Objective: To study the antimicrobial activity of actinomycetes isolated from sabkha of Kenadsa and identification of the isolate interesting. Methods: Eighteen strains were isolated, using four culture media from seb...Objective: To study the antimicrobial activity of actinomycetes isolated from sabkha of Kenadsa and identification of the isolate interesting. Methods: Eighteen strains were isolated, using four culture media from sebkha of Kenadsa(Bechar, Southwestern Algeria). Screening of antimicrobial activity consisted of two steps: in primary screening, antibacterial activity was determined by using the agar plug method against test strains; in secondary screening, better isolate which showed a good activity in the first screening was selected to extract antimicrobial substances. The antimicrobial activities of extracts were evaluated by using Kirby-Bauer disc diffusion method. Partial characterization of antimicrobial products was performed on the basis of chemical revelations, UV-vis spectrometry and infrared spectroscopy. The identification of isolate interesting was performed through morphological, chemical, biochemical and physiological characteristics. Results: All isolates showed antimicrobial activity against at least one microorganism test. One isolate, LAM143 cG 3, was selected for its broad spectrum and high antimicrobial activity. The isolate LAM143 c G3 was identified as Spirillospora sp. The comparison between the species of this genus(Spirillospora rubra and Spirillospora albida) and our isolate indicated the existence of several physiological and biochemical differences which led us to suppose that this was a new member of this genus. Primary characterization of antimicrobial substances produced by the isolate LAM143 c G3 indicated the presence of amines and phenols. The UV–vis spectrum suggested a non-polyenic nature of substances secreted by our isolate, while infrared confirmed the presence of amine groups.Conclusions: The result of the present study revealed that sebkha of Kenadsa was rich in rare actinomycetes, that secreted interesting antimicrobial substance.展开更多
In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linea...In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linear operator.展开更多
On the basis of analyzing and testing of common inverting circuits, a new type inverter, which has a special inverting circuit called complex isolated, has been put forward. In turn, an applicable air plasma cutting ...On the basis of analyzing and testing of common inverting circuits, a new type inverter, which has a special inverting circuit called complex isolated, has been put forward. In turn, an applicable air plasma cutting machine has also been put into use. Testing results show that this kind inverter has lots of properties as high reliability, high efficiency, good EMC(electromagnetic compatibility) and easy operating. The complex isolated inverting circuit can be considered as a quite valuable reference for the research of high power welding inverter.展开更多
When initial radius Rinitial 0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of Rinit...When initial radius Rinitial 0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of Rinitial 0 are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged Sentropy=0.3rH2/a2 for a time dependent horizon radius rH in cosmology, with for flat space conditions rH= for conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with ~H2/G H≈a-1. The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the length gets, Sentropy if it is entanglement entropy, will not go to zero. The requirement is that the smallest length of time, t, re scaled does not go to zero. Even if the length goes to zero. This preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial 0.展开更多
In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete form...In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5<sup>th</sup> order Butcher’s algorithm in predictor-corrector form.展开更多
The work illustrates the impossibility of decreasing entropy in a strictly random thermodynamic process in a non-isolated system using the example of heating a planet by solar radiation flux without and taking into ac...The work illustrates the impossibility of decreasing entropy in a strictly random thermodynamic process in a non-isolated system using the example of heating a planet by solar radiation flux without and taking into account its rotation around its own axis. That is, the second law of thermodynamics formulated for isolated systems continues to govern such systems. We have shown that in order to achieve a stationary state at lower values of temperature and entropy far from thermodynamic equilibrium at a maximum of temperature and entropy, it is necessary to have regular factors of nonrandom nature, one of which in this example is the rotation of the planet around its own axis. This means that the reason for the appearance of ordered structured objects in non-isolated thermodynamic systems is not the random process itself, but the action of dynamic control mechanisms, such as periodic external influences, nonlinear elements with positive feedback, catalysts for chemical reactions, etc. We present the plots with dependences of temperature and entropy versus time in non-isolated systems with purely random processes and in the presence of a control factor of non-random nature-rotation.展开更多
When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit ...When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit calculations as to a space time length factor Without the drop off of the vacuum energy as given by is at least the value of . We review the work by Ng as to quantum foam as to how that affects a general expression as to energy when , with determined at least approximately by arguments he presented in 2008 in the Dark side of the universe conference. Well before certain effects make themselves apparent, in ways which are illustrated in the manuscript. Having at a point singularity would remove expansion by the scale factor, so that the extreme version of Stoica’s treatment in an isolated 4-dimensional universe would be no expansion at all.展开更多
Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region....Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.展开更多
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are co...In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.展开更多
A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon's information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.展开更多
The application of intelligent disinfection robot in designated non-negative pressure isolation ward during the outbreak in novel coronavirus pneumonia. The construction and competition, disinfection mode of intellige...The application of intelligent disinfection robot in designated non-negative pressure isolation ward during the outbreak in novel coronavirus pneumonia. The construction and competition, disinfection mode of intelligent disinfection robot, the setting of disinfection point built on area and number of isolation ward, can be introduced below. Frequency can realize remote control when staff uses a table to give instruction and set disinfection mode, and then the intelligent disinfection robot returns automatically to the charging pile to charge when the instruction is completed. It can also autonomously move to sterilize without human participation, which makes man-machine separation and accurate disinfection come true. The chance of contact infection and exposure is decreased when an intelligent disinfection robot is used to sterilize the environment and object surface in an isolation ward, which can also reduce occupational exposure, achieve occupational protection of medical workers and ensure there is no hospital infection.展开更多
This paper describes the installation and management of the monitoring system of the “Our Lady of Tears Shrine” in Syracuse, whose dome is an imposing r.c. and prestressed r.c. structure of about 22,000 ton that was...This paper describes the installation and management of the monitoring system of the “Our Lady of Tears Shrine” in Syracuse, whose dome is an imposing r.c. and prestressed r.c. structure of about 22,000 ton that was seismically isolated by flat sliding devices with hysteretic dampers. The monitoring system, representing an upgrading and improvement of an old system never made working, has some innovative features, because it allows to manage with the same dedicated hardware and software both the slow (thermal variations, relative humidity, wind direction and velocity) and the fast acquisitions (dynamic vibrations by wind and earthquake). The monitoring system was inserted among those structures maintained and controlled by the Seismic Observatory of Structures of the National Department of Civil Protection. Some records of low magnitude earthquakes allowed to validate the correct behaviour of the whole structure, as well as to make a dynamic identification of the complex construction and to calibrate a detailed finite element model of the Sanctuary, thus predicting isolators’ behaviour under design earthquake.展开更多
The paper discusses how to reduce higher singularity order of a boundary integral equation. The approach will be discussed in some detail for plane elasticity.Numerical results for the meshes of unequal length boundar...The paper discusses how to reduce higher singularity order of a boundary integral equation. The approach will be discussed in some detail for plane elasticity.Numerical results for the meshes of unequal length boundary elements are reported.Higher precision for both deflection and force is obtained than that obtained with a general boundary element method.展开更多
A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theor...A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame' constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular (but sometimes singular or even hypersingular) stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.展开更多
In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems...In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.展开更多
We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, ...We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or?θ(p,l,q) as the induced subgraph. In this paper, by using three graph transformations which do not change the singularity of the graph, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained.展开更多
We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We ...We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .展开更多
In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usu...In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usual pointwise HSrmander condition.展开更多
When kernel density is in the class of continuous function to possessing sufficient derivative of high order(and needn't in the class of corresponding Holder function),in this paper it is given the continuity and...When kernel density is in the class of continuous function to possessing sufficient derivative of high order(and needn't in the class of corresponding Holder function),in this paper it is given the continuity and the differential formulas for singular integrals of high non--integral order. The above results themselves and in order to prove in future the formulas to changing order of integration for singular integrals of high non-integral order(another paper) will have important significance. The method to prove in this paper is more different from the method in the corresponding cass of singular integrals of high integral order.展开更多
基金Supported by the Ministry of Higher Education and Scientific Research of People’s Democratic Republic of Algeria(Grant No.F02020110081)
文摘Objective: To study the antimicrobial activity of actinomycetes isolated from sabkha of Kenadsa and identification of the isolate interesting. Methods: Eighteen strains were isolated, using four culture media from sebkha of Kenadsa(Bechar, Southwestern Algeria). Screening of antimicrobial activity consisted of two steps: in primary screening, antibacterial activity was determined by using the agar plug method against test strains; in secondary screening, better isolate which showed a good activity in the first screening was selected to extract antimicrobial substances. The antimicrobial activities of extracts were evaluated by using Kirby-Bauer disc diffusion method. Partial characterization of antimicrobial products was performed on the basis of chemical revelations, UV-vis spectrometry and infrared spectroscopy. The identification of isolate interesting was performed through morphological, chemical, biochemical and physiological characteristics. Results: All isolates showed antimicrobial activity against at least one microorganism test. One isolate, LAM143 cG 3, was selected for its broad spectrum and high antimicrobial activity. The isolate LAM143 c G3 was identified as Spirillospora sp. The comparison between the species of this genus(Spirillospora rubra and Spirillospora albida) and our isolate indicated the existence of several physiological and biochemical differences which led us to suppose that this was a new member of this genus. Primary characterization of antimicrobial substances produced by the isolate LAM143 c G3 indicated the presence of amines and phenols. The UV–vis spectrum suggested a non-polyenic nature of substances secreted by our isolate, while infrared confirmed the presence of amine groups.Conclusions: The result of the present study revealed that sebkha of Kenadsa was rich in rare actinomycetes, that secreted interesting antimicrobial substance.
文摘In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linear operator.
文摘On the basis of analyzing and testing of common inverting circuits, a new type inverter, which has a special inverting circuit called complex isolated, has been put forward. In turn, an applicable air plasma cutting machine has also been put into use. Testing results show that this kind inverter has lots of properties as high reliability, high efficiency, good EMC(electromagnetic compatibility) and easy operating. The complex isolated inverting circuit can be considered as a quite valuable reference for the research of high power welding inverter.
文摘When initial radius Rinitial 0 if Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of Rinitial 0 are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto, and show that there are consequences due to initial entanged Sentropy=0.3rH2/a2 for a time dependent horizon radius rH in cosmology, with for flat space conditions rH= for conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time in line with ~H2/G H≈a-1. The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the length gets, Sentropy if it is entanglement entropy, will not go to zero. The requirement is that the smallest length of time, t, re scaled does not go to zero. Even if the length goes to zero. This preserves a minimum non zero vacuum energy, and in doing so keep the bits, for computational bits cosmological evolution even if Rinitial 0.
文摘In this paper, we state and prove the conditions for the non-singularity of the <em>D</em> matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5<sup>th</sup> order Butcher’s algorithm in predictor-corrector form.
文摘The work illustrates the impossibility of decreasing entropy in a strictly random thermodynamic process in a non-isolated system using the example of heating a planet by solar radiation flux without and taking into account its rotation around its own axis. That is, the second law of thermodynamics formulated for isolated systems continues to govern such systems. We have shown that in order to achieve a stationary state at lower values of temperature and entropy far from thermodynamic equilibrium at a maximum of temperature and entropy, it is necessary to have regular factors of nonrandom nature, one of which in this example is the rotation of the planet around its own axis. This means that the reason for the appearance of ordered structured objects in non-isolated thermodynamic systems is not the random process itself, but the action of dynamic control mechanisms, such as periodic external influences, nonlinear elements with positive feedback, catalysts for chemical reactions, etc. We present the plots with dependences of temperature and entropy versus time in non-isolated systems with purely random processes and in the presence of a control factor of non-random nature-rotation.
文摘When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit calculations as to a space time length factor Without the drop off of the vacuum energy as given by is at least the value of . We review the work by Ng as to quantum foam as to how that affects a general expression as to energy when , with determined at least approximately by arguments he presented in 2008 in the Dark side of the universe conference. Well before certain effects make themselves apparent, in ways which are illustrated in the manuscript. Having at a point singularity would remove expansion by the scale factor, so that the extreme version of Stoica’s treatment in an isolated 4-dimensional universe would be no expansion at all.
基金supported by the Educational Department Foundation of Fujian Province of China(Nos. JA08140 and A0610025)the Scientific Research Foundation of Zhejiang University of Scienceand Technology (No. 2008050)the National Natural Science Foundation of China (No. 50679074)
文摘Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
基金Supported in part by the National Thousand Talents Program of Chinathe National Natural Science Foundation of China(61473054)the Fundamental Research Funds for the Central Universities of China
文摘In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon's information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
文摘The application of intelligent disinfection robot in designated non-negative pressure isolation ward during the outbreak in novel coronavirus pneumonia. The construction and competition, disinfection mode of intelligent disinfection robot, the setting of disinfection point built on area and number of isolation ward, can be introduced below. Frequency can realize remote control when staff uses a table to give instruction and set disinfection mode, and then the intelligent disinfection robot returns automatically to the charging pile to charge when the instruction is completed. It can also autonomously move to sterilize without human participation, which makes man-machine separation and accurate disinfection come true. The chance of contact infection and exposure is decreased when an intelligent disinfection robot is used to sterilize the environment and object surface in an isolation ward, which can also reduce occupational exposure, achieve occupational protection of medical workers and ensure there is no hospital infection.
文摘This paper describes the installation and management of the monitoring system of the “Our Lady of Tears Shrine” in Syracuse, whose dome is an imposing r.c. and prestressed r.c. structure of about 22,000 ton that was seismically isolated by flat sliding devices with hysteretic dampers. The monitoring system, representing an upgrading and improvement of an old system never made working, has some innovative features, because it allows to manage with the same dedicated hardware and software both the slow (thermal variations, relative humidity, wind direction and velocity) and the fast acquisitions (dynamic vibrations by wind and earthquake). The monitoring system was inserted among those structures maintained and controlled by the Seismic Observatory of Structures of the National Department of Civil Protection. Some records of low magnitude earthquakes allowed to validate the correct behaviour of the whole structure, as well as to make a dynamic identification of the complex construction and to calibrate a detailed finite element model of the Sanctuary, thus predicting isolators’ behaviour under design earthquake.
基金The project supported by National Natural Science Foundation of China.
文摘The paper discusses how to reduce higher singularity order of a boundary integral equation. The approach will be discussed in some detail for plane elasticity.Numerical results for the meshes of unequal length boundary elements are reported.Higher precision for both deflection and force is obtained than that obtained with a general boundary element method.
基金supported by the General Secretariat of Research and Technology(GSRT)of Greece(Helenic/ERC-13(88257-IL-GradMech-ASM)ARISTEIA II(5152-SEDEMP)THALES/INTERMONU68/1117)
文摘A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame' constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular (but sometimes singular or even hypersingular) stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.
文摘In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.
文摘We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or?θ(p,l,q) as the induced subgraph. In this paper, by using three graph transformations which do not change the singularity of the graph, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained.
文摘We prove the existence of a ground state solution for the qusilinear elliptic equation in , under suitable conditions on a locally Holder continuous non-linearity , the non-linearity may exhibit a singularity as . We also prove the non-existence of radially symmetric solutions to the singular elliptic equation in , as where .
文摘In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usual pointwise HSrmander condition.
文摘When kernel density is in the class of continuous function to possessing sufficient derivative of high order(and needn't in the class of corresponding Holder function),in this paper it is given the continuity and the differential formulas for singular integrals of high non--integral order. The above results themselves and in order to prove in future the formulas to changing order of integration for singular integrals of high non-integral order(another paper) will have important significance. The method to prove in this paper is more different from the method in the corresponding cass of singular integrals of high integral order.