Variations of Weyl’s Tube Formula

In 1939 Weyl showed that the volume of spherical tubes around compact submanifolds M of Euclidean space depends solely on the induced Riemannian metric on M. Can this intrinsic nature of the tube volume be preserved for tubes with more general cross sections $$\mathbb {D}$$ D than the round ball? Under sufficiently strong symmetry conditions on $$\mathbb {D}$$ D the answer turns out to be yes.

Looking at shadows of entanglement wedges

We present a new method of deriving shapes of entanglement wedges directly from conformal field theory (CFT) calculations. We point out that a reduced density matrix in holographic CFTs possesses a sharp wedge structure such that inside the wedge we can distinguish two local excitations, while outside we cannot. We can determine this wedge, which we call a CFT wedge, by computing a distinguishability measure. We find that CFT wedges defined by the fidelity or Bures distance as a distinguishability measure coincide perfectly with shadows of entanglement wedges in anti-de Sitter (AdS)/CFT. We confirm this agreement between CFT wedges and entanglement wedges for two-dimensional holographic CFTs where the subsystem is chosen to be an interval or double intervals, as well as higher-dimensional CFTs with a round ball subsystem. On the other hand, if we consider a free scalar CFT, we find that there are no sharp CFT wedges. This shows that sharp entanglement wedges emerge only for holographic CFTs owing to the large-$N$ factorization. We also generalize our analysis to a time-dependent example and to a holographic boundary conformal field theory (AdS/BCFT). Finally, we study other distinguishability measures to define CFT wedges. We observe that some of the measures lead to CFT wedges which slightly deviate from the entanglement wedges in AdS/CFT, and we give a heuristic explanation for this. This paper is an extended version of our earlier letter (arXiv:1908.09939 [hep-th]) and includes various new observations and examples.

PENGARUH LATIHAN KECEPATAN DAN KELINCAHAN TERHADAP LEMPAR TANGKAP BOLA KASTI UNTUK SISWA- SISWI KELAS IV SEKOLAH DASAR NEGERI 19 KOTA BENGKULU

This study aims to determine whether speed and agility exercises have a significant effect on improving catching abilities in roundball games. The method used in this study is the experimental method, with the independent variables being speed and agility, and the dependent variable is the round ball catching technique. The sample used in this study was 40 students - 19 public elementary school students and as a comparison for students at the base of the city of Bengkulu. The data collection instrument or tool used in this study is a 30-meter sprint, running back and forth with a distance of 10 meters with 4 times back and forth and throwing a catch into the target wall of 2 meters in 30 seconds. Based on the management and analysis of the data obtained, the results of this study are the initial test average of 42.65. agility 19.66 and catching 59.60 the average test finally speeds 56.14. Agility 5.06 and throw catch 7.20 - the average difference of 1.9. The conclusion of this study, judging from the data, is that speed and agility training have a significant effect on round ball catching. Keywords: exercise speed and agility

Estimating Lead Fragmentation from Ammunition for Muzzleloading and Black Powder Cartridge Rifles

Lead bullet fragments pose a health risk to scavengers and hunters consuming game meat, but lead or lead-core bullets are still commonly employed for big and small game hunting. Bullet fragmentation has been assessed for modern, high-velocity rifles, but has not been well documented for black-powder cartridge rifles or muzzleloading firearms. We used two established methods to estimate bullet fragmentation. We evaluated a traditional .54 round ball and a modern-designed .54 conical bullet for muzzleloaders, two types of .45-70 black powder rifle cartridges, and a modern lead-core high-velocity bullet (.30-06) as our comparison control. We tested penetration and fragmentation in water (n = 12) and ballistics gel (n = 2) for each bullet type. We measured lead mass lost to fragmentation and x-rayed ballistic gels to visualize fragmentation patterns. The modern .30-06 bullets we tested (Remington Core-Lokt) retained a mean of only 57.5% of original mass, whereas mean retention by muzzleloader and black powder cartridge bullets ranged 87.8-99.7%. Round balls and .45-70 bullets shed less lead (i.e., 0.04g and 0.19g on average respectively) than the modern conical .54 muzzleloading bullets (3.08g) or the .30-06 control (4.14g). Fragments from round balls and black powder cartridge bullets showed far less lateral spread compared to the high-velocity modern bullet. Our findings suggest that round balls for muzzleloaders and black powder cartridge bullets may leave far fewer lead fragments in game than the conical muzzleloader bullet or modern high-velocity rifle bullet we tested, and thus could pose a lower risk of secondary lead poisoning for humans and wildlife. Artificial tests cannot replicate conditions encountered in the field, but the striking differences we observed in bullet fragmentation even under severe testing conditions suggests that follow-up tests on game animals may be warranted.

Entanglement temperature for black branes with hyperscaling violation

Entanglement temperature is an interesting quantity which relates the increased amount of entanglement entropy to that of energy for a weakly excited state in the first-law of entanglement entropy, it is proportional to the inverse of the size of entanglement subsystem and only depends on the shape of the entanglement region. We find the explicit formula of entanglement temperature for the general hyperscaling violation backgrounds with a strip-subsystem. We then investigate the entanglement temperature for a round ball-subsystem, we check that the entanglement temperature has a universal form when the hyperscaling violation exponent is near zero.

Tennis Transmitter Design and Parameter Optimization

Design of tennis transmitter design parameters, structure design, choice of institution, etc., the transmitter in accordance with the standards of the international tennis federation (ITF) to carry on the design. Design and institutional selection includes the realization of the crank connecting rod mechanism and control motor sports, ball tray and ball under the control of the speed of tennis, crowded ball wheel speed regulating motor selection, crowded round ball structure design and checking calculation, the design and checking calculation of shaft, casing and bracket material design and the selection, selection of walking wheel, etc.