Let $K$ be a field of characteristic zero, and $L_{m,c}$ the free metabelian nilpotent Lie algebra class $c$ rank $m$ over $K$. We call an automorphism $\phi$ pointwise inner, if there exists inner $\xi_i$ for each generator $x_i$, $i=1,\ldots,m$, such that $\phi(x_i)=\xi_i(x_i)$. In this study, we exemine group $PI(L_{m,c})$ pintwise automorphisms $L_{m,c}$, provide set generators group.

We construct a hitting set generator for sparse multivariate polynomials over the reals. The seed length of our generator is O(log2(mn/ )) where m is the number of monomials, n is number of variables, and 1− is the hitting probability. The generator can be evaluated in time polynomial in logm, n, and log 1/ . This is the first hitting set generator whose seed length is independent of the degree...

Let Λ be an artin algebra and M n-cluster tilting subcategory of mod Λ. We show that has additive generator if only the n-almost split sequences form a basis for relations Grothendieck group every effaceable functor M→Ab finite length. As consequence we type then

a critical protection requirement for grid connected distributed generators (dg) is anti-islanding protection. in this paper, a new islanding detection method for any possible network loading is proposed based on utilizing and combining various system parameter indices. in order to secure the detection of islanding, eight intentional disturbances are imposed to the system under study in which t...

Let M " be a smooth, closed, orientable 2«-manifold and suppose that Kx"~ is an orientable submanifold of M " dual to a cohomology class x . If d is a positive integer, the signatures of Kd"~ and K"~ are related by a numerical congruence. If n is odd, then any codimension 2 submanifold of CP" fixed by a diffeomorphism of odd prime order is dual to the generator of the cohomology algebra.

State symmetries are defined as permutations which act on vector spaces of column vectors and square matrices, resulting in isotropy groups for specific vector spaces. A large number of properties for such objects is shown, to provide a rigorous basis for future applications. The main statement characterises the state symmetry of vector sequences (v) which are generated by powers of a generator...

Multi-dimensional @I-D) fast Fourier transform (FFT) is an essential algorithm in array signal processing. However, the calculation of M-D indexing and transposition of data matrix required by the M-D FFT are the algorithm's performance killer. The paper will propose a novel M-D to l-D FFT signal flow graph (SFG) mapping. Thus, the M-D FlV can be efficiently implemented by the unified l-D index...

AC 0 circuits of size n log n augmented with log n MODm gates, for every odd integer m and any sufficiently small . As a consequence, for every odd integer m, we obtain a pseudorandom generator, based on the MOD2 function, for circuits of size S containing log S MODm gates. Our results are based on recent bounds of exponential sums that were previously introduced for proving lower bounds for MA...

in the restructured environment of electricity market, firstly the generating companies and the customers are looking for maximizing their profit and secondly independent system operator is looking for the stability of the power network and maximizing social welfare. in this paper, a one way auction in the electricity market for the generator companies is considered in both perfect and imperfec...

Lagged Fibonacci Generators (LFG) are used as a building block of key-stream generator in stream cipher cryptography. In this note, we have used the self-shrinking concept in LFG and given an upper bound 2 n+m 8 for the self-shrinking LFG, where n is the number of stage and m is the word size of the LFG. We have also shown that the bound is attained by all the LFGs of degree n < 28, result supp...