Background: Formation and rupture of cerebral aneurysms may be related to certain types of configuration of the circle of Willis. Analysis of their interdependence can be of great importance. Methods: A group of 114 patients treated operatively for the cerebral aneurysm rupture and a group of 56 autopsied subjects were involved in the study. Four basic types of the circle of Willis configurations were formed–two symmetric types A and C, and two asymmetric types B and D. Results: A statistically significantly higher presence of asymmetry of the circle of Willis in the group of surgically treated subjects (p=0.006) with a significant presence of asymmetric Type B in this group (p=0.017) were determined. The presence of changes in the A1 segment in the group of subjects with solitary aneurysms on the anterior communicating artery showed a statistically significant presence in the group of autopsied subjects (p=0.0004). Analyzing the presence of symmetry of the circle of Willis between the two groups, that is, the total presence of symmetric types A and C indicated their statistically significant presence in the group of autopsied patients (p=0.043). Conclusion: Changes such as hypoplasia or aplasia of A1 and the resulting asymmetry of the circle of Willis directly affect the possibility of the rupture of cerebral aneurysms. Detection of the corresponding types of the circle of Willis after diagnostic examination can be the basis for the development of a protocol for monitoring such patients.

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation, and for the first time the worldlines equations are given. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson-Morley interferometer is solved, and we described an experiment where a new relativistic paradox appears --- a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

This paper aims to introduce the notions of various types of Qc-contractions for which we establish some fixed circle and fixed disc theorems in the setting of metric spaces. Some illustrative examples are also provided to support our results. Moreover, we present some fixed circle and fixed disc results of integral type contractive self-mappings.

An adaptive spatial clustering (ASC) algorithm is proposed in this present study, which employs sweep-circle techniques and a dynamic threshold setting based on the Gestalt theory to detect spatial clusters. The proposed algorithm can automatically discover clusters in one pass, rather than through the modification of the initial model (for example, a minimal spanning tree, Delaunay triangulation or Voronoi diagram). It can quickly identify arbitrarily-shaped clusters while adapting efficiently to non-homogeneous density characteristics of spatial data, without the need of prior knowledge or parameters. The proposed algorithm is also ideal for use in data streaming technology with dynamic characteristics flowing in the form of spatial clustering in large data sets.

In the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe”, and further in the Article “Distance Between Two Circles in Any Number of Dimensions is a Vector Ellipse”, it has been mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Using this mathematical methodology, a method is provided in this Article as a measure for the amount of interaction between two international economies, which are two countries or economic zones, by modelling each economy in terms of a “circle in four dimensions”. Based on this method, the proximity of the two economies at the end of each fiscal period, which is generally a fiscal year, is then measured by the distance between points at the end of the given period on the two circles in four dimensions, associated with these two economies in our model.

Iterations of continuous maps are the simplest models of generic dynamical systems. In particular, circle maps display several key properties of complex dynamics, such as phase-locking and the quasi-periodicity route to chaos. Our work points out that Planck’s constant may be derived from the scaling behavior of circle maps in the asymptotic limit.

This paper presents a new approach to a different proof of "Fermat's Last Theorem.” For the proof of the theorem, it is proposed to use a more straightforward geometrical approach. A special family of curves, the Elba curves, is introduced to facilitate the proof. This approach makes the proof easier to comprehend by mathematicians and those interested in the subject.

In the paper, the author finds bounds of the sine and cosine along a circle on the complex plane in terms of two double inequalities for the norms of the sine and cosine along a circle on the complex plane.

The application of 3D LiDAR technology has become increasingly extensive in tunnel monitoring due to the large density and high accuracy of the acquired spatial data. The proposed processing method aims at circle tunnels and provides a clear workflow to automatically process raw point data and easily interpretable results to analyze tunnel health state. The proposed automatic processing method employs a series of algorithms to extract point cloud of a single tunnel segment without obvious noise from entire raw tunnel point cloud mainly by three steps: axis acquisition, segments extraction and denoising. Tunnel axis is extracted by fitting boundaries of the tunnel point cloud rejection in plane with RANSAC algorithm. With guidance of axis, the entire preprocessed tunnel point cloud is segmented by equal division to get a section of tunnel point cloud which corresponds to a single tunnel segment. Then the noise in every single point cloud segment is removed by clustering algorithm twice, based on distance and intensity. Finally, clean point clouds of tunnel segments are processed by effective deformation extraction processor to get ovality and three-dimensional deformation nephogram.

Taiwan is the world’s leading country regarding tuna longline fisheries; the combined catches with those from Japan account for more than half of the global total. However, the bycatch of sea turtles, seabirds, and dolphins in longline fisheries has attracted international concern. Regarding sea turtle conservation, the use of circle hooks in longline fisheries will inevitably become a trend. Meanwhile, Taiwanese fishermen are concerned whether the use of circle hooks will have a negative impact on the catch efficiency of target species. This study was conducted to compare the catch efficiency of circle and tuna hooks by the Taiwanese commercial tuna longline fishing vessels in the eastern Pacific Ocean. The results indicated that if the effects of immersion time were considered, the catch rates of all groups were the same between 4.2-sun circle and tuna hooks. However, the catch rate of 4.0-sun circle hooks was significantly higher than the two types of 4.2-sun circle and tuna hooks. Regarding survival rates, fish caught with circle hooks showed higher survival rates than tuna hooks for total commercial fish, tunas and yellowfin tuna (Thunnus albacares). However, the survival rate was only determined at haulback; the relationship between survival rate and immersion time still needs further investigation. Regarding catch sizes, there were no significant differences in the sizes of bigeye (Thunnus obesus) and yellowfin tuna between circle and tuna hooks. But based solely on mean weight, the value of yellowfin tuna caught using circle hooks may be higher than those using tuna hooks. In summary, the circle hooks used in this study did not show a negative impact on the catch efficiency of Taiwanese longline fisheries, and could show a superior performance than that of tuna hooks. These results could be actively promoted in the industry through the education and training of fishermen; thus enabling Taiwan to comply with international sea turtle conservation trends.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1^st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.

Discrete Double Hilbert Exponential sums along polynomials. This is preprint version (not peer reviewed) And we now check the proof of (ii) of Lemma 3.2 whether it is really true.

In the Brazilian Amazon, rural settlements are increasingly isolated by large-scale production farms, jeopardizing their sustainability and the good living of family farmers. Works were carried out in settlements to measure sustainability. However, the majority does not consider the participation and the collectively of those involved. In this way, we propose to evaluate, in a collective and participatory way, the sustainability and good living of the SDP São Paulo Rural Settlement, of the northern Amazon of Mato Grosso. We used the didactic-pedagogical method Circle of Sustainability, developed from five points: 1st - circle of investigation of generating themes; 2nd - circle of the history of the subject world; 3rd - circle of diagnosis of rural settlements; 4th - circle of exchange of knowledge; and 5th - circle of sustainable perceptions and narratives. The historical, socioeconomic and cultural characterization of the settlement allowed us to understand how sustainability and good living are being built in the settlement history process. Sustainability and good living are dialectical processes, are under construction, in movement.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.