The efficiency of the cache mapping technique depends on how the cache lines are organized and the way that is used to look for and hit the target cache line. In this paper, an efficient technique is proposed to obtain a significant improvement in average hit time of a line in the cache. The paper presents Distributive Comparison Approach (DCA) that significantly minimizes the hit time and improve cache hit ratio. The efficient of DCA is based on how the cache lines are compared and picked up the coveted one leading to a low cache hit ratio. In DCA, the cache line is assigned by multi tags where each individual tag is only one character. Then, instead of one line tag of complete characters per a comparison cycle, the comparator is flushed by multi tags of different lines in the cache. Also the cache lines that are come from the main memory classified into two groups; even and odd line's tags to reject the unwanted lines form the multi-tag comparison. These two procedures practically speed up the repelling of misfit tagged lines and consequently the hitting of the target line in the cache. Simulation results show that the DCA outperforms well-known mapping techniques including FAMT and SMT.
This paper discussed the derivation of two-stage explicit Stochastic Rational Runge-Kutta (SRRK) methods for the solution of stochastic first order ordinary differential equations. The derivation is based on the use of Taylor series expansion for the deterministic and stochastic parts of the stochastic differential equation. Efforts were made to analyse the stability of the methods and also applied the methods to test some numerical problems to solve Stochastic Differential Equations (SDE). From the results obtained it is obvious that the methods derived performed better than the ones with which we compared our results.
The problem of pricing contingent claims has been extensively studied for non-Gaussian models and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was originally studied in Insurance pricing where the distortion function was defined in terms of the normal distribution. It was also used to compare the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using the Cauchy simulation analysis via MATLAB to compare the Wang distortion and NIG distortion operator with their pricing model. The results show that we can recuperate the Black-Scholes and NIG pricing model using the simulation of Cauchy distortion operator.
It is known that the composition of a convex, increasing functional with a subharmonic function is subharmonic. In this paper we show that the composition of a superquadratic functional with a subharmonic function is subharmonic, with a sharper submean inequality. It is further demonstrated that the composition of an increasing convex functional with a nonnegative superquadratic functional with a subharmonic function is subharmonic, with a sharper submean inequality.
In the paper, generally,we solve a irregular vector functions inverse Riemann boundary value problem(R-problem). The kernel of our method is to regularize those equations via introducing some diagonal matrices. Then, we get the solution of the problem at the end of the paper.
This paper study mathematical theory, called the max-plus algebra, which have the wherewithal for a uniform treatment of most problems that arise in the area of Operations Research. The basic properties of max-plus algebra is also explained including how to solve systems of max-plus equations. In this paper, the discrepancy method of max-plus is used to solve n×n and m×n system of linear equations where m ≤ n. From the examples presented, it is clear that an n × n system of linear equations in (max, ⊕,⊗) and (,+, ·) either had One solution, an In nite number of solutions or No solution. Also, both m × n system of linear equations (where m < n) in (max,⊕,⊗) and (,+, ·) have either an in nite number of solutions or no solution. It is therefore clear that many charateristics of the max-plus algebraic structure can be likened to the conventional mathematical structures. Max-plus is used to solve di erent types of matrix operations. We also applied max-plus algebra in solving linear programming problem involving linear equations and inequalities.