The maximum likelihood estimator does not always maximize the expected log-likelihood when estimating the exponential distribution using a small data set. The maximum likelihood estimator should be multiplied by a positive constant that only depends on the amount of data.

This paper discusses a design problem of a variable gain robust controller with guaranteed gain performance for a class of uncertain switched linear systems. The uncertainties included in the switched linear system under consideration are supposed to satisfy the matching condition and the proposed variable gain robust controller consists of a switching rule, state feedback laws with fixed and variable feedback gain matrices. The switching rule and the fixed feedback gain matrices are derived by using the nominal system. In this paper, we show that a design method of the variable gain robust controller with guaranteed gain performance are reduced to matrix inequalities. Besides, it is presented that the number of matrix inequalities in the proposed design is less than one for the existing results. Finally, an illustrative example is included.

Let X be a Banach space, and E ⊂ X be a non-empty closed bounded subset of X. The set E is called proximinal in X if for all x∈X there is some e ∈ E such that Çx - eÇ = inf{Çx - yÇ : y ∈ E}. E is called remotal in X if for all x ∈ X, there exists e ∈ E such that Çx - eÇ = sup{Çx - yÇ : y ∈ E}. The concept of strong proximinality is well known by now in the literature, and many results were obtained. In this paper we introduce the concept of strong remotality of sets. Many results are presented.

A hybrid of the new Conjugate gradient method and Galerkin theory has been used to find the maximum deflection of a beam under uniformly distributed load. Maximum deflection of a beam under a given pressure was found by solving a two-point linear, second order, boundary value problem with homogeneous boundary conditions without evaluating the inverse of a matrix. An objective function associated with a given member of this class of boundary value problems was optimized. The numerical results obtained from solving some of these problems are very close to the exact solutions. This method is easy to implement and automate computer-wise.

A quasi-orthogonal space time block coding (QO-STBC) scheme that exploits Hadamard matrix properties is studied and evaluated. At first, an analytical solution is derived as an extension of some earlier proposed QO-STBC scheme based on Hadamard matrices, called diagonalized Hadamard space-time block coding (DHSBTC). It explores the ability of Hadamard matrices that can translate into amplitude gains for a multi-antenna system, such as the QO-STBC system, to eliminate some off-diagonal (interference) terms that limit the system performance towards full diversity. This property is used in diagonalizing the decoding matrix of the QO-STBC system without such interfering elements. Results obtained quite agree with the analytical solution and also reflect the full diversity advantage of the proposed QO-STBC system design scheme. Secondly, the study is extended over an interference-free QO-STBC multi-antenna scheme, which does not include the interfering terms in the decoding matrix. Then, following the Hadamard matrix property advantages, the gain obtained (for example, in 4x1 QO-STBC scheme) in this study showed 4-times louder amplitude (gain) than the interference-free QO-STBC and much louder than earlier DHSTBC for which the new approach is compared with.

Even though imaging mass spectrometry (IMS) technique is evolving rapidly, its data analysis capability lags behind. Especially with the improving of IMS data resolution, faster and more accurate data analysis algorithms are required. To meet such challenges in IMS data analysis, an effective and efficient algorithm for IMS data biomarker selection and classification using multiresolution (wavelet) analysis method is proposed. We first applied wavelet transform to IMS data de-noising. The idea of wavelet pyramid method for image matching was then applied for biomarker selection, in which Jaccard similarity was used to measure the similarity of wavelet coefficients. Last, the Naive Bayes classifier was used for classification based on feature vectors in terms of wavelet coefficients. Performance of the algorithm was evaluated in real data applications. Experimental results show that this multi-resolution method has advantages of fast computing and accuracy.

Exotic collections include all non-traditional financial assets that investors pursue for investments and psychological satisfaction purposes. This paper proposes a dynamic Lagrangian model to price these assets, which carry special features compared to traditional assets. The model assumes two types of agents: one has a fixed ratio of traditional investment and the other faces the tradeoff between traditional and exotic investment. The model also incorporates risks of various assets in the utility function to best mimic the real world investor decision. This paper develops the dynamic model and derives the conditions that maximize the agent’s utility in infinite lives. This paper also solves the optimization conditions to present a solution to investment decision.

The present paper deals with the definition and study of new kinds of hypergeometric matrix functions within complex analysis. We also get the radius of regularity and matrix recurrence relations are then developed for l(m, n)-hypergeometric matrix function of two complex variables. We give a different approach to prove the effect of the differential operator on this function. Finally, another hypergeometric matrix function, namely, p l(m, n)-hypergeometric matrix function of two complex variables are defined, its components when the positive integer p is greater than one, provide a matrix partial differential equation satisfied by these function and some of their properties are investigated.

This paper presents stochastic volatility in the valuation of European options. Stochastic volatility models treat the volatility of the underlying asset as a random process rather than the constant volatility assumption of the Black-Scholes model. By changing the model parameters, almost all kinds of asset distributions can be generated by a negative correlation between the stock price process and the volatility process. It is observed that an asset’s log-return distribution is non-Gaussian which is characterized by heavy tails and high peaks. Heston model presents a new approach for a closed form valuation of options specifying the dynamics of the squared volatility as a square-root process and applying Fourier inversion techniques for the pricing procedure. Determination of the market growth rate of the stock share was considered. We also considered the effect of volatility and correlation parameter on the kurtosis and skewness of the density function.

In the paper [1], Pusz and Woronowicz first gave the geometric mean of two positive definite matrices. This mean has similar properties to those of the geometric mean of two positive numbers. In [2], Ando, Li and Mathias listed ten properties that a geometric mean of m positive definite matrices should satisfy. Then gave a definition of geometric mean of m matrices by a iteration which satisfies these ten properties. For the geometric mean of two positive definite matrices, there is an interesting relationship between matrix geometric mean and the information metric. Consider the set of all positive matrices as a Riemannian manifold with the information metric. Then the geometric mean of two matrices in the manifold is just the middle point of the geodesic connecting them. In this paper, we review this notion and present two different proofs, the variation method and the exponential map method, for proving the relationship.