Wind loading is one of the most important loads for controlling the design of large-span roof structures. Equivalent static wind loads, which can generally aim at determining a specific response, are widely used by st...Wind loading is one of the most important loads for controlling the design of large-span roof structures. Equivalent static wind loads, which can generally aim at determining a specific response, are widely used by structural designers. A method for equivalent static wind loads applicable to multi-responses is proposed in this paper. A modified load- response-correlation （LRC） method corresponding to a particular peak response is presented, and the similarity algorithm implemented for the group response is described. The main idea of the algorithm is that two responses can be put into one group if the value of one response is close to that of the other response, when the structure is subjected to equivalent static wind loads aiming at the other response. Based on the modified LRC, the grouping response method is put forward to construct equivalent static wind loading. This technique can simultaneously reproduce peak responses for some grouped responses. To verify its computational accuracy, the method is applied to an actual large-span roof structure. Calculation results show that when the similarity of responses in the same group is high, equivalent static wind loads with high accuracy and reasonable magnitude of equivalent static wind distribution can be achieved.展开更多
Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state ...Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map_germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.展开更多
Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules an...Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer Burkhard in a p-modular system for an arbitrary subgroup H of G. It is proved that naturally Morita equivalent blocks are equivalent blocks and Morita equivalent via a bimodule with trivial source.展开更多
Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pytha...Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv<sup>2</sup> leads to Einstein’s celebrated maximal energy equation E = mc<sup>2</sup> and how in turn this can be dissected into the ordinary energy density E(O) = mc<sup>2</sup>/22 and the dark energy density E(D) = mc<sup>2</sup>(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.展开更多
We analyze the phenomena of phase group synchronization between the different nominal frequency signals and propose a new theory of the equivalent comparison between them. The exact expression of the equivalent compar...We analyze the phenomena of phase group synchronization between the different nominal frequency signals and propose a new theory of the equivalent comparison between them. The exact expression of the equivalent comparison is deduced. High resolution frequency measurement and phase comparison can be realized using this theory with the divider. For avoiding the frequency mixing, multiplication and synthesis, the system phase noise is improved and the higher resolution comparison and measurement are achieved between the different nominal frequencies by theory.展开更多
The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and Myasnikov also prove that ...The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and Myasnikov also prove that the elementary theory of free groups is decidable. For a group ring they have proved that the first-order theory (in the language of ring theory) is not decidable and have studied equations over group rings, especially for torsion-free hyperbolic groups. In this note we examine and survey extensions of Tarksi-like results to the collection of group rings and examine relationships between the universal and elementary theories of the corresponding groups and rings and the corresponding universal theory of the formed group ring. To accomplish this we introduce different first-order languages with equality whose model classes are respectively groups, rings and group rings. We prove that if R[G] is elementarily equivalent to S[H] then simultaneously the group G is elementarily equivalent to the group H and the ring R is elementarily equivalent to the ring S with respect to the appropriate languages. Further if G is universally equivalent to a nonabelian free group F and R is universally equivalent to the integers Z then R[G] is universally equivalent to Z[F] again with respect to an ap-propriate language.展开更多
Let IHn be the (2n+1)-dimensional Heisenberg group. In this paper, we shall give among other things, the properties of some homogeneous norms relative to dilations on the IHn and prove the equivalence of these norms.
We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Pro...We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that ifT, T1 and T2 are irreducible operators with T T1≌T T2, then T1≌T2. Finally,weshow that K0 (A(D))≌Z, giving a new result on the K0-group of Banach algebras.展开更多
This study is to investigate the effectiveness and safety of bloodletting puncture(BP)for acute ischemic stroke(AIS)when used in combination with standard treatment,as well as the patients'feelings and attitudes t...This study is to investigate the effectiveness and safety of bloodletting puncture(BP)for acute ischemic stroke(AIS)when used in combination with standard treatment,as well as the patients'feelings and attitudes toward the treatment.This is a mixed method research which includes a multi-center,superiority,randomized controlled clinical trial,and focus group interview.A total of 360 AIS participants will be enrolled.They will be randomized into one of the following two groups for 7 d:(a)BP with standard treatment group(n=180);(b)standard treatment group(n=180).The primary outcome will be National Institute of Health stroke scale(NIHSS)score at day 7 after treatment.Secondary outcomes will be changes of Glasgow Coma Scale score,NIHSS score,mRS and Traditional Chinese Medicine syndrome score from baseline to 7,14,and 30 d after treatment,recurrence rate and all-cause mortality rate within 30 d,and the safety assessments.The focus group will be conducted with a purposive sample of 1-2 acupuncturists and 1-2 patients respectively at each center at 7 and 30 d after treatment.We designed a mixed method study to evaluate the effect of BP,an acupuncture therapy for patients with AIS.If the findings of this study confirm the effectiveness of BP to reduce the NIHSS score and other related outcomes and patients are willing to accept the therapy,we believe this study will help the implementation of this therapy in clinical practice,and provide new evidence for the treatment of AIS.展开更多
Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract ...Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.展开更多
The relationship between symmetries and Gauss kernels for the SchrSdinger equation iut = uxx ＋ f（x）u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral...The relationship between symmetries and Gauss kernels for the SchrSdinger equation iut = uxx ＋ f（x）u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schroedinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.展开更多
The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ...The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.展开更多
The aim of this study is to establish that, the equivalent class <img src="Edit_d35dd794-39a5-4ce4-992b-5130559b3c82.png" width="70" height="22" alt="" /> which is made up...The aim of this study is to establish that, the equivalent class <img src="Edit_d35dd794-39a5-4ce4-992b-5130559b3c82.png" width="70" height="22" alt="" /> which is made up of homotopic loops is a group with respect to <img src="Edit_3577ec7c-e6f5-4d71-8bd5-c63ea8fdb24f.png" width="30" height="15" alt="" /> in the general interval <span style="white-space:nowrap;">[m,n]. The study proved from homotopical point of view that <img src="Edit_4cb511c3-e469-47e3-bd9c-e971594f939c.png" width="70" height="22" alt="" /> is associative, has an identity and inverse function. The study established with proof that <img src="Edit_39497a4b-b0e9-40d9-8f31-49816e760d6a.png" width="70" height="22" alt="" /> is a fundamental group in <span style="white-space:nowrap;">[m,n] ,<img src="Edit_077b19f1-afb3-41f5-8d39-df073165c9dc.png" width="75" height="18" alt="" />.展开更多
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) ...Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.展开更多
基金Ministry of Science and Technology of China Under Grant No.SLDRCE10-B-04the National Natural Science Foundation Under Grant No.50621062
文摘Wind loading is one of the most important loads for controlling the design of large-span roof structures. Equivalent static wind loads, which can generally aim at determining a specific response, are widely used by structural designers. A method for equivalent static wind loads applicable to multi-responses is proposed in this paper. A modified load- response-correlation （LRC） method corresponding to a particular peak response is presented, and the similarity algorithm implemented for the group response is described. The main idea of the algorithm is that two responses can be put into one group if the value of one response is close to that of the other response, when the structure is subjected to equivalent static wind loads aiming at the other response. Based on the modified LRC, the grouping response method is put forward to construct equivalent static wind loading. This technique can simultaneously reproduce peak responses for some grouped responses. To verify its computational accuracy, the method is applied to an actual large-span roof structure. Calculation results show that when the similarity of responses in the same group is high, equivalent static wind loads with high accuracy and reasonable magnitude of equivalent static wind distribution can be achieved.
文摘Based on the left_right equivalent relation of smooth map_germs in singularity theory, the unfoldings of multiparameter equivariant bifurcation problems with respect to left_right equivalence are discussed. The state variables of such an equivariant bifurcation problem were divided into two groups, in which the first can vary independently, while the others depend on the first in the varying process. By applying related methods and techniques in the unfolding theory of smooth map_germs, the necessary and sufficient condition for an unfolding of a multiparameter equivariant bifurcation problem with two groups of state variables to be versal is obtained.
基金Supported by the National Programfor the BasicScience Researches of China(G19990751)
文摘Let （K, O, k） be a p-modular system and G be a finite group. We prove that block A of RG and block B of RH are nalurally Morita equivalent of degree n if and only if A≌B＋…＋B}→n^2 as right R[H×H]-modules and A and B have the same defect（where R∈{k,O}）, which is a generalization of the result of Külshammer Burkhard in a p-modular system for an arbitrary subgroup H of G. It is proved that naturally Morita equivalent blocks are equivalent blocks and Morita equivalent via a bimodule with trivial source.
文摘Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv<sup>2</sup> leads to Einstein’s celebrated maximal energy equation E = mc<sup>2</sup> and how in turn this can be dissected into the ordinary energy density E(O) = mc<sup>2</sup>/22 and the dark energy density E(D) = mc<sup>2</sup>(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.
基金supported by the National Natural Science Foundation of China(Grant Nos.10978017 and 61201288)the Fundamental Research Funds for the Central Universities,China(Grant No.JB140413)
文摘We analyze the phenomena of phase group synchronization between the different nominal frequency signals and propose a new theory of the equivalent comparison between them. The exact expression of the equivalent comparison is deduced. High resolution frequency measurement and phase comparison can be realized using this theory with the divider. For avoiding the frequency mixing, multiplication and synthesis, the system phase noise is improved and the higher resolution comparison and measurement are achieved between the different nominal frequencies by theory.
文摘The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and Myasnikov also prove that the elementary theory of free groups is decidable. For a group ring they have proved that the first-order theory (in the language of ring theory) is not decidable and have studied equations over group rings, especially for torsion-free hyperbolic groups. In this note we examine and survey extensions of Tarksi-like results to the collection of group rings and examine relationships between the universal and elementary theories of the corresponding groups and rings and the corresponding universal theory of the formed group ring. To accomplish this we introduce different first-order languages with equality whose model classes are respectively groups, rings and group rings. We prove that if R[G] is elementarily equivalent to S[H] then simultaneously the group G is elementarily equivalent to the group H and the ring R is elementarily equivalent to the ring S with respect to the appropriate languages. Further if G is universally equivalent to a nonabelian free group F and R is universally equivalent to the integers Z then R[G] is universally equivalent to Z[F] again with respect to an ap-propriate language.
文摘Let IHn be the (2n+1)-dimensional Heisenberg group. In this paper, we shall give among other things, the properties of some homogeneous norms relative to dilations on the IHn and prove the equivalence of these norms.
基金The 973 Project of China and the NNSF (Grant No. 19631070) of China.
文摘We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that ifT, T1 and T2 are irreducible operators with T T1≌T T2, then T1≌T2. Finally,weshow that K0 (A(D))≌Z, giving a new result on the K0-group of Banach algebras.
基金Scientific and Technological Innovation Project of China Academy of Chinese Medical Sciences:Research Design and Application of Mixed Methods in Traditional Chinese Medicine (No.CI2021B003)Evidence-based Ability Construction Project of National Administration of Traditional Chinese Medicine:Evidencebased Ability Improvement and Platform Construction of Traditional Chinese Medicine in Encephalopathy (No.2019XZZX-NB014)+2 种基金CACMS Innovation Fund:Research Priorities on Screening and Evaluating Appropriate and Effective Health Technologies in Specific Disease Field of TCM (No.CI2021A05503)CACMS Innovation Fund:Evaluation Method and Demonstration Research of Traditional Chinese Medicine Health Technology Assessment (No.CI2021A00701-3)the Fundamental Research Funds for the Central Public Welfare Research Institutes:Evidence Mapping and Scoping Review of Chinese Patent Medicines for Clearing Heat and Detoxifying (No.ZZ13-YQ-075)
文摘This study is to investigate the effectiveness and safety of bloodletting puncture(BP)for acute ischemic stroke(AIS)when used in combination with standard treatment,as well as the patients'feelings and attitudes toward the treatment.This is a mixed method research which includes a multi-center,superiority,randomized controlled clinical trial,and focus group interview.A total of 360 AIS participants will be enrolled.They will be randomized into one of the following two groups for 7 d:(a)BP with standard treatment group(n=180);(b)standard treatment group(n=180).The primary outcome will be National Institute of Health stroke scale(NIHSS)score at day 7 after treatment.Secondary outcomes will be changes of Glasgow Coma Scale score,NIHSS score,mRS and Traditional Chinese Medicine syndrome score from baseline to 7,14,and 30 d after treatment,recurrence rate and all-cause mortality rate within 30 d,and the safety assessments.The focus group will be conducted with a purposive sample of 1-2 acupuncturists and 1-2 patients respectively at each center at 7 and 30 d after treatment.We designed a mixed method study to evaluate the effect of BP,an acupuncture therapy for patients with AIS.If the findings of this study confirm the effectiveness of BP to reduce the NIHSS score and other related outcomes and patients are willing to accept the therapy,we believe this study will help the implementation of this therapy in clinical practice,and provide new evidence for the treatment of AIS.
基金supported by the National Key Basic Research Project of China (973 Program)(No. 2004CB318000)
文摘Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.
基金supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No.10925104)the National Natural Science Foundation of China (Grant No.11001220)the Ph.D.Program Foundation of the Ministry of Education of China (Grant No.20106101110008)
文摘The relationship between symmetries and Gauss kernels for the SchrSdinger equation iut = uxx ＋ f（x）u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schroedinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified.
文摘The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.
文摘The aim of this study is to establish that, the equivalent class <img src="Edit_d35dd794-39a5-4ce4-992b-5130559b3c82.png" width="70" height="22" alt="" /> which is made up of homotopic loops is a group with respect to <img src="Edit_3577ec7c-e6f5-4d71-8bd5-c63ea8fdb24f.png" width="30" height="15" alt="" /> in the general interval <span style="white-space:nowrap;">[m,n]. The study proved from homotopical point of view that <img src="Edit_4cb511c3-e469-47e3-bd9c-e971594f939c.png" width="70" height="22" alt="" /> is associative, has an identity and inverse function. The study established with proof that <img src="Edit_39497a4b-b0e9-40d9-8f31-49816e760d6a.png" width="70" height="22" alt="" /> is a fundamental group in <span style="white-space:nowrap;">[m,n] ,<img src="Edit_077b19f1-afb3-41f5-8d39-df073165c9dc.png" width="75" height="18" alt="" />.
文摘Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal subgroup of G . For principal fibre bundle (E,p, E/G;G) and (E/H,p′,E/G;G/H), the relation between aut G(E) (resp. aut * G(E) ) and aut G/H (E/H) (resp.aut * G/H (E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group F G(E) (resp. E G(E)) while the group F G/H (E/H) is known.
