The response and energy dissipation of rock under stochastic stress waves were analyzed based on dynamic fracture criterion of brittle materials integrating with Fourier transform methods of spectral analysis. When th...The response and energy dissipation of rock under stochastic stress waves were analyzed based on dynamic fracture criterion of brittle materials integrating with Fourier transform methods of spectral analysis. When the stochastic stress waves transmit through rocks, the frequency and energy ratio of harmonic components were calculated by analytical and discrete analysis methods. The stress waves in shale, malmstone and liparite were taken as examples to illustrate the proposed analysis methods. The results show the harder the rock, the less absorption of energy, the more the useless elastic waves transmitting through rock, and the narrower the cutoff frequency to fracture rock. When the whole stress energy doubles either by doubling the duration time or by increasing the amplitude of stress wave, ratio of the energy of elastic waves transmitting through rock to the whole stress energy (i.e. energy dissipation ratio) is decreased to 10%-15%. When doubling the duration time, the cutoff frequency to fracture rock remains constant. However, with the increase of the amplitude of stress wave, the cutoff frequency increases accordingly.展开更多
Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.
A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and th...A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of hell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.展开更多
One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equatio...One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.展开更多
Transition metal carbides have been shown to exhibit good catalytic performance that depends on their compositions and morphologies,and understanding such catalytic properties requires knowledge of their precise geome...Transition metal carbides have been shown to exhibit good catalytic performance that depends on their compositions and morphologies,and understanding such catalytic properties requires knowledge of their precise geometry,determination of which is challenging,particularly for clusters formed by multiple elements.In this study,we investigate the geometries and electronic structures of binary V_(n)C_(3)-(n=1-6)clusters and their neutrals using photoelectron spectroscopy and theoretical calculations based on density functional theory.The adiabatic detachment energies of V_(n)C_(3)-,or equally,the electron affinities of V_(n)C_(3),have been determined from the measured photoelectron spectra.Theoretical calculations reveal that the carbon atoms become separate when the number of V atoms increases in the clusters,i.e.,the C-C interactions present in small clusters are replaced by V-C and/or V-V interactions in larger ones.We further explore the composition dependent formation of cubic or cube-like structures in 8-atom VnCm(n+m=8)clusters.展开更多
A shift sampling theory established by author (1997a) is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error (A-E) equation of potential field transformatio...A shift sampling theory established by author (1997a) is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error (A-E) equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η(0.5, 0.5) reduction-to-pole (RTP) technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law (origin, form mechanism, and essential properties) of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.展开更多
This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and...This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.展开更多
Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method wa...Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.展开更多
Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is p...Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.展开更多
In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the tr...In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated.展开更多
In this paper, we describe a new batch process monitoring method based on multilevel independent component analysis and principal component analysis (MLICA-PCA). Unlike the conventional multi-way principal component a...In this paper, we describe a new batch process monitoring method based on multilevel independent component analysis and principal component analysis (MLICA-PCA). Unlike the conventional multi-way principal component analysis (MPCA) method, MLICA-PCA provides a separated interpretation for multilevel batch process data. Batch process data are partitioned into two levels: the within-batch level and the between-batch level. In each level, the Gaussian and non-Gaussian components of process information can be separately extracted. I2, T2 and SPE statistics are individually built and monitored. The new method facilitates fault diagnosis. Since the two variation levels are decomposed, the variables responsible for faults in each level can be identified and interpreted more easily. A case study of the Dupont benchmark process showed that the proposed method was more efficient and interpretable in fault detection and diagnosis, compared to the alternative batch process monitoring method.展开更多
Geography is a kind of differential calculus in the sense that the three-dimensional, that is, the act of tangentially accessing things, is mapped on to the two-dimensional or the concrete. It is why we can say that t...Geography is a kind of differential calculus in the sense that the three-dimensional, that is, the act of tangentially accessing things, is mapped on to the two-dimensional or the concrete. It is why we can say that the East-West or Occidental versus Oriental dichotomy is so limited in its binary dualism. We could easily criticize not only Said's Orientalism, but also in turn, a critical self-defense by turning itself upon its own head. It can indeed be said that the cross or cardinal directions run four different ways and not two. "The East" is not just Far Eastern, that is, the so-called "Asian," but extends to the Far West or to California. Parts of Europe and the Dionysian are not simply limited to Central Europe and Southeastern Asia. We can see in Asia, that is, Eurasia and in North Africa, that 1-2% of non-Sub-saharan human DNA is genotypically Neanderthal in addition to being Homo Sapiens in DNA. 1 The task, it might be said, is to continually remediate binary directions and to reweave Apollo and Dionysos in Friedrich Nietzsche. We can see the limitations of Continentalism in categorizing the human.展开更多
An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be f...An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.展开更多
As grammatical words, conjunction and relative pronoun play a similar role. They join clauses, phrases, and even words. The terms independent and dependent clauses have become popular for quite a long time. When the c...As grammatical words, conjunction and relative pronoun play a similar role. They join clauses, phrases, and even words. The terms independent and dependent clauses have become popular for quite a long time. When the concept of clause and sentence meets at the presence of NP (Noun Phrase) and VP (Verb Phrase), there is a right to consider construction as an S or a sentence leaving the conjunction and relative pronoun as means of uniting device and leaving every NP-VP construction as equal units. By employing an embedding theory, we can see hidden parts of a sentence and their roles in other sentences. This article tries to see if it is still necessary to distinguish between dependent and independent clauses.展开更多
Cyber security lacks comprehensive theoretical guidance. General security theory, as a set of basic security theory concepts, is intended to guide cyber security and all the other security work. The general theory of ...Cyber security lacks comprehensive theoretical guidance. General security theory, as a set of basic security theory concepts, is intended to guide cyber security and all the other security work. The general theory of security aims to unify the main branches of cyber security and establish a unified basic theory. This paper proposal an overview on the general theory of security, which is devoted to constructing a comprehensive model of network security. The hierarchical structure of the meridian-collateral tree is described. Shannon information theory is employed to build a cyberspace security model. Some central concepts of security, i.e., the attack and defense, are discussed and several general theorems on security are presented.展开更多
Based on the technique of integral within a Weyl ordered product of operators, we present applications of the Weyl ordered two-mode Wigner operator for quantum mechanical entangled system, e.g., we derive the complex ...Based on the technique of integral within a Weyl ordered product of operators, we present applications of the Weyl ordered two-mode Wigner operator for quantum mechanical entangled system, e.g., we derive the complex Wigner transform and its relation to the complex fractional Fourier transform, as well as the entangled Radon transform.展开更多
Let n be any positive integer, and S(n) be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x(n/S(n))^k (k ≥ 1). And by using the elementary methods, it intends to...Let n be any positive integer, and S(n) be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x(n/S(n))^k (k ≥ 1). And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.展开更多
基金Projects(50404010, 50574098) supported by the National Natural Science Foundation of Chinaproject(05jj10010) supported by the Hunan Provincial Natural Science Foundation of Distinguished Young Scholars
文摘The response and energy dissipation of rock under stochastic stress waves were analyzed based on dynamic fracture criterion of brittle materials integrating with Fourier transform methods of spectral analysis. When the stochastic stress waves transmit through rocks, the frequency and energy ratio of harmonic components were calculated by analytical and discrete analysis methods. The stress waves in shale, malmstone and liparite were taken as examples to illustrate the proposed analysis methods. The results show the harder the rock, the less absorption of energy, the more the useless elastic waves transmitting through rock, and the narrower the cutoff frequency to fracture rock. When the whole stress energy doubles either by doubling the duration time or by increasing the amplitude of stress wave, ratio of the energy of elastic waves transmitting through rock to the whole stress energy (i.e. energy dissipation ratio) is decreased to 10%-15%. When doubling the duration time, the cutoff frequency to fracture rock remains constant. However, with the increase of the amplitude of stress wave, the cutoff frequency increases accordingly.
文摘Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.
基金*The project supported by National Natural Science Foundation of China under Grant No. 10471139 and Hong Kong Research Grant Council under Grant No. HKBU/2016/03P
文摘A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of hell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10474076 and 10375041
文摘One of the basic problems about the inverse scattering transform for solving a completely integrable nonlinear evolutions equation is to demonstrate that the Jost solutions obtained from the inverse scattering equations of Cauchy integral satisfy the Lax equations. Such a basic problem still exists in the procedure of deriving the dark soliton solutions of the NLS equation in normal dispersion with non-vanishing boundary conditions through the inverse scattering transform. In this paper, a pair of Jost solutions with same analytic properties are composed to be a 2 × 2 matrix and then another pair are introduced to be its right inverse confirmed by the Liouville theorem. As they are both 2 × 2 matrices, the right inverse should be the left inverse too, based upon which it is not difficult to show that these Jost solutions satisfy both the first and second Lax equations. As a result of compatibility condition, the dark soliton solutions definitely satisfy the NLS equation in normal dispersion with non-vanishing boundary conditions.
基金the Doctoral Start-up Funding of Zhengzhou University of Light Industry(No.2017BSJJ030)Henan Province Science Fund for Excellent Young Scholars(No.202300410494)+4 种基金the Beijing Municipal Science and Technology Commission(No.Z191100007219009)for supportsthe VSC(Flemish Supercomputer Center),funded by the Research Foundation-Flanders(FWO)the Flemish Government-department EWIthe support of Xi’an Jiaotong University via the“Young Talent Support Plan”the“Fundamental Research Funds for Central Universities”。
文摘Transition metal carbides have been shown to exhibit good catalytic performance that depends on their compositions and morphologies,and understanding such catalytic properties requires knowledge of their precise geometry,determination of which is challenging,particularly for clusters formed by multiple elements.In this study,we investigate the geometries and electronic structures of binary V_(n)C_(3)-(n=1-6)clusters and their neutrals using photoelectron spectroscopy and theoretical calculations based on density functional theory.The adiabatic detachment energies of V_(n)C_(3)-,or equally,the electron affinities of V_(n)C_(3),have been determined from the measured photoelectron spectra.Theoretical calculations reveal that the carbon atoms become separate when the number of V atoms increases in the clusters,i.e.,the C-C interactions present in small clusters are replaced by V-C and/or V-V interactions in larger ones.We further explore the composition dependent formation of cubic or cube-like structures in 8-atom VnCm(n+m=8)clusters.
文摘A shift sampling theory established by author (1997a) is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error (A-E) equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η(0.5, 0.5) reduction-to-pole (RTP) technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law (origin, form mechanism, and essential properties) of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.
基金Supported by the Chinese Academy of Sciences (No. KJ 951-B1-704), the National Natural Science Foundation of China (No. 59736130) and the State Key Fundamental Research Plan of China (No. G2000026305).
文摘This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.
基金Supported by the National Natural Science Foundation of China under Grant No.50921001973 Program under Grant No. 2010CB83270
文摘Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.
基金Supported by the National Natural Science Foundation of China under Grant No.10735030 the National Basic Research Programs of China (973 Programs) under Grant Nos.2007CB814800 and 2005CB422301the PCSIRT (IRT0734)
文摘Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.
基金The project supported by National Natural Science Foundation of China under Grant No. 10401022
文摘In this paper, we employ the bifurcation method of dynamical systems to study the solitary waves and periodic waves of a generalized Boussinesq equations. All possible phase portraits in the parameter plane for the travelling wave systems are obtained. The possible solitary wave solutions, periodic wave solutions and cusp waves for the general Boussinesq type fluid model are also investigated.
基金Project (No. 60774067) supported by the National Natural ScienceFoundation of China
文摘In this paper, we describe a new batch process monitoring method based on multilevel independent component analysis and principal component analysis (MLICA-PCA). Unlike the conventional multi-way principal component analysis (MPCA) method, MLICA-PCA provides a separated interpretation for multilevel batch process data. Batch process data are partitioned into two levels: the within-batch level and the between-batch level. In each level, the Gaussian and non-Gaussian components of process information can be separately extracted. I2, T2 and SPE statistics are individually built and monitored. The new method facilitates fault diagnosis. Since the two variation levels are decomposed, the variables responsible for faults in each level can be identified and interpreted more easily. A case study of the Dupont benchmark process showed that the proposed method was more efficient and interpretable in fault detection and diagnosis, compared to the alternative batch process monitoring method.
文摘Geography is a kind of differential calculus in the sense that the three-dimensional, that is, the act of tangentially accessing things, is mapped on to the two-dimensional or the concrete. It is why we can say that the East-West or Occidental versus Oriental dichotomy is so limited in its binary dualism. We could easily criticize not only Said's Orientalism, but also in turn, a critical self-defense by turning itself upon its own head. It can indeed be said that the cross or cardinal directions run four different ways and not two. "The East" is not just Far Eastern, that is, the so-called "Asian," but extends to the Far West or to California. Parts of Europe and the Dionysian are not simply limited to Central Europe and Southeastern Asia. We can see in Asia, that is, Eurasia and in North Africa, that 1-2% of non-Sub-saharan human DNA is genotypically Neanderthal in addition to being Homo Sapiens in DNA. 1 The task, it might be said, is to continually remediate binary directions and to reweave Apollo and Dionysos in Friedrich Nietzsche. We can see the limitations of Continentalism in categorizing the human.
文摘An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.
文摘As grammatical words, conjunction and relative pronoun play a similar role. They join clauses, phrases, and even words. The terms independent and dependent clauses have become popular for quite a long time. When the concept of clause and sentence meets at the presence of NP (Noun Phrase) and VP (Verb Phrase), there is a right to consider construction as an S or a sentence leaving the conjunction and relative pronoun as means of uniting device and leaving every NP-VP construction as equal units. By employing an embedding theory, we can see hidden parts of a sentence and their roles in other sentences. This article tries to see if it is still necessary to distinguish between dependent and independent clauses.
基金supported by the National Key R&D Program of China (2016YFF0204001)the National Key Technology Support Program (2015BAH08F02)+3 种基金the CCF-Venustech Hongyan Research Initiative (2016-009)the PAPD fundthe CICAEET fundthe Guizhou Provincial Key Laboratory of Public Big Data Program
文摘Cyber security lacks comprehensive theoretical guidance. General security theory, as a set of basic security theory concepts, is intended to guide cyber security and all the other security work. The general theory of security aims to unify the main branches of cyber security and establish a unified basic theory. This paper proposal an overview on the general theory of security, which is devoted to constructing a comprehensive model of network security. The hierarchical structure of the meridian-collateral tree is described. Shannon information theory is employed to build a cyberspace security model. Some central concepts of security, i.e., the attack and defense, are discussed and several general theorems on security are presented.
基金The project supported by National Natural Science Foundation of China under Grant No.10175057
文摘Based on the technique of integral within a Weyl ordered product of operators, we present applications of the Weyl ordered two-mode Wigner operator for quantum mechanical entangled system, e.g., we derive the complex Wigner transform and its relation to the complex fractional Fourier transform, as well as the entangled Radon transform.
文摘Let n be any positive integer, and S(n) be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x(n/S(n))^k (k ≥ 1). And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.