Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle

This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation.

TOBACCO PRODUCTS MARKET: FISCAL AND REGULATORY ROLE OF TAXATION

Background.The tobacco taxation policy’s fiscal efficiency should be compre­hensively examined, taking into account both the criteria for the amount of the collected tax revenues to the budget system and the specific share of the hidden tax base, which is part of the shadow economy. The analysis of recent research and publications has shown that despite the availability of some scientific investigations, it is advisable to further develop the main provisions on the tobacco excise tax collection for Ukraine, taking the current market trends and the potential threats into account. The aim of this article is to assess the potential development challenges for the domestic tobacco market and to develop both scientific and practical proposals to increase the fiscal and regulatory effectiveness of the excise tax on tobacco and tobacco products. Materials and methods. In the course of research, the system approach, the methods of analytical estimation, synthesis, economic and mathematical modeling, and scientific abstraction were used. Results. The directions for the further improvement in the tobacco excise taxation practice were offered, taking into account its fiscal and regulatory aspects. The modern peculiarities of the development of the tobacco products market in Ukraine were determined. The main causes and consequences of the illicit excisable goods’ production and circulation have been studied. The excise tax potential index’s calculations without the implementation of systematic measures in the field of counteracting the illicit market were presented. The government policy’s vectors in the field of reducing the cigarette market’s shadow segment have been identified. Conclusion. Taking the excisable goods shadow market’s indicators and its expansion potential into account, the balanced adjustments of the state fiscal policy is important. Counteracting the illicit tobacco and tobacco products trafficking is an important element of the national and economic security strategy. It is advisable to systematize the reliable information on the prevalence of smoking, consumer preferences and the relevant products’ consumption intensity in the territorial context, and the illicit market share as well. On the part of the authorized state institutions, the priority measures are modeling the supply and demand for tobacco products; systematization of information on its illegal circulation; description of the modus operandi of the main participants in the shadow market of tobacco and tobacco products; assessment of institutional capacity, transparency and accountability of fiscal and other authorized bodies for counteracting illicit products trafficking.

Development and Validation of a Novel RP-HPLC Analytical Method for Sitagliptin Determination in Human Plasma

Background: Different bio-analytic methods have been developed for determining drug concentration in plasma, but methods for sitagliptin determination are still very rare. In this study, RP-HPLC based method has been developed for assessing sitagliptin concentration in plasma. Aim: To develop and validate RP-HPLC based analytical method for estimating sitagliptin in human plasma for pharmacokinetic applications. Methods: In the present study, the mobile phase composed of acetonitrile: 0.5% triethanolamine (20:80) with pH 6.5 has been utilized. Samples of plasma containing sitagliptin and internal standard (IS)-rosiglitazone were extracted with dichloromethane:diethyl ether (4:6; v/v) at pH 7.4. The rate of flow was 1 ml/min. The retention time was about 5,232 and 6,903 minutes respectively for sitagliptin and rosiglitazone. Results: At concentrations of 100-3200 ng/ml in plasma, calibration curves of sitagliptin were linear. The inter- and intra-day precision and accuracy ranged in between 93.56-98.56% and 1.09-4.55% respectively. For specificity, the study findings showed no co-eluting peaks occurring with IS drug (rosiglitazone) and confirmed that no percentage of interferences at analyte (sitagliptin) retention in presence of rosiglitazone. The sitagliptin recovery was 96.442%. Chromatographic separations were performed on HI Qsil C-18 HS column (250mm x 4.6mm x 5μm). The stability of stock solutions of sitagliptin and IS at room temperature was 98.06% and 100.79% respectively while under refrigerated conditions stability was 98.19% and 96.59% respectively. Freeze-thaw stability for sitagliptin was performed with low & high QC and shown as 98.26% for and 97.45% respectively. The limits of detection and quantification were 8.592 ng/ml and 28.641 ng/ml respectively. Conclusion: A simple, sensitive and accurate method was developed for bio analytical estimation of sitagliptin in human plasma using liquid-liquid extraction technique. The validation results of linearity, accuracy, precision, stability, selectivity, ruggedness, LOD and LOQ were good under acceptable limit and can be applied for pharmacokinetic studies.

Joint modeling for the analytical estimation of dynamic behaviors of beam-coupled structures

In this study, analytical method is applied for the estimation of dynamic behaviors of beam-coupled structures. Mathematical expressions are given with terms of shape factors, material information and assembly angles of each sub-component. Based on Euler-Bernoulli beam theory, entire formulation is built with compatibility of system dynamics. The coupled structures are divided into two types, point coupling and mass coupling, related with the properties of coupling points. Point coupling is commonly used assumption that two sub-components are combined with lumped spring or damping, and mass coupling has undeformable rigid joint which has mass and inertia like welded structures. Dynamic properties of coupled structures are predicted in forms of frequency response functions and spectral responses about given forces. The verification process is conducted for assessing the accuracy of the estimation formula by using modal frequencies and mode shapes of beam-coupled structures. Extracted modal parameters from experimental modal analysis and finite element method are adopted as reference values for verification.

Analytical Estimation of Data-Motivated Time-Dependent Disease Transmission Rate: An Application to Ebola and Selected Public Health Problems

Obtaining reasonable estimates for transmission rates from observed data is a challenge when using mathematical models to study the dynamics of ?infectious? diseases, like Ebola. Most models assume the transmission rate of a contagion either does not vary over time or change in a fixed pre-determined adhoc ways. However, these rates do vary during an outbreak due to multitude of factors such as environmental conditions, social behaviors, and public-health interventions deployed to control the disease, which are in-part guided by changing size of an outbreak. We derive analytical estimates of time-dependent transmission rate for an epidemic in terms of either incidence or prevalence using a standard mathematical SIR-type epidemic model. We illustrate applicability of our method by applying data on various public health problems, including infectious diseases (Ebola, SARS, and Leishmaniasis) and social issues (obesity and alcohol drinking) to compute transmission rates over time. We show that time-dependent transmission rate estimates can have a large variation, depending on the type of available data and other epidemiological parameters. Time-dependent estimation of transmission rates captures the dynamics of the problem better and can be utilized to understand disease progression more accurately.