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[en] In principle, the local cosmic void can be simply modeled by the spherically symmetric Lemaitre-Tolman-Bondi (LTB) metric. In practice, the real local cosmic void is probably not spherically symmetric. In this paper, to reconstruct a more realistic profile of the local cosmic void, we divide it into several segments. Each segment with certain solid angle is modeled by its own LTB metric. Meanwhile, we divide the 1048 type Ia supernovae (SNIa) of the Pantheon Survey into corresponding subsets according to their distribution in the galactic coordinate system. Obviously, each SNIa subset can only be used to reconstruct the profile of one segment. Finally, we can patch together an irregular profile for the local cosmic void with the whole Pantheon sample. Note that, the paucity of each data subset lead us to focus on the inner part of each void segment and assume that the half radii of the void segments are sufficient to constrain the whole segment. We find that, despite 2σ signals of anisotropy limited to the depth of the void segments, the constraints on every void segment are consistent with ΛCDM model at 95% CL. Moreover, our constraints are too weak to challenge the cosmic homogeneity and isotropy.

[en] It is proved that for any transitive Lie algebroid L on a compact oriented connected manifold with unimodular isotropy Lie algebras and trivial monodromy the cohomology algebra is a Poincare algebra with trivial signature. Examples of such algebroids are algebroids on simply connected manifolds, algebroids such that the outer automorphism group of the isotropy Lie algebra is equal to its inner automorphism group, or such that the adjoint Lie algebra bundle g induces a trivial homology bundle H*( g) in the category of flat bundles

[en] This paper deals with the counterweight optimization of an asymmetrical hybrid machine tool based on dynamic isotropy. The dynamic model is derived and the dynamic manipulability ellipsoid is studied. Based on dynamic manipulability ellipsoid, the dynamic isotropy is defined. Counterweight block and fluid counterweight are presented to balance the weight of moving parts. The mass of the counterweight block is optimized to obtain the maximum dynamic isotropy in the workspace. The dynamic isotropy of the machine tool after counterweight optimization is compared with that before counterweight optimization. Furthermore, the dynamic isotropy of the machine tool with fluid counterweight is investigated and compared with that of the machine tool with counterweight block.

[en] We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition. (paper)

[en] We solve the Einstein equations in the Randall-Sundrum framework using an isotropic ansatz for the metric and obtain an exact expression to first order in the gravitational coupling. The solution is free from metric singularities away from the source and it satisfies the Israel matching condition on a straight brane. At distances far away from the source and on the physical brane this solution coincides with the 4D Schwarzschild metric in isotropic coordinates. Furthermore, we show that the extension of the standard Schwarzschild horizon in the bulk is tubular for any diagonal form of the metric while there is no restriction for the extension of the Schwarzschild horizon in isotropic coordinates

[en] To improve the auxeticity and isotropy behavior of standard hexachiral structures at large elasto-plastic deformation, the authors have earlier proposed a modified hexachiral structure with wavy ligaments (Zhu et al 2018 Smart Material Structures 27 055001). While a significant improvement was achieved with the proposed modified chiral structure, it was reported therewith that its auxeticity and isotropy degrade rapidly at large tensile deformation, in contrast to the excellent performance in compression. The present work builds upon the basic structure proposed in (Zhu et al 2018 Smart Material Structures 27 055001), to further improve the mechanical behavior in tension, without compromising the already excellent performance achieved at large compressive deformation. To reduce the distortion of the central ring in a hexachiral structure—the deformation mechanism that degrades its mechanical performance in tension—a hierarchical hexachiral structure is proposed, where a standard hexachiral structure reinforces the central ring of the basic hexachiral structure in (Zhu et al 2018 Smart Material Structures 27 055001). A significant improvement in mechanical behavior over the basic structure is demonstrated, with potential applications in a protective system. (paper)

[en] Hubble tension is among the most crucial unresolved issues in modern cosmology. In addition, search for preferred direction has also been explored in the last two decades. Different measurements of the Hubble constant provide significantly different values, and this is known as the Hubble tension. The cosmological principle assumes that the universe is homogeneous and isotropic; however, deviations from the isotropy have often been claimed.

d1e587^>We apply the Bayesian tools and the Extreme Value theory dependent statistic to address the above issues. These techniques have been applied to the Panstarrs1 type Ia supernovae data. Our analysis for Hubble constant does not reject the Hubble tension. However, our value is smaller than that of the SHoES program and agrees with the CCHP value. Extreme value theory-based analysis indicates that the data does not show directional dependence. As a byproduct of our technique, we show that the errors in the data are non-Gaussian in nature.

[en] Ultrasonic pulse-echo methods measuring the transit time through specimens have been widely used in determination of ultrasonic velocity and thickness of specimens. Usually, to determine the velocity of the ultrasonic. Tthe transit time of the ultrasonic pulse through specimen is measured by using the ultrasonic measuring equipment such as the oscilloscope including ultrasonic pulser/receiver and the thickness of the specimen is measured by using the length measuring instrument such as micrometer or vernier calipers etc., i. e. each parameter is measured by using each measuring method. In the case of the measuring the thickness of a specimen by using the ultrasonics. the ultrasonic equipment, which measure the thickness, such as the ultrasonic thickness gauge must be calibrated by using the reference block of which the ultrasonic velocity is known beforehand. In the present work, we proposed a new method for simultaneous measurement of ultrasonic velocity and thickness without reference blocks. Experimental results for several specimens show that proposed method have good agreements with those by traditional ultrasonic method

[en] In this paper the question of the isotropy of the one-way speed of light is addressed from an experimental perspective. In particular, we analyse two experimental methods commonly used in its determination. The analysis is aimed at clarifying the view that the one-way speed of light cannot be determined by techniques in which physical entities close paths. The procedure employed here will provide epistemological tools so that physicists understand that a direct measurement of the speed not only of light but of any physical entity is by no means trivial. Our results shed light on the physics behind the experiments which may be of interest for both physicists with an elemental knowledge in special relativity and philosophers of science.