This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilt...This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.展开更多
In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-...In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-COLE transformation to linearize the problems and explicitly solve them. Next we study the Burgers equation and solve the initial value problem for it. We study the asymptotic behavior of solutions and we show that the exact solution of boundary value problem for viscid Burgers equation as viscosity parameter is sufficiently small approach the shock type solution of boundary value problem for inviscid Burgers equation. We discuss both confluence and interacting shocks. In this article a new approach has been developed to find the exact solutions. The results are formulated in classical mathematics and proved with infinitesimal technique of non standard analysis.展开更多
Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The gen...Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement <sup>*</sup><em>X </em>of the space <em>X</em> which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every <em>f</em> in <em>C</em>(<em>X</em>,<em>R</em>) (the space of bounded continuous real valued functions on <em>X</em>) or <em>Cc</em>(<em>X</em>,<em>R</em>) (the space of continuous real valued functions on <em>X</em> with compact support) or the dual group <span style="white-space:nowrap;">Γ </span>of the locally compact Abelian group <em>G</em> is extended to the set <img alt="" src="Edit_b9535172-924d-44f0-bab3-c49db17a3b7a.png" /> of the above mentioned equivalence classes. A compact topology on <img alt="" src="Edit_9d7962a3-b8a3-4693-b62a-078c8c4b4853.png" /> is obtained as the weak topology generated by these extensions of <em>f</em>. Then <em>X</em> is naturally imbedded densely in <img alt="" src="Edit_f7d403b2-eff3-4555-b8e7-1b106e06d2e7.png" />.展开更多
Based on the features of the non-standard equipment executing work, a project management and decision support system oriented to the non-standard equipment is developed, and the information model, function model as we...Based on the features of the non-standard equipment executing work, a project management and decision support system oriented to the non-standard equipment is developed, and the information model, function model as well as the structure framework of the system are also introduced in this paper.展开更多
Spectral analysis was a method of identifying substances, determining their chemical composition and calculating their content based on their spectral characteristics. This paper mainly discussed the application of va...Spectral analysis was a method of identifying substances, determining their chemical composition and calculating their content based on their spectral characteristics. This paper mainly discussed the application of various spectroscopic techniques, mainly including atomic absorption spectrometry (AAS) inductively coupled plasma emission spectrometry (ICP-AES) X-ray fluorescence spectroscopy (XRF) atomic fluorescence spectroscopy (AFS) direct reading spectroscopy (OES) glow discharge emission spectroscopy (GD-OSE) laser-induced breakdown spectroscopy (LIBS), in the formulation of non-ferrous metal standards in China. The AAS method was the most widely used single-element microanalysis method among the non-ferrous metal standards. The ICP-AES method was good at significant advantages in the simultaneous detection of multiple elements. The XRF method was increasingly used in the determination of primary and secondary trace elements due to its simple sample preparation and high efficiency. The AFS was mostly detected by single-element trace analysis. OES GD-OES and LIBS were playing an increasingly important role in the new demand area for non-ferrous metals. This paper discussed matrix elimination, sample digestion, sample preparation, instrument categories and other aspects of some standards, and summarized the advantages of spectral analysis and traditional chemical analysis methods. The new methods of future spectroscopic technology had been illustrated in the process of developing non-ferrous metal standards.展开更多
[Objectives]This study was conducted to provide an accurate and reliable method for rapid high-throughput screening of veterinary drug preparations.[Methods]For the matrixes of veterinary drug preparations,high-perfor...[Objectives]This study was conducted to provide an accurate and reliable method for rapid high-throughput screening of veterinary drug preparations.[Methods]For the matrixes of veterinary drug preparations,high-performance liquid chromatography-high resolution quadrupole time-of-flight mass spectrometry(UPLC-QTOF/MS)was used to establish a fast screening method for 59 non-standard components in five categories of antiviral agents,aminoglycosides,quinolones,sulfonamides,and tetracyclines in veterinary drugs.The target drugs were separated by a Waters ACQUITY UPLC HSS T3 chromatographic column(50 mm×2.1 mm,1.8μm),and data were collected in the positive ion mode.Good separation of the 59 drugs was achieved within 7 min.[Results]In the concentration range of 0-100 ng/ml,each drug showed a good linear relationship,and the correlation coefficients were all greater than 0.999.The detection limits of the 59 drugs were in the range of 0.1-0.5 mg/ml,and the recovery under the addition concentration of 5 mg/ml was in the range of 85.2%-103.8%.[Conclusions]The method is fast,simple,accurate,and highly sensitive,and is suitable for high-throughput screening and qualitative identification of non-standard components in veterinary drug preparations.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227)the Innovation Program of Suzhou University of Science and Technology,China(Grant No.SKYCX16 012)
文摘This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.
文摘In this paper we study inviscid and viscid Burgers equations with initial conditions in the half plane . First we consider the Burgers equations with initial conditions admitting two and three shocks and use the HOPF-COLE transformation to linearize the problems and explicitly solve them. Next we study the Burgers equation and solve the initial value problem for it. We study the asymptotic behavior of solutions and we show that the exact solution of boundary value problem for viscid Burgers equation as viscosity parameter is sufficiently small approach the shock type solution of boundary value problem for inviscid Burgers equation. We discuss both confluence and interacting shocks. In this article a new approach has been developed to find the exact solutions. The results are formulated in classical mathematics and proved with infinitesimal technique of non standard analysis.
文摘Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods. The general procedure is as follows: A suitable equivalence relation is defined on an enlargement <sup>*</sup><em>X </em>of the space <em>X</em> which is a completely regular space or a locally compact Hausdorff space or a locally compact Abelian group. Accordingly, every <em>f</em> in <em>C</em>(<em>X</em>,<em>R</em>) (the space of bounded continuous real valued functions on <em>X</em>) or <em>Cc</em>(<em>X</em>,<em>R</em>) (the space of continuous real valued functions on <em>X</em> with compact support) or the dual group <span style="white-space:nowrap;">Γ </span>of the locally compact Abelian group <em>G</em> is extended to the set <img alt="" src="Edit_b9535172-924d-44f0-bab3-c49db17a3b7a.png" /> of the above mentioned equivalence classes. A compact topology on <img alt="" src="Edit_9d7962a3-b8a3-4693-b62a-078c8c4b4853.png" /> is obtained as the weak topology generated by these extensions of <em>f</em>. Then <em>X</em> is naturally imbedded densely in <img alt="" src="Edit_f7d403b2-eff3-4555-b8e7-1b106e06d2e7.png" />.
文摘Based on the features of the non-standard equipment executing work, a project management and decision support system oriented to the non-standard equipment is developed, and the information model, function model as well as the structure framework of the system are also introduced in this paper.
文摘Spectral analysis was a method of identifying substances, determining their chemical composition and calculating their content based on their spectral characteristics. This paper mainly discussed the application of various spectroscopic techniques, mainly including atomic absorption spectrometry (AAS) inductively coupled plasma emission spectrometry (ICP-AES) X-ray fluorescence spectroscopy (XRF) atomic fluorescence spectroscopy (AFS) direct reading spectroscopy (OES) glow discharge emission spectroscopy (GD-OSE) laser-induced breakdown spectroscopy (LIBS), in the formulation of non-ferrous metal standards in China. The AAS method was the most widely used single-element microanalysis method among the non-ferrous metal standards. The ICP-AES method was good at significant advantages in the simultaneous detection of multiple elements. The XRF method was increasingly used in the determination of primary and secondary trace elements due to its simple sample preparation and high efficiency. The AFS was mostly detected by single-element trace analysis. OES GD-OES and LIBS were playing an increasingly important role in the new demand area for non-ferrous metals. This paper discussed matrix elimination, sample digestion, sample preparation, instrument categories and other aspects of some standards, and summarized the advantages of spectral analysis and traditional chemical analysis methods. The new methods of future spectroscopic technology had been illustrated in the process of developing non-ferrous metal standards.
基金Supported by Key R&D Project of Hebei Province(19227516D)Hebei Provincial Phase II Modern Agricultural Industry Technology System Innovation Team Building Project(HBCT2018120207)+2 种基金Hebei Provincial Phase II Modern Agricultural Industry Technology System Grass Industry Innovation Team Building Project(HBCT2018160403)Hebei Provincial Science and Technology Innovation Leading Talents(21130243A)The Fourth Batch of High-end Talent Project in Hebei Province。
文摘[Objectives]This study was conducted to provide an accurate and reliable method for rapid high-throughput screening of veterinary drug preparations.[Methods]For the matrixes of veterinary drug preparations,high-performance liquid chromatography-high resolution quadrupole time-of-flight mass spectrometry(UPLC-QTOF/MS)was used to establish a fast screening method for 59 non-standard components in five categories of antiviral agents,aminoglycosides,quinolones,sulfonamides,and tetracyclines in veterinary drugs.The target drugs were separated by a Waters ACQUITY UPLC HSS T3 chromatographic column(50 mm×2.1 mm,1.8μm),and data were collected in the positive ion mode.Good separation of the 59 drugs was achieved within 7 min.[Results]In the concentration range of 0-100 ng/ml,each drug showed a good linear relationship,and the correlation coefficients were all greater than 0.999.The detection limits of the 59 drugs were in the range of 0.1-0.5 mg/ml,and the recovery under the addition concentration of 5 mg/ml was in the range of 85.2%-103.8%.[Conclusions]The method is fast,simple,accurate,and highly sensitive,and is suitable for high-throughput screening and qualitative identification of non-standard components in veterinary drug preparations.
