In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
Trinomial permutation polynomials of the form xr(ax2s + bxs + c) over Fq have been studied where 3|q-1 and s = (q-1)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynom...Trinomial permutation polynomials of the form xr(ax2s + bxs + c) over Fq have been studied where 3|q-1 and s = (q-1)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynomials, and construct some examples. Moreover, we discuss the relationship between permutation trinomials of the given type over a tower of finite fields.展开更多
The problem in practice of determining the proper combination of Z<sub>i</sub> in a set of changegears may be abstracted to the problem of finding the proper combination and permutation ofthe elements a<...The problem in practice of determining the proper combination of Z<sub>i</sub> in a set of changegears may be abstracted to the problem of finding the proper combination and permutation ofthe elements a<sub>i,i+1</sub> of the set A<sub>1</sub> to give maximum M-d. Some results to find optimal combina-tions of the elements of the set A<sub>1</sub> have been reported in part I. In this part, some rules forpermuting these elements are introduced. By means of these rules, three kinds of intercalated setsof A<sub>1</sub> have been found, namely: （1） Sets with an even left wing, （2） Sets with coincidence of bothwings, and （3） Sets with circulated elements.展开更多
The traditional academic warning methods for students in higher vocational colleges are relatively backward,single,and have many influencing factors,which have a limited effect on improving their learning ability.A da...The traditional academic warning methods for students in higher vocational colleges are relatively backward,single,and have many influencing factors,which have a limited effect on improving their learning ability.A data set was established by collecting academic warning data of students in a certain university.The importance of the school,major,grade,and warning level for the students was analyzed using the Pearson correlation coefficient,random forest variable importance,and permutation importance.It was found that the characteristic of the major has a great impact on the academic warning level.Countermeasures such as dynamic adjustment of majors,reform of cognitive adaptation of courses,full-cycle academic support,and data-driven precise intervention were proposed to provide theoretical support and practical paths for universities to improve the efficiency of academic warning and enhance students’learning ability.展开更多
The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because o...The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.展开更多
A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)...A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)which avoid patternsσ_(1),σ_(2),...,σ_(r).The aim of this paper is to investigate when,for certain patternsσ_(1),σ_(2),...,σ_(r),S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.We prove that for any{σ_(1),σ_(2),...,σ_(r)}?S_3,if{σ_(1),σ_(2),...,σ_(r)}is sign-balanced except for{132,213,231,312},then S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.In addition,we give some results in the case of avoiding some patterns of length 4.展开更多
Purpose–High-speed turnouts are more complex in structure and thus may cause abnormal vibration of highspeed train car body,affecting driving safety and passenger riding experience.Therefore,it is necessary to analyz...Purpose–High-speed turnouts are more complex in structure and thus may cause abnormal vibration of highspeed train car body,affecting driving safety and passenger riding experience.Therefore,it is necessary to analyze the data characteristics of continuous hunting of high-speed trains passing through turnouts and propose a diagnostic method for engineering applications.Design/methodology/approach–First,Complete Ensemble Empirical Mode Decomposition with Adaptive Noise(CEEMDAN)is performed to determine the first characteristic component of the car body’s lateral acceleration.Then,the Short-Time Fourier Transform(STFT)is performed to calculate the marginal spectra.Finally,the presence of a continuous hunting problem is determined based on the results of the comparison calculations and diagnostic thresholds.To improve computational efficiency,permutation entropy(PE)is used as a fast indicator to identify turnouts with potential problems.Findings–Under continuous hunting conditions,the PE is less than 0.90;the ratio of the maximum peak value of the signal component to the original signal peak value exceeded 0.7,and there is an energy band in the STFT time-frequency map,which corresponds to a frequency distribution range of 1–2 Hz.Originality/value–The research results have revealed the lateral vibration characteristics of the high-speed train’s car body during continuous hunting when passing through turnouts.On this basis,an effective diagnostic method has been proposed.With a focus on practical engineering applications,a rapid screening index for identifying potential issues has been proposed,significantly enhancing the efficiency of diagnostic processes.展开更多
Constructing permutation polynomials is a hot topic in finite fields,and permutation polynomials have many applications in dif‐ferent areas.In this paper,by using monomials on the cosets of a subgroup to characterize...Constructing permutation polynomials is a hot topic in finite fields,and permutation polynomials have many applications in dif‐ferent areas.In this paper,by using monomials on the cosets of a subgroup to characterize the permutational property of rational functions onμq+1,we construct a class of permutation quadrinomials with the form f_(r,a,b,c,s,t,u)(x)=x^(r)(1+ax^(s(q-1))+bx^(t(q-1))+cxu(q-1))of F_(q^(2)).展开更多
As data becomes increasingly complex,measuring dependence among variables is of great interest.However,most existing measures of dependence are limited to the Euclidean setting and cannot effectively characterize the ...As data becomes increasingly complex,measuring dependence among variables is of great interest.However,most existing measures of dependence are limited to the Euclidean setting and cannot effectively characterize the complex relationships.In this paper,we propose a novel method for constructing independence tests for random elements in Hilbert spaces,which includes functional data as a special case.Our approach is using distance covariance of random projections to build a test statistic that is computationally efficient and exhibits strong power performance.We prove the equivalence between testing for independence expressed on the original and the projected covariates,bridging the gap between measures of testing independence in Euclidean spaces and Hilbert spaces.Implementation of the test involves calibration by permutation and combining several p-values from different projections using the false discovery rate method.Simulation studies and real data examples illustrate the finite sample properties of the proposed method under a variety of scenarios.展开更多
Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar ...Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.展开更多
The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,tr...The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,traditional encryption algorithms demand considerable computational effort for real-time audio encryption.To address these challenges,this paper presents a permutation for secure audio encryption using a combination of Tent and 1D logistic maps.The audio data is first shuffled using Tent map for the random permutation.The high random secret key with a length equal to the size of the audio data is then generated using a 1D logistic map.Finally,the Exclusive OR(XOR)operation is applied between the generated key and the shuffled audio to yield the cipher audio.The experimental results prove that the proposed method surpassed the other techniques by encrypting two types of audio files,as mono and stereo audio files with large sizes up to 122 MB,different sample rates 22,050,44,100,48,000,and 96,000 for WAV and 44,100 sample rates for MP3 of size 11 MB.The results show high Mean Square Error(MSE),low Signal-to-Noise Ratio(SNR),spectral distortion,100%Number of Sample Change Rate(NSCR),high Percent Residual Deviation(PRD),low Correlation Coefficient(CC),large key space 2^(616),high sensitivity to a slight change in the secret key and that it can counter several attacks,namely brute force attack,statistical attack,differential attack,and noise attack.展开更多
In this paper,the transferable belief model established on power sets is extended to the permutation event space(PES)and is referred to as the layer-2 transferable belief model.Our goal is to provide a comprehensive a...In this paper,the transferable belief model established on power sets is extended to the permutation event space(PES)and is referred to as the layer-2 transferable belief model.Our goal is to provide a comprehensive approach for handling and modeling uncertainty,capable of representing both quantitative and qualitative information.First,the motivation for proposing the layer-2 transferable belief model and its information processing principles are explored from the perspective of weak propensity.Then,based on these principles,the corresponding information processing methods for the credal and pignistic levels are developed.Finally,the advantages of this model are validated through a classifier that leverages attribute fusion to enhance performance and decision-making accuracy.展开更多
The cascade of reversible logic gate network with n inputs and n outputs forms a group isomorphic to the symmetric group S2^n. Characteristics of a number of gates from the set of all generalized Toffoli gates are stu...The cascade of reversible logic gate network with n inputs and n outputs forms a group isomorphic to the symmetric group S2^n. Characteristics of a number of gates from the set of all generalized Toffoli gates are studied. Any permutation Sn is proved to be generated by a n-cycle 9 and a permutation τ= （ij,ik） together. It shows that any neighboring 2-cycle permutation can be generated by at most two NOT gates without ancilla bit. Based on the above theory, a cascade algorithm for reversible logic gate networks is proposed. A reversible example of logic gate network cascade is given to show the correctness of the algorithm.展开更多
A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship amon...A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship among the components of a graphic object. Using two kinds of matching constraints dynamically generated in the matching process, the proposed approach can prune most improper mappings between SRGs during the matching process. According to our theoretical analysis in this paper, the time complexity of our approach is O(n 2) in the best case, and O(n!) in the worst case, which occurs infrequently. The spatial complexity is always O(n) for all cases. Implemented in Smart Sketchpad, our proposed strategy is of good performance.展开更多
Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is...Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is any transcendental entire function with h′(z)=0 having infinitely many solutions, p(z) is a polynomial with deg p ≥2 and a(≠0) ∈ C .展开更多
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘Trinomial permutation polynomials of the form xr(ax2s + bxs + c) over Fq have been studied where 3|q-1 and s = (q-1)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynomials, and construct some examples. Moreover, we discuss the relationship between permutation trinomials of the given type over a tower of finite fields.
文摘The problem in practice of determining the proper combination of Z<sub>i</sub> in a set of changegears may be abstracted to the problem of finding the proper combination and permutation ofthe elements a<sub>i,i+1</sub> of the set A<sub>1</sub> to give maximum M-d. Some results to find optimal combina-tions of the elements of the set A<sub>1</sub> have been reported in part I. In this part, some rules forpermuting these elements are introduced. By means of these rules, three kinds of intercalated setsof A<sub>1</sub> have been found, namely: （1） Sets with an even left wing, （2） Sets with coincidence of bothwings, and （3） Sets with circulated elements.
基金supported by the Basic Ability Improvement Project of Young and Middle-Aged Teachers in Colleges and Universities of Guangxi(2022KY1922,2021KY1938).
文摘The traditional academic warning methods for students in higher vocational colleges are relatively backward,single,and have many influencing factors,which have a limited effect on improving their learning ability.A data set was established by collecting academic warning data of students in a certain university.The importance of the school,major,grade,and warning level for the students was analyzed using the Pearson correlation coefficient,random forest variable importance,and permutation importance.It was found that the characteristic of the major has a great impact on the academic warning level.Countermeasures such as dynamic adjustment of majors,reform of cognitive adaptation of courses,full-cycle academic support,and data-driven precise intervention were proposed to provide theoretical support and practical paths for universities to improve the efficiency of academic warning and enhance students’learning ability.
基金supported in part by the National Key Research and Development Program of China under Grant No.2021YFF0901300in part by the National Natural Science Foundation of China under Grant Nos.62173076 and 72271048.
文摘The distributed permutation flow shop scheduling problem(DPFSP)has received increasing attention in recent years.The iterated greedy algorithm(IGA)serves as a powerful optimizer for addressing such a problem because of its straightforward,single-solution evolution framework.However,a potential draw-back of IGA is the lack of utilization of historical information,which could lead to an imbalance between exploration and exploitation,especially in large-scale DPFSPs.As a consequence,this paper develops an IGA with memory and learning mechanisms(MLIGA)to efficiently solve the DPFSP targeted at the mini-malmakespan.InMLIGA,we incorporate a memory mechanism to make a more informed selection of the initial solution at each stage of the search,by extending,reconstructing,and reinforcing the information from previous solutions.In addition,we design a twolayer cooperative reinforcement learning approach to intelligently determine the key parameters of IGA and the operations of the memory mechanism.Meanwhile,to ensure that the experience generated by each perturbation operator is fully learned and to reduce the prior parameters of MLIGA,a probability curve-based acceptance criterion is proposed by combining a cube root function with custom rules.At last,a discrete adaptive learning rate is employed to enhance the stability of the memory and learningmechanisms.Complete ablation experiments are utilized to verify the effectiveness of the memory mechanism,and the results show that this mechanism is capable of improving the performance of IGA to a large extent.Furthermore,through comparative experiments involving MLIGA and five state-of-the-art algorithms on 720 benchmarks,we have discovered that MLI-GA demonstrates significant potential for solving large-scale DPFSPs.This indicates that MLIGA is well-suited for real-world distributed flow shop scheduling.
基金Supported by the National Natural Science Foundation of China(Grant No.12061030)the Natural Science Foundation of Hainan Province(Grant No.122RC652)2023 Excellent Science and Technology Innovation Team of Jiangsu Province Universities(Real-Time Industrial Internet of Things).
文摘A set of permutations is called sign-balanced if the set contains the same number of even permutations as odd permutations.Let S_(n)(σ_(1),σ_(2),...,σ_(r))denote the set of permutations in the symmetric group S_(n)which avoid patternsσ_(1),σ_(2),...,σ_(r).The aim of this paper is to investigate when,for certain patternsσ_(1),σ_(2),...,σ_(r),S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.We prove that for any{σ_(1),σ_(2),...,σ_(r)}?S_3,if{σ_(1),σ_(2),...,σ_(r)}is sign-balanced except for{132,213,231,312},then S_(n)(σ_(1),σ_(2),...,σ_(r))is sign-balanced for every integer n>1.In addition,we give some results in the case of avoiding some patterns of length 4.
基金support from the funds of National Natural Science Foundation of China(52308473)China Academy of Railway Science Corporation Limited(2022YJ192)are gratefully acknowledged。
文摘Purpose–High-speed turnouts are more complex in structure and thus may cause abnormal vibration of highspeed train car body,affecting driving safety and passenger riding experience.Therefore,it is necessary to analyze the data characteristics of continuous hunting of high-speed trains passing through turnouts and propose a diagnostic method for engineering applications.Design/methodology/approach–First,Complete Ensemble Empirical Mode Decomposition with Adaptive Noise(CEEMDAN)is performed to determine the first characteristic component of the car body’s lateral acceleration.Then,the Short-Time Fourier Transform(STFT)is performed to calculate the marginal spectra.Finally,the presence of a continuous hunting problem is determined based on the results of the comparison calculations and diagnostic thresholds.To improve computational efficiency,permutation entropy(PE)is used as a fast indicator to identify turnouts with potential problems.Findings–Under continuous hunting conditions,the PE is less than 0.90;the ratio of the maximum peak value of the signal component to the original signal peak value exceeded 0.7,and there is an energy band in the STFT time-frequency map,which corresponds to a frequency distribution range of 1–2 Hz.Originality/value–The research results have revealed the lateral vibration characteristics of the high-speed train’s car body during continuous hunting when passing through turnouts.On this basis,an effective diagnostic method has been proposed.With a focus on practical engineering applications,a rapid screening index for identifying potential issues has been proposed,significantly enhancing the efficiency of diagnostic processes.
基金Supported by the National Natural Science Foundation of China(11926344)Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202401601)+1 种基金Doctor Talent Program of Chongqing University of Education(2023BSRC003)Undergraduate Science Research Program of Chongqing University of Education(KY20240046)。
文摘Constructing permutation polynomials is a hot topic in finite fields,and permutation polynomials have many applications in dif‐ferent areas.In this paper,by using monomials on the cosets of a subgroup to characterize the permutational property of rational functions onμq+1,we construct a class of permutation quadrinomials with the form f_(r,a,b,c,s,t,u)(x)=x^(r)(1+ax^(s(q-1))+bx^(t(q-1))+cxu(q-1))of F_(q^(2)).
基金Supported by the Grant of National Science Foundation of China(11971433)Zhejiang Gongshang University“Digital+”Disciplinary Construction Management Project(SZJ2022B004)+1 种基金Institute for International People-to-People Exchange in Artificial Intelligence and Advanced Manufacturing(CCIPERGZN202439)the Development Fund for Zhejiang College of Shanghai University of Finance and Economics(2023FZJJ15).
文摘As data becomes increasingly complex,measuring dependence among variables is of great interest.However,most existing measures of dependence are limited to the Euclidean setting and cannot effectively characterize the complex relationships.In this paper,we propose a novel method for constructing independence tests for random elements in Hilbert spaces,which includes functional data as a special case.Our approach is using distance covariance of random projections to build a test statistic that is computationally efficient and exhibits strong power performance.We prove the equivalence between testing for independence expressed on the original and the projected covariates,bridging the gap between measures of testing independence in Euclidean spaces and Hilbert spaces.Implementation of the test involves calibration by permutation and combining several p-values from different projections using the false discovery rate method.Simulation studies and real data examples illustrate the finite sample properties of the proposed method under a variety of scenarios.
基金supported by the National Natural Science Foundation of China under Grant Nos.92265209,11174081 and 62305285the Natural Science Foundation of Chongqing under Grant No.CSTB2024NSCQ-MSX0643the Shanghai Municipal Science and Technology Major Project under Grant No.2019SHZDZX01。
文摘Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when solving specific tasks.In this study,we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field.The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO.Through the application of multi-target optimal control theory,we strategically design microwave pulses to execute logical operations,including Fourier transform,oracle U_(f)operation,and inverse Fourier transform within a three-level molecular qutrit structure.The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit,which quantifies the maximum speed of quantum state manipulation.Subsequently,we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule,achieving remarkable fidelity.Consequently,a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation.Therefore,our results indicate that the optimal control theory can be well applied to the quantum computation of polar molecular systems.
文摘The exponential growth of audio data shared over the internet and communication channels has raised significant concerns about the security and privacy of transmitted information.Due to high processing requirements,traditional encryption algorithms demand considerable computational effort for real-time audio encryption.To address these challenges,this paper presents a permutation for secure audio encryption using a combination of Tent and 1D logistic maps.The audio data is first shuffled using Tent map for the random permutation.The high random secret key with a length equal to the size of the audio data is then generated using a 1D logistic map.Finally,the Exclusive OR(XOR)operation is applied between the generated key and the shuffled audio to yield the cipher audio.The experimental results prove that the proposed method surpassed the other techniques by encrypting two types of audio files,as mono and stereo audio files with large sizes up to 122 MB,different sample rates 22,050,44,100,48,000,and 96,000 for WAV and 44,100 sample rates for MP3 of size 11 MB.The results show high Mean Square Error(MSE),low Signal-to-Noise Ratio(SNR),spectral distortion,100%Number of Sample Change Rate(NSCR),high Percent Residual Deviation(PRD),low Correlation Coefficient(CC),large key space 2^(616),high sensitivity to a slight change in the secret key and that it can counter several attacks,namely brute force attack,statistical attack,differential attack,and noise attack.
文摘In this paper,the transferable belief model established on power sets is extended to the permutation event space(PES)and is referred to as the layer-2 transferable belief model.Our goal is to provide a comprehensive approach for handling and modeling uncertainty,capable of representing both quantitative and qualitative information.First,the motivation for proposing the layer-2 transferable belief model and its information processing principles are explored from the perspective of weak propensity.Then,based on these principles,the corresponding information processing methods for the credal and pignistic levels are developed.Finally,the advantages of this model are validated through a classifier that leverages attribute fusion to enhance performance and decision-making accuracy.
基金the National Natural Science Foundation of China(60673127)the National High Technology Research and Development Program of China(863Program)(2007AA01Z404)~~
文摘The cascade of reversible logic gate network with n inputs and n outputs forms a group isomorphic to the symmetric group S2^n. Characteristics of a number of gates from the set of all generalized Toffoli gates are studied. Any permutation Sn is proved to be generated by a n-cycle 9 and a permutation τ= （ij,ik） together. It shows that any neighboring 2-cycle permutation can be generated by at most two NOT gates without ancilla bit. Based on the above theory, a cascade algorithm for reversible logic gate networks is proposed. A reversible example of logic gate network cascade is given to show the correctness of the algorithm.
文摘A constrained partial permutation strategy is proposed for matching spatial relation graph (SRG), which is used in our sketch input and recognition system Smart Sketchpad for representing the spatial relationship among the components of a graphic object. Using two kinds of matching constraints dynamically generated in the matching process, the proposed approach can prune most improper mappings between SRGs during the matching process. According to our theoretical analysis in this paper, the time complexity of our approach is O(n 2) in the best case, and O(n!) in the worst case, which occurs infrequently. The spatial complexity is always O(n) for all cases. Implemented in Smart Sketchpad, our proposed strategy is of good performance.
文摘Let f and g be two permutable transcendental entire functions. In this paper, we first prove that J(fg)=J(f n g m) for any positive integers n and m . Then we prove that the function h(p(z))+az ∈/ B , where h(z) is any transcendental entire function with h′(z)=0 having infinitely many solutions, p(z) is a polynomial with deg p ≥2 and a(≠0) ∈ C .
