Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind o...Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind of binary codebooks are constructed by using the subspace of the singular linear space over the finite fields.According to the anzahl theorem,the parameters and the maximum correlation amplitude I_(max)(C)of the codebooks are calculated,and then given the conditions that the I_(max)(C)asymptotically reaches the Welch bound.On this basis,by mixing with Hadamard matrices,the number of columns are increased and obtain another class of new code,which further relaxes the conditions that the I_(max)(C)asymptotically reaches the Welch bound.展开更多
In this paper,we investigate the properties of strongly coapproximation in normed linear spaces and lo- cally,convex spaces.The relations between strongly coapproximation and strongly unique approximation and of the f...In this paper,we investigate the properties of strongly coapproximation in normed linear spaces and lo- cally,convex spaces.The relations between strongly coapproximation and strongly unique approximation and of the f-coapproximation and f-approximation,are also considered.展开更多
Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best...Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.展开更多
This work is a contribution to the classification of linear spaces admitting a pointtransitive automorphism group. Let S be a regular linear space with 51 points, with lines of size 6, and G be an automorphism group o...This work is a contribution to the classification of linear spaces admitting a pointtransitive automorphism group. Let S be a regular linear space with 51 points, with lines of size 6, and G be an automorphism group of S. We prove that G cannot be point-transitive.展开更多
In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.
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
Some results from the theory of best (or best simultaneous) approximation in a narmed linear space have been extended to a normed almost linear space [strong normed almost linear space].
Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent develo...Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent development of using fractional telegraph equations as models in some fields (e.g., the thermal diffusion in fractal media) has heightened the importance of examining the method of solutions for such equations (both approximate and analytic). The present work is designed to serve as a valuable contribution to work in this field. The key objective of this work is to propose a general framework that can be used to guide quadratic spline functions in order to create a numerical method for obtaining an approximation solution using the linear space-fractional telegraph equation. Additionally, the Von Neumann method was employed to measure the stability of the analytical scheme, which showed that the proposed method is conditionally stable. What’s more, the proposal contains a numerical example that illustrates how the proposed method can be implemented practically, whilst the error estimates and numerical stability results are discussed in depth. The findings indicate that the proposed model is highly effective, convenient and accurate for solving the relevant problems and is suitable for use with approximate solutions acquired through the two-dimensional differential transform method that has been developed for linear partial differential equations with space- and time-fractional derivatives.展开更多
In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the ...In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.展开更多
In this article,we study the projective class ring of bosonization B(G,g,x)of quantum linear space.We classify all finite-dimensional indecomposable projective B(G,g,x)-modules and simple B(G,g,x)-modules.The decompos...In this article,we study the projective class ring of bosonization B(G,g,x)of quantum linear space.We classify all finite-dimensional indecomposable projective B(G,g,x)-modules and simple B(G,g,x)-modules.The decomposition rules for tensor products of indecomposable projective B(G,g,x)-modules and simple B(G,g,x)-modules are given,and the structures of projective class ring r_(p)(B(G,g,x))are described.It turns out that r_(p)(B(G,g,x))is a commutative ring generated by n+1 elements subject to certain relations.Finally,we classify all finite-dimensional indecomposable modules over the complexified projective class ring R_(p)(B(G,g,x)).展开更多
In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and t...In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.展开更多
Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of （ψ）-hemicontractive mapping in normed l...Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of （ψ）-hemicontractive mapping in normed linear spaces by the modified Ishikawa iterative sequences with errors is investigated. The results presented in this paper improve and extend the results of the others.展开更多
In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increa...In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.展开更多
The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a...The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a theorem of Camina and the fifth author that identifies three kinds of line-transitive automorphism groups of linear spaces. In two of these cases the group may be imprimitive on points, that is, the group leaves invariant a nontrivial partition of the point set. In the first of these cases the group is almost simple with point-transitive simple socle, and may or may not be point-primitive, while in the second case the group has a non-trivial point-intransitive normal subgroup and hence is definitely point-imprimitive. The theory presented here focuses on point-imprimitive groups. As a non-trivial application a classification is given of the point-imprimitive, line-transitive groups, and the corresponding linear spaces, for which the greatest common divisor gcd（k, v - 1） ≤ 8, where v is the number of points, and k is the line size. Motivation for this classification comes from a result of Weidong Fang and Huffing Li in 1993, that there are only finitely many non-trivial point-imprimitive, linetransitive linear spaces for a given value of gcd（k, v - 1）. The classification strengthens the classification by Camina and Mischke under the much stronger restriction k ≤ 8： no additional examples arise. The paper provides the backbone for future computer-based classifications of point-imprimitive, line- transitive linear spaces with small parameters. Several suggestions for further investigations are made.展开更多
Let G be a subgroup of the automorphism group of a non-trivial finite linear space $. In this paper we prove that if G is line-primitive with Fang-Li parameter gcd（k, r） = 11 and 12, then G is also point-primitive. ...Let G be a subgroup of the automorphism group of a non-trivial finite linear space $. In this paper we prove that if G is line-primitive with Fang-Li parameter gcd（k, r） = 11 and 12, then G is also point-primitive. This extends the results of Fang and Li （1993） and Li and Liu （2001） which combined gives the result for gcd（k,r） ≤ 10.展开更多
As a generalization of singular linear spaces, we introduce the concept of t-singular linear spaces, make some anzahl formulas of subspaces, and determine the suborbits of t-singular linear groups.
This paper is a further contribution to the classification of line- transitive finite linear spaces. We prove that if y is a non-trivial finite linear space such that the Fang-Li parameter gcd（k, r） is 9 or 10, and ...This paper is a further contribution to the classification of line- transitive finite linear spaces. We prove that if y is a non-trivial finite linear space such that the Fang-Li parameter gcd（k, r） is 9 or 10, and the group G ≤ Aut（Y） is line-transitive and point-imprimitive, then y is the Desarguesian projective plane PG（2, 9）.展开更多
This paper presents an advanced control strategy for DC-DC buck converters utilizing Non-Minimal State Space (NMSS) representation combined with Proportional-Integral-Plus (PIP) control, optimized through Linear Quadr...This paper presents an advanced control strategy for DC-DC buck converters utilizing Non-Minimal State Space (NMSS) representation combined with Proportional-Integral-Plus (PIP) control, optimized through Linear Quadratic Regulator (LQR) design. The proposed approach leverages NMSS to eliminate the need for state observers, enhancing robustness against model mismatch and improving overall system performance. The PIP controller extends traditional PI control by incorporating additional dynamic feedback. Experimental results demonstrate that the NMSS-PIP-LQR controlled buck converter achieves excellent dynamic performance. The design procedure is fully documented, and microcontroller implementation issues are discussed.展开更多
After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is u...After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is usually easy by the theorem of Delandtsheer and Doyen.The primitive ones are now subdivided,according to the O'Nan-Scotte theorem and some further work by Camina,into the socles which are an elementary abelian or non-abelian simple.In this paper,we consider the latter.Namely,T ≤ G ≤ Aut(T) and G acts line-transitively on finite linear spaces,where T is a non-abelian simple.We obtain some useful lemmas.In particular,we prove that when T is isomorphic to 3D4(q),then T is line-transitive,where q is a power of the prime p.展开更多
文摘Codebooks are widely applied in code division multiple access communication systems.Based on the subspaces of singular linear spaces over the finite fields,two classes of new codebooks are constructed.Firstly,a kind of binary codebooks are constructed by using the subspace of the singular linear space over the finite fields.According to the anzahl theorem,the parameters and the maximum correlation amplitude I_(max)(C)of the codebooks are calculated,and then given the conditions that the I_(max)(C)asymptotically reaches the Welch bound.On this basis,by mixing with Hadamard matrices,the number of columns are increased and obtain another class of new code,which further relaxes the conditions that the I_(max)(C)asymptotically reaches the Welch bound.
文摘In this paper,we investigate the properties of strongly coapproximation in normed linear spaces and lo- cally,convex spaces.The relations between strongly coapproximation and strongly unique approximation and of the f-coapproximation and f-approximation,are also considered.
文摘Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11801311 11626141)
文摘This work is a contribution to the classification of linear spaces admitting a pointtransitive automorphism group. Let S be a regular linear space with 51 points, with lines of size 6, and G be an automorphism group of S. We prove that G cannot be point-transitive.
文摘In [1],a family of angles are defined in normed linear spaces. In this paper,it is shown that if anyone of the angles satisfies certain euclidean triangle congruence properties,the space must be an inner product space.
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Some results from the theory of best (or best simultaneous) approximation in a narmed linear space have been extended to a normed almost linear space [strong normed almost linear space].
文摘Over the last few years, there has been a significant increase in attention paid to fractional differential equations, given their wide array of applications in the fields of physics and engineering. The recent development of using fractional telegraph equations as models in some fields (e.g., the thermal diffusion in fractal media) has heightened the importance of examining the method of solutions for such equations (both approximate and analytic). The present work is designed to serve as a valuable contribution to work in this field. The key objective of this work is to propose a general framework that can be used to guide quadratic spline functions in order to create a numerical method for obtaining an approximation solution using the linear space-fractional telegraph equation. Additionally, the Von Neumann method was employed to measure the stability of the analytical scheme, which showed that the proposed method is conditionally stable. What’s more, the proposal contains a numerical example that illustrates how the proposed method can be implemented practically, whilst the error estimates and numerical stability results are discussed in depth. The findings indicate that the proposed model is highly effective, convenient and accurate for solving the relevant problems and is suitable for use with approximate solutions acquired through the two-dimensional differential transform method that has been developed for linear partial differential equations with space- and time-fractional derivatives.
文摘In this paper,the k major cone and strict k major cone in real infinite dimensional linear space are introduced,through which the k major order is defined,and their properties are also discussed.Therefore,with the help of them any two elements in real infinite dimensional linear space can be compared.
文摘In this article,we study the projective class ring of bosonization B(G,g,x)of quantum linear space.We classify all finite-dimensional indecomposable projective B(G,g,x)-modules and simple B(G,g,x)-modules.The decomposition rules for tensor products of indecomposable projective B(G,g,x)-modules and simple B(G,g,x)-modules are given,and the structures of projective class ring r_(p)(B(G,g,x))are described.It turns out that r_(p)(B(G,g,x))is a commutative ring generated by n+1 elements subject to certain relations.Finally,we classify all finite-dimensional indecomposable modules over the complexified projective class ring R_(p)(B(G,g,x)).
基金the National Natural Science Foundation of China (60274016)the Project of Scientific Research in Hight Education Bureau Liaoning Province (2023901018).
文摘In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.
文摘Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of （ψ）-hemicontractive mapping in normed linear spaces by the modified Ishikawa iterative sequences with errors is investigated. The results presented in this paper improve and extend the results of the others.
文摘In detailed aerodynamic design optimization,a large number of design variables in geometry parameterization are required to provide sufficient flexibility and obtain the potential optimum shape.However,with the increasing number of design variables,it becomes difficult to maintain the smoothness on the surface which consequently makes the optimization process progressively complex.In this paper,smoothing methods based on B-spline functions are studied to improve the smoothness and design efficiency.The wavelet smoothing method and the least square smoothing method are developed through coordinate transformation in a linear space constructed by B-spline basis functions.In these two methods,smoothing is achieved by a mapping from the linear space to itself such that the design space remains unchanged.A design example is presented where aerodynamic optimization of a supercritical airfoil is conducted with smoothing methods included in the optimization loop.Affirmative results from the design example confirm that these two smoothing methods can greatly improve quality and efficiency compared with the existing conventional non-smoothing method.
基金Supported by Australian Research Council(Grant Nos. DP0557587 and DP0209706)The fifth author is supported by Australian Research Council Federation Fellowship FF0776186The sixth author is partly supported by the NSF of Guangdong Province
文摘The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a theorem of Camina and the fifth author that identifies three kinds of line-transitive automorphism groups of linear spaces. In two of these cases the group may be imprimitive on points, that is, the group leaves invariant a nontrivial partition of the point set. In the first of these cases the group is almost simple with point-transitive simple socle, and may or may not be point-primitive, while in the second case the group has a non-trivial point-intransitive normal subgroup and hence is definitely point-imprimitive. The theory presented here focuses on point-imprimitive groups. As a non-trivial application a classification is given of the point-imprimitive, line-transitive groups, and the corresponding linear spaces, for which the greatest common divisor gcd（k, v - 1） ≤ 8, where v is the number of points, and k is the line size. Motivation for this classification comes from a result of Weidong Fang and Huffing Li in 1993, that there are only finitely many non-trivial point-imprimitive, linetransitive linear spaces for a given value of gcd（k, v - 1）. The classification strengthens the classification by Camina and Mischke under the much stronger restriction k ≤ 8： no additional examples arise. The paper provides the backbone for future computer-based classifications of point-imprimitive, line- transitive linear spaces with small parameters. Several suggestions for further investigations are made.
文摘Let G be a subgroup of the automorphism group of a non-trivial finite linear space $. In this paper we prove that if G is line-primitive with Fang-Li parameter gcd（k, r） = 11 and 12, then G is also point-primitive. This extends the results of Fang and Li （1993） and Li and Liu （2001） which combined gives the result for gcd（k,r） ≤ 10.
文摘As a generalization of singular linear spaces, we introduce the concept of t-singular linear spaces, make some anzahl formulas of subspaces, and determine the suborbits of t-singular linear groups.
文摘This paper is a further contribution to the classification of line- transitive finite linear spaces. We prove that if y is a non-trivial finite linear space such that the Fang-Li parameter gcd（k, r） is 9 or 10, and the group G ≤ Aut（Y） is line-transitive and point-imprimitive, then y is the Desarguesian projective plane PG（2, 9）.
文摘This paper presents an advanced control strategy for DC-DC buck converters utilizing Non-Minimal State Space (NMSS) representation combined with Proportional-Integral-Plus (PIP) control, optimized through Linear Quadratic Regulator (LQR) design. The proposed approach leverages NMSS to eliminate the need for state observers, enhancing robustness against model mismatch and improving overall system performance. The PIP controller extends traditional PI control by incorporating additional dynamic feedback. Experimental results demonstrate that the NMSS-PIP-LQR controlled buck converter achieves excellent dynamic performance. The design procedure is fully documented, and microcontroller implementation issues are discussed.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10471152).
文摘After the classification of flag-transitive linear spaces,attention has now turned to line-transitive linear spaces.Such spaces are first divided into the point-imprimitive and the point-primitive,the first class is usually easy by the theorem of Delandtsheer and Doyen.The primitive ones are now subdivided,according to the O'Nan-Scotte theorem and some further work by Camina,into the socles which are an elementary abelian or non-abelian simple.In this paper,we consider the latter.Namely,T ≤ G ≤ Aut(T) and G acts line-transitively on finite linear spaces,where T is a non-abelian simple.We obtain some useful lemmas.In particular,we prove that when T is isomorphic to 3D4(q),then T is line-transitive,where q is a power of the prime p.
