Weak form of basic equations in elasticity
The correct weak form of basic equations in elasticity is the foundation of finite element analysis.The weak form obtained by means of the basic equations is often not correct because each basic equation could have a difference in sign(positive or negative).The correct weak form of basic equations in elasticity is presented by means of dual space conception and basic theorem in functional analysis.The conditions on discontinuous surfaces of displacements or elasticity constants for continua are given.The dynamic equations of elasticity defined on 3-D are taken as the equations defined on a domain in 4-D,and the weak forms of dynamic equations of elasticity are given.The same results as Hamilton′s variational principle are derived from the weak form.
The modelling of short-term interest rates in emerging markets is an important research area, especially in view of the growth of new financial markets and of the financial securities traded in these countries. Over the last decade, a number of researchers have looked at different models of short-term interest rates. An important paper in this area is the study by Chan, Karolyi, Longstaff and Sanders (1992, CKLS hereafter), who considered various one-factor models nested in their general interest rate model. The CKLS general model captured various aspects of interest rate behaviour, including drift and mean reversion of interest rates. It also allowed for a general relationship between the level of interest rates and the volatility of rates. By imposing restrictions on these parameters, various well-known models in the literature that are used extensively by financial market operators can be utilized.