In this paper, the performance of a universal mobile telecommunication system (UMTS)-based passive multistatic radar in a line-of-sight (LoS) environment is studied. The presence of LoS component from the target considerably alters the received signal model, therefore, its characterization is necessary and is the main subject of this work where the transceivers and a target are localized in a three-dimensional Euclidean space. The probability density function (PDF) of the received signal in the presence of LoS is derived and the closed-form expressions of the modified Cramer-Rao lower bounds (MCRLBs) on the Euclidean coordinates of target's position and velocity are found. It is shown that modified Fisher information matrix (MFIM) is a combination of MFIMs due to non-LoS (NLoS) components and LoS component. With the aid of numerical examples, it is verified that by exploiting LoS, the target radar cross section (RCS) increases, which improves the accuracy of target's detection and parameter estimation. In addition, it is also shown that by exploiting LoS component, the performance limits of a waveform can be determined for a generalized radar cross section model (GRCSM), which provides the characterization of a waveform for a broader range of radar applications.

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Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the LaneEmden type equations which have roots in the study of stellar structures are presented and discussed.

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We present the use of complex Lie symmetries in variational problems by defining a complex Lagrangian and considering its Euler-Lagrange ordinary differential equation. This Lagrangian results in two real "Lagrangians" for the corresponding system of partial differential equations, which satisfy Euler-Lagrange like equations. Those complex Lie symmetries that are also Noether symmetries (i.e. symmetries of the complex Lagrangian) result in two real Noether symmetries of the real "Lagrangians". Also, a complex Noether symmetry of a second order complex ordinary differential equation results in a double reduction of the complex ordinary differential equation. This implies a double reduction in the corresponding system of partial differential equations.

The objective of this study is to investigate the impact of financial leverage on corporate financial performance of Pakistan's textile sector from 1999-2012 using panel data. The leverage-performance relationship is examined with a special focus on the Global Financial Crisis of [2007][2008]. Both accountingbased (Return on Assets -ROA) and market-based (Tobin's Q) measures of corporate financial performance are used. Regression analysis is performed with and without inclusion of financial crisis dummy. Total Debt to Total Assets (TDTA), Long Term Debt to Total Assets (LDTA), Short Term Debt to Total Assets (SDTA) and Debt to Equity (DE) ratios are used as proxies for financial leverage whereas firm's size and firm's efficiency are used as control variables. The results indicate that financial leverage has a negative impact on corporate performance when measured with ROA. Whereas in case of Tobin's Q, SDTA coefficient is positive. It can be concluded that since cost of borrowing is high in Pakistan and debt capital markets are less developed, firms are forced to resort to banks as their source of debt finance and thus have to repay huge amount of principal and interest which has a heavy toll on their financial health. In addition to this, financial crisis was found to have a negative impact on corporate performance and also affect the leverage-performance relationship.

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