The photodegradation of 4-chlorobiphenyl in hexane by UV irradiation has been investigated. For the first time, the UV spectral changes of 4-chlorobiphenyl and formation of chloride in the photoreaction have been disc...The photodegradation of 4-chlorobiphenyl in hexane by UV irradiation has been investigated. For the first time, the UV spectral changes of 4-chlorobiphenyl and formation of chloride in the photoreaction have been discussed. The main pathway for the degradation of 4-chlorobiphenyl in hexane was dechlorination to follow a ftrst order kinetics. The products were formed by the cleavage of carbon-chlorine bond to produce a biphenyl free radical, which then abstracted hydrogen from the solvent hexane to form biphenyl. With irradiation, biphenyl was also decomposed to lower hydrocarbons as the final products, which was further confirmed by the degradation experiment of biphenyl.展开更多
In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are ...In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.展开更多
Local susceptibility variations result in <em>B</em><sub>0</sub> field inhomogeneities, causing distortions and signal losses in MR imaging. Susceptibility variations become stronger with incre...Local susceptibility variations result in <em>B</em><sub>0</sub> field inhomogeneities, causing distortions and signal losses in MR imaging. Susceptibility variations become stronger with increasing <em>B</em><sub>0</sub> magnetic field strength. Active shimming is used to generate corrective magnetic fields, which can be used to improve <em>B</em><sub>0</sub> field homogeneity. FASTMAP is an effective shimming technique for computing optimal coil currents, which uses data from six projection directions (or columns): this technique is routinely used for shimming cubic volumes of interest (VOIs). In this paper, we propose several improvements to FASTMAP at 4T. For each shim coil, using a modified 3D gradient-echo pulse sequence, we compute <em>B</em><sub>0</sub> inhomogeneity maps and project them onto eight 1<sup>st</sup> and 2<sup>nd</sup> order spherical harmonic functions. This process is repeated for shim currents between -15,000 to 15,000 with increments of 5000 Digital to Analog Converter (DAC) units, and is used to compute the gradient between spherical harmonic coefficients and DAC values for all 8 shim coils—along with the R<sup>2</sup> values of linear fits. A method is proposed (based on R<sup>2</sup> values) to further refine optimal shim currents in respective coils. We present an analysis that is numerically robust and completely flexible in the selection of the VOIs for shimming. Performance analyses, phantom results, and <em>in vivo</em> results of a human brain are presented, comparing our methods with the FASTMAP method.展开更多
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
Dipeptides are stereo-specifically involved in several biological functions that are challenging to separate enantiomerically. Elution order of enantiomers is an important issue in chiral chromatography. Amylose tris-...Dipeptides are stereo-specifically involved in several biological functions that are challenging to separate enantiomerically. Elution order of enantiomers is an important issue in chiral chromatography. Amylose tris-(3,5-dimethylphenylcarbamate) chiral stationary phase(CSP) is the best and most-widely-used CSP in chiral separations, but experimental data of enantiomeric separation of dipeptides on this CSP is lacking. Simulation studies were conducted to determine the order of elution and the chiral recognition mechanism of didpetides on this CSP. Results indicated that the docking energy of SR-enantiomers were higher than SS-antipodes. The range of docking energies for SR-enantiomers was -7.44 to -5.92 kcal/mol with CSP, but -7.15 to -5.87 kcal/mol for SS-stereoisomers. Therefore it is predicted that SS-enantiomer will elute first, followed by SR-antipode. Furthermore, hydrogen bondings, van der Waal's interactions and electrostatic interactions were observed among SR- and SSenantiomers and chiral grooves of CSP. The number of hydrogen bonds was one in each enantiomer binding except S-Ala-R-Tyr, which contained two hydrogen bonds. No hydrogen bond was found in S-Ala-R-Trp, S-Leu-S-Trp, and S-Leu-S-Tyr dipeptides bindings. The chiral recognition mechanisms dictate different strengths of stereoselective bindings of the enantiomers on CSP.展开更多
This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all...This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5<sup>th</sup>-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.展开更多
基金Project supported by the National Natural Science Foundation of China （No. 2003CB415007） and the Ministry of Education of China （No. 20030027008）.
文摘The photodegradation of 4-chlorobiphenyl in hexane by UV irradiation has been investigated. For the first time, the UV spectral changes of 4-chlorobiphenyl and formation of chloride in the photoreaction have been discussed. The main pathway for the degradation of 4-chlorobiphenyl in hexane was dechlorination to follow a ftrst order kinetics. The products were formed by the cleavage of carbon-chlorine bond to produce a biphenyl free radical, which then abstracted hydrogen from the solvent hexane to form biphenyl. With irradiation, biphenyl was also decomposed to lower hydrocarbons as the final products, which was further confirmed by the degradation experiment of biphenyl.
文摘In this paper, by using a block-operator matrix technique, we study mixed-type reverse order laws for {1,3}-, {1,2,3}- and {1,3,4}-generalized inverses over Hilbert spaces. It is shown that and when the ranges of are closed. Moreover, a new equivalent condition of is given.
文摘Local susceptibility variations result in <em>B</em><sub>0</sub> field inhomogeneities, causing distortions and signal losses in MR imaging. Susceptibility variations become stronger with increasing <em>B</em><sub>0</sub> magnetic field strength. Active shimming is used to generate corrective magnetic fields, which can be used to improve <em>B</em><sub>0</sub> field homogeneity. FASTMAP is an effective shimming technique for computing optimal coil currents, which uses data from six projection directions (or columns): this technique is routinely used for shimming cubic volumes of interest (VOIs). In this paper, we propose several improvements to FASTMAP at 4T. For each shim coil, using a modified 3D gradient-echo pulse sequence, we compute <em>B</em><sub>0</sub> inhomogeneity maps and project them onto eight 1<sup>st</sup> and 2<sup>nd</sup> order spherical harmonic functions. This process is repeated for shim currents between -15,000 to 15,000 with increments of 5000 Digital to Analog Converter (DAC) units, and is used to compute the gradient between spherical harmonic coefficients and DAC values for all 8 shim coils—along with the R<sup>2</sup> values of linear fits. A method is proposed (based on R<sup>2</sup> values) to further refine optimal shim currents in respective coils. We present an analysis that is numerically robust and completely flexible in the selection of the VOIs for shimming. Performance analyses, phantom results, and <em>in vivo</em> results of a human brain are presented, comparing our methods with the FASTMAP method.
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
基金the Department of Science and Technology, New Delhi, India (DST/INT/RFBR/P-147)the Russian Foundation of Basic Research, Russia (RFBR 13-03-92692) for financial assistance
文摘Dipeptides are stereo-specifically involved in several biological functions that are challenging to separate enantiomerically. Elution order of enantiomers is an important issue in chiral chromatography. Amylose tris-(3,5-dimethylphenylcarbamate) chiral stationary phase(CSP) is the best and most-widely-used CSP in chiral separations, but experimental data of enantiomeric separation of dipeptides on this CSP is lacking. Simulation studies were conducted to determine the order of elution and the chiral recognition mechanism of didpetides on this CSP. Results indicated that the docking energy of SR-enantiomers were higher than SS-antipodes. The range of docking energies for SR-enantiomers was -7.44 to -5.92 kcal/mol with CSP, but -7.15 to -5.87 kcal/mol for SS-stereoisomers. Therefore it is predicted that SS-enantiomer will elute first, followed by SR-antipode. Furthermore, hydrogen bondings, van der Waal's interactions and electrostatic interactions were observed among SR- and SSenantiomers and chiral grooves of CSP. The number of hydrogen bonds was one in each enantiomer binding except S-Ala-R-Tyr, which contained two hydrogen bonds. No hydrogen bond was found in S-Ala-R-Trp, S-Leu-S-Trp, and S-Leu-S-Tyr dipeptides bindings. The chiral recognition mechanisms dictate different strengths of stereoselective bindings of the enantiomers on CSP.
基金supported by NSFC(No.11271301,No.11171364,No.11001226)Science and Technology Project of Chongqing Education Committee(No.KJ110609)+1 种基金Natural Science Foundation Project of CQ CSTC(No.cstc2011jjA00020)Foundation Project of Chongqing Normal University(No.12XLB029)
文摘This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5<sup>th</sup>-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5<sup>th</sup>-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5<sup>th</sup>-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.
