By virtue of the normal ordering of vacuum projector we directly derive some new complicated operatoridentities, regarding to the generalized Stirling number.
The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation....The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation. This partially answers a question of Domigo A. Herrero.展开更多
Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neith...Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.展开更多
Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical oper...Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector ｜q〉λ,v of linear combination of the coordinate and momentum operator, （λQ ＋ vP）, where λ,v are real numbers, and ｜q〉λv is complete, then the projector ｜q〉λ,vλ,v〈q｜ must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.展开更多
A dandelion algorithm(DA) is a recently developed intelligent optimization algorithm for function optimization problems. Many of its parameters need to be set by experience in DA,which might not be appropriate for all...A dandelion algorithm(DA) is a recently developed intelligent optimization algorithm for function optimization problems. Many of its parameters need to be set by experience in DA,which might not be appropriate for all optimization problems. A self-adapting and efficient dandelion algorithm is proposed in this work to lower the number of DA's parameters and simplify DA's structure. Only the normal sowing operator is retained;while the other operators are discarded. An adaptive seeding radius strategy is designed for the core dandelion. The results show that the proposed algorithm achieves better performance on the standard test functions with less time consumption than its competitive peers. In addition, the proposed algorithm is applied to feature selection for credit card fraud detection(CCFD), and the results indicate that it can obtain higher classification and detection performance than the-state-of-the-art methods.展开更多
For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all gen...For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.展开更多
Integrated continuous stirred-tank reactors and distillation columns with recycle(CSTR-DC-recycle)are essential components in chemical processes.This paper proposes a method to establish a normal operating zone(NOZ)mo...Integrated continuous stirred-tank reactors and distillation columns with recycle(CSTR-DC-recycle)are essential components in chemical processes.This paper proposes a method to establish a normal operating zone(NOZ)model to represent allowable variations of the CSTR-DC-recycle chemical processes.The NOZ is a geometric space containing all safe operating points of the CSTR-DC-recycle chemical processes,so that it is an effective model for process monitoring.The novelty of the proposed method is to establish the NOZ model based on boundary points.The boundary points make it possible to capture the actual geometric space irrespective of the space shape.In contrast,existing methods represent the NOZ of processes by fixed mathematical models such as ellipsoidal and convex-hull models;they are not suitable for the CSTR-DC-recycle chemical processes whose NOZs cannot be exactly defined by fixed mathematical structures.Simulated case studies based on Aspen Hysys software are given to illustrate the proposed method.展开更多
Global warming has led to a gradual extension of the navigable window for the Arctic Route,providing a realistic possibility for the normalized commercial operation of the Northeast Passage(NEP).Based on the changes i...Global warming has led to a gradual extension of the navigable window for the Arctic Route,providing a realistic possibility for the normalized commercial operation of the Northeast Passage(NEP).Based on the changes in the navigable window of the NEP,Russia’s proposed nuclear-powered icebreaker construction scheme,and China’s potential development of a moderately sized ice-class fleet,this study establishes three scenarios for the commercial operation of the NEP.These scenarios include:(a)normalized summer operational scenario(from July to October each year),(b)normalized summer-autumn operational scenario(from June to January of the following year),and(c)normalized year-round operational scenario(12 months per year).The cargo transportation potential of the NEP under three normalized operational scenarios was predicted based on the grey prediction model.On this basis,construction scale plans for China’s ice-class fleet to meet cargo transportation demands under the three normalized operational scenarios were designed.The economic benefits of different plans were evaluated using a profit-maximization linear programming model.The research results show the following:(1)The cargo transportation potential of the NEP demonstrates a rapid growth trend in the future,with annual throughput under year-round normalized operations expected to exceed 100 million tonnes and reach 297 million tonnes.(2)Under different normalized operational scenarios,the fleet scale and vessel type composition vary.Under the normalized summer operational scenario,the optimal scale for China’s ice-class fleet is 20 vessels,consisting solely of ships classed as PC7 by the International Association of Classification Societies(IACS).Under the normalized summer-autumn operational scenario,the optimal fleet scale is 31 vessels,including 30 IACS PC7 ships and 1 IACS PC3 ship.Under the normalized year-round operational scenario,the optimal fleet scale is 45 vessels,composed of 30 IACS PC7 ships,8 IACS PC3 ships,and 7 IACS PC2 ships.(3)Among the three normalized operational scenarios,the normalized year-round operational scenario yields the best economic benefits for the fleet scale,while the normalized summer operational scenario yields the lowest economic benefits.展开更多
Maximum Power Point Tracking (MPPT) algorithms are now widely used in PV systems independently of the weather conditions. In function of the application, a DC-DC converter topology is chosen without any previous perfo...Maximum Power Point Tracking (MPPT) algorithms are now widely used in PV systems independently of the weather conditions. In function of the application, a DC-DC converter topology is chosen without any previous performance test under normal weather conditions. This paper proposes an experimental evaluation of MPPT algorithms according to DC-DC converters topologies, under normal operation conditions. Four widely used MPPT algorithms <i><i><span>i.e.</span></i><span></span></i> Perturb and Observe (P & O), Hill Climbing (HC), Fixed step Increment of Conductance (INCF) and Variable step Increment of Conductance (INCV) are implemented using two topologies of DC-DC converters <i><span>i.e.</span></i><span> buck and boost converters. As input variables to the PV systems, recorded irradiance and temperature, and extracted photovoltaic parameters (ideality factor, series resistance and reverse saturation current) were used. The obtained results show that buck converter has a lot of power losses when controlled by each of the four MPPT algorithms. Meanwhile, boost converter presents a stable output power during the whole day. Once more, the results show that INCV algorithm has the best performance.</span>展开更多
In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and fo...In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.展开更多
A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is sai...A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called quasi-n-normal.We shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of 2-normal.We also give some examples of type I k-quasi-n-normal and typeⅡk-quasi-n-normal.We also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.展开更多
Given an essentially normal operator T with connected spectrum and ind (λ-T)>0 for λ in ρ F(T)∩σ(T) , and a positive number ∈ ,the authors show that theree xists a compact K with ‖K‖&...Given an essentially normal operator T with connected spectrum and ind (λ-T)>0 for λ in ρ F(T)∩σ(T) , and a positive number ∈ ,the authors show that theree xists a compact K with ‖K‖<∈ such that T+K is strongly irreducible.展开更多
The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B^n in C^n is modified....The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B^n in C^n is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ_(G,γ)(f)](z) preserves the properties of S_Ω~*(A, B), as well as strong and almost spirallikeness of type β and order α on B^n. Thus, the mappings in S_Ω~*(A, B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.展开更多
We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10874174 and 10947017/A05 the Specialized Research Fund for the Doctorial Progress of Higher Education of China under Grant No.20070358009
文摘By virtue of the normal ordering of vacuum projector we directly derive some new complicated operatoridentities, regarding to the generalized Stirling number.
文摘The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation. This partially answers a question of Domigo A. Herrero.
文摘Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.
基金Supported by National Natural Science Foundation of China under Grant Nos. 10874174 and 10775097
文摘Using the normally ordered Gaussian form of the Wigner operator we recapitulate the quantum phase space representation, we derive a new formula for searching for the classical correspondence of quantum mechanical operators; we also show that if there exists the eigenvector ｜q〉λ,v of linear combination of the coordinate and momentum operator, （λQ ＋ vP）, where λ,v are real numbers, and ｜q〉λv is complete, then the projector ｜q〉λ,vλ,v〈q｜ must be the Radon transform of Wigner operator. This approach seems concise and physical appealing.
基金supported by the Institutional Fund Projects(IFPIP-1481-611-1443)the Key Projects of Natural Science Research in Anhui Higher Education Institutions(2022AH051909)+1 种基金the Provincial Quality Project of Colleges and Universities in Anhui Province(2022sdxx020,2022xqhz044)Bengbu University 2021 High-Level Scientific Research and Cultivation Project(2021pyxm04)。
文摘A dandelion algorithm(DA) is a recently developed intelligent optimization algorithm for function optimization problems. Many of its parameters need to be set by experience in DA,which might not be appropriate for all optimization problems. A self-adapting and efficient dandelion algorithm is proposed in this work to lower the number of DA's parameters and simplify DA's structure. Only the normal sowing operator is retained;while the other operators are discarded. An adaptive seeding radius strategy is designed for the core dandelion. The results show that the proposed algorithm achieves better performance on the standard test functions with less time consumption than its competitive peers. In addition, the proposed algorithm is applied to feature selection for credit card fraud detection(CCFD), and the results indicate that it can obtain higher classification and detection performance than the-state-of-the-art methods.
文摘For an integer n ≥2, we say that an operator A is an n-idempotent if A^n = A; A is a generalized n-idempotent if A^n = A^＊; A is a hyper-generalized n. idempotent if A^n = A^＋. The set of all n-idempotents, all generalized n-idempotents and all hyper-generalized n-idempotents are denoted by In（H）, gIn（H） and HgIn（H）, respectively. In this note, we obtain a chain of proper inclusions gIn（H） belong to HgIn（H） belong to In＋2（H）.
基金partially funded by the National Natural Science Foundation of China(62273215)。
文摘Integrated continuous stirred-tank reactors and distillation columns with recycle(CSTR-DC-recycle)are essential components in chemical processes.This paper proposes a method to establish a normal operating zone(NOZ)model to represent allowable variations of the CSTR-DC-recycle chemical processes.The NOZ is a geometric space containing all safe operating points of the CSTR-DC-recycle chemical processes,so that it is an effective model for process monitoring.The novelty of the proposed method is to establish the NOZ model based on boundary points.The boundary points make it possible to capture the actual geometric space irrespective of the space shape.In contrast,existing methods represent the NOZ of processes by fixed mathematical models such as ellipsoidal and convex-hull models;they are not suitable for the CSTR-DC-recycle chemical processes whose NOZs cannot be exactly defined by fixed mathematical structures.Simulated case studies based on Aspen Hysys software are given to illustrate the proposed method.
基金Funding by Social Science Research of Ministry of Education of the People’s Republic of China“Study on issues related on the development and utilization of the Arctic Passage”(Grant no.20JHQ016)is acknowledged.
文摘Global warming has led to a gradual extension of the navigable window for the Arctic Route,providing a realistic possibility for the normalized commercial operation of the Northeast Passage(NEP).Based on the changes in the navigable window of the NEP,Russia’s proposed nuclear-powered icebreaker construction scheme,and China’s potential development of a moderately sized ice-class fleet,this study establishes three scenarios for the commercial operation of the NEP.These scenarios include:(a)normalized summer operational scenario(from July to October each year),(b)normalized summer-autumn operational scenario(from June to January of the following year),and(c)normalized year-round operational scenario(12 months per year).The cargo transportation potential of the NEP under three normalized operational scenarios was predicted based on the grey prediction model.On this basis,construction scale plans for China’s ice-class fleet to meet cargo transportation demands under the three normalized operational scenarios were designed.The economic benefits of different plans were evaluated using a profit-maximization linear programming model.The research results show the following:(1)The cargo transportation potential of the NEP demonstrates a rapid growth trend in the future,with annual throughput under year-round normalized operations expected to exceed 100 million tonnes and reach 297 million tonnes.(2)Under different normalized operational scenarios,the fleet scale and vessel type composition vary.Under the normalized summer operational scenario,the optimal scale for China’s ice-class fleet is 20 vessels,consisting solely of ships classed as PC7 by the International Association of Classification Societies(IACS).Under the normalized summer-autumn operational scenario,the optimal fleet scale is 31 vessels,including 30 IACS PC7 ships and 1 IACS PC3 ship.Under the normalized year-round operational scenario,the optimal fleet scale is 45 vessels,composed of 30 IACS PC7 ships,8 IACS PC3 ships,and 7 IACS PC2 ships.(3)Among the three normalized operational scenarios,the normalized year-round operational scenario yields the best economic benefits for the fleet scale,while the normalized summer operational scenario yields the lowest economic benefits.
文摘Maximum Power Point Tracking (MPPT) algorithms are now widely used in PV systems independently of the weather conditions. In function of the application, a DC-DC converter topology is chosen without any previous performance test under normal weather conditions. This paper proposes an experimental evaluation of MPPT algorithms according to DC-DC converters topologies, under normal operation conditions. Four widely used MPPT algorithms <i><i><span>i.e.</span></i><span></span></i> Perturb and Observe (P & O), Hill Climbing (HC), Fixed step Increment of Conductance (INCF) and Variable step Increment of Conductance (INCV) are implemented using two topologies of DC-DC converters <i><span>i.e.</span></i><span> buck and boost converters. As input variables to the PV systems, recorded irradiance and temperature, and extracted photovoltaic parameters (ideality factor, series resistance and reverse saturation current) were used. The obtained results show that buck converter has a lot of power losses when controlled by each of the four MPPT algorithms. Meanwhile, boost converter presents a stable output power during the whole day. Once more, the results show that INCV algorithm has the best performance.</span>
文摘In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found.
文摘A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called quasi-n-normal.We shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of 2-normal.We also give some examples of type I k-quasi-n-normal and typeⅡk-quasi-n-normal.We also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.
文摘Given an essentially normal operator T with connected spectrum and ind (λ-T)>0 for λ in ρ F(T)∩σ(T) , and a positive number ∈ ,the authors show that theree xists a compact K with ‖K‖<∈ such that T+K is strongly irreducible.
基金supported by the National Natural Science Foundation of China(Nos.11271359,11471098)the Joint Funds of the National Natural Science Foundation of China(No.U1204618)the Science and Technology Research Projects of Henan Provincial Education Department(Nos.14B110015,14B110016)
文摘The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The RoperSuffridge operator on the unit ball B^n in C^n is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ_(G,γ)(f)](z) preserves the properties of S_Ω~*(A, B), as well as strong and almost spirallikeness of type β and order α on B^n. Thus, the mappings in S_Ω~*(A, B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.
基金Supported by National Research Foundation of Korea(Grant No.NRF-2011-220-1-C00002)partially supported by MCT(Grant No.MTM2010-18099)supported by NRF(Grant No.NRF-2012-R1A2A2A-01043023)
文摘We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.
