Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach ge...Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].展开更多
Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the mu...Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.展开更多
Public procurement denotes the attainment of goods,works,or services required by governments through contracts.Public procurement is usually plagued with covert practices and exclusive forms of corruption in Banglades...Public procurement denotes the attainment of goods,works,or services required by governments through contracts.Public procurement is usually plagued with covert practices and exclusive forms of corruption in Bangladesh.The cost of development finance is much higher in public procurement than that of others in Bangladesh.There have been no unified rules or laws regarding government purchases since 2006.The Government of Bangladesh enacted its ever first act of public procurement,the Public Procurement Act,2006(PPA,2006),and the Public Procurement Rules,2008(PPR,2008).The procurement entity must disseminate procurement information through electronic medium i.e.Electronic Government Procurement(hereinafter e-GP).Despite passing over an era since its enactment,the role of the PPA,2006 remains seriously under-researched area,specifically there is no research on the issue of the grievance redress mechanisms.The study has been done using a qualitative case study methodology,backed by both primary and secondary documentary analysis.Based on empirical data,this paper explained the role of digitalization in the process of government procurement and depicted changes that have been brought by the implementation of e-GP in government purchases.However,it concluded that the grievance redress mechanism in the process of procurement is only existing in the policy papers which need mandatory implementation for a transparent and accountable governance system.Despite the significant changes and up-gradation in digital government procurement,it is hardly found that the GRM process is digitalized.And the mass tenderers are yet to be acquainted with the improvised system apart from the consistent efforts of the government.展开更多
文摘Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].
文摘Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.
文摘Public procurement denotes the attainment of goods,works,or services required by governments through contracts.Public procurement is usually plagued with covert practices and exclusive forms of corruption in Bangladesh.The cost of development finance is much higher in public procurement than that of others in Bangladesh.There have been no unified rules or laws regarding government purchases since 2006.The Government of Bangladesh enacted its ever first act of public procurement,the Public Procurement Act,2006(PPA,2006),and the Public Procurement Rules,2008(PPR,2008).The procurement entity must disseminate procurement information through electronic medium i.e.Electronic Government Procurement(hereinafter e-GP).Despite passing over an era since its enactment,the role of the PPA,2006 remains seriously under-researched area,specifically there is no research on the issue of the grievance redress mechanisms.The study has been done using a qualitative case study methodology,backed by both primary and secondary documentary analysis.Based on empirical data,this paper explained the role of digitalization in the process of government procurement and depicted changes that have been brought by the implementation of e-GP in government purchases.However,it concluded that the grievance redress mechanism in the process of procurement is only existing in the policy papers which need mandatory implementation for a transparent and accountable governance system.Despite the significant changes and up-gradation in digital government procurement,it is hardly found that the GRM process is digitalized.And the mass tenderers are yet to be acquainted with the improvised system apart from the consistent efforts of the government.
