Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for a...Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.展开更多
In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic s...In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.展开更多
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y）...We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.展开更多
In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on ...In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on fixed point results in ordered spaces proved recently by the author. A concrete example is solved to demonstrate the obtained results.展开更多
In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and ...In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.展开更多
This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implici...This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implicit functions to simulate large deformations. In the translational interpolation function, two parameters which affect lateral deflection geometry are defined implicitly through nonlinear equations. The proposed translational interpolation function is shown to be more accurate than Hermitian function at large deformations. In the rotational interpolation function, twist rate is defined implicitly through a torsional continuity equation. Cross-sectional rotation which is strictly consistent to beam axis is obtained through separate bending rotation interpolation and torsional rotation interpolation. The element model fully accounts for geometric nonlinearities and coupling effects,and thus,can simulate cables with zero bending stiffness. Stiffness matrix and load vector have been derived using symbolic computation. Source code has been generated automatically.Numerical examples show that the proposed element has significantly higher accuracy than conventional 2-node beam elements under the same meshes for geometrically nonlinear problems.展开更多
In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.
We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improveme...We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.展开更多
BACKGROUND： Previous studies have shown that lesions in the anterior limb of the internal capsule contribute to obsessive-compulsive symptoms in patients with refractory obsessive-compulsive disorder （OCD）. However...BACKGROUND： Previous studies have shown that lesions in the anterior limb of the internal capsule contribute to obsessive-compulsive symptoms in patients with refractory obsessive-compulsive disorder （OCD）. However, few reports have addressed the effects of lesions in the anterior limb of the internal capsule on cognition, learning, and memory functions in patients with refractory OCD. OBJECTIVE： To investigate the degree of damage to memory tasks in refractory OCD patients following lesions to the anterior limb of the internal capsule. DESIGN, TIME AND SETTING： A case-controlled, observational study was performed at the Department of Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao-Tong University, China from May 2007 to March 2008. PARTICIPANTS： A total of 10 refractory OCD patients were admitted to the Department of Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao-Tong University, China from May 2007 to March 2008 and were recruited for this study. The OCD patients were of equal gender, with an average age of （25.1 ± 9.6） years. An additional 10 healthy volunteers were enrolled from a community of Shanghai City as controls; they were of equal gender and aged （25.1 ± 8.6） years. METHODS： A total of 10 refractory OCD patients were subjected to lesions in the anterior limbs of the bilateral internal capsules. Wechsler Memory Scale-Chinese Revision （WMS-CR, as a task of explicit memory） and the Nissen Version （serial reaction time task） software （SRTT, as a task of implicit memory） were applied to determine memory functions and learning performance in pre- and post-operative OCD patients and controls. MAIN OUTCOME MEASURES： WMS scores, reaction time in SRTT, and Yale-Brown obsessive compulsive scale scores were measured in pre- and post-operative OCD patients and controls. RESULTS： Compared to controls, the pre-operative OCD patients exhibited reduced memory task scores （P = 0.005）, whereas scores for reciting numbers of backwards digits were greater （P = 0.000）. Figure recall and associative memory were less in OCD patients at 1 week following surgery than in the pre-operative OCD patients （P = 0.042, P = 0.002, respectively）. Reaction time in implicit SRTT was significantly longer in pre-operative OCD patients compared with controls and post-operative OCD patients （P = 0.01, P = 0.03, respectively）. These results suggested ameliorated SRTT following neurosurgery. Yale-Brown Obsessive Compulsive Scale results revealed significantly improved OCD following lesions in the internal capsule （P = 0.04）. Some post-operative OCD patients suffered from deficits in short-term memory and implicit memory. CONCLUSION： Lesions in anterior limbs of bilateral internal capsules improve obsessive- compulsive symptoms and implicit memory in OCD patients, but result in aggravated short-term memory deficits.展开更多
In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of commo...In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.展开更多
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent im...In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.展开更多
By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative a...By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61502402 and 61379080)the Natural Science Foundation of Fujian Province of China(Grant No.2015J05129).
文摘Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.
文摘In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.
文摘We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g（x, y） ＋ h（x, y）y＇ =0.
文摘In this paper we shall study the solvability of discontinuous functional equations, and apply the so-obtained results to discontinuous implicit initial value problems in ordered Banach spaces. The proofs are based on fixed point results in ordered spaces proved recently by the author. A concrete example is solved to demonstrate the obtained results.
文摘In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.
基金Sponsored by the National Natural Science Foundation of China(Grant No.91215302)
文摘This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implicit functions to simulate large deformations. In the translational interpolation function, two parameters which affect lateral deflection geometry are defined implicitly through nonlinear equations. The proposed translational interpolation function is shown to be more accurate than Hermitian function at large deformations. In the rotational interpolation function, twist rate is defined implicitly through a torsional continuity equation. Cross-sectional rotation which is strictly consistent to beam axis is obtained through separate bending rotation interpolation and torsional rotation interpolation. The element model fully accounts for geometric nonlinearities and coupling effects,and thus,can simulate cables with zero bending stiffness. Stiffness matrix and load vector have been derived using symbolic computation. Source code has been generated automatically.Numerical examples show that the proposed element has significantly higher accuracy than conventional 2-node beam elements under the same meshes for geometrically nonlinear problems.
基金Supported by the National Science Foundation of China（60802045） Supported by the Science and Technology Foundation of Guizhou（20052004） Supported by the Science Foundation of Qiannan Normal College for Nationalities
文摘In this paper,we prove the converse of gem is right equivalent is also true in[1] and[2],obtain the necessary and sufficient conditions of equivalence of a class gems of C∞ function on Banach spaces.
文摘We use Radial Basis Functions （RBFs） to reconstruct smooth surfaces from 3D scattered data. An object＇s surface is defined implicitly as the zero set of an RBF fitted to the given surface data. We propose improvements on the methods of surface reconstruction with radial basis functions. A sparse approximation set of scattered data is constructed by reducing the number of interpolating points on the surface. We present an adaptive method for finding the off-surface normal points. The order of the equation decreases greatly as the number of the off-surface constraints reduces gradually. Experimental results are provided to illustrate that the proposed method is robust and may draw beautiful graphics.
基金the Key Program of International Communication Foundation of Psychiatry and Neurology Department of Shanghai Jiao-Tong University, No. 200901
文摘BACKGROUND： Previous studies have shown that lesions in the anterior limb of the internal capsule contribute to obsessive-compulsive symptoms in patients with refractory obsessive-compulsive disorder （OCD）. However, few reports have addressed the effects of lesions in the anterior limb of the internal capsule on cognition, learning, and memory functions in patients with refractory OCD. OBJECTIVE： To investigate the degree of damage to memory tasks in refractory OCD patients following lesions to the anterior limb of the internal capsule. DESIGN, TIME AND SETTING： A case-controlled, observational study was performed at the Department of Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao-Tong University, China from May 2007 to March 2008. PARTICIPANTS： A total of 10 refractory OCD patients were admitted to the Department of Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao-Tong University, China from May 2007 to March 2008 and were recruited for this study. The OCD patients were of equal gender, with an average age of （25.1 ± 9.6） years. An additional 10 healthy volunteers were enrolled from a community of Shanghai City as controls; they were of equal gender and aged （25.1 ± 8.6） years. METHODS： A total of 10 refractory OCD patients were subjected to lesions in the anterior limbs of the bilateral internal capsules. Wechsler Memory Scale-Chinese Revision （WMS-CR, as a task of explicit memory） and the Nissen Version （serial reaction time task） software （SRTT, as a task of implicit memory） were applied to determine memory functions and learning performance in pre- and post-operative OCD patients and controls. MAIN OUTCOME MEASURES： WMS scores, reaction time in SRTT, and Yale-Brown obsessive compulsive scale scores were measured in pre- and post-operative OCD patients and controls. RESULTS： Compared to controls, the pre-operative OCD patients exhibited reduced memory task scores （P = 0.005）, whereas scores for reciting numbers of backwards digits were greater （P = 0.000）. Figure recall and associative memory were less in OCD patients at 1 week following surgery than in the pre-operative OCD patients （P = 0.042, P = 0.002, respectively）. Reaction time in implicit SRTT was significantly longer in pre-operative OCD patients compared with controls and post-operative OCD patients （P = 0.01, P = 0.03, respectively）. These results suggested ameliorated SRTT following neurosurgery. Yale-Brown Obsessive Compulsive Scale results revealed significantly improved OCD following lesions in the internal capsule （P = 0.04）. Some post-operative OCD patients suffered from deficits in short-term memory and implicit memory. CONCLUSION： Lesions in anterior limbs of bilateral internal capsules improve obsessive- compulsive symptoms and implicit memory in OCD patients, but result in aggravated short-term memory deficits.
文摘In this paper, we introduce a new class U of 3-dimensional real functions, use U and a 2-dimensional real function ? to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results goodly generalize and improve the corresponding conclusions in references.
文摘In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.
文摘By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.
