The Mostafa Maged four-stitch technique to avoid leaving dead space during repairing the episiotomy

Most women who are primigravida are mostly confronted with episiotomy during child-birth to prevent the perineal and vaginal lacerations which could be performed at birth. There are many types of episiotomies which are median, mediolateral and J-shaped episiotomy. In here, we performed the mediolateral suture due to its safety. All episiotomy were taken by the Mostafa Maged four-stitch technique. Prevention of the formation of the dead space during the repair of episiotomy so avoiding hematoma formation in the episiotomy area after child-birth. It is an Interventional study. The Mostafa Maged four-stitch technique uses the absorbable vicryls treads with round needles 75 mm. the results of this new technique are Prevention of the dead space formation, Good and tight hemostasis of the episiotomy is achieved, strong approximation of the two edges of the episiotomy, cosmetically, it is so good. The invention of this new technique (Mostafa Maged technique) has shown its effectiveness in those fifteen patients in preventing the dead space during suturing the episiotomy in primigravida cases.

Approximation of SDE solutions using local asymptotic expansions

We develop an asymptotic expansion for small time of the density of the solution of a non-degenerate system of stochastic differential equations with smooth coefficients, and apply this to the stepwise approximation of solutions. The asymptotic expansion, which takes the form of a multivariate Edgeworth-type expansion, is obtained from the Kolmogorov forward equation using some standard PDE results. To generate one step of the approximation to the solution, we use a Cornish–Fisher type expansion derived from the Edgeworth expansion. To interpret the approximation generated in this way as a strong approximation we use couplings between the (normal) random variables used and the Brownian path driving the SDE. These couplings are constructed using techniques from optimal transport and Vaserstein metrics. The type of approximation so obtained may be regarded as intermediate between a conventional strong approximation and a weak approximation. In principle approximations of any order can be obtained, though for higher orders the algebra becomes very heavy. In order 1/2 the method gives the usual Euler approximation; in order 1 it gives a variant of the Milstein method, but which needs only normal variables to be generated. However the method is somewhat limited by the non-degeneracy requirement.

Strong Embeddings for Transitory Queueing Models

In this paper, we establish strong embedding theorems, in the sense of the Komlós-Major-Tusnády framework, for the performance metrics of a general class of transitory queueing models of nonstationary queueing systems. The nonstationary and non-Markovian nature of these models makes the computation of performance metrics hard. The strong embeddings yield error bounds on sample path approximations by diffusion processes in the form of functional strong approximation theorems.

Pointwise (H, Φ) Strong Approximation by Fourier Series of LΨ Integrable Functions

We essentially extend and improve the classical result of G. H. Hardy and J. E. Littlewood on strong summability of Fourier series. We will present an estimation of the generalized strong mean (H, Φ) as an approximation version of the Totik type generaliza- tion of the result of G. H. Hardy, J. E. Littlewood, in case of integrable functions from LΨ. As a measure of such approximation we will use the function constructed by function Ψ com- plementary to Φ on the base of definition of the LΨ points. Some corollary and remarks will also be given.