In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.展开更多
目的探讨骨转换与老年女性髋部脆性骨折(fragile hip fracture,HF)风险及与高密度脂蛋白胆固醇(HDLc)的相关性。方法选取2021年1月至2022年12月年龄≥60岁女性住院骨质疏松症患者共661例,分为无骨折组(A组)266例和HF组(B组)395例。检测...目的探讨骨转换与老年女性髋部脆性骨折(fragile hip fracture,HF)风险及与高密度脂蛋白胆固醇(HDLc)的相关性。方法选取2021年1月至2022年12月年龄≥60岁女性住院骨质疏松症患者共661例,分为无骨折组(A组)266例和HF组(B组)395例。检测总胆固醇(Tch)、甘油三酯(TG)、HDLc、低密度脂蛋白胆固醇(LDLc)、骨钙素N段中分子片段(N-MID OC)、Ⅰ型胶原羧基端肽β特殊序列(β-CTX)、总蛋白(TP)、白蛋白(Alb)、钙(Ca)、磷(P)、镁(Mg)、尿素(Urea)、肌酐(Cr)、胱抑素C(Cys-C)、肾小球滤过率(eGFR)、骨形成率(MoMF)、骨吸收率(MoMR)及骨转化率(MoT)。结果(1)HF组TP[118(108,128)vs 124(114,131)]、Alb[38.4±3.7 vs 40.0±4.3]、HDLc[1.51(1.24,1.71)vs 1.54(1.37,1.73)]、Ca[2.21±0.12 vs 2.29±0.12]、P[1.03±0.16 vs 1.08±0.17]含量较无骨折组降低,年龄[76(68,83)vs 73(67,78)]、β-CTX[0.57(0.40,0.77)vs 0.34(0.19,0.56)]、MoMR[1.84(1.30,2.51)vs 1.09(0.61,1.83)]及MoT[2.16(1.56,2.85)vs 1.56(1.09,2.38)]较无骨折组增加,差异有统计学意义(P<0.05)。N-MID OC、MoMF、Urea、Cr、Cys-C、eGFR、Tch、TG、LDLc及Mg差异无统计学意义(P>0.05)。(2)老年女性HF与HDLc、TP、ALB、Ca、P、Mg呈负相关(r=-0.09、-0.26、-0.16、-0.28、-0.12、-0.03,P<0.05),与年龄、β-CTX、MoMR、MoT呈正相关(r=0.17、0.36、0.36、0.26,P<0.05),与N-MID OC、MoMF、Urea、Cr、Cys-C、eGFR、Tch、TG、LDLc无相关性(P>0.05)。(3)年龄、MoT、TP、Ca、P为老年女性HF的风险因素,OR分别为1.03(95%CI:1.01~1.06)、1.75(95%CI:1.44~2.12)、0.96(95%CI:0.92~0.99)、0.06(95%CI:0.01~0.37)、0.18(95%CI:0.06~0.6),P<0.05。(4)HDLc与骨转化间存在“U”型关系,P<0.01,其切点为1.692 mmol/L。结论高骨转换是老年女性HF的危险因素,其骨转化率与HDLc存在U型相关。展开更多
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
文摘目的探讨骨转换与老年女性髋部脆性骨折(fragile hip fracture,HF)风险及与高密度脂蛋白胆固醇(HDLc)的相关性。方法选取2021年1月至2022年12月年龄≥60岁女性住院骨质疏松症患者共661例,分为无骨折组(A组)266例和HF组(B组)395例。检测总胆固醇(Tch)、甘油三酯(TG)、HDLc、低密度脂蛋白胆固醇(LDLc)、骨钙素N段中分子片段(N-MID OC)、Ⅰ型胶原羧基端肽β特殊序列(β-CTX)、总蛋白(TP)、白蛋白(Alb)、钙(Ca)、磷(P)、镁(Mg)、尿素(Urea)、肌酐(Cr)、胱抑素C(Cys-C)、肾小球滤过率(eGFR)、骨形成率(MoMF)、骨吸收率(MoMR)及骨转化率(MoT)。结果(1)HF组TP[118(108,128)vs 124(114,131)]、Alb[38.4±3.7 vs 40.0±4.3]、HDLc[1.51(1.24,1.71)vs 1.54(1.37,1.73)]、Ca[2.21±0.12 vs 2.29±0.12]、P[1.03±0.16 vs 1.08±0.17]含量较无骨折组降低,年龄[76(68,83)vs 73(67,78)]、β-CTX[0.57(0.40,0.77)vs 0.34(0.19,0.56)]、MoMR[1.84(1.30,2.51)vs 1.09(0.61,1.83)]及MoT[2.16(1.56,2.85)vs 1.56(1.09,2.38)]较无骨折组增加,差异有统计学意义(P<0.05)。N-MID OC、MoMF、Urea、Cr、Cys-C、eGFR、Tch、TG、LDLc及Mg差异无统计学意义(P>0.05)。(2)老年女性HF与HDLc、TP、ALB、Ca、P、Mg呈负相关(r=-0.09、-0.26、-0.16、-0.28、-0.12、-0.03,P<0.05),与年龄、β-CTX、MoMR、MoT呈正相关(r=0.17、0.36、0.36、0.26,P<0.05),与N-MID OC、MoMF、Urea、Cr、Cys-C、eGFR、Tch、TG、LDLc无相关性(P>0.05)。(3)年龄、MoT、TP、Ca、P为老年女性HF的风险因素,OR分别为1.03(95%CI:1.01~1.06)、1.75(95%CI:1.44~2.12)、0.96(95%CI:0.92~0.99)、0.06(95%CI:0.01~0.37)、0.18(95%CI:0.06~0.6),P<0.05。(4)HDLc与骨转化间存在“U”型关系,P<0.01,其切点为1.692 mmol/L。结论高骨转换是老年女性HF的危险因素,其骨转化率与HDLc存在U型相关。
