Online stochastic UAV mission planning with time windows and time-sensitive targets

In this paper we simultaneously consider three extensions to the standard Orienteering Problem (OP) to model characteristics that are of practical relevance in planning reconnaissance missions of Unmanned Aerial Vehicles (UAVs). First, travel and recording times are uncertain. Secondly, the information about each target can only be obtained within a predefined time window. Due to the travel and recording time uncertainty, it is also uncertain whether a target can be reached before the end of its time window. Finally, we consider the appearance of new targets during the flight, so-called time-sensitive targets, which need to be visited immediately if possible. We tackle this online stochastic UAV mission planning problem with time windows and time-sensitive targets using a re-planning approach. To this end, we introduce the Maximum Coverage Stochastic Orienteering Problem with Time Windows (MCS-OPTW). It aims at constructing a tour with maximum expected profit of targets that were already known before the flight. Secondly, it directs the planned tour to predefined areas where time-sensitive targets are expected to appear. We have developed a fast heuristic that can be used to re-plan the tour, each time before leaving a target. In our computational experiments we illustrate the benefits of the MCS-OPTW planning approach with respect to balancing the two objectives: the expected profits of foreseen targets, and expected percentage of time-sensitive targets reached on time. We compare it to a deterministic planning approach and show how it deals with uncertainty in travel and recording times and the appearance of time-sensitive targets.     

On some properties of a linguistic classifier

A general structure of a linguistic classifier wherein sub-subclassifiers are the building blocks is suggested. Some properties of these sub-subclassifiers are proposed and proved. The physical significances of these properties are explored and it is shown that a condensed measure of belongingness of patterns to any class can be obtained which can conveniently be used for forming classification rules.     

Randomized distributions in event recording models for multiple processes

We consider the problem of allowing for fluctuations in "recording intensity," which is reducible to randomization by an appropriate parameter. The properties (including asymptotic properties) of randomized convolutions with uniform and gamma distributions are considered. Constructive algorithms are developed for computing randomized distributions. Numerical implementation of these algorithms has made it possible to compare randomized and nonrandomized distribution for some characteristic parameter values.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 84–93, 1985.     

Analysis of rounded data from dependent sequences

Observations on continuous populations are often rounded when recorded due to the precision of the recording mechanism. However, classical statistical approaches have ignored the effect caused by the rounding errors. When the observations are independent and identically distributed, the exact maximum likelihood estimation (MLE) can be employed. However, if rounded data are from a dependent structure, the MLE of the parameters is difficult to calculate since the integral involved in the likelihood equation is intractable. This paper presents and examines a new approach to the parameter estimation, named as “short, overlapping series” (SOS), to deal with the α-mixing models in presence of rounding errors. We will establish the asymptotic properties of the SOS estimators when the innovations are normally distributed. Comparisons of this new approach with other existing techniques in the literature are also made by simulation with samples of moderate sizes.     

Application of optimization methods for finding equilibrium states of two-dimensional crystals

A two-dimensional model of a multilayer material and a procedure for simulating its properties based on global optimization methods are proposed. This model is applied for the case of a two-dimensional crystal. Global minima of the interaction energy of the material’s atoms are found, and geometric characteristics of its corresponding equilibrium states are described. The resulting lattices, in particular graphene’s lattices, agree with experimental data, which confirms the validity of the proposed approach. This approach can be extended to a wider class of layered structures, and it can be used for determining the mechanical properties of materials.     

Existence for a model arising from the in situ vitrification process

Existence of a solution is established for a time-dependent problem that can be used to model the in situ vitrification process. Certain properties of the solution are also presented.     

包含—受扭迴转轴的半空间的性质*

本文研究包含有一根部份嵌入的迴转轴的半空间的性质.不用知道一给定的嵌入的轴的扭转问题的精确解,这些性质能指出此半空间的位移或应力场的某些特点并且有时可以用来检查数值解.文中给出嵌入半空间的受扭的刚性圆柱的轴的表面上的正确的应力分布的检查的例子.     

Experimental Investigation of Elastodissipative Characteristics of Carbon-Fiber-Reinforced Plastics

A procedure is described for the experimental study of elastodissipative properties of carbon-fiber-reinforced plastic (CFRP) structures. Experimental values of dissipation factors are given for angle-ply structures with a reinforcing angle varying from 0 to 90°. Elastodissipative characteristics of two types of CFRP are identified. The values obtained can be used for predicting the properties of complex CFRP structures. It is shown that the energy absorption in sandwich structures with CFRP skins and a honeycomb core is mainly governed by properties of the skins.     

Morphological and functional aspects of the study of some mechanical properties of the human aorta

Some mechanical properties (strength, stretchability, rupture stress, and the like) of the walls of various sections of the aorta have been studied by application of methods and apparatus used in textile materials science. In experiments on unpedigreed dogs, the possibility was studied of recording pulsed oscillations of aorta walls by rheographic methods. The method of polyrheoaortography, which allows, during one's lifetime, determination of the viscoelastic properties of the walls of the human aorta at its various levels, was suggested and tested. High correlation was shown upon comparison of the results of morphological and functional studies. Data have been obtained on the age, individual, and topographic features of the mechanical properties of the aorta, which allows determination of the hemodynamic state in different sections of the aorta for different states of the organism.     

软群

Molodtsov提出了软集——一种处理不确定性信息的数学工具．本文在进行了阐述软集的相关概念和性质后,接下来给出了软群的定义,并对软群的软同态做了进一步研究．     

软群

Molodtsov提出了软集——一种处理不确定性信息的数学工具.本文在进行了阐述软集的相关概念和性质后,接下来给出了软群的定义,并对软群的软同态做了进一步研究.     

Uniform stability and ISS of discrete-time impulsive hybrid systems

This paper studies the uniform stability and ISS (input-to-state stability) properties for DIHS (discrete-time impulsive hybrid systems) via comparison approach. By employing the vector-value function, the comparison principle is established for DIHS with external inputs. Then the comparison principle is used to establish the uniform stability and ISS criteria for DIHS, respectively. Moreover, regions in which the uniform stability and ISS properties can be guaranteed are estimated. As applications, the comparison principle and the results of uniform stability and ISS are used to study the robustly globally uniformly exponential stability for uncertain DIHS and exponential ISS of DIHS. It is shown that impulses contribute to stability and ISS properties for a discrete-time system which has no such properties. Two examples with numerical simulations are worked out for illustration.     

A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.     

Graph transformations preserving the stability number

We analyse the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin deletions. We also show how some of these transformations are related to the notion of even pair introduced to color some classes of perfect graphs. Then, some properties of edge deletion and twin deletion are given and a conjecture is formulated about the class of graphs for which these transformations can be used to determine the stability number.     

Homothetic transformations and geometric loci: properties of triangles and quadrilaterals

In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the figure are considered. These loci are studied in paragraphs 3 and 4. By means of the homothetic transformations some properties of triangles and quadrilaterals are found. The study of these properties can be used, with profit, in a classroom activity supported by Dynamic Geometry System.     

Estimating production test properties from test measurement data

A complex sequence of tests on components and the system is a part of many manufacturing processes. Statistical imperfect test and repair models can be used to derive the properties of such test sequences but require model parameters to be specified. We describe a technique for estimating such parameters from typical data that are available from past testing. A Gaussian mixture model is used to illustrate the approach and as a model that can represent the wide variety of statistical properties of test data, including outliers, multimodality and skewness. Model fitting was carried out using a Bayesian approach, implemented by MCMC. Copyright © 2011 John Wiley & Sons, Ltd.     

二项式系数幂和序列在模p2下的几个性质

利用同余理论和多项式理论研究二项式系数幂和序列在模p2下的同余性质,得到了一些非平凡结果.为进一步研究二项式系数幂和序列的多项式递推公式提供有利的工具.     

Removing dead transitions in timed-arc Petri nets

Timed-arc Petri nets (TAPNs) are a timed extension of Petri nets where tokens are assigned an age indicating the time elapsed from its creation, and PT-arcs (place to transition arcs) are labelled with time intervals that are used to restrict the age of the tokens that can be used to fire the adjacent transition. This is a rather pathological model, as reachability is undecidable, whereas some other known properties of Petri nets, like boundedness, coverability and even termination, are decidable. This article focuses on the problem of detecting dead transitions, i.e. transitions that can be removed from the model since they can never become enabled. We prove that this problem is decidable for TAPNs with natural times, and we present an algorithm that can be used to find dead transitions in the particular case of 1-safe TAPNs.     

Vaginal bleeding patterns — the problem and an example data set

Data concerning the vaginal bleeding patterns of women using different forms of fertility regulation are presented. The data were collected in the form of diaries which were completed by the women themselves by recording the presence or absence of vaginal bleeding on a daily basis. The object of the paper is to invite suggestions for suitable methods of presentation and analysis of such data so that the results of studies on methods of fertility regulation can be better summarized and interpreted.