When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ...When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.展开更多
Background: 4D-CT has been used to localize the parathyroid adenomas and hyperplasia since 2006 as a second line study after TC-99 m MIBI and ultrasonography. However, multiple studies have shown that 4D-CT is a robus...Background: 4D-CT has been used to localize the parathyroid adenomas and hyperplasia since 2006 as a second line study after TC-99 m MIBI and ultrasonography. However, multiple studies have shown that 4D-CT is a robust imaging method with high diagnostic accuracy, becoming increasingly popular among surgeons and radiologists. Purpose: To assess the diagnostic performance of 4D-CT scans to identify the pathologic gland(s), using pathology and intraoperative findings as gold standards. Methods: We analyzed patients with primary and secondary hyperparathyroidism who had intraoperative reports, pathology, parathyroid hormone levels, and preoperative 4D-CT. Histology, surgical findings, and decreased parathyroid hormone levels were used as gold standards. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), accuracy and 95% confidence interval were calculated. Fleiss’ kappa was used to assess the inter-observer agreement. Results: Sixty-seven patients were included. Sixty-two patients had a single adenoma, and five patients had a multiple gland disease (adenomas or hyperplasia). A total of 72 glands were proven to have parathyroid adenomas or hyperplasia. The sensitivity, specificity, PPV, NPV and accuracy are 85%, 97%, 96%, 87% and 91% for lateralization and 76%, 96%, 85%, 92% and 90% for quadrant localization, respectively in single-gland disease. The sensitivity, specificity, PPV, NPV and accuracy are 88%, 100%, 100%, 50% and 90% for lateralization and 71%, 100%, 100%, 60% and 80% for quadrant localization respectively in multiple-gland disease. Fleiss’ kappa value is 5.6 (moderate inter-observer agreement). Conclusion: 4D-CT is a robust method in the localization of hyperfunctioning parathyroid glands with high accuracy and at least moderate inter-observer agreement.展开更多
Initiation, growth, and rupture of cerebral aneurysms are caused by hemodynamic factors. It is extensively accepted that the cerebral aneurysm wall is assumed to be rigid using computational fluid dynamics (CFD). Furt...Initiation, growth, and rupture of cerebral aneurysms are caused by hemodynamic factors. It is extensively accepted that the cerebral aneurysm wall is assumed to be rigid using computational fluid dynamics (CFD). Furthermore, fluid-structure interactions have been recently applied for simulation of an elastic cerebral aneurysm model. Herein, we examined cerebral aneurysm hemodynamics in a realistic moving boundary deformation model based on 4-dimensional computed tomographic angiography (4D-CTA) obtained by high time-resolution using numerical simulation. The aneurysm of the realistic moving deformation model based on 4D-CTA at each phase was constructed. The effect of small wall deformation on hemodynamic characteristics might be interested. So, four hemodynamic factors (wall shear stress, wall shear stress divergence, oscillatory shear index and residual residence time) were determined from the numerical simulation, and their behaviors were assessed in the basilar bifurcation aneurysm.展开更多
In this paper,we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras.We prove the realization theorem,offer a concrete example realizing all type of 4-dimensional 3-Lie algebras,and also...In this paper,we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras.We prove the realization theorem,offer a concrete example realizing all type of 4-dimensional 3-Lie algebras,and also give some properties about semi-simple n-Lie algebras.展开更多
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> with integers (a, b, c) are generalized to 3D-Pythagorean ...The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> with integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>=d<sup>2</sup> with integers (a, b, c, d). Rules for a parametrization of the numbers (a, b, c, d) are derived and a list of all possible nonequivalent cases without common divisors up to d<sup>2</sup> is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>+d<sup>2</sup>=e<sup>2</sup> and a parametrization is derived. Relations to the 4-square identity are discussed which leads also to the N-dimensional case. The initial 3D- and 4D-Pythagorean numbers are explicitly calculated up to d<sup>2</sup>, respectively, e<sup>2</sup>.展开更多
As a zero-carbon fuel,hydrogen can be produced via electrochemical water splitting using clean electric energy by the hydrogen evolution reaction(HER)process.The ultimate goal of HER catalyst is to replace the expensi...As a zero-carbon fuel,hydrogen can be produced via electrochemical water splitting using clean electric energy by the hydrogen evolution reaction(HER)process.The ultimate goal of HER catalyst is to replace the expensive Pt metal benchmark with a cheap one with equivalent activities.In this work,we investigated the possibility of HER process on single-atom catalysts(SACs)doped on two-dimensional(2D)GaPS_(4)materials,which have a large intrinsic band gap that can be regulated by doping and tensile strain.Based on the machine learning regression analysis,we can expand the prediction of HER performance to more catalysts without expensive DFT calculation.The electron affinity and first ionization energy are the two most important descriptors related to the HER behavior.Furthermore,constrain molecular dynamics with solvation models and constant potentials were applied to understand the dynamics barrier of HER process of Pt SAC on GaPS_(4)materials.These findings not only provide important insights into the catalytic properties of single-atom catalysts on GaPS_(4)2D materials,but also provides theoretical guidance paradigm for exploration of new catalysts.展开更多
A heterojunction structure design is a very good method for improving the properties of semiconductors in many research fields.This method is employed in the present study to promote the gas-sensing performance of Ag_...A heterojunction structure design is a very good method for improving the properties of semiconductors in many research fields.This method is employed in the present study to promote the gas-sensing performance of Ag_(3)PO_(4)nanocomposites at room temperature(25℃).A nanocomposite of Ag_(3)PO_(4)nanoparticles and three-dimensional peony-like WO_(3)(WO_(3)/Ag_(3)PO_(4))was successfully prepared by the precipitation method.The crystalline phases were analyzed by xray diffraction and the microstructure was characterized by scanning electron microscopy and transmission electron microscopy.The chemical bonding states were analyzed by x-ray photoelectron spectroscopy.The gas-sensing performance of WO_(3)/Ag_(3)PO_(4)sensors was systematically explored at room temperature.The composite sensors possessed a higher response and lower detection limit(1 ppm)to NH_(3)than those made of a single type of material;this is ascribed to the synergistic effect achieved by the heterojunction structure.Among the different composite sensors tested,gas sensor A5W5(Ag_(3)PO_(4):WO3mass ratio of 5:5)displayed the highest response to NH_(3)at room temperature.Interestingly,the A5W5 gas sensor exhibited relatively good stability and excellent selectivity to NH_(3).The A5W5 sensor also displayed a relatively good response under high humidity.The gas-sensing mechanism of the WO_(3)/Ag_(3)PO_(4)sensors is explained in detail.Taken together,the as-prepared sensor is highly efficient at detecting NH_(3)and could be suitable for practical applications.In addition,this study also provides a new method for developing Ag_(3)PO_(4)-based sensors in the gas-sensing field.展开更多
Layered magnetic materials,such as MnBi_(2)Te_(4),have drawn much attention owing to their potential for realizing twodimensional(2D)magnetism and possible topological states.Recently,FeBi_(2)Te_(4),which is isostruct...Layered magnetic materials,such as MnBi_(2)Te_(4),have drawn much attention owing to their potential for realizing twodimensional(2D)magnetism and possible topological states.Recently,FeBi_(2)Te_(4),which is isostructural to MnBi_(2)Te_(4),has been synthesized in experiments,but its detailed magnetic ordering and band topology have not been clearly understood yet.Here,based on first-principles calculations,we investigate the magnetic and electronic properties of FeBi_(2)Te_(4)in bulk and 2D forms.We show that different from MnBi_(2)Te_(4),the magnetic ground states of bulk,single-layer,and bilayer FeBi_(2)Te_(4)all favor a 120°noncollinear antiferromagnetic ordering,and they are topologically trivial narrow-gap semiconductors.For the bilayer case,we find that a quantum anomalous Hall effect with a unit Chern number is realized in the ferromagnetic state,which may be achieved in experiment by an external magnetic field or by magnetic proximity coupling.Our work clarifies the physical properties of the new material system of FeBi_(2)Te_(4)and reveals it as a potential platform for studying magnetic frustration down to 2D limit as well as quantum anomalous Hall effect.展开更多
文摘When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.
文摘Background: 4D-CT has been used to localize the parathyroid adenomas and hyperplasia since 2006 as a second line study after TC-99 m MIBI and ultrasonography. However, multiple studies have shown that 4D-CT is a robust imaging method with high diagnostic accuracy, becoming increasingly popular among surgeons and radiologists. Purpose: To assess the diagnostic performance of 4D-CT scans to identify the pathologic gland(s), using pathology and intraoperative findings as gold standards. Methods: We analyzed patients with primary and secondary hyperparathyroidism who had intraoperative reports, pathology, parathyroid hormone levels, and preoperative 4D-CT. Histology, surgical findings, and decreased parathyroid hormone levels were used as gold standards. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), accuracy and 95% confidence interval were calculated. Fleiss’ kappa was used to assess the inter-observer agreement. Results: Sixty-seven patients were included. Sixty-two patients had a single adenoma, and five patients had a multiple gland disease (adenomas or hyperplasia). A total of 72 glands were proven to have parathyroid adenomas or hyperplasia. The sensitivity, specificity, PPV, NPV and accuracy are 85%, 97%, 96%, 87% and 91% for lateralization and 76%, 96%, 85%, 92% and 90% for quadrant localization, respectively in single-gland disease. The sensitivity, specificity, PPV, NPV and accuracy are 88%, 100%, 100%, 50% and 90% for lateralization and 71%, 100%, 100%, 60% and 80% for quadrant localization respectively in multiple-gland disease. Fleiss’ kappa value is 5.6 (moderate inter-observer agreement). Conclusion: 4D-CT is a robust method in the localization of hyperfunctioning parathyroid glands with high accuracy and at least moderate inter-observer agreement.
文摘Initiation, growth, and rupture of cerebral aneurysms are caused by hemodynamic factors. It is extensively accepted that the cerebral aneurysm wall is assumed to be rigid using computational fluid dynamics (CFD). Furthermore, fluid-structure interactions have been recently applied for simulation of an elastic cerebral aneurysm model. Herein, we examined cerebral aneurysm hemodynamics in a realistic moving boundary deformation model based on 4-dimensional computed tomographic angiography (4D-CTA) obtained by high time-resolution using numerical simulation. The aneurysm of the realistic moving deformation model based on 4D-CTA at each phase was constructed. The effect of small wall deformation on hemodynamic characteristics might be interested. So, four hemodynamic factors (wall shear stress, wall shear stress divergence, oscillatory shear index and residual residence time) were determined from the numerical simulation, and their behaviors were assessed in the basilar bifurcation aneurysm.
文摘In this paper,we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras.We prove the realization theorem,offer a concrete example realizing all type of 4-dimensional 3-Lie algebras,and also give some properties about semi-simple n-Lie algebras.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
文摘The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>=c<sup>2</sup> with integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>=d<sup>2</sup> with integers (a, b, c, d). Rules for a parametrization of the numbers (a, b, c, d) are derived and a list of all possible nonequivalent cases without common divisors up to d<sup>2</sup> is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) which satisfy the equation a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>+d<sup>2</sup>=e<sup>2</sup> and a parametrization is derived. Relations to the 4-square identity are discussed which leads also to the N-dimensional case. The initial 3D- and 4D-Pythagorean numbers are explicitly calculated up to d<sup>2</sup>, respectively, e<sup>2</sup>.
基金supported by the National Natural Science Foundation of China (Grant No.12164009),which is received by Xuefei Liuthe Guizhou Science and Technology Foundation-ZK[2022]General 308,which is received by Xuefei Liu+2 种基金Top scientific and technological talents in Guizhou Province of Qian Jiaoji[2022]No.078,which is received by Xuefei LiuGraduate Research Fund Project of Guizhou Province (YJSKYJJ[2021]088),which is received by Tianyun Liuthe Haihe Laboratory of Sustainable Chemical Transformation for financial support。
文摘As a zero-carbon fuel,hydrogen can be produced via electrochemical water splitting using clean electric energy by the hydrogen evolution reaction(HER)process.The ultimate goal of HER catalyst is to replace the expensive Pt metal benchmark with a cheap one with equivalent activities.In this work,we investigated the possibility of HER process on single-atom catalysts(SACs)doped on two-dimensional(2D)GaPS_(4)materials,which have a large intrinsic band gap that can be regulated by doping and tensile strain.Based on the machine learning regression analysis,we can expand the prediction of HER performance to more catalysts without expensive DFT calculation.The electron affinity and first ionization energy are the two most important descriptors related to the HER behavior.Furthermore,constrain molecular dynamics with solvation models and constant potentials were applied to understand the dynamics barrier of HER process of Pt SAC on GaPS_(4)materials.These findings not only provide important insights into the catalytic properties of single-atom catalysts on GaPS_(4)2D materials,but also provides theoretical guidance paradigm for exploration of new catalysts.
基金financial support from the Collaborative Education Project of IndustryUniversity Cooperation of the Ministry of Education of China(Grant No.202101256024)the National Natural Science Foundation of China(Grant Nos.11904209 and 61802144)。
文摘A heterojunction structure design is a very good method for improving the properties of semiconductors in many research fields.This method is employed in the present study to promote the gas-sensing performance of Ag_(3)PO_(4)nanocomposites at room temperature(25℃).A nanocomposite of Ag_(3)PO_(4)nanoparticles and three-dimensional peony-like WO_(3)(WO_(3)/Ag_(3)PO_(4))was successfully prepared by the precipitation method.The crystalline phases were analyzed by xray diffraction and the microstructure was characterized by scanning electron microscopy and transmission electron microscopy.The chemical bonding states were analyzed by x-ray photoelectron spectroscopy.The gas-sensing performance of WO_(3)/Ag_(3)PO_(4)sensors was systematically explored at room temperature.The composite sensors possessed a higher response and lower detection limit(1 ppm)to NH_(3)than those made of a single type of material;this is ascribed to the synergistic effect achieved by the heterojunction structure.Among the different composite sensors tested,gas sensor A5W5(Ag_(3)PO_(4):WO3mass ratio of 5:5)displayed the highest response to NH_(3)at room temperature.Interestingly,the A5W5 gas sensor exhibited relatively good stability and excellent selectivity to NH_(3).The A5W5 sensor also displayed a relatively good response under high humidity.The gas-sensing mechanism of the WO_(3)/Ag_(3)PO_(4)sensors is explained in detail.Taken together,the as-prepared sensor is highly efficient at detecting NH_(3)and could be suitable for practical applications.In addition,this study also provides a new method for developing Ag_(3)PO_(4)-based sensors in the gas-sensing field.
基金funding support from the Singapore MOE Ac RF 308 Tier 2(Grant No.T2EP50220-0026)funding support from Shandong Provincial Natural Science Foundation(Grant No.ZR2023QA012)+3 种基金the Special Fund-ing in the Project of Qilu Young Scholar Program of Shandong Universityfunding support from Australian Research Council Future Fellowship(Grant No.FT220100290)funding support from the AINSE postgraduate awardfunding support from the Research and Development Administration Office at the University of Macao(Grants Nos.MYRG2022-00088-IAPME and SRG2021-00003-IAPME)。
文摘Layered magnetic materials,such as MnBi_(2)Te_(4),have drawn much attention owing to their potential for realizing twodimensional(2D)magnetism and possible topological states.Recently,FeBi_(2)Te_(4),which is isostructural to MnBi_(2)Te_(4),has been synthesized in experiments,but its detailed magnetic ordering and band topology have not been clearly understood yet.Here,based on first-principles calculations,we investigate the magnetic and electronic properties of FeBi_(2)Te_(4)in bulk and 2D forms.We show that different from MnBi_(2)Te_(4),the magnetic ground states of bulk,single-layer,and bilayer FeBi_(2)Te_(4)all favor a 120°noncollinear antiferromagnetic ordering,and they are topologically trivial narrow-gap semiconductors.For the bilayer case,we find that a quantum anomalous Hall effect with a unit Chern number is realized in the ferromagnetic state,which may be achieved in experiment by an external magnetic field or by magnetic proximity coupling.Our work clarifies the physical properties of the new material system of FeBi_(2)Te_(4)and reveals it as a potential platform for studying magnetic frustration down to 2D limit as well as quantum anomalous Hall effect.
