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\"Xaxon Yellowbearyd was the fiercest Viking warrior of his time. Now a map to his hidden treasure lies in the hands of Radius and Per. Together the cousins must decode the strange numbered grid on the map-- and figure out the secret of the Viking's X and Y axes\"--P. [4] of cover

The affine coherent state (ACS) quantisation method represents an effective approach to quantisation that can be adapted for the construction of a quantum spherical symmetric gravitational model. The ACS quantisation method is characterised by a relatively straightforward mathematical formalism. The method permits the quantisation of both the spatial and temporal coordinates, thereby enabling the reproduction of the classical quantity as an expectation value of an appropriate quantum observable. This paper presents the ACS quantisation of the Oppenheimer-Snyder (OS) model and discusses the general construction of the ACS quantum space. It also presents a quantum description of the OS model based on the analysis of characteristic quantum observables, with particular emphasis on the gravitational singularity area.

Izračunali smo povprečno odstopanje, postopek transformacije pa nadaljevali tako, da smo za vezne točke vzeli vse trigonometrične točke, ki smo jim odčitali grafično koordinato, za vse preostale trigonometrične točke, za katere smo imeli samo numerične koordinate, pa smo vzeli razliko numeričnih koordinat in povprečnega odstopanja. Na sliki 5 sta prikazana primerjava lokacij stare in transformirane mreže listov načrtov v sistemu Gellért ter primer karte razdelitve na liste, ki smo jih izdelali za vse katastrske občine. 3 UREDITEV OPISNE TABELE LISTOV V SISTEMU GELLÉRT K vsakemu listu mreže so atributno pripisani pripadajoči grafični načrti. 2021. https://www. primorsko-geodetsko-drustvo.si/wp-content/uploads/2021/09/03_ GD49_l_1-Kataster_v_PrekmurJu-Joc_TKglav_compressed.pdf, prídobljeno 31.5.

Based on the transformation of the spatial variables between the orthogonal curvilinear coordinate system and the Cartesian coordinate system, the derivation of spatial variables in orthogonal curvilinear system to the ones in Cartesian coordinate system is derived. The derivatives of the spatial variables in cylindrical, spherical, and elliptic cylindrical coordinate system are derived respectively.

This report continues the practice where the IAU Working Group on Cartographic Coordinates and Rotational Elements revises recommendations regarding those topics for the planets, satellites, minor planets, and comets approximately every 3 years. The Working Group has now become a “functional working group” of the IAU, and its membership is open to anyone interested in participating. We describe the procedure for submitting questions about the recommendations given here or the application of these recommendations for creating a new or updated coordinate system for a given body. Regarding body orientation, the following bodies have been updated: Mercury, based on MESSENGER results; Mars, along with a refined longitude definition; Phobos; Deimos; (1) Ceres; (52) Europa; (243) Ida; (2867) Šteins; Neptune; (134340) Pluto and its satellite Charon; comets 9P/Tempel 1, 19P/Borrelly, 67P/Churyumov–Gerasimenko, and 103P/Hartley 2, noting that such information is valid only between specific epochs. The special challenges related to mapping 67P/Churyumov–Gerasimenko are also discussed. Approximate expressions for the Earth have been removed in order to avoid confusion, and the low precision series expression for the Moon’s orientation has been removed. The previously online only recommended orientation model for (4) Vesta is repeated with an explanation of how it was updated. Regarding body shape, text has been included to explain the expected uses of such information, and the relevance of the cited uncertainty information. The size of the Sun has been updated, and notation added that the size and the ellipsoidal axes for the Earth and Jupiter have been recommended by an IAU Resolution. The distinction of a reference radius for a body (here, the Moon and Titan) is made between cartographic uses, and for orthoprojection and geophysical uses. The recommended radius for Mercury has been updated based on MESSENGER results. The recommended radius for Titan is returned to its previous value. Size information has been updated for 13 other Saturnian satellites and added for Aegaeon. The sizes of Pluto and Charon have been updated. Size information has been updated for (1) Ceres and given for (16) Psyche and (52) Europa. The size of (25143) Itokawa has been corrected. In addition, the discussion of terminology for the poles (hemispheres) of small bodies has been modified and a discussion on cardinal directions added. Although they continue to be used for planets and their satellites, it is assumed that the planetographic and planetocentric coordinate system definitions do not apply to small bodies. However, planetocentric and planetodetic latitudes and longitudes may be used on such bodies, following the right-hand rule. We repeat our previous recommendations that planning and efforts be made to make controlled cartographic products; newly recommend that common formulations should be used for orientation and size; continue to recommend that a community consensus be developed for the orientation models of Jupiter and Saturn; newly recommend that historical summaries of the coordinate systems for given bodies should be developed, and point out that for planets and satellites planetographic systems have generally been historically preferred over planetocentric systems, and that in cases when planetographic coordinates have been widely used in the past, there is no obvious advantage to switching to the use of planetocentric coordinates. The Working Group also requests community input on the question submitting process, posting of updates to the Working Group website, and on whether recommendations should be made regarding exoplanet coordinate systems.

In some hospitals or similar institutions, it can be helpful to anonymously monitor patients’ activities so that self-harm and violence against others can be detected and prevented early. The ISAS 2025 Challenge addresses this problem by looking for the best method to classify eight predefined types of human activities based on 2D-skeleton data.To solve this problem, we consider two different approaches: In our first approach, we apply TinyHAR directly on the given 2D-skeleton data and test different feature scaling techniques and a body-centered coordinate system with different origins. In our second approach, we transform the 2D-skeleton data back into a video sequence and use these videos as input for video classification models. Finally, we state the Leave-One-Subject-Out (LOSO) mean and standard deviation of accuracy and macro F1-Score. Since our chosen models vary a lot in the number of parameters and size, we also state the power consumption in Wh and the VRAM usage of the GPU.

For the graph’s vertex coloring, it is required that for every vertex in a graph, the colors used in its open neighborhood or closed neighborhood must be able to form a continuous integer interval. A coloring is called an open neighborhood interval vertex coloring or a closed neighborhood interval vertex coloring of a graph if the neighborhood satisfying the condition is open or closed. In this paper, the interval vertex coloring of cartesian products and strong products of two paths is studied, and the low bound of the interval chromatic number is given.

The 17th and 18th century opposition between Cartesian and Newtonian science is often depicted as a contest between a priorism and speculation on one hand, and observation and mathematical proof on the other, one of which won out. This is a simplification. In 17th century England Cartesian natural philosophy, including the vortex theory of the planetary orbits, was (intentionally) easy to understand. It was seen however as poorly disguised atheism and widely disparaged on that account by influential theologians. Amongst the 18th century French philosophes, this aspect of Cartesianism was hardly a problem. Newtonianism now denoted an appetite for exciting experimental demonstrations as against the dead letter of scientific books, including not only René Descartes’s Principles but also Isaac Newton’s (for most readers) largely impenetrable Principia .

Aiming at the problem that the hand-eye calibration of the uncalibrated non-standard manipulator cannot be addressed by the general calibration method, i.e., the eye-in-hand and eye-to-hand calibration method of the visual servo system was proposed to guide the manipulator without calibration. First, a camera was installed on the manipulator to complete the eye-in-hand calibration and achieve transformation from the end coordinate system to the camera coordinate system. Second, a second camera was used to achieve eye-to-hand calibration and obtain the transformation relationship from the end coordinate system to the calibration board. The entire calibration process only requires the collection of images from two scenarios, i.e., the docking and the completion of the docking processes. The implementation results show that the rotation error between groups is less than 1.5°, and the translation error between groups is less than 8 mm. Therefore, the proposed visual servo strategy can accurately guide the uncalibrated non-standard manipulator.

The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam’s razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system.We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.