Let K be a proper cone in R^x,let A be an n×n real matrix that satisfies AK(?)K,letb be a given vector of K,and let λbe a given positive real number.The following two lin-ear equations are considered in this pap...Let K be a proper cone in R^x,let A be an n×n real matrix that satisfies AK(?)K,letb be a given vector of K,and let λbe a given positive real number.The following two lin-ear equations are considered in this paper:(i)(λⅠ_n-A)x=b,x∈K,and(ii)(A-λⅠ_n)x=b,x∈K.We obtain several equivalent conditions for the solvability of the first equation.展开更多
This paper presents the effect of magnetic field, indicated by Hartmann number (Ha), on the free convective flow of Magneto-hydro-dynamic (MHD) fluid in a square cavity with a heated cone of different orientation. Alt...This paper presents the effect of magnetic field, indicated by Hartmann number (Ha), on the free convective flow of Magneto-hydro-dynamic (MHD) fluid in a square cavity with a heated cone of different orientation. Although similar studies abound, the novelty of this work lies in the presence of the heated cone, whose orientation is varied at different angles. The mathematical model includes the system of governing mass, momentum and energy equations. The system is solved by finite element method. The calculations are performed for Prandtl number Pr = 0.71;the Rayleigh number Ra = 10, 1000, 100,000;and for Hartmann number Ha = 0, 20, 50, 100. The results are illustrated with streamlines, velocity profiles and isotherms. From the results, it is found that for the present configuration, magnetic field (Hartmann number) has no effect on the shape of the streamlines for low Rayleigh numbers. However, for high values of Ra, the effect of Ha becomes quite visible. Magnetic field affects the flow by retarding the fluid movement, and thus affects convective heat transfer. At low Ra, the fluid movement and heat transfer rate are already slowing, thus impressing a magnetic field does not produce much effect. At high Ra, fluid particles move at high velocity and change the stream lines, in absence of any magnetic force. Impressing magnetic field in this situation produced noticeable effect by slowing down the fluid movement and changing the streamlines back to low Ra situations. It is noted that a combination of low Ra with zero or low Ha produces similar effects with the combination of high Ra and high Ha. It can be concluded that with increasing Ha, heat transfer mode in MHD fluid gradually changes toward conduction from convection. It can be surmised that sufficiently large Ha can potentially stop the fluid movement altogether. In that case, heat transfer would be fully by conduction.展开更多
Purpose: To improve the accuracy in megavoltage photon beam dose calculation in CBCT-based radiation treatment (RT) plans, using a kilovoltage cone-beam computed tomography (CBCT)-to-density-step (CBCT-SF) function. M...Purpose: To improve the accuracy in megavoltage photon beam dose calculation in CBCT-based radiation treatment (RT) plans, using a kilovoltage cone-beam computed tomography (CBCT)-to-density-step (CBCT-SF) function. Materials and Methods: The CBCT-SF table is constructed from differential histograms of the voxel values of CBCT and Fan-beam CT (FBCT). From the CBCT histograms, frequency peaks representing air, lung, soft tissue and bone are observed and their widths in CT numbers are assigned to the lower and higher bounds of the steps in the CBCT-SF. The CBCT-SF is entered into a planning system as an alternative to the clinical CT-to-density table. The CT image sets studied in this work consist of FBCT and CBCT scans of three patients: a prostate cancer patient, a lung cancer patient and a head and neck patient;and of a humanoid phantom at sections of the pelvis, the thorax and the head. Deformable image registration is used to map the patient FBCT scans to the corresponding CBCT images to minimize anatomical variations. Three-dimensional conformal radiotherapy (3D-CRT) and intensity-modulated radiotherapy (IMRT) plans are made on the FBCT image sets of the patients and the phantom. The plans are recalculated on the CBCT scans using both the conventional CT-to-density table and the CBCT-SF. Dose calculations on the CBCT images and FBCT images are compared using dose differences, distance to agreement (DTA), Gamma analyses and dose volume histogram (DVH) analyses. Results: The results show that IMRT plans optimized using CBCT scans and FBCT scans agree dosimetrically within 1% when the CBCT-SF is used for the CBCT-based plans, including thoracic IMRT plan. In contrast, up to 5% dose difference is observed between IMRT plans optimized on FBCT scans and CBCT scans for thoracic cases if conventional CT-to-density table is used on CBCT images. Conclusions: The simple stepwise mapping of the CBCT numbers to density using the CBCT-SF resolves the inaccuracies in dose calculations previously reported in CBCT-based RT plans. CBCT-SF can be used in Image-Guided adaptive radiotherapy planning.展开更多
文摘Let K be a proper cone in R^x,let A be an n×n real matrix that satisfies AK(?)K,letb be a given vector of K,and let λbe a given positive real number.The following two lin-ear equations are considered in this paper:(i)(λⅠ_n-A)x=b,x∈K,and(ii)(A-λⅠ_n)x=b,x∈K.We obtain several equivalent conditions for the solvability of the first equation.
文摘This paper presents the effect of magnetic field, indicated by Hartmann number (Ha), on the free convective flow of Magneto-hydro-dynamic (MHD) fluid in a square cavity with a heated cone of different orientation. Although similar studies abound, the novelty of this work lies in the presence of the heated cone, whose orientation is varied at different angles. The mathematical model includes the system of governing mass, momentum and energy equations. The system is solved by finite element method. The calculations are performed for Prandtl number Pr = 0.71;the Rayleigh number Ra = 10, 1000, 100,000;and for Hartmann number Ha = 0, 20, 50, 100. The results are illustrated with streamlines, velocity profiles and isotherms. From the results, it is found that for the present configuration, magnetic field (Hartmann number) has no effect on the shape of the streamlines for low Rayleigh numbers. However, for high values of Ra, the effect of Ha becomes quite visible. Magnetic field affects the flow by retarding the fluid movement, and thus affects convective heat transfer. At low Ra, the fluid movement and heat transfer rate are already slowing, thus impressing a magnetic field does not produce much effect. At high Ra, fluid particles move at high velocity and change the stream lines, in absence of any magnetic force. Impressing magnetic field in this situation produced noticeable effect by slowing down the fluid movement and changing the streamlines back to low Ra situations. It is noted that a combination of low Ra with zero or low Ha produces similar effects with the combination of high Ra and high Ha. It can be concluded that with increasing Ha, heat transfer mode in MHD fluid gradually changes toward conduction from convection. It can be surmised that sufficiently large Ha can potentially stop the fluid movement altogether. In that case, heat transfer would be fully by conduction.
文摘Purpose: To improve the accuracy in megavoltage photon beam dose calculation in CBCT-based radiation treatment (RT) plans, using a kilovoltage cone-beam computed tomography (CBCT)-to-density-step (CBCT-SF) function. Materials and Methods: The CBCT-SF table is constructed from differential histograms of the voxel values of CBCT and Fan-beam CT (FBCT). From the CBCT histograms, frequency peaks representing air, lung, soft tissue and bone are observed and their widths in CT numbers are assigned to the lower and higher bounds of the steps in the CBCT-SF. The CBCT-SF is entered into a planning system as an alternative to the clinical CT-to-density table. The CT image sets studied in this work consist of FBCT and CBCT scans of three patients: a prostate cancer patient, a lung cancer patient and a head and neck patient;and of a humanoid phantom at sections of the pelvis, the thorax and the head. Deformable image registration is used to map the patient FBCT scans to the corresponding CBCT images to minimize anatomical variations. Three-dimensional conformal radiotherapy (3D-CRT) and intensity-modulated radiotherapy (IMRT) plans are made on the FBCT image sets of the patients and the phantom. The plans are recalculated on the CBCT scans using both the conventional CT-to-density table and the CBCT-SF. Dose calculations on the CBCT images and FBCT images are compared using dose differences, distance to agreement (DTA), Gamma analyses and dose volume histogram (DVH) analyses. Results: The results show that IMRT plans optimized using CBCT scans and FBCT scans agree dosimetrically within 1% when the CBCT-SF is used for the CBCT-based plans, including thoracic IMRT plan. In contrast, up to 5% dose difference is observed between IMRT plans optimized on FBCT scans and CBCT scans for thoracic cases if conventional CT-to-density table is used on CBCT images. Conclusions: The simple stepwise mapping of the CBCT numbers to density using the CBCT-SF resolves the inaccuracies in dose calculations previously reported in CBCT-based RT plans. CBCT-SF can be used in Image-Guided adaptive radiotherapy planning.
文摘【目的】挖掘与华山松球果数量相关的基因。【方法】以华山松球果数量性状表型数据筛选华山松高、低球果数量单株,利用前期已开发的单核苷酸多态性(single-nucleotide polymorphism,SNP)标记结合表型数据进行全基因组关联分析(genome-wide association study,GWAS),构建华山松样品的系统发育树,发掘与华山松球果数量性状相关的SNP标记与候选基因,并进一步分析筛选出的基因在华山松针叶、木质部、韧皮部、树皮、幼嫩球果和树根的qPCR基因组织特异性表达。【结果】系统发育树显示:同一种源的单株基本处于相近的位置,而来自巍山的单株广泛分布于各个群体中,与主成分分析结果基本一致。全基因组关联分析共检测到12个与球果数量显著关联的SNP位点,其中,Marker193307的序列与纤维素合成相关基因Korrigan (KOR1,编码跨膜内切β-1,4-D葡聚糖酶)的序列相似度较高(74.74%)。qPCR基因组织特异性表达分析结果显示:该基因在华山松枝条韧皮部的表达量最高,幼嫩球果中次之,在根系的表达量最少,初步判断该基因与球果数量相关。【结论】华山松种源地相近的单株基本处于相近的位置。巍山种源的材料较其他种源拥有较为广泛的遗传变异。GWAS分析仅检索到1个与植物纤维素合成相关的基因(KOR1),该基因可能参与球果数量性状的表达。
