In this work, we prove by employing mapping Cone that the sequence and the subsequence of the characteristic-zero are exact and subcomplex respectively in the case of partition (6,6,4) .

In this paper the diagrams and divided power of the place polarization
(k )
ij  , with
its capelli identities have been used, to study the complex of Lascoux in case of the
partition (4,4,4).

In this paper we study the relation between the resolution of Weyl Module F K ) 3 , 4 , 4 (
in
characteristic-free mode and in the Lascoux mode (characteristic zero), more precisely we
obtain the Lascoux resolution of F K ) 3 , 4 , 4 (
in characteristic zero as an application of the
resolution of F K ) 3 , 4 , 4 (
in characteristic-free.
Key word : Resolution, Weyl module, Lascoux mode, divided power, characteristic-free.

     The Syriac language is one of the ancient Semitic languages that appeared in the first century AD. It is currently used in a number of cities in Iraq, Turkey, and others. In this research paper, we tried to apply the work of  Ali and Mahmood 2020  on the letters and words in the Syriac language to find a new encoding for them and increase the possibility of reading the message by other people.

In the partition theory, there is more then one form of representation of dedication, most notably the Abacus diagram, which gives an accurate and specific description. In the year 2019, Mahmood and Mahmood presented the idea of merging more than two plans, and then the following question was raised: Is the process of separating any somewhat large diagram into smaller schemes possible? The general formula to split e-abacus diagram into two or more equal or unequal parts was achieved in this study now.

In this article, the inverse source problem is determined by the partition hyperbolic equation under the left end flux tension of the string, where the extra measurement is considered. The approximate solution is obtained in the form of splitting and applying the finite difference method (FDM). Moreover, this problem is ill-posed, dealing with instability of force after adding noise to the additional condition. To stabilize the solution, the regularization matrix is considered. Consequently, it is proved by error estimates between the regularized solution and the exact solution. The numerical results show that the method is efficient and stable.

     Minimizing the power consumption of electronic systems is one of the most critical concerns in the design of integrated circuits for very large-scale integration (VLSI). Despite the reality that VLSI design is known for its compact size, low power, low price, excellent dependability, and high functionality, the design stage remains difficult to improve in terms of time and power. Several optimization algorithms have been designed to tackle the present issues in VLSI design. This study discusses a bi-objective optimization technique for circuit partitioning based on a genetic algorithm. The motivation for the proposed research is derived from the basic concept that, if some portions of a circuit's system are deactivated during th