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This paper aims to integrate the concepts of $F$-contraction and $S^B$-contraction within the context of super metric spaces. Specifically, we introduce the concepts of $S^F$-contraction and Bianchini $S^F$-contraction. We demonstrate that these new concepts are genuine generalizations of $S^B$- and $S^K$-contractions by providing nontrivial examples. Furthermore, we establish the existence and uniqueness of fixed points for mappings that satisfy these contractions. Lastly, we apply our findings to a model describing an airplane capable of automatically following a terrain.

Next-generation networks explore the opportunistic assistance of airliner/high-altitude platforms (HAPs) in delivering high data rates for terrestrial networks to ensure consistent and reliable communication. When an airliner/HAP moves at very high speeds, its mobility has a substantial impact on ensuring seamless connectivity, stable signal strength, and reliable data transmission. Orthogonal time frequency space (OTFS) modulation has been shown to provide notable improvement in performance when handling Doppler effects during high-mobility situations. This paper presents an OTFS-based airplane-aided next-generation networking system. In the proposed system, the airliner/HAPs are equipped with a planar antenna array that applies null steering beamforming (NSB) at the transmitter for communication with terrestrial users. A comprehensive performance comparison between OTFS and orthogonal frequency division multiplexing (OFDM) is performed under varying airliner altitude, velocity, array dimension, and Rician factor conditions. The simulation results show that OTFS consistently outperforms OFDM, achieving a lower bit error rate (BER) and more stable performance across different airli

Fear of flying is a serious problem that affects millions of individuals. Exposure therapy for fear of flying is an effective therapy technique. However, exposure therapy is also expensive, logistically difficult to arrange, and presents significant problems of patient confidentiality and potential embarrassment. We have developed a virtual airplane for use in fear of flying therapy. Using the virtual airplane for exposure therapy is a potential solution to many of the current problems of fear of flying exposure therapy. We describe the design of the virtual airplane and present a case report on its use for fear of flying exposure therapy.

This paper is devoted to the analysis and resolution of a pathological phenomenon in airplane encounters called blocking mode. As autonomy in airplane systems increases, a pathological phenomenon can be observed in two-aircraft encounter scenarios, where airplanes stick together and fly in parallel for an extended period. This parallel flight results in a temporary blocking that significantly delays progress. In contrast to widely studied deadlocks in multi-robot systems, such transient blocking is often overlooked in existing literature. Since such prolonged parallel flying places high-speed airplanes at elevated risks of near-miss collisions, encounter conflicts must be resolved as quickly as possible in the context of aviation. We develop a mathematical model for a two-airplane encounter system that replicates this blocking phenomenon. Using this model, we analyze the conditions under which blocking occurs, quantify the duration of the blocking period, and demonstrate that the blocking condition is significantly less restrictive than that of deadlock. Based on these analytical insights, we propose an intention-aware strategy with an adaptive priority mechanism that enables effic

How can a stack of identical blocks be arranged to extend beyond the edge of a table as far as possible? We consider a generalization of this classic puzzle to blocks that differ in width and mass. Despite the seemingly simple premise, we demonstrate that it is unlikely that one can efficiently determine a stack configuration of maximum overhang. Formally, we prove that the Block-Stacking Problem is NP-hard, partially answering an open question from the literature. Furthermore, we demonstrate that the restriction to stacks without counterweights has a surprising connection to the Airplane Refueling Problem, another famous puzzle, and to Robust Appointment Scheduling, a problem of practical relevance. In addition to revealing a remarkable relation to the real-world challenge of devising schedules under uncertainty, their equivalence unveils a polynomial-time approximation scheme, that is, a $(1+ε)$-approximation algorithm, for Block Stacking without counterbalancing and a $(2+ε)$-approximation algorithm for the general case.

The airplane, the basilica and the Douady rabbit (and, more generally, rabbits with more than two ears) are well-known Julia sets of complex quadratic polynomials. In this paper we study the groups of all homeomorphisms of such fractals and of all automorphisms of their laminations. In particular, we identify them with some kaleidoscopic group or universal groups and thus realize them as Polish permutation groups. From these identifications, we deduce algebraic, topological and geometric properties of these groups.

The disperse structure distributions (discreteness) and variant scattering characteristics (variability) of SAR airplane targets lead to special challenges of object detection and recognition. The current deep learning-based detectors encounter challenges in distinguishing fine-grained SAR airplanes against complex backgrounds. To address it, we propose a novel physics-guided detector (PGD) learning paradigm for SAR airplanes that comprehensively investigate their discreteness and variability to improve the detection performance. It is a general learning paradigm that can be extended to different existing deep learning-based detectors with "backbone-neck-head" architectures. The main contributions of PGD include the physics-guided self-supervised learning, feature enhancement, and instance perception, denoted as PGSSL, PGFE, and PGIP, respectively. PGSSL aims to construct a self-supervised learning task based on a wide range of SAR airplane targets that encodes the prior knowledge of various discrete structure distributions into the embedded space. Then, PGFE enhances the multi-scale feature representation of a detector, guided by the physics-aware information learned from PGSSL. P

This paper describes how intentional and unintentional radio emission from airplanes is recorded with the Radio Neutrino Observatory Greenland (RNO-G). We characterize the received signals and define a procedure to extract a clean set of impulsive signals. These signals are highly suitable for instrument calibration, also for future experiments. A set of signals is used to probe the timing precision of RNO-G in-situ, which is found to match expectations. We also discuss the impact of these signals on the ability to detect neutrinos with RNO-G.

The airplane refueling problem is a nonlinear combinatorial optimization problem, and its equivalent problem the $n$-vehicle exploration problem is proved to be NP-complete (arXiv:2304.03965v1, The $n$-vehicle exploration problem is NP-complete). In Article (arXiv:2210.11634v2, A polynomial-time algorithm to solve the aircraft refueling problem: the sequential search algorithm), we designed the sequential search algorithm for solving large scale of airplane refueling instances, and we proved that the computational complexity increases to polynomial time with increasing number of airplanes. Thus the airplane refueling problem, as an NP-complete problem, is solvable in polynomial time when its input scale is sufficiently large.

This paper is concerned with the minimum-time path-planning problem for a Dubins airplane under the influence of steady wind. The path-planning problem, by transforming into the air-relative frame, is equivalent to finding the minimum-time control strategy for a Dubins airplane to intercept a moving target. In the air-relative frame, by applying Pontryagin's maximum principle, the candidates for the minimum-time solution are categorized into a family of four types: SC, CC, CCC, CSC, where S denotes a straight line segment and C denotes a circular segment. Furthermore, the geometric properties for each type are analyzed, indicating that the paths of SC and CC can be obtained by finding the roots of a quadratic equation, while the paths of CCC and CSC are determined by the roots of some nonlinear transcendental equations. An improved bisection method is presented in the paper so that all the roots of the transcendental equations can be computed within a constant time. As a consequence, the globally optimal path can be obtained within a constant time by comparing all the candidates of the four types. Finally, numerical examples are presented, showing that the closed-form solutions der

In this work, we start with a generic mathematical framework for the equations of motion (EOM) in flight mechanics with six degrees of freedom (6-DOF) for a general (not necessarily symmetric) fixed-wing aircraft. This mathematical framework incorporates (1) body axes (fixed in the airplane at its center of gravity), (2) inertial axes (fixed in the earth/ground at the take-off point), wind axes (aligned with the flight path/course), (3) spherical flight path angles (azimuth angle measured clockwise from the geographic north, and elevation angle measured above the horizon plane), and (4) spherical flight angles (angle of attack and sideslip angle). We then manipulate these equations of motion to derive a customized version suitable for inverse simulation flight mechanics, where a target flight trajectory is specified while a set of corresponding necessary flight controls to achieve that maneuver are predicted. We then present a numerical procedure for integrating the developed inverse simulation (InvSim) system in time; utilizing (1) symbolic mathematics, (2) explicit fourth-order Runge-Kutta (RK4) numerical integration technique, and (3) expressions based on the finite difference m

Instance segmentation of compound objects in XXL-CT imagery poses a unique challenge in non-destructive testing. This complexity arises from the lack of known reference segmentation labels, limited applicable segmentation tools, as well as partially degraded image quality. To asses recent advancements in the field of machine learning-based image segmentation, the "Instance Segmentation XXL-CT Challenge of a Historic Airplane" was conducted. The challenge aimed to explore automatic or interactive instance segmentation methods for an efficient delineation of the different aircraft components, such as screws, rivets, metal sheets or pressure tubes. We report the organization and outcome of this challenge and describe the capabilities and limitations of the submitted segmentation methods.

Automatic airplane detection in aerial imagery has a variety of applications. Two of the significant challenges in this task are variations in the scale and direction of the airplanes. To solve these challenges, we present a rotation-and-scale invariant airplane proposal generator. We call this generator symmetric line segments (SLS) that is developed based on the symmetric and regular boundaries of airplanes from the top view. Then, the generated proposals are used to train a deep convolutional neural network for removing non-airplane proposals. Since each airplane can have multiple SLS proposals, where some of them are not in the direction of the fuselage, we collect all proposals corresponding to one ground-truth as a positive bag and the others as the negative instances. To have multiple instance deep learning, we modify the loss function of the network to learn from each positive bag at least one instance as well as all negative instances. Finally, we employ non-maximum suppression to remove duplicate detections. Our experiments on NWPU VHR-10 and DOTA datasets show that our method is a promising approach for automatic airplane detection in very high-resolution images. Moreove

Airplane refueling problem is a nonlinear unconstrained optimization problem with $n!$ feasible solutions. Given a fleet of $n$ airplanes with mid-air refueling technique, the question is to find the best refueling policy to make the last remaining airplane travel the farthest. In order to solve airplane refueling problem, we proposed the definition of sequential feasible solution by employing the refueling properties of data structure. We proved that if an airplane refueling instance has feasible solutions, it must have sequential feasible solutions; and the optimal feasible solution must be the optimal sequential feasible solution. So we need to numerate all the sequential feasible solutions to get an exact algorithm. We proposed the sequential search algorithm which consists of two steps, the first step of which aims to seek out all of the sequential feasible solutions, and the second step aims to search for the maximal sequential feasible solution by bubble sorting all of the sequential feasible solutions. We observed that the number of the sequential feasible solutions will change to grow at a polynomial rate when the input size of $n$ is greater than an inflection point $N$.

Airplane detection from satellite imagery is a challenging task due to the complex backgrounds in the images and differences in data acquisition conditions caused by the sensor geometry and atmospheric effects. Deep learning methods provide reliable and accurate solutions for automatic detection of airplanes; however, huge amount of training data is required to obtain promising results. In this study, we create a novel airplane detection dataset called High Resolution Planes (HRPlanes) by using images from Google Earth (GE) and labeling the bounding box of each plane on the images. HRPlanes include GE images of several different airports across the world to represent a variety of landscape, seasonal and satellite geometry conditions obtained from different satellites. We evaluated our dataset with two widely used object detection methods namely YOLOv4 and Faster R-CNN. Our preliminary results show that the proposed dataset can be a valuable data source and benchmark data set for future applications. Moreover, proposed architectures and results of this study could be used for transfer learning of different datasets and models for airplane detection.

This paper investigates the problem of planning a minimum-length tour for a three-dimensional Dubins airplane model to visually inspect a series of targets located on the ground or exterior surface of objects in an urban environment. Objects are 2.5D extruded polygons representing buildings or other structures. A visibility volume defines the set of admissible (occlusion-free) viewing locations for each target that satisfy feasible airspace and imaging constraints. The Dubins traveling salesperson problem with neighborhoods (DTSPN) is extended to three dimensions with visibility volumes that are approximated by triangular meshes. Four sampling algorithms are proposed for sampling vehicle configurations within each visibility volume to define vertices of the underlying DTSPN. Additionally, a heuristic approach is proposed to improve computation time by approximating edge costs of the 3D Dubins airplane with a lower bound that is used to solve for a sequence of viewing locations. The viewing locations are then assigned pitch and heading angles based on their relative geometry. The proposed sampling methods and heuristics are compared through a Monte-Carlo experiment that simulates vi

The Me 163 was a Second World War fighter airplane and a result of the German air force secret developments. One of these airplanes is currently owned and displayed in the historic aircraft exhibition of the Deutsches Museum in Munich, Germany. To gain insights with respect to its history, design and state of preservation, a complete CT scan was obtained using an industrial XXL-computer tomography scanner. Using the CT data from the Me 163, all its details can visually be examined at various levels, ranging from the complete hull down to single sprockets and rivets. However, while a trained human observer can identify and interpret the volumetric data with all its parts and connections, a virtual dissection of the airplane and all its different parts would be quite desirable. Nevertheless, this means, that an instance segmentation of all components and objects of interest into disjoint entities from the CT data is necessary. As of currently, no adequate computer-assisted tools for automated or semi-automated segmentation of such XXL-airplane data are available, in a first step, an interactive data annotation and object labelling process has been established. So far, seven 512 x 512

For dealing with traffic bottlenecks at airports, aircraft object detection is insufficient. Every airport generally has a variety of planes with various physical and technological requirements as well as diverse service requirements. Detecting the presence of new planes will not address all traffic congestion issues. Identifying the type of airplane, on the other hand, will entirely fix the problem because it will offer important information about the plane's technical specifications (i.e., the time it needs to be served and its appropriate place in the airport). Several studies have provided various contributions to address airport traffic jams; however, their ultimate goal was to determine the existence of airplane objects. This paper provides a practical approach to identify the type of airplane in airports depending on the results provided by the airplane detection process using mask region convolution neural network. The key feature employed to identify the type of airplane is the surface area calculated based on the results of airplane detection. The surface area is used to assess the estimated cabin length which is considered as an additional key feature for identifying the

We consider the airplane refueling problem, where we have a fleet of airplanes that can refuel each other. Each airplane is characterized by specific fuel tank volume and fuel consumption rate, and the goal is to find a drop out order of airplanes that last airplane in the air can reach as far as possible. This problem is equivalent to the scheduling problem $1||\sum w_j (- \frac{1}{C_j})$. Based on the dominance properties among jobs, we reveal some structural properties of the problem and propose a recursive algorithm to solve the problem exactly. The running time of our algorithm is directly related to the number of schedules that do not violate the dominance properties. An experimental study shows our algorithm outperforms state of the art exact algorithms and is efficient on larger instances.