In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...

When power systems are expanded and connected together with weak tie lines, the low-frequency oscillations are increased and the stability margin of the power system decreases. Therefore, when designing the transmission system to be used, it is necessary to maintain the dynamic stability of the power system, and to make sure to have the most possible stability margin. SSSC is a FACTS device con...

We study analytically plane strain static deformations of functionally graded eccentric and non-axisymmetrically loaded circular cylinders comprised of isotropic and incompressible linear elastic materials. Normal and tangential surface tractions on the inner and the outer surfaces of a cylinder may vary in the circumferential direction. The shear modulus is taken to vary either as an exponenti...

Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of self-maps of P1 with ramification to order ei at general points Pi, in the case that all ei are less than the characteristic. We also develop a new, more functorial construction for the basic theory of limit linear series, which works transparently in posi...

When power systems are expanded and connected together with weak tie lines, the low-frequency oscillations are increased and the stability margin of the power system decreases. Therefore, when designing the transmission system to be used, it is necessary to maintain the dynamic stability of the power system, and to make sure to have the most possible stability margin. SSSC is a FACTS device con...