In this paper,we introduce a new geometric constant R_(X)(κ)based on isosceles orthogonality.First,we explore some basic properties of this new constant and then provide several examples to estimate its exact values ...In this paper,we introduce a new geometric constant R_(X)(κ)based on isosceles orthogonality.First,we explore some basic properties of this new constant and then provide several examples to estimate its exact values in certain specific Banach spaces.Next,we investigate the relationships between this new constant and other classical constants.Specifically,we establish an inequality relationship between it and the J(X)constant,as well as an identity relationship between it and theρX(t)constant.Furthermore,we characterize some geometric properties of Banach spaces by means of this new constant.Finally,by restricting the above-mentioned constant to the unit sphere,we introduce another new constant,calculate its upper and lower bounds,and present a relevant example.展开更多
In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can sa...In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.展开更多
The article initially reviews various works describing the physical model (PM) of Michelson’s interferometric experiment (ME), represented by the race between two swimmers Sw1, Sw2 (or boats, or planes, or sound sign...The article initially reviews various works describing the physical model (PM) of Michelson’s interferometric experiment (ME), represented by the race between two swimmers Sw1, Sw2 (or boats, or planes, or sound signals, etc.). The two swimmers must each swim the same distance, but Sw1 will swim along the river flow, and Sw2 will swim perpendicularly to this direction. In all such works, it is considered that Sw2’s path will require less time and that it will reach the start point first. However, in this work, it has been determined that in order to make this possible, Sw2 must not observe the orthogonality rule of his start direction. This action would be deceitful to the arbiters and thus considered as non-fair-play towards Sw1. The article proves by swimming times calculus, that if the fair-play rules are observed, then the correct crosswise path (in water reference frame) is a right triangle instead of the isosceles triangle considered by Michelson. Consequently, the two times shall be perfectly equal and the race ends in a tie, and the myth of Sw2 as the race winner shall be debunked. Note that the same result shall also be applicable to Michelson’s interferometric experiment (ME) as well as to any similar experiment. Therefore, utilising the isosceles triangle as the transversal path in PM and also in ME is an erroneous act.展开更多
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
Finite element (FE) coupled thermal-mechanical analysis is widely used to predict the deformation and residualstress of wire arc additive manufacturing (WAAM) parts. In this study, an innovative single-layermulti-bead...Finite element (FE) coupled thermal-mechanical analysis is widely used to predict the deformation and residualstress of wire arc additive manufacturing (WAAM) parts. In this study, an innovative single-layermulti-bead profilegeometric modeling method through the isosceles trapezoid function is proposed to build the FE model of theWAAMprocess. Firstly, a straight-line model for overlapping beads based on the parabola function was establishedto calculate the optimal center distance. Then, the isosceles trapezoid-based profile was employed to replace theparabola profiles of the parabola-based overlapping model to establish an innovative isosceles trapezoid-basedmulti-bead overlapping geometric model. The rationality of the isosceles trapezoid-based overlapping model wasconfirmed by comparing the geometric deviation and the heat dissipation performance index of the two overlappingmodels. In addition, the FE-coupled thermal-mechanical analysis, as well as a comparative experiment of thesingle-layer eight-bead deposition process show that the simulation results of the above two models agree with theexperimental results. At the same time, the proposed isosceles trapezoid-based overlappingmodels are all straightlineprofiles, which can be divided into high-quality FE elements. It can improve the modeling efficiency andshorten the simulation calculation time. The innovative modeling method proposed in this study can provide anefficient and high-precision geometricmodelingmethod forWAAMpart FE coupled thermal-mechanical analysis.展开更多
以单极子、偶极子和四极子声源为例,研究了在包围声源的四面体等腰三角形测量面上采用等腰三角形扫描路径应用扫描声强法测量声功率的收敛特性,并以扫描声强测量误差为目标函数,以等腰三角形扫描测量面的大小、测量面到声源的距离和扫...以单极子、偶极子和四极子声源为例,研究了在包围声源的四面体等腰三角形测量面上采用等腰三角形扫描路径应用扫描声强法测量声功率的收敛特性,并以扫描声强测量误差为目标函数,以等腰三角形扫描测量面的大小、测量面到声源的距离和扫描线密度为设计变量,应用遗传算法进行了优化.依此优化方法确定测量面的各几何参数,保证了测量精度,提高了测量效率,为快速准确地测量声功率提供了依据.
Abstract：
To measure the measuring surfaces of isosceles triangle from tetrahedron which surround sound source by the method of isosceles triangle path scanning, the monopole source, dipole source and quadrupole source are taken as examples. The scanning sound intensity method can get the convergent feature of sound power. The convergent feature is studied. The error analysis of scanning sound intensity as objective function, the design variable which made up of the sizeof scanning measuring surfaces of isosceles triangle, the distance between measuring surface and sound source, and the density of scanning line, all of which optimized by GA. This optimization determines the geometry parameters of measuring surface, ensures the measuring accuracy, also improves the measuring efficiency . They lays a solid foundation for swiftly and accurately measuring sound power of sound source.展开更多
Deformation twinning serves as an important mode of plastic dissipation processes in nanoscale body-centered cubic(BCC)metals,but its origin and spatio-temporal features are mysterious.Here,applying in situ tensile ex...Deformation twinning serves as an important mode of plastic dissipation processes in nanoscale body-centered cubic(BCC)metals,but its origin and spatio-temporal features are mysterious.Here,applying in situ tensile experiments,we report a strong size effect on mediating the twinning behaviors and twin boundary(TB)-dislocation interaction mechanisms in BCC iron(Fe)nanowires(NWs).There exists a critical diameter(d)of∼2.5 nm,above which the deformation twinning rather than dislocation slip dominates the plasticity.Unlike the traditional reflection TBs,the intermediate isosceles TBs are consis-tently observed as mediated by the 1/12<111>partial dislocations.Moreover,we uncover two distinct TB-related deformation mechanisms,including twin variant re-orientation and TB cracking for NWs with d<17 nm and d>17 nm,respectively.Further molecular dynamics and statics simulations provide the basic underlying mechanisms for size-dependent plasticity,which have been largely overlooked in previous experimental investigations.Our findings highlight the importance of grain size in mediating the deformation behaviors in Fe,serving as possible guidance for exploring single-crystalline and poly-crystalline Fe-based materials(e.g.steel)with optimized mechanical performance.展开更多
The ternary rare-earth aluminum germanide GdAlGe with tetragonal structure is systematically studied by x-ray diffraction,magnetic and electric measurements.The magnetic and electric properties of GdAlGe are strongly ...The ternary rare-earth aluminum germanide GdAlGe with tetragonal structure is systematically studied by x-ray diffraction,magnetic and electric measurements.The magnetic and electric properties of GdAlGe are strongly related to its special magnetic structure formed by magnetic Gd3 isosceles triangles△s.The GdAlGe orders ferromagnetically at 21 K due to the exchanging interaction of Gd3△↑-△↑Gd3.The mechanism of magnetic transport originates from the slip scattering induced by Stoner spin fluctuation in the magnetic ordering region and the spin wave scattering induced by the thermal photon excitation and phonon scattering in the paramagnetic region.The positive magnetoresistance is observed in GdAlGe,which might be due to the disordered magnetic scatter induced by magnetic anisotropy in GdAlGe.展开更多
We investigate heat and mass transfer in an isosceles trapezoidal cavity, filled with charcoal considered as a granular porous medium. The Darcy-Brinkman-Forchheimer flow model is coupled to the energy and mass equati...We investigate heat and mass transfer in an isosceles trapezoidal cavity, filled with charcoal considered as a granular porous medium. The Darcy-Brinkman-Forchheimer flow model is coupled to the energy and mass equations with the assumption of non-thermal equilibrium. These equations are discretized by the finite volume method with an offset mesh and then solved by the line-by-line method of Thomas. The coupling between pressure and velocity is obtained by Semi-Implicit Method for Pressure Linked Equations. (SIMPLE) algorithm. The results show that the temperature in the cavity increases when the inclination angle of the sides walls decreases. The 15° inclination is selected as being able to offer better thermal performance in the cookstove combustion chamber.展开更多
Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and ge...Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the <em>l<sub>p</sub></em> space.展开更多
In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make us...In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make use of the notion of natural extension.Furthermore,using our methods,several sufficient conditions for Tingley＇s problem on symmetric absolute normalized norms on R2 are given.As applications,we present various new examples including the two-dimensional Lorentz sequence space d^（2）（ω,q） and its dual d^（2）（ω,q）＊by simple arguments.展开更多
基金Supported by the Higher Education Science Research Project(Natural Science)of Anhui Province(Grant No.2023AH050487)。
文摘In this paper,we introduce a new geometric constant R_(X)(κ)based on isosceles orthogonality.First,we explore some basic properties of this new constant and then provide several examples to estimate its exact values in certain specific Banach spaces.Next,we investigate the relationships between this new constant and other classical constants.Specifically,we establish an inequality relationship between it and the J(X)constant,as well as an identity relationship between it and theρX(t)constant.Furthermore,we characterize some geometric properties of Banach spaces by means of this new constant.Finally,by restricting the above-mentioned constant to the unit sphere,we introduce another new constant,calculate its upper and lower bounds,and present a relevant example.
文摘In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.
文摘The article initially reviews various works describing the physical model (PM) of Michelson’s interferometric experiment (ME), represented by the race between two swimmers Sw1, Sw2 (or boats, or planes, or sound signals, etc.). The two swimmers must each swim the same distance, but Sw1 will swim along the river flow, and Sw2 will swim perpendicularly to this direction. In all such works, it is considered that Sw2’s path will require less time and that it will reach the start point first. However, in this work, it has been determined that in order to make this possible, Sw2 must not observe the orthogonality rule of his start direction. This action would be deceitful to the arbiters and thus considered as non-fair-play towards Sw1. The article proves by swimming times calculus, that if the fair-play rules are observed, then the correct crosswise path (in water reference frame) is a right triangle instead of the isosceles triangle considered by Michelson. Consequently, the two times shall be perfectly equal and the race ends in a tie, and the myth of Sw2 as the race winner shall be debunked. Note that the same result shall also be applicable to Michelson’s interferometric experiment (ME) as well as to any similar experiment. Therefore, utilising the isosceles triangle as the transversal path in PM and also in ME is an erroneous act.
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the National Natural Science Foundation of China(Grant No.51705287)the Scientific Research Foundation of Hubei Provincial Education Department(Grant No.D20211203).
文摘Finite element (FE) coupled thermal-mechanical analysis is widely used to predict the deformation and residualstress of wire arc additive manufacturing (WAAM) parts. In this study, an innovative single-layermulti-bead profilegeometric modeling method through the isosceles trapezoid function is proposed to build the FE model of theWAAMprocess. Firstly, a straight-line model for overlapping beads based on the parabola function was establishedto calculate the optimal center distance. Then, the isosceles trapezoid-based profile was employed to replace theparabola profiles of the parabola-based overlapping model to establish an innovative isosceles trapezoid-basedmulti-bead overlapping geometric model. The rationality of the isosceles trapezoid-based overlapping model wasconfirmed by comparing the geometric deviation and the heat dissipation performance index of the two overlappingmodels. In addition, the FE-coupled thermal-mechanical analysis, as well as a comparative experiment of thesingle-layer eight-bead deposition process show that the simulation results of the above two models agree with theexperimental results. At the same time, the proposed isosceles trapezoid-based overlappingmodels are all straightlineprofiles, which can be divided into high-quality FE elements. It can improve the modeling efficiency andshorten the simulation calculation time. The innovative modeling method proposed in this study can provide anefficient and high-precision geometricmodelingmethod forWAAMpart FE coupled thermal-mechanical analysis.
文摘以单极子、偶极子和四极子声源为例,研究了在包围声源的四面体等腰三角形测量面上采用等腰三角形扫描路径应用扫描声强法测量声功率的收敛特性,并以扫描声强测量误差为目标函数,以等腰三角形扫描测量面的大小、测量面到声源的距离和扫描线密度为设计变量,应用遗传算法进行了优化.依此优化方法确定测量面的各几何参数,保证了测量精度,提高了测量效率,为快速准确地测量声功率提供了依据.
Abstract：
To measure the measuring surfaces of isosceles triangle from tetrahedron which surround sound source by the method of isosceles triangle path scanning, the monopole source, dipole source and quadrupole source are taken as examples. The scanning sound intensity method can get the convergent feature of sound power. The convergent feature is studied. The error analysis of scanning sound intensity as objective function, the design variable which made up of the sizeof scanning measuring surfaces of isosceles triangle, the distance between measuring surface and sound source, and the density of scanning line, all of which optimized by GA. This optimization determines the geometry parameters of measuring surface, ensures the measuring accuracy, also improves the measuring efficiency . They lays a solid foundation for swiftly and accurately measuring sound power of sound source.
基金supported by the National Natural Science Foundation of China (Nos.52071237,12074290,51871169,52101021,and 12104345)the Natural Science Foundation of Jiangsu Province (No.BK20191187)+1 种基金the Young Top-notch Talent Cultivation Program of Hubei Province,the Science and Technology Program of Shenzhen (No.JCYJ20190808150407522)the China Postdoctoral Science Foundation (No.2019M652685).
文摘Deformation twinning serves as an important mode of plastic dissipation processes in nanoscale body-centered cubic(BCC)metals,but its origin and spatio-temporal features are mysterious.Here,applying in situ tensile experiments,we report a strong size effect on mediating the twinning behaviors and twin boundary(TB)-dislocation interaction mechanisms in BCC iron(Fe)nanowires(NWs).There exists a critical diameter(d)of∼2.5 nm,above which the deformation twinning rather than dislocation slip dominates the plasticity.Unlike the traditional reflection TBs,the intermediate isosceles TBs are consis-tently observed as mediated by the 1/12<111>partial dislocations.Moreover,we uncover two distinct TB-related deformation mechanisms,including twin variant re-orientation and TB cracking for NWs with d<17 nm and d>17 nm,respectively.Further molecular dynamics and statics simulations provide the basic underlying mechanisms for size-dependent plasticity,which have been largely overlooked in previous experimental investigations.Our findings highlight the importance of grain size in mediating the deformation behaviors in Fe,serving as possible guidance for exploring single-crystalline and poly-crystalline Fe-based materials(e.g.steel)with optimized mechanical performance.
文摘The ternary rare-earth aluminum germanide GdAlGe with tetragonal structure is systematically studied by x-ray diffraction,magnetic and electric measurements.The magnetic and electric properties of GdAlGe are strongly related to its special magnetic structure formed by magnetic Gd3 isosceles triangles△s.The GdAlGe orders ferromagnetically at 21 K due to the exchanging interaction of Gd3△↑-△↑Gd3.The mechanism of magnetic transport originates from the slip scattering induced by Stoner spin fluctuation in the magnetic ordering region and the spin wave scattering induced by the thermal photon excitation and phonon scattering in the paramagnetic region.The positive magnetoresistance is observed in GdAlGe,which might be due to the disordered magnetic scatter induced by magnetic anisotropy in GdAlGe.
文摘We investigate heat and mass transfer in an isosceles trapezoidal cavity, filled with charcoal considered as a granular porous medium. The Darcy-Brinkman-Forchheimer flow model is coupled to the energy and mass equations with the assumption of non-thermal equilibrium. These equations are discretized by the finite volume method with an offset mesh and then solved by the line-by-line method of Thomas. The coupling between pressure and velocity is obtained by Semi-Implicit Method for Pressure Linked Equations. (SIMPLE) algorithm. The results show that the temperature in the cavity increases when the inclination angle of the sides walls decreases. The 15° inclination is selected as being able to offer better thermal performance in the cookstove combustion chamber.
文摘Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the <em>l<sub>p</sub></em> space.
文摘In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make use of the notion of natural extension.Furthermore,using our methods,several sufficient conditions for Tingley＇s problem on symmetric absolute normalized norms on R2 are given.As applications,we present various new examples including the two-dimensional Lorentz sequence space d^（2）（ω,q） and its dual d^（2）（ω,q）＊by simple arguments.
