Abstract:
Power system oscillations are a characteristic of the system and they are inevitable. Power System Stabilizer (PSS) can help the damping of power system oscillations. This controller has become an accepted solution for oscillatory instability problems and thus improves system stability. Small signal stability is the system ability to maintain synchronism when a small disturbance occurs. This study provides an analysis of the small signal stability of the power system under different system conditions and operating loads. Several simulations have been done to show the effect of the line parameters on the power system oscillations stability.

Abstract:
The direct thrust force control which is the direct torque control linear type method is modified in this article in order to eliminate the defects that are variable switching frequency and existing large ripples of force and flux, by keeping the advantages of thrust force control method which include simplicity of structure, low dependency to motor parameters and no requirement to coordination transformations. In previous works, the structure simplicity of DTC and low calculations, to reduce the force ripples and fixing switching frequency are disaffirmed, but with regards to keeping DTC advantages, a new method is presented in this article to eliminate the defects by the aid of neural network. for the first time, in this article, the precise non-linear behavior of PMLSM motor and effect of speed in voltage vectors selection in DTC has been considered by using space vector modulation and it has been shown that despite considering motors non-linear behavior, the results concluded by the submitted intelligent DTC-SVM method, is more satisfactory than other methods

Abstract:
Using a compactness argument, we introduce a Phragmen Lindelof type theorem for functions with bounded Laplacian. The technique is very useful in studying unbounded free boundary problems near the infinity point and also in approximating integrable harmonic functions by those that decrease rapidly at infinity. The method is flexible in the sense that it can be applied to any operator which admits the standard elliptic estimate.

Abstract:
We prove that if the given compact set $K$ is convex then a minimizer of the functional $$ I(v)=\int_{B_R} |\nabla v|^p dx+\text{Per}(\{v>0\}),\,1

Abstract:
In this paper we study the fully nonlinear free boundary problem $$ {{array}{ll} F(D^2u)=1 & \text{a.e. in}B_1 \cap \Omega |D^2 u| \leq K & \text{a.e. in}B_1\setminus\Omega, {array}. $$ where $K>0$, and $\Omega$ is an unknown open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that $W^{2,n}$ solutions are locally $C^{1,1}$ inside $B_1$. Under the extra condition that $\Omega \supset \{D u\neq 0 \}$, and a uniform thickness assumption on the coincidence set $\{D u = 0 \}$, we also show local regularity for the free boundary $\partial\Omega\cap B_1$.

Abstract:
Consider the following coupled elliptic system of equations $$ (-\Delta)^s u_i = |u|^{p-1} u_i \quad \text{in} \ \ \mathbb{R}^n $$ where $01$, $m\ge1$, $u=(u_i)_{i=1}^m$ and $u_i: \mathbb{R}^n \to \mathbb{R}$. The qualitative behaviour of solutions of the above system has been studied from various perspectives in the literature including the free boundary problems and the classification of solutions for Sobolev sub- and super-critical exponents. In this paper, we derive monotonicity formulae for entire solutions of the above local, when $s=1,2$, and nonlocal, when $0

Abstract:
In this paper we consider a minimization problem for the functional $$ J(u)=\int_{B_1^+}|\nabla u|\sp 2+\lambda_{+}^2\chi_{\{u>0\}}+\lambda_{-}^2\chi_{\{u\leq0\}}, $$ in the upper half ball $B_1^+\subset\R^n, n\geq 2$ subject to a Lipschitz continuous Dirichlet data on $\partial B_1^+$. More precisely we assume that $0\in \partial \{u>0\}$ and the derivative of the boundary data has a jump discontinuity. If $0\in \bar{\partial(\{u>0\} \cap B_1^+)}$ then (for $n=2$ or $n>3$ and one-phase case) we prove, among other things, that the free boundary $\partial \{u>0\}$ approaches the origin along one of the two possible planes given by $$ \gamma x_1 = \pm x_2, $$ where $\gamma$ is an explicit constant given by the boundary data and $\lambda_\pm$ the constants seen in the definition of $J(u)$. Moreover the speed of the approach to $\gamma x_1=x_2$ is uniform.

Abstract:
In this paper we consider the fully nonlinear parabolic free boundary problem $$ \left\{\begin{array}{ll} F(D^2u) -\partial_t u=1 & \text{a.e. in}Q_1 \cap \Omega\\ |D^2 u| + |\partial_t u| \leq K & \text{a.e. in}Q_1\setminus\Omega, \end{array} \right. $$ where $K>0$ is a positive constant, and $\Omega$ is an (unknown) open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that $W_x^{2,n} \cap W_t^{1,n} $ solutions are locally $C_x^{1,1}\cap C_t^{0,1} $ inside $Q_1$. A key starting point for this result is a new BMO-type estimate which extends to the parabolic setting the main result in \cite{CH}. Once optimal regularity for $u$ is obtained, we also show regularity for the free boundary $\partial\Omega\cap Q_1$ under the extra condition that $\Omega \supset \{u \neq 0 \}$, and a uniform thickness assumption on the coincidence set $\{u = 0 \}$,

Abstract:
In this paper we introduce the multi-phase version of the so-called Quadrature Domains (QD), which refers to a generalized type of mean value property for harmonic functions. The well-established and developed theory of one-phase QD was recently generalized to a two-phase version, by one of the current authors (in collaboration). Here we introduce the concept of the multi-phase version of the problem, and prove existence as well as several properties of such solutions. In particular, we discuss possibilities of multi-junction points.

Abstract:
For a periodic vector field $\h F$, let $\h X^\e$ solve the dynamical system \begin{equation*} \frac{d\h X^\e}{dt} = \h F\lb\frac {\h X^\e}\e\rb . \end{equation*} In \cite{DeGiorgi} Ennio De Giorgi enquiers whether from the existence of the limit $\h X^0(t):=\lim\limits_{\e\to 0}\h X^\e(t)$ one can conclude that $ \frac{d\h X^0}{dt}= constant$. Our main result settles this conjecture under fairly general assumptions on $\h F$, which may also depend on $t$-variable. Once the above problem is solved, one can apply the result to the transport equation, in a standard way. This is also touched upon in the text to follow.