On-line arbitrarily vertex decomposable suns

We give a complete characterization of on-line arbitrarily vertex decomposable graphs in the family of unicycle graphs called suns. A sun is a graph with maximum degree three, such that deleting vertices of degree one results in a cycle. This result has already been used in another paper to prove some Ore-type conditions for on-line arbitrarily decomposable graphs.     

Heavy-tails and regime-switching in electricity prices

In this paper we first analyze the stylized facts of electricity prices, in particular, the extreme volatility and price spikes which lead to heavy-tailed distributions of price changes. Then we calibrate Markov regime-switching (MRS) models with heavy-tailed components and show that they adequately address the aforementioned characteristics. Contrary to the common belief that electricity price models ‘should be built on log-prices’, we find evidence that modeling the prices themselves is more beneficial and methodologically sound, at least in case of MRS models.     

On a Unique Ergodicity of Some Markov Processes

It is proved that the sufficient condition for the uniqueness of an invariant measure for Markov processes with the strong asymptotic Feller property formulated by Hairer and Mattingly (Ann Math 164(3):993–1032, 2006) entails the existence of at most one invariant measure for e-processes as well. Some application to time-homogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise is also given.     

Solving the discrete-continuous project scheduling problem via its discretization

In this paper a discrete-continuous project scheduling problem is considered. In this problem activities simultaneously require discrete and continuous resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resources are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a classical (i.e. discrete) project scheduling problem in the multi-mode version is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. In the former case a nonlinear solver is used for solving a corresponding convex programming problem. The results are compared with the results obtained using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each iteration. The results of a computational experiment are analyzed and some conclusions are included.     

Solid phase synthesis of two muramyl pentapeptide derivatives

Solid phase peptide synthesis (SPPS) of two selected muramyl pentapeptide derivatives is described. The simplicity of removing the protecting groups via one-step deprotection and cleavage from the resin is the biggest advantage of SPPS. Using this method, two muramyl pentapeptide derivatives, D-MurN₃-L-Ala-D-iGlu-L-Lys-D-Ala-D-Ser (5) and D-MurN₃-L-Ala-D-iGlu-L-Lys-D-Ala-D-Ala (6), were obtained. Their chemical structures were confirmed by high-resolution mass spectrometry (HRMS) and nuclear magnetic resonance (NMR) spectroscopy. To determine the absolute configuration of the carbon atom in the side chain of the muramic acid derivative, single-crystal X-ray diffraction measurements were recorded.     

Optoelectronic Thresholder for Pattern Recognition with Double Feedback Module

The present paper proposes a modification of a simple optoelectronic architecture (A. Bergeron et al.: Appl. Opt. 33 (1994) 1463) for carrying out optical thresholding operations. The threshold operation is achieved by means of a feedback loop. The setup is modified by inserting an attenuator adapted in each iteration to the total incident energy measured by an intensity detector. The proposed architecture does not need an additional light source, assures translation invariance and does not break the beam propagation path. The adaptive attenuator permits working under different lighting conditions (illumination, partially occluded objects, etc.). This kind of architecture is suitable for an optical pattern recognition task, optical neural network or optical associative memory. Application of the modified thresholder to the recognition task based on an optical correlator is reported.     

Normal-Phase TLC Separation of Some Antiarrhythmics. Densitometric Determination of Mexiletine Hydrochloride in Capsules

JPC – Journal of Planar Chromatography – Modern TLC - A normal-phase (NP) TLC method has been established for separation of the five antiarrhythmics - disopyramide, flecainide,...