Time sensitive functionals of marked Cox processes

This paper continues studies on a multivariate marked Cox process C_t observed upon some random epochs τ={τ₁,τ₂,…} initiated in [J. Math. Anal. Appl. 293 (2004) 1-13]. The goal is to connect the continuous time parameter process C_t with C_τ for which closed-form transforms were presented in that paper. This work does not only restore some or much of the information on C_t lost due to its limited observation, but it also manages to scrutinize the behavior of C_τ around the first passage time of C_τ (that takes place upon one of the observation epochs τ) within some random time intervals. Again, analytically tractable formulas for functionals of C_τ are derived.     

Stability of functional equations in single variable

This paper discusses Hyers-Ulam stability for functional equations in single variable, including the forms of linear functional equation, nonlinear functional equation and iterative equation. Surveying many known and related results, we clarify the relations between Hyers-Ulam stability and other senses of stability such as iterative stability, continuous dependence and robust stability, which are used for functional equations. Applying results of nonlinear functional equations we give the Hyers-Ulam stability of Böttcher's equation. We also prove a general result of Hyers-Ulam stability for iterative equations.     

Infinite interval problems arising in non-linear mechanics and non-Newtonian fluid flows

Existence results are presented for second-order boundary value problems on the infinite interval modelling phenomena which arise in non-Newtonian fluid theory and in circular membranes.     

Monotone iterative technique for periodic boundary value problems with causal operators

In this paper, we develop the monotone iterative technique for periodic boundary value problems with causal operators.     

Lead-insensitive fiber optic pH sensor and performance under bending

We have designed and tested a lead-insensitive fiber optic pH sensor that is based on the absorption of an indicator dye immobilized in a polymer bead. The fiber optic pH sensor uses two wavelengths; one senses the change in absorption of the indicator dye and the other provides a reference signal. In a view to desired time modulation and the dual wavelength time division multiplexing, we used light emitting diodes for sources, a phototransistor for the detector, and electronics process the detected signal. The sensor has demonstrated fast response, repeatable calibration, reversibility, and stability. This inexpensive device may also be used during bending of the optical fiber for applications in the field.     

Queues with hysteretic control by vacation and post-vacation periods

The paper investigates the queueing process in stochastic systems with bulk input, batch state dependent service, server vacations, and three post-vacation disciplines. The policy of leaving and entering busy periods is hysteretic, meaning that, initially, the server leaves the system on multiple vacation trips whenever the queue falls below r (⩾1), and resumes service when during his absence the system replenishes to N or more customers upon one of his returns. During his vacation trips, the server can be called off on emergency, limiting his trips by a specified random variable (thereby encompassing several classes of vacation queues, such as ones with multiple and single vacations). If by then the queue has not reached another fixed threshold M (⩽ N), the server enters a so-called “post-vacation period” characterized by three different disciplines: waiting, or leaving on multiple vacation trips with or without emergency. For all three disciplines, the probability generating functions of the discrete and continuous time parameter queueing processes in the steady state are obtained in a closed analytic form. The author uses a semi-regenerative approach and enhances fluctuation techniques (from his previous studies) preceding the analysis of queueing systems. Various examples demonstrate and discuss the results obtained. This revised version was published online in June 2006 with corrections to the Cover Date.     

Direct fail-proof triangularization algorithms for AX + XB = C with Error-Free and parallel implementations

Two 0(mn³) inversion-free direct algorithms to compute a solution of the linear system AX +XB = C by triangularizing a Hessenberg matrix are presented. Without any loss of generality the matrix A is assumed upper Hessenberg and the order m of A the order n of B. The algorithms have an in-built consistency check, are capable of pruning redundant rows and converting the resulting matrix into a full row rank matrix, and permit A and —B to be any square matrices with common or distinct eigenvalues. In addition, these algorithms can also solve the homogeneous system AX +XB = 0 (null matrix C). An error-free implementation of the solution X using multiple modulus residue arithmetic as well as a parallelization of the algorithms is discussed.     

Silyl group deprotection by Pd/C/H2. A facile and selective method

An easy, high yield, RT, short-reaction-time Pd/C hydrogenation of silyl groups is described. This includes TES, TPS, TBS, TBDMS, TIPS, and TBDPS. The relative selectivity of the process has been investigated and we can show, for example, that TES, TPS, TBS, and TBDMS removal can be performed in the presence of TIPS and TBDPS.     

Silhouette Analysis for Performance Evaluation in Machine Learning with Applications to Clustering

Grouping the objects based on their similarities is an important common task in machine learning applications. Many clustering methods have been developed, among them k-means based clustering methods have been broadly used and several extensions have been developed to improve the original k-means clustering method such as k-means ++ and kernel k-means. K-means is a linear clustering method; that is, it divides the objects into linearly separable groups, while kernel k-means is a non-linear technique. Kernel k-means projects the elements to a higher dimensional feature space using a kernel function, and then groups them. Different kernel functions may not perform similarly in clustering of a data set and, in turn, choosing the right kernel for an application could be challenging. In our previous work, we introduced a weighted majority voting method for clustering based on normalized mutual information (NMI). NMI is a supervised method where the true labels for a training set are required to calculate NMI. In this study, we extend our previous work of aggregating the clustering results to develop an unsupervised weighting function where a training set is not available. The proposed weighting function here is based on Silhouette index, as an unsupervised criterion. As a result, a training set is not required to calculate Silhouette index. This makes our new method more sensible in terms of clustering concept.