One of the important issues being explored in Industry 4.0 is a collaborative mobile robots. This collaboration requires precise navigation systems, especially indoor navigation systems where GNSS (Global Navigation Satellite System) cannot be used. To enable precise localization of robots, different variations of navigation systems are being developed, mainly based on trilateration and triangulation methods. Triangulation systems are distinguished by the fact that they allow precise determination of an object’s orientation, which is important for mobile robots. An important feature of positioning systems is the frequency of position updates based on measurements. For most systems it is 10-20 Hz. In our work, we propose a high-speed 50 Hz positioning system based on the triangulation method with infrared transmitters and receivers. In addition, our system is completely static, i.e. it has no moving/rotating measurement sensors, which makes it more resistant to disturbances (caused by vibrations, wear and tear of components, etc.). In this paper we describe the principle of the system as well as its design. Finally, we present tests of the built system, which show centimeter positioning accuracy with a position update frequency of 50 Hz.

Directional dithering of a laser beam potentially limits the detection accuracy of a laser triangulation displacement probe. A theoretical analysis indicates that the measurement accuracy will linearly decrease as the laser dithering angle increases. To suppress laser dithering, a laser triangulation displacement probe with laser beam pointing control, which consists of a collimated red laser, a laser beam pointing control setup, a receiver lens, and a charge-coupled device, is proposed in this paper. The laser beam pointing control setup is inserted into the source laser beam and the measured object and can separate the source laser beam into two symmetrical laser beams. Hence, at the angle at which the source laser beam dithers, the positional averages of the two laser spots are equal and opposite. Moreover, a laser dithering compensation algorithm is used to maintain a stable average of the positions of the two spots on the imaging side. Experimental results indicate that with laser beam pointing control, the standard variance of the fitting error decreases from 0.3531 to 0.0100, the repeatability accuracy can be decreased from ±7mm to ±5 μm, and the nonlinear error can be reduced from ±6 %FS to ±0.16 %FS.

Abstract: Droughts are complex and gradually evolving conditions of extreme water deficits which can compromise livelihoods and ecological integrity, especially in fragile arid and semi-arid regions that depend on rainfed farming, such as Kitui West in south-eastern Kenya. Against the background of low ground-station density, 10 gridded rainfall products and four gridded temperature products were used to generate an ensemble of 40 calculations of the Standardized Precipitation Evapotranspiration Index (SPEI) to assess uncertainties in the onset, duration and magnitude of past droughts. These uncertainties were driven more by variations between the rainfall products than variations between the temperature products. Remaining ambiguities in drought occurrence could be resolved by complementing the quantitative analysis with ground-based information from key informants engaged in disaster relief, effectively formulating an ensemble approach to SPEI-based drought identification to aid decision making. The reported trend towards drier conditions in Eastern Africa was confirmed for Kitui West by the majority of data products, whereas the rainfall effect on the increasingly dry conditions was more subtle than annual and seasonal declines and greater annual variation, which warrants further investigation. Nevertheless, the effects of increasing droughts are already felt on the ground and warrant decisive action.

The paper deals with exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination of multiples of primes. These elementary number theory activities, appropriate for technology-enhanced secondary mathematics education courses, are supported by a spreadsheet, Wolfram Alpha, Maple, and the Online Encyclopedia of Integer Sequences. General formulas for subsequences of polygonal numbers referred to in the paper as polygonal number sieves of order k that include base-two exponential functions of k have been developed. Different problem-solving approaches to the derivation of such and other sieves based on the technology-immune/technology-enabled framework have been used. The accuracy of computations and mathematical reasoning is confirmed through the technique of computational triangulation enabled by using more than one digital tool. A few relevant excerpts from the history of mathematics are briefly featured.

The triangulation process represents a violation of the boundary between parental and child relational subsystems which, in turn, affects family dynamics and relationships. The paper, with distinct reference to marital conflict and divorced couples, describes the main causes of the triangulation process and its impact on children (and adolescents) as significant third participants within the parental conflict. Besides, it fo-cuses on long-term consequences associated with triangulation process to parental conflict exposure, that can adversely affect the well-being of children during their life-cycle, and even into adulthood. A data-search was carried out for articles to be included in the review and articles were retrieved from different electronic databases (first: Scopus and Web of Science, then: PsychINFO, Google Scholar, EBSCO and ScienceDirect,). After having initially considered 152 articles, 58 studies were selected for this research. A qualitative analysis was conducted on selected studies, focusing on: (1) different types of triangulation commonly used in intergenerational family relationships; (2) an updated summary of the research around the impact of triangulation on the well-being of children and the parent-child conflict; and (3) the main characteristics of successful intervention of preventative and psychotherapeutic treatments. In conclusion, the results, examining the long-term effects of the triangulation process, highlight the developmental paths of children that are more exposed and at risk, and focuses on the importance of preventing the intergenerational transmission of marital conflict, as a way to reduce mental health costs and to improve the well-being of children and families who are all involved in these conflicting and destructive dynamics.

Using the orbit decomposition, a new enumerative polynomial P(x) is introduced for abstract (simplicial) complexes of a given type, e.g., trees with a fixed number of vertices or triangulations of the torus with a fixed graph. The polynomial has the following three useful properties. (I) The value P(1) is equal to the total number of unlabeled complexes (of a given type). (II) The value of the derivative P'(1) is equal to the total number of nontrivial automorphisms when counted across all unlabeled complexes. (III) The integral of P(x) from 0 to 1 is equal to the total number of vertex-labeled complexes, divided by the order of the acting group. The enumerative polynomial P(x) is demonstrated for trees and then is applied to the triangulations of the torus with the vertex-labeled complete four-partite graph G = K_{2,2,2,2}, in which specific case P(x) = x^{31}. The graph G embeds in the torus as a triangulation, T(G). The automorphism group of G naturally acts on the set of triangulations of the torus with the vertex-labeled graph G. For the first time, by a combination of algebraic and symmetry techniques, all vertex-labeled triangulations of the torus (twelve in number) with the graph G are classified intelligently without using computing technology, in a uniform and systematic way. It is helpful to notice that the graph G can be converted to the Cayley graph of the quaternion group Q_8 with the three imaginary quaternions i, j, k as generators.

Splines and quasi-interpolation operators are important both in approximation theory and applications. In this paper, we construct a family of quasi-interpolation operators for the bivariate quintic spline spaces S₅³ (∆_mn⁽²⁾). Moreover, the properties of the proposed quasi-interpolation operators are studied, as well as its applications for solving two-dimensional Burgers’ equation and image reconstruction. Some numerical examples show that these methods, which are easy to implement, provide accurate results.

The nuclear lamina consists of a dense fibrous meshwork made of nuclear lamins, Type V intermediate filaments, and is ~14 nm thick according to recent cryo-electron tomography studies. Recent advances in light microscopy have extended the resolution to a scale allowing for the fine structure of the lamina to be imaged in the context of the whole nucleus. We review quantitative approaches to analyze the imaging data of the nuclear lamina as acquired by structured illumination microscopy (SIM) and single molecule localization microscopy (SMLM), as well as the requisite cell preparation techniques. In particular, we discuss the application of steerable filters and graph based methods to segment the structure of the four mammalian lamin isoforms (A, C, B1, and B2) and extract quantitative information.

The proliferation of the Internet of Things (IoT) has revolutionized traditional services, giving rise to emerging smart infrastructures by connecting the physical and digital worlds. Sensory data is essential in IoT-based systems for providing context-aware and location-based services. Hence, the accurate localization of IoT devices is paramount. Anchor misplacement can significantly affect location information and coverage services in IoT. We study the effect of anchor misplacement in typical IoT settings where sensors are randomly deployed, can be mobile and may belong to multiple providers. We identify sensing coverage holes formed by anchor misplacement and analyze their presence and impact. To mitigate the impact of anchor misplacement on network reliability, we propose a framework to identify the affected sensor nodes and then identify and remove misplaced anchor nodes. The validity of our approach is verified, and its effectiveness is demonstrated by several experiments with different network topologies and parameters. Our results are promising and can be utilized in multiple coverage applications, such as smart agriculture systems and habitat monitoring, regardless of the sensors or deployment types. It also sheds light on best practices and methods for a reliable design of IoT-based systems.

Black hole temperature T_BH = T_P/2πd as a function of its Planck length real diameter multiplier d is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured d = 1/2π describes primordial Big Bang singularity as in this case T_BH = T_P. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -c² if all its vertices have black hole gravitational potential of -c²/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier d. It is shown that black holes feature wave-particle duality only if d ≤ 8π, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.

Due to the complexity, high-risk, and conservative character of construction companies, advanced digital technologies do not become widely adopted in the short term, while vendors make determined efforts to overcome this and disseminate their technologies. This paper presents the methods of an investigation addressing the extremely complex issues related to the current practices of digital technology adoption in construction. It discusses how construction companies follow a specific logical process linked to need, project objectives, characteristics of the adopting organization, and the characteristics of the new technology to be adopted. The study aims to demonstrate a novel method of data collection and analysis including data and methodological triangulation techniques including the use of NVivo and AHP to explore how companies make the decision to uptake a new technology (e.g. advanced crane, tunnel boring machine or drones) by focusing on customer and vendor activities, their interactions, contributing factors, and people involved in the process. The major original contribution of this paper is to develop an innovative methodological Cube for investigating the Construction Technology Adoption Process (CTAP) covering technology adoption, acceptance, diffusion and implementation concepts. CTAP is a framework that delineates the phases of the process that customer organizations use when deciding to adopt a new digital technology and the parallel vendor activities. The significance of these contributions is that they enable vendors to understand how to match their strategies with customer expectations in each phase of the CTAP. It also provides a benchmark for new construction companies to use the current best practice of decision making. Future research is warranted to more clearly delineate any differences with developing nations or related industries such as mining and property management.