Two-fold symmetry of the in-plane resistance in kagome superconductor Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with enhanced superconductivity

The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V_(1-x)Ta_(x))_(3)Sb_(5) by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T_(c) ~ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V_(1-x)Ta_(x))_(3)Sb_(5)(x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance(AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V_(1-x)Ta_(x))_(3)Sb_(5). Our findings demonstrate that Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum classical correspondence in terms of the coherent wave functions of a charged particle in two-dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than h is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 27r-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

We study quantum–classical correspondence in terms of the coherent wave functions of a charged particle in two- dimensional central-scalar potentials as well as the gauge field of a magnetic flux in the sense that the probability clouds of wave functions are well localized on classical orbits. For both closed and open classical orbits, the non-integer angular-momentum quantization with the level space of angular momentum being greater or less than is determined uniquely by the same rotational symmetry of classical orbits and probability clouds of coherent wave functions, which is not necessarily 2π-periodic. The gauge potential of a magnetic flux impenetrable to the particle cannot change the quantization rule but is able to shift the spectrum of canonical angular momentum by a flux-dependent value, which results in a common topological phase for all wave functions in the given model. The well-known quantum mechanical anyon model becomes a special case of the arbitrary quantization, where the classical orbits are 2π-periodic.

LIOUVILLE PROPERTY FOR A CLASS OF QUASI-HARMONIC SPHERE

In this paper we obtain a Liouville type result for a class of quasi-harmonic spheres with rotational symmetry.

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction.It is shown that,in the absence of the on-site interaction,the system possesses the SU(2)symmetry arising from the time reversal symmetry.The influence of the on-site interaction on the symmetry depends on the topology of the networks:The SU(2)symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction.On the contrary,the on-site interaction breaks the SU(2)symmetry of a multi-connected lattice.This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system.The obtained rigorous result is illustrated by a simple ring system.

A NEW METHOD FOR NUMERICAL SIMULATION OF TWO TRAINS PASSING BY EACH OTHER AT THE SAME SPEED

A new method is proposed to numerically simulate problems of trains passing by each other at the same speed, and is implemented in UDF language of commercial software Fluent. Because only a half of the computational domain is required and the dynamic mesh technique is avoided, the computational efficiency is greatly improved. A two-dimensional test case is used for validation, which shows that the flow field and the pressure wave during the train-passing events can be correctly calculated by this new method. This method can be easily extended to three-dimensional simulations, to deal with practical problems.

A Zernike-moment-based non-local denoising filter for cryo-EM images

Cryo-electron microscopy (cryo-EM) plays an important role in determining the structure of proteins, viruses, and even the whole cell. It can capture dynamic structural changes of large protein complexes, which other methods such as X-ray crystallography and nuclear magnetic resonance analysis find difficult. The signal-to-noise ratio of cryo-EM images is low and the contrast is very weak, and therefore, the images are very noisy and require filtering. In this paper, a filtering method based on non-local means and Zernike moments is proposed. The method takes into account the rotational symmetry of some biological molecules to enhance the signal-to-noise ratio of cryo-EM images. The method may be useful in cryo-EM image processing such as the automatic selection of particles, orientation determination, and the building of initial models.

Classification of gradient steady Ricci solitons with linear curvature decay

In this paper,we study steady Ricci solitons with a linear decay of sectional curvature.In particular,we give a complete classification of 3-dimensional steady Ricci solitons and 4-dimensional K-noncollapsed steady Ricci solitons with non-negative sectional curvature under the linear curvature decay.

Weighted polyharmonic equation with Navier boundary conditions in a half space

We study positive solutions of the following polyharmonic equation with Hardy weights associated to Navier boundary conditions on a half space：where rn is any positive integer satisfying 0 〈 2m 〈 n. We first prove that the positive solutions of （0.1） are super polyharmonic, i.e.,where x＊ = （x1,... ,Xn-1, --Xn） is the reflection of the point x about the plane Rn-1. Then, we use the method of moving planes in integral forms to derive rotational symmetry and monotonicity for the positive solution of （0.3）, in which α can be any real number between 0 and n. By some Pohozaev type identities in integral forms, we prove a Liouville type theorem--the non-existence of positive solutions for （0.1）.

Liouville type theorems for Schrdinger systems

We study positive solutions to the following higher order SchrSdinger system with Dirichlet boundary conditions on a half space： where a is any even number between 0 and n. This PDE system is closely related to the integral system where G is the corresponding Green＇s function on the half space. More precisely, we show that every solution to （0.2） satisfies （0.1）, and we believe that the converse is also true. We establish a Liouville type theorem the non-existence of positive solutions to （0.2） under a very weak condition that u and v are only locally integrable. Some new ideas are involved in the proof, which can be applied to a system of more equations.

Spherical Logistic Distribution

Some of the spherical distributions can be constructed through proper transformation of the densities on plane.Since the logistic density on the Euclidean space has similar behavior to the normal distribution,it is of interest to extend it for spherical data.In this paper,we introduce spherical logistic distribution on the unit sphere and then study relevant statistical inferences including parameters estimation through method of moments and maximum likelihood techniques.It is shown that the spherical logistic distribution is a multimodal distribution with the marginal logistic density function.Proposed density has rotational symmetry property and this plays a key role to drive some important results related to first two moments.To investigate the proposed density in more details,some simulation studies along with analyzing real-life data are also considered.

Qualitative tool for designing natural protected areas and ecological restoration projects

The rotational symmetry connection between the Species-Area Relationship(SAR)and Endemics-Area Relationship(EAR)was discovered in the frame of Species-Area Theory.In this paper,this paired connection was applied into the impact of variation of number of species and area and dynamic change of species-abundance distribution on the curve shape of SAR and EAR,which can be integrated into the assessment of Natural Protected Areas and Ecological Restoration Projects.The results indicate that the underestimate or overestimate of total number of species can lead to the underestimate or overestimate of extinction rate,while the reduction or expansion of area can lead to the increase or decrease in extinction rate.In addition,the species-abundance distribution change of community causes the shape tuning of SAR and EAR,which leads to inconsistent change of extinction rate.Thus,this SAT frame can be used as a qualitative tool in conservation and restoration management.