Green’s Function for Static Klein–Gordon Equation Stated on a Rectangular Region and Its Application in Meteorology Data Assimilation

The meteorology data assimilation applications often encounter variational problems with unknown weights, where the corresponding Euler equation is an elliptic partial differential equation. This research focused on retrieving the weights in remote sensing data assimilation by means of the computer-friendly form of the Green’s function obtained by eigenfunction expansion for the boundary value problem of the static Klein–Gordon equation on a rectangular region. With the help of the proposed retrieving method, the assimilation problem of estimating regional precipitation with weather radar and rain-gauge is solved in the Green’s function method. Results show that high accuracy of the proposed method makes it a good candidate for data assimilation problems in operational use.

Scene Text Detection Based on Expanding the Text Center Region for Bilingual Tibetan-Chinese

Scene text detection is an important research branch of artificial intelligence technology whose goal is to locate text in scene images. In the Tibetan areas of China, scene images containing both Tibetan and Chinese texts are ubiquitous. Thus, detecting bilingual Tibetan-Chinese scene texts is important in promoting intelligent applications for minority languages. In this study, a scene text detection database for bilingual Tibetan-Chinese is constructed using a manually labeled method and an automatic synthesis method, and a text detection method is proposed. First, we predict a text rectangular region and the text center region for each text instance and simultaneously learned the expansion distance of the text center region. Second, based on the classification score of the text center region and the text rectangular region, we obtain the final confidence of each text instance and then filter out the text center region with lower confidence. Third, through the learned expansion distance, the full-text instance from the remaining text center region is recovered. The results show that our method obtains good detection performance; it achieves an accuracy of up to 75.47% during the text detection phase, laying the foundation for scene text recognition in the subsequent step.

Imperfect Repair Strategies for Two-Dimensional Warranty

<p>When a repairable product under warranty fails, the manufacturer (warrantor) has the choice to either repair or replace the failed product. When repairing a failed product, the degree of repair which affects the working condition of the product can vary, and this is assumed to have an impact on the cost of the repair. The main motivation of this study is to develop a warranty repair strategy that minimizes the costs associated with servicing the warranty. In this research, the product coverage is represented by a two-dimensional rectangular region with a free-replacement warranty. We propose an imperfect repair strategy that suggests employing imperfect repairs of a predefined degree, in prespecified subregions of the warranty region. The aim is to then minimize the expected warranty servicing cost to the manufacturer by determining the optimal partitioning of the warranty region for the chosen degrees of repair. Two imperfect repair models are considered, and for both, the expressions for the distribution of the times to imperfect repair and the expected warranty servicing cost per product sold are derived. We numerically illustrate our findings and compare the expected costs of the proposed imperfect repair strategy with those of previously developed repair-replacement warranty strategies.</p>

Imperfect Repair Strategies for Two-Dimensional Warranty

<p>When a repairable product under warranty fails, the manufacturer (warrantor) has the choice to either repair or replace the failed product. When repairing a failed product, the degree of repair which affects the working condition of the product can vary, and this is assumed to have an impact on the cost of the repair. The main motivation of this study is to develop a warranty repair strategy that minimizes the costs associated with servicing the warranty. In this research, the product coverage is represented by a two-dimensional rectangular region with a free-replacement warranty. We propose an imperfect repair strategy that suggests employing imperfect repairs of a predefined degree, in prespecified subregions of the warranty region. The aim is to then minimize the expected warranty servicing cost to the manufacturer by determining the optimal partitioning of the warranty region for the chosen degrees of repair. Two imperfect repair models are considered, and for both, the expressions for the distribution of the times to imperfect repair and the expected warranty servicing cost per product sold are derived. We numerically illustrate our findings and compare the expected costs of the proposed imperfect repair strategy with those of previously developed repair-replacement warranty strategies.</p>

Imperfect Repair Strategies for Two-Dimensional Warranty

<p>When a repairable product under warranty fails, the manufacturer (warrantor) has the choice to either repair or replace the failed product. When repairing a failed product, the degree of repair which affects the working condition of the product can vary, and this is assumed to have an impact on the cost of the repair. The main motivation of this study is to develop a warranty repair strategy that minimizes the costs associated with servicing the warranty. In this research, the product coverage is represented by a two-dimensional rectangular region with a free-replacement warranty. We propose an imperfect repair strategy that suggests employing imperfect repairs of a predefined degree, in prespecified subregions of the warranty region. The aim is to then minimize the expected warranty servicing cost to the manufacturer by determining the optimal partitioning of the warranty region for the chosen degrees of repair. Two imperfect repair models are considered, and for both, the expressions for the distribution of the times to imperfect repair and the expected warranty servicing cost per product sold are derived. We numerically illustrate our findings and compare the expected costs of the proposed imperfect repair strategy with those of previously developed repair-replacement warranty strategies.</p>

A Simple Guide to Lawn Mowing

This paper presents the total time required to mow a two-dimensional rectangular region of grass using a push mower. In deriving the total time, each of the three ‘well known’ (or intuitive) mowing patterns to cut the entire rectangular grass area is used. Using basic mathematics, analytical and empirical time results for each of the three patterns taken to completely cover this rectangular region are presented, and examples are used to determine which pattern provides an optimal total time to cut a planar rectangular region. This paper provides quantitative information to aid in deciding which mowing pattern to use when cutting one’s lawn.

Algorithms for Finding Vulnerabilities and Deploying Additional Sensors in a Region with Obstacles

Consider a two-dimensional rectangular region guarded by a set of sensors, which may be smart networked surveillance cameras or simpler sensor devices. In order to evaluate the level of security provided by these sensors, it is useful to find and evaluate the path with the lowest level of exposure to the sensors. Then, if desired, additional sensors can be placed at strategic locations to increase the level of security provided. General forms of these two problems are presented in this paper. Next, the minimum exposure path is found by first using the sensing limits of the sensors to compute an approximate “feasible area” of interest, and then using a grid within this feasible area to search for the minimum exposure path in a systematic manner. Two algorithms are presented for the minimum exposure path problem, and an additional subsequently executed algorithm is proposed for sensor deployment. The proposed algorithms are shown to require significantly lower computational complexity than previous methods, with the fastest proposed algorithm requiring O(n2.5) time, as compared to O(mn3) for a traditional grid-based search method, where n is the number of sensors, m is the number of obstacles, and certain assumptions are made on the parameter values.

Guided Visibility Sampling++

Visibility computation is a common problem in the field of computer graphics. Examples include occlusion culling, where parts of the scene are culled away, or global illumination simulations, which are based on the mutual visibility of pairs of points to calculate lighting. In this paper, an aggressive from-region visibility technique called Guided Visibility Sampling++ (GVS++) is presented. The proposed technique improves the Guided Visibility Sampling algorithm through improved sampling strategies, thus achieving low error rates on various scenes, and being over four orders of magnitude faster than the original CPU-based Guided Visibility Sampling implementation. We present sampling strategies that adaptively compute sample locations and use ray casting to determine a set of triangles visible from a flat or volumetric rectangular region in space. This set is called a potentially visible set (PVS). Based on initial random sampling, subsequent exploration phases progressively grow an intermediate solution. A termination criterion is used to terminate the PVS search. A modern implementation using the Vulkan graphics API and RTX ray tracing is discussed. Furthermore, we show optimizations that allow for an implementation that is over 20 times faster than a naive implementation.

Non-stationary dynamics of anisotropic Kirchhoff-Love type shel

Строится нестационарная функция прогиба для тонкой бесконечной цилиндрической оболочки постоянной толщины при воздействии на ее боковую поверхность вынужденной нестационарной движущейся нагрузки, распределенной по прямоугольной области. Материал рассматриваемой цилиндрической оболочки принят упругим и анизотропным, обладающим симметрией относительно ее срединной плоскости. Теория тонких упругих оболочек строится на гипотезах Кирхгофа-Лява. Для математического описания мгновенно приложенной нагрузки используются дельта-функции Дирака. A non-stationary deflection function is determined for a thin infinite cylindrical shell of constant thickness under the influence of non-stationary moving pressure. The pressure is distributed over a rectangular region, which belongs to the side surface of the shell. The shell material is elastic, anisotropic, and has symmetry to the median surface. The theory of thin elastic shells is based on the Kirchhoff-Love’s hypotheses. The Dirac delta-functions are used to describe an instantaneously applied pressure.