum stable state output error remains under ±10 nm in the closed loop positioning system.
文摘In this work, we have selected three number of stepped type solar stills of the same overall dimensions 620 mm (W) × 808 mm (L) but with different absorber surface areas due to the variation in the shape of the basin surface. The other design parameters like depth of water, thickness of glass cover, insulation thickness, type of condensing cover, absorbing material provided over the basin, and angle of inclination of the still were kept constant to study the effect of shape of the absorber surface over the distillate yield obtained. The shape of the absorber surface provided in the basins of solar stills A, E and F was flat, convex and concave respectively. When the convex and concave type stepped solar stills are used, the average daily water production has been found to be 56.60% and 29.24% higher than that of flat type stepped solar still respectively. Also an economic analysis was made. The payback period of flat type, convex type and concave type stepped solar still is 823 days, 525 days and 637 days respectively. Thus, the convex type solar still gives the returns within the least possible time as compared to other two types of stepped solar stills. The laboratory tests were conducted to test the quality of water after distillation. The tests indicate that the quality of water in terms of pH, electrical conductivity, total hardness, TDS, Alkalinity, Nitrates etc. is well within the desirable limits as prescribed by WHO for Indian specific conditions.
文摘The differential equations of movement along the concave profile of the grate, consisting of three broken lines, are integrated on Maple 9.5 under initial conditions, using separate functions, and graphs of the dependence of movement and speed over time are presented. The graphs show the patterns of change in displacement and speed at different angles, friction coefficient of seeds along grate with a broken line of a concave profile.
基金National Natural Science Foundation of China(No.59235101)
文摘Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diameter, is larger than 1, there exists two-dimensional tensile stress in the deformed body, when the ratio is smaller than 1, there exists shear stress in static hydraulic zone. The former breaks through the theory that there is three-dimensional compressive stress irrespective of any ratio of height to diameter. The latter satisfactorily explains the mechanism of layer-like cracks in disk-shaped forgings and the flanges of forged gear axles. The representation of the two models makes the upsetting, theory into correct and perfect stage.