Search Results (81)

This study develops a high-accuracy indoor positioning system using ultra-wideband (UWB) technology and the time-of-arrival (TOA) method. The system is built using Arduino Nano microcontrollers and DW1000 UWB chips to measure distances between anchor nodes and a mobile tag. Three positioning algorithms are tested: the triangle centroid algorithm (TCA), inner triangle centroid algorithm (ITCA), and the proposed intersection midpoint algorithm (IMA). Experiments conducted in a 732 × 488 × 220 cm indoor environment show that TCA performs well near the center but suffers from reduced accuracy at the edges. In contrast, IMA maintains stable and accurate positioning across all test points, achieving an average error of 12.87 cm. The system offers low power consumption, fast computation, and high positioning accuracy, making it suitable for real-time indoor applications such as hospital patient tracking and shopping malls where GPS is unavailable or unreliable. Full article

In a multi-point source system, increasing the jamming power can expand the distribution area of the equivalent radiation center, but significantly increases the system exposure risk. Therefore, in order to achieve an optimal balance between the two, this paper proposes a joint optimization method for jamming power and an array of multi-point source systems. First, based on determining the spatial geometric relationship between the triplet antenna and the target, the distribution law of the equivalent radiation center of the triplet antenna under the condition of the target echo is derived. Second, by introducing the angle factor, the jamming power and equivalent radiation center distribution area are combined to construct the joint optimization model of jamming power and array in omnidirectional and non-omnidirectional situations. Third, based on the non-dominated sorting whale optimization algorithm (NSWOA), an adaptive inertia weight based on the cosine function and logistic chaotic map is introduced to obtain the optimal arrangement. The experimental results show that in the omnidirectional case, when the average jamming-to-signal ratio is 13.83 dB, the equilateral triangle array can achieve the goal of protecting the target while avoiding the exposure of the triplet antenna position. In the non-omnidirectional case, when the average jamming-to-signal ratio is 13.90 dB, the equilateral triangle array can achieve the optimal balance between the jamming power and the area of the distribution area of the equivalent radiation center, and control the distribution of the equivalent radiation center to strictly meet the preset angular domain constraints. Furthermore, the optimal JSR value was reduced by an average of 1.14 dB compared with that of the conventional selection scheme. Full article

In this design, foam packaging for consumer products is replaced by the kraft paper cushioning system. The kraft paper is made into a cylindrical structure, with small cylindrical structures pasted to its outer walls. The cylindrical structure can withstand a high amount of stress, internally and externally. These cylindrical structures’ center points make an imaginary equilateral triangle. Therefore, the applied load is distributed equally across the cylinders and hexagonal structures. We can replace foam packaging with this kraft paper packaging. This design is expected to provide a more eco-friendly product than a normal packaging system. The interior design for the kraft paper is created as integrated cylindrical structures designed using Computer Aided Drawing (CAD). Various tests, such as on compression, impact, and vibration, were carried out. In this design, stimulation, cost comparison of the design, and manufacturing feasibility were examined. Full article

Performing secondary tasks affects the performance of primary tasks. Engaging in secondary tasks while driving often leads to accidents. Therefore, this study aimed to investigate the impact on reaction time when drivers perform secondary tasks while driving. The participants of this study were 30 participants, including 11 males and 19 females. During driving, participants watched a driving video. When a warning triangle appeared in the center of the road, participants immediately pressed the Enter button. When the participant pressed the Enter button, the computer automatically recorded the time of the button press. In a within-subjects design, all participants took part in secondary tasks during the primary driving task, and outcomes were compared between secondary tasks (no task, conversation with the passenger, and listening to the radio). The results show that the reaction time during conversation with the passenger in the primary task was significantly longer than that during listening to the radio or having no task. However, there was no significant difference in reaction time between having no task and listening to the radio. The average reaction time with no task was longer than while listening to the radio. Fatigue increased the reaction time for no task. Having a conversation with the passenger did not affect the average reaction time for both tests due to the conversation with the passenger mitigating the effects of fatigue. The results of this study provide a reference for further research on driving behavior. Full article

In the face of the urgent need for the coordinated development of regional rural functions and the orderly and efficient integration of urban and rural areas, the problem of how to accurately identify the spatial correlation relationships and characteristics of rural elements among regions in Northeast China has become a key issue that urgently needs to be resolved. The results show the following: (1) The overall spatial correlation network (SCN) in the Northeast region from the perspective of rural element gravity has obvious differences. Each province has generated a strong connection center, and “strip-shaped” connection belts have been formed across provinces and cities. (2) From the perspective of the spatial pattern of the strong connection attributes of rural elements, Heilongjiang Province presents a polygonal “rhombus network”, Jilin Province presents a closed-loop “triangle network”, and Liaoning Province presents an irregular “trapezoid network”. (3) The connection relationships of rural element nodes within the provincial scope show that Yichun is an important hub connecting all directions within the province; Changchun and Siping have become the central nodes connecting the nodes on the northwest–southeast wings; Fuxin and Yingkou have become the central locations connecting the nodes on the southwest–northeast sides. (4) There are four sectors in the network, and the rural element transfer mechanism among the sectors shows that Block I and Block II are net spillover sectors, playing the role of “resource-based” sectors, and transmitting information to the net inflow Block IV through the broker Block III, presenting a “gradient” transmission mode. Full article

It is well known that the four ancient Greek triangle centers and others have homogeneous barycentric coordinates that are polynomials in the sidelengths $a,b,$ and c of a triangle $ABC$. For example, the circumcenter is represented by the polynomial $a(b^2+c^2-a^2)$. It is not so well known that triangle centers have barycentric coordinates, such as $\tan A : \tan B : \tan C$, that are also representable by polynomials, in this case, by $p(a, b, c) : p(b, c, a) : p(c, a, b)$, where $p(a, b, c)=a(a^2+b^2-c^2)(a^2+c^2-b^2)$. This paper presents and discusses the polynomial representations of triangle centers that have barycentric coordinates of the form $f(a, b, c) : f(b, c, a) : f(c, a, b)$, where f depends on one or more of the functions in the set $\{\cos , \sin , \tan , \sec , \csc , \cot \}$. The topics discussed include infinite trigonometric orthopoints, the n-Euler line, and symbolic substitution. Full article

The five-bar linkage, used in the form of a planar manipulator, benefits from easy controllability and relatively simple kinematic structures, which mean that it can be used in several applications in robotics, rehabilitation, and haptic devices, etc. This paper proposes an optimal synthesis method for a symmetrical five-bar linkage of type 5-RRRRR, with a singularity-free dexterous workspace, based on workspaces with predefined shapes, like squares, rectangles, triangles, circles, and ellipses. The synthesis conditions, to avoid singularities, are given as inequations, which can be further substituted with a system of equations, by introducing the supraunitary coefficient, k. The analytical solutions of the resulting system of equations enable the computation of the link lengths of the five-bar linkage. The optimization method provides the optimal value of the supraunitary coefficient, in order to obtain a maximum value for the minimum input transmission angle and a minimum value for the manipulator size. In this paper, the authors present an analytical approach to the optimal synthesis of a symmetrical five-bar linkage for different shapes of workspace, with the same surface and coordinates in terms of the mass center, as well as the resulting link lengths. In regard to the numerical examples, the authors considered and compared performance indices, such as manipulability, the condition number, and stiffness. The considered examples showed that an equilateral triangle-shaped workspace achieved higher global manipulability, a square-shaped workspace achieved higher global dexterity and the minimum input transmission angle, and circular workspaces achieved the highest mean stiffness and total surface size. It was observed that the synthesis method generates structures that are well-suited to singularity-free dexterous workspaces, with nonzero stiffness values. Full article

This paper focuses on a comprehensive study of a four-axle vehicle, including dynamics analysis, equivalent modeling methods, and their comparison. Firstly, a linear two-degree lateral dynamic model is established, which has four drive axles and two steer axles. Secondly, the mathematical transfer function expressions for the yaw rate and the centroid sideslip angle were derived on the basis of the model. The steady-state parameters, such as yaw rate gain G_γss, centroid sideslip angle gain G_βss, stability factor K_n, equivalent axial distance l_n, and equivalent centroid sideslip angle coefficient K_n’ were obtained by using the transfer functions. Then, the steady-state and transient characteristics are roundly discussed, including steady-state parameters, system root trajectory, frequency domain, and time domain. Some recommendations for the four-axle vehicle’s parameter design are also given. Finally, for a more simple and efficient analysis of response characteristics of four-axle vehicles and even n (n > 4) axle vehicles, the equivalent model is developed for the four-axle vehicle, and comprehensive analyses are presented with four equalization methods, which are based on the inner heart of the approximation triangle, the outer heart of the approximation triangle, the center of gravity of the approximation triangle and the compensation point. Following a thorough analysis of the four, it is determined that the inner approximation triangle solution approach is most suited for four-axle vehicles. Full article

We propose a Ramsey-theory-based approach for the analysis of the behavior of isolated mechanical systems containing interacting particles. The total momentum of the system in the frame of the center of masses is zero. The mechanical system is described by a Ramsey-theory-based, bi-colored, complete graph. Vectors of momenta of the particles ${\overrightarrow{p}}_i$ serve as the vertices of the graph. We start from the graph representing the system in the frame of the center of masses, where the momenta of the particles in this system are ${\overrightarrow{p}}_{cmi}.$ If ${(\overrightarrow{p}}_{cmi}(t)·{\overrightarrow{p}}_{cmj}(t))\ge 0$ is true, the vectors of momenta of the particles numbered i and j are connected with a red link; if ${(\overrightarrow{p}}_{cmi}(t)·{\overrightarrow{p}}_{cmj}(t))<0$ takes place, the vectors of momenta are connected with a green link. Thus, the complete, bi-colored graph emerges. Considering an isolated system built of six interacting particles, according to the Ramsey theorem, the graph inevitably comprises at least one monochromatic triangle. The coloring procedure is invariant relative to the rotations/translations of frames; thus, the graph representing the system contains at least one monochromatic triangle in any of the frames emerging from the rotation/translation of the original frame. This gives rise to a novel kind of mechanical invariant. Similar coloring is introduced for the angular momenta of the particles. However, the coloring procedure is sensitive to Galilean/Lorenz transformations. Extensions of the suggested approach are discussed. Full article

In this study, the resonant characteristics of the off-center-driven Chladni plates were systematically investigated for the square and equilateral triangle shapes. Experimental results reveal that the number of the resonant modes is considerably increased for the plates under the off-center-driving in comparison to the on-center-driving. The Green’s functions derived from the nonhomogeneous Helmholtz equation are exploited to numerically analyze the information entropy distribution and the resonant nodal-line patterns. The experimental resonant modes are clearly confirmed to be in good agreement with the maximum entropy states in the Green’s functions. Furthermore, the information entropy distribution of the Green’s functions can be used to reveal that more eigenmodes can be triggered in the plate under the off-center-driving than the on-center-driving. By using the multiplication of the resonant modes in the off-center-driving, the dispersion relation between the experimental frequency and the theoretical wave number can be deduced with more accuracy. It is found that the deduced dispersion relations agree quite well with the Kirchhoff–Love plate theory. Full article

Structural DNA nanotechnology is an emerging field and is expected to be used for various applications in materials science. In this study, we designed a DNA tensegrity triangle to accommodate the bipyridine complexes with metal ions (Ni²⁺ and Fe²⁺) at the center of the space within the triangle. A metal–bipyridine-incorporated DNA tensegrity triangle was crystalized, and the presence of metals within it was confirmed through X-ray crystal structure analysis. A signal of the anomalous dispersion effect derived from metal was observed in the center of the DNA triangle. Full article

The chemistry of heterometallic metal complexes continues to attract the interest of molecular inorganic chemists mainly because of the properties that different metal ions can bring to compounds. Contrary to the plethora of 3d–4f- and 3d–3d′-metal complexes, complexes containing both 3d- and 4d-metal ions are much less studied. The choice of the bridging organic ligand is of paramount importance for the synthesis of such species. In the present work, we describe the use of the potentially tetradentate NOO′O″ Schiff bases N-(2-carboxyphenyl)salicylideneimine (saphHCOOH) and N-(4-chloro-carboxyphenyl)salicylideneimine (4ClsaphHCOOH) in Cd^II-M^III (M = Fe, Cr) chemistry. The complexes [Cd₂Fe₂(saphCOO)₄(NO₃)₂(H₂O)₂] (1), [Cd₂Cr₂(saphCOO)₄(NO₃)₂(H₂O)₂] (2), [Cd₂Fe₂(4ClsaphCOO)₄(NO₃)₂(H₂O)₂] (3) and [CdCr₂(4ClsaphCOO)₄(H₂O)₃(EtOH)] (4) have been structurally characterized, the quality of the structure of the latter being poor but, permitting the knowledge of the connectivity and the main structural features. Complexes 1–3 are isostructural, but not isomorphous, possessing a variety of lattice solvent molecules (EtOH, MeCN, CH₂Cl₂, H₂O). The metal topology can be described as two isosceles triangles sharing a common Cd^II…Cd^II edge. The two Cd^II atoms are doubly bridged by two μ-aqua groups. The M^III…Cd^II sides of the triangles are each asymmetrically bridged by one carboxylate oxygen atom of a 2.2111 saphCOO²⁻/4ClsaphCOO²⁻ ligand. The core of the molecules is {Cd₂M₂(μ-O_aqua)₂(μ-OR)₄}⁶⁺, where the OR oxygen atoms are the bridging carboxylate oxygens. The coordination spheres of the metal ions in the centrosymmetric molecules are [Cd(O_aqua)₂(O_carboxylato)₄(O_nitrato)₂] and [M(N_imino)₂(O_carboxylato)₂(O_phenolato)₂]. The biaugmented trigonal prism is the most appropriate for the description of the coordination geometry of the Cd^II atoms in 1 and 3, while the geometry of these metal ions in 2 is best described as distorted triangular dodecahedral. A combination of H-bonding and π–π stacking interactions give interesting supramolecular patterns in the three tetranuclear compounds. The three metal ions in 4 define an isosceles triangle with two almost equal Cd^II…Cr^III sides. The Cd^II center is linked to each Cr^III atom through one carboxylato oxygen of a 2.2111 4ClsaphCOO²⁻ ligand. The core of the molecule is {CdCr₂(μ-OR)₂}⁶⁺, where the OR oxygen atoms are the bridging carboxylato oxygens. A tridentate chelating 1.1101 4ClsaphCOO²⁻ ligand is bonded to each Cr^III. The coordination spheres are [Cd(O_aqua)₃(O_ethanol)(O_{bridging carboxylato})₂(O_{terminal carboxylate})₂] and [Cr(O_{bridging carboxylato})(O_{terminal carboxylato})(O_phenolato)₂(N_imino)₂]. Complexes 1–4 are the first heterometallic 3d–4d complexes based on saphHCOOH and 4ClsaphCOOH. The structures are critically compared with those of previous reported Zn^II-M^III (M = Fe, Cr) complexes. The IR and Raman spectra of the complexes are discussed in terms of the coordination modes of the ligands involved. UV/VIS spectra in CH₂Cl₂ are also reported, and the bands are assigned to the corresponding transitions. The δ and ΔE_Q⁵⁷Fe-Mössbauer parameters of 1 and 3 at room temperature and 80 K suggest the presence of isolated high-spin Fe^III centers. Variable-temperature (1.8–310 K) and variable-field (0–50 kOe) magnetic studies for 1 and 2 indicate the absence of M^III…M^III exchange interactions, in agreement with the long distances (~8 Å) between the paramagnetic metal ions. The combined work demonstrates the ability of saphCOO²⁻ and 4ClsaphCOO²⁻ to give 3d–4d metal complexes. Full article

The combinatorial problem in this paper is motivated by a variant of the famous traveling salesman problem where the salesman must return to the starting point after each delivery. The total length of a delivery route is related to a metric known as closeness centrality. The closeness centrality of a vertex v in a graph G was defined in 1950 by Bavelas to be $CC\left(v\right)={\displaystyle \frac{\left|V\right(G\left)\right|-1}{SD\left(v\right)}}$, where $SD\left(v\right)$ is the sum of the distances from v to each of the other vertices (which is one-half of the total distance in the delivery route). We provide a real-world example involving the Metro Atlanta Rapid Transit Authority rail network and identify stations whose $SD$ values are nearly identical, meaning they have a similar proximity to other stations in the network. We then consider theoretical aspects involving asymmetric trees. For integer values of k, we considered the asymmetric tree with paths of lengths $k,2k,\dots ,nk$ that are incident to a center vertex. We investigated trees with different values of k, and for $k=1$ and $k=2$, we established necessary and sufficient conditions for the existence of two vertices with identical $SD$ values, which has a surprising connection to the triangular numbers. Additionally, we investigated asymmetric trees with paths incident to two vertices and found a sufficient condition for vertices to have equal $SD$ values. This leads to new combinatorial proofs of identities arising from Pascal’s triangle. Full article

The aim of this study is to explore the impact of the main determinants on the rapid increase in fertilizer prices in Poland and to foresee the consequences of this situation regarding sustainable policy developments. We developed linear regression models for N, P, and K fertilizers to show the direction of influence of explaining variables and make a decomposition of the fertilizer price increases. The models illustrate that four major factors were responsible for the fertilizer price increases in Poland in 2020–2022, i.e., wheat, gas, GHGE allowance prices, and domestic production volumes. These factors explained the variation in the price of fertilizers concerned with different strengths. There were also other impacts associated with the ‘black swans’ occurrence (the COVID-19 pandemic and the war in Ukraine). High mineral fertilizer prices provide an opportunity to revise agricultural policy and legislation, taking into account environmental concerns and the latest technological developments. Fertilizer management practices are at the center of a triangle of critical objectives that track the progress toward sustainable agricultural systems, such as (1) an increase in farm incomes, (2) environmental protection, and (3) food and nutrition security. We recommend adjusting the set of explaining variables in the models (i.e., wheat/corn price) to the specificities of the domestic agri-food system. This study provides important guidance for agricultural policymaking, emphasizing the need to integrate sustainable fertilizer management practices to achieve synergies between economic growth, environmental protection, and food security. Such an approach can support the long-term development of agriculture in Poland and contribute to the economic and environmental stability of the agricultural sector. Full article

The accuracy of relative pose estimation is an important foundation for ensuring the safety and stability of autonomous aerial refueling (AAR) of unmanned aerial vehicles (UAV), and in response to this problem, a relative pose estimation method of UAVs based on the spatial equivalent plane is proposed in this paper. The UAV is equivalent to a spatial polygonal plane, and according to the measurement information of the Global Navigation Satellite System (GNSS) receivers, the equivalent polygonal plane equation is solved through the three-point normal vector and the minimum sum of squares of the distance from the four points to the plane. The equations of the distance between the geometric centers of the two polygonal planes, the angle between planes, and the angle between lines are used to calculate the relative pose information of the UAVs. Finally, the simulation environment and initial parameters are utilized for numerical simulation and results analysis. The simulation results show that without considering the motion model of the UAV, the proposed method can accurately estimate the relative pose information of the UAVs. In addition, in the presence of measurement errors, the relative pose estimation method based on the equivalent triangle plane can identify the position of the measurement point with the error, and the relative pose estimation method based on the equivalent quadrilateral plane has good robustness. The simulation results verify the feasibility and effectiveness of the proposed method. Full article