We prove that θ-methods with the Lagrange interpolation process is GP-stable if and only if 1/2≤θ≤1.The one-leg θ-methods is GP-stable if and only if θ=1.

In chapter 2, we prove that G(c,p,q)-algebraically stable one-leg methods with linear interpolation are GR(p/2,q/2)-stable and weak GAR(p/2,q/2)-stable for c<1 and GAR(p/2,q/2)-stable for c

It is proved that one-leg θ-methods are stable for 1/2≤θ≤1 and asymptotically stable for 1/2<θ≤1 when the methods are applied to the class R_(α,β) of nonlinear neutral delay differential equations.

This paper is concerned with the numerical stability of one-leg θ-methods for nonlinear Volterra integral equations with delay. It is shown that one-leg θ-methods are globally stable for 1/2 ≤ θ ≤ 1 and asymptotically stable for 1/2 ≤ θ≤ 1.

We focus on the behaviour of the one-leg method and the linear method in the solution of the linear test equation U'(t)=λ(t)U(t)+μ(t)U(t-τ)with τ>0 and λ,μ functions from R to C.

This paper deals with the stability analysis of θ─methods for the solution of double de- lay differential equations u'(t)= au(t) + bu(t - τ)+ cu(t - kτ), and proves that one-leg θ─method and linear θ─method are stable respectively when θ= 1 and 1/2 ≤ 0 ≤ 1 .*

The linear θ- method and one - leg θ- method are applied to the delay differential equation with piece-wise continuous arguments with one delay[t]. The asymptotic stability of numerical solutions is studied.

One-leg methods and linear multistep methods are two class of important numerical methods applied to stiff initial value problems of ordinary differential equations.

Convergence Results of One-Leg and Linear Multistep Methods for Multiply Stiff Singular Perturbation Problems

The results obtained in this paper can be extended for one-leg VSVFM's and for VSVFM's based on predictorcorrector schemes of different types.

Thus, we adapt our local-global step size selection strategy to one-leg methods.

We show that the error control is more complicated in one-leg methods, especially when applied to stiff problems.

Multilead electromyographic studies were made on 15 healthy young adult males to investigate the action of the postural muscles of the lower extremity,especially the gastro- cnemius.The results were as follows: 1.In standing position,either both legs or one leg supported the body weight,the gastrocnemius of the weight bearing leg or legs as well as hamstring muscles showed some potentials.When changing the body position from standing to squatting or the re- verse,the gastrocnemius showed similar activity.It...

Multilead electromyographic studies were made on 15 healthy young adult males to investigate the action of the postural muscles of the lower extremity,especially the gastro- cnemius.The results were as follows: 1.In standing position,either both legs or one leg supported the body weight,the gastrocnemius of the weight bearing leg or legs as well as hamstring muscles showed some potentials.When changing the body position from standing to squatting or the re- verse,the gastrocnemius showed similar activity.It indicates that the gastrocnemius acts together with the hamstring muscles to counteract the action of the quadriceps in main- taining the extended position of the knee joint. 2.When one leg stands on the ground and the other hangs freely,then flex and extend the free leg slowly,no activity was recorded in the gastrocnemius.Similarly no activity was recorded in the gastrocnemius when flexing the knee joint in sitting position. It is,therefore,assumed that the gastrocnemius is not necessarily a flexor of the knee joint as usually considered,but an important extensor under certain conditions. 3.When rotate the leg medially or laterally on siting position,the both heads of the gastrocnemius showed activities.The rotation of the leg towards either direction is not the action of a single head although the medial head is always more active than the lateral one. 4.The activities were also shown in the gastrocnemius when standing on the toes or stepping forward of the weight-bearing leg in walking.It confirms the common view that the gastrocnemius is a flexor of the ankle joint. The activities of the quadriceps,hamstring muscles and soleus were also recorded and discussed.

In this paper we investigate the behavior of the B-S wave function as the squared momentum on one leg becomes infinte while the squared momentum on the other leg remians fixed by using the property of asymptotic freedom in QCD. Using the obtained wave function we compute the cross section of the process e~++e~- → π+q+(?)(where the pion has large transverse momentum perpendicular to the axis of a stratonic jet). We find that the contribution of this process to the cross section of e~++e~-→hadrons is much smaller...

In this paper we investigate the behavior of the B-S wave function as the squared momentum on one leg becomes infinte while the squared momentum on the other leg remians fixed by using the property of asymptotic freedom in QCD. Using the obtained wave function we compute the cross section of the process e~++e~- → π+q+(?)(where the pion has large transverse momentum perpendicular to the axis of a stratonic jet). We find that the contribution of this process to the cross section of e~++e~-→hadrons is much smaller than the process e~++e~-→g+q+(?).

Single angle members are commonly used in trusses, joists, and other types of structures. According to the loading condition, single angle members in compression can be classified as two following categories. One is concentrically loaded angles and the other is eccentrically loaded angles with connection in one leg only.In this paper a finite element method which takes into account the effects of residual stresses, initial crookedness and end restraints provided by gusset plates is used to obtain ultimate strength...

Single angle members are commonly used in trusses, joists, and other types of structures. According to the loading condition, single angle members in compression can be classified as two following categories. One is concentrically loaded angles and the other is eccentrically loaded angles with connection in one leg only.In this paper a finite element method which takes into account the effects of residual stresses, initial crookedness and end restraints provided by gusset plates is used to obtain ultimate strength solutions for compression members of both categories.The strength of simply supported and warping restrained angles with equal or unequal legs and subjected to concentrical load is first presented in the form of column curves. The results show that the strength of unequal leg angles (on a non-dimensional basis) is lower than that of equal leg angles.Numerical calculations also have been carried out for equal and unequal leg angles and the results are compared with test results.Finally, by the use of the concept of effective length as adopted in the codes of some other countries'a family of column curves for eccentrically loaded equal or unequal leg angles with connection in one leg only is given. For convenience of designer, the effective length factor is taken as the parameter for these curves.