An Example of Utilizing Stochastic Approach for Investigating Network Constraints (Congestions) on Horizontally Operated Power Systems with Distributed Generation

This paper shows an example of a stochastic approach to study the impact of distributed generation (DG) on the network constraints (congestions) in power systems. We assume the DG units to be customer-owned, so that they can be connected to or disconnected from the power system by their owners at random. Therefore, the DG units generate power in a stochastic way. The load in the system shows a random behavior too, and the probability distribution of the aggregated generated power and load demand of the distribution system are calculated using Monte Carlo Simulation (MCS).The network constraints (congestions) are evaluated based on the probability distributions of the power flows that result from the simulations. The method that is applied in this paper, shows that looking at the network constraints with a stochastic approach gives a more complete picture of the network than applying a deterministic method, especially when non-dispatchable DG units play a dominant role

Twisted Quantum Affine Superalgebra Uq[sl(2∣2)(2)]U_q[sl(2|2)^{(2)}], Uq[osp(2∣2)]U_q[osp(2|2)] Invariant R-matrices and a New Integrable Electronic Model

We describe the twisted affine superalgebra $sl(2|2)^{(2)}$ and its quantized version $U_q[sl(2|2)^{(2)}]$. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra $U_q[osp(2|2)]$. We work out the tensor product decomposition explicitly and find the decomposition is not completely reducible. Associated with this 4-dimensional grade star representation we derive two $U_q[osp(2|2)]$ invariant R-matrices: one of them corresponds to $U_q[sl(2|2)^{(2)}]$ and the other to $U_q[osp(2|2)^{(1)}]$. Using the R-matrix for $U_q[sl(2|2)^{(2)}]$, we construct a new $U_q[osp(2|2)]$ invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly, this model reduces, in the $q=1$ limit, to the one proposed by Essler et al which has a larger, $sl(2|2)$, symmetry.Comment: 17 pages, LaTex fil

Quadratic automaton algebras and intermediate growth

We present an example of a quadratic algebra given by three generators and three relations, which is automaton (the set of normal words forms a regular language) and such that its ideal of relations does not possess a finite Gr\"obner basis with respect to any choice of generators and any choice of a well-ordering of monomials compatible with multiplication. This answers a question of Ufnarovski. Another result is a simple example (4 generators and 7 relations) of a quadratic algebra of intermediate growth.Comment: To appear in Journal of Cobinatorial Algebr

On the algebra A_{\hbar,\eta}(osp(2|2)^{(2)}) and free boson representations

A two-parameter quantum deformation of the affine Lie super algebra $osp(2|2)^{(2)}$ is introduced and studied in some detail. This algebra is the first example associated with nonsimply-laced and twisted root systems of a quantum current algebra with the structure of a so-called infinite Hopf family of (super)algebras. A representation of this algebra at $c=1$ is realized in the product Fock space of two commuting sets of Heisenberg algebras.Comment: 14 pages, LaTe

On some metabelian 2-group whose abelianization is of type (2, 2, 2) and applications

Let $G$ be some metabelian $2$-group satisfying the condition $G/G'\simeq \mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/2\mathbb{Z}$. In this paper, we construct all the subgroups of $G$ of index $2$ or $4$, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem of the $2$-ideal classes of some fields $\mathbf{k}$ satisfying the condition $\mathrm{G}al(\mathbf{k}_2^{(2)}/\mathbf{k})\simeq G$, where $\mathbf{k}_2^{(2)}$ is the second Hilbert $2$-class field of $\mathbf{k}$.Comment: in Journal of Taibah University for Science (2015