Constructing Hopf Insulator from Geometric Perspective of Hopf Invariant

We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.

Optimized Evaluation of Mobile Base Station by Modern Topological Invariants

Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifthgeneration(5G)cellular networks.For the formal reason,the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory.Any number that can be uniquely calculated by a graph is known as a graph invariant.During the last two decades,innumerable numerical graph invariants have been portrayed and used for correlation analysis.In any case,no efficient assessment has been embraced to choose,how much these invariants are connected with a network graph.This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks.Since K-banhatti sombor invariants(KBSO)and Contrharmonic-quadratic invariants(CQIs)are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks.As the hexagonal networks are used in mobile base stations in layered,forms called honeycomb.The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms.The deduced outcomes can be utilized for the modeling of mobile cellular networks,multiprocessors interconnections,microchips,chemical compound synthesis and memory interconnection networks.The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network(MBSN)for the high load of traffic and minimal traffic also.

On the Construction and Classification of the Common Invariant Solutions for Some P(1,4) -Invariant Partial Differential Equations

We consider the following (1 + 3)-dimensional P(1,4)-invariant partial differential equations (PDEs): the Eikonal equation, the Euler-Lagrange-Born-Infeld equation, the homogeneous Monge-Ampère equation, the inhomogeneous Monge-Ampère equation. The purpose of this paper is to construct and classify the common invariant solutions for those equations. For this aim, we have used the results concerning construction and classification of invariant solutions for the (1 + 3)-dimensional P(1,4)-invariant Eikonal equation, since this equation is the simplest among the equations under investigation. The direct checked allowed us to conclude that the majority of invariant solutions of the (1 + 3)-dimensional Eikonal equation, obtained on the base of low-dimensional (dimL ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4), satisfy all the equations under investigation. In this paper, we present obtained common invariant solutions of the equations under study as well as the classification of those invariant solutions.

Invariant measures for the strong-facilitated exclusion process

Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed.The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements.The method is made invar-iant domain preserving for the Euler equations using convex limiting and is tested on vari-ous benchmarks.

Invariant manifold growth formula in cylindrical coordinates and its application for magnetically confined fusion

For three-dimensional vector fields,the governing formula of invariant manifolds grown from a hyperbolic cycle is given in cylindrical coordinates.The initial growth directions depend on the Jacobians of Poincarémap on that cycle,for which an evolution formula is deduced to reveal the relationship among Jacobians of different Poincarésections.The evolution formula also applies to cycles in arbitrary finite n-dimensional autonomous continuous-time dynamical systems.Non-Möbiusian/Möbiusian saddle cycles and a dummy X-cycle are constructed analytically as demonstration.A real-world numeric example of analyzing a magnetic field timeslice on EAST is presented.

Lie symmetry analysis and invariant solutions for the(3+1)-dimensional Virasoro integrable model

Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.

A road map to higher genus Gromov-Witten invariants of Calabi-Yau quintics

This is a survey of using NMSP method to study higher genus Gromov-Witten invariants of Calabi-Yau quintics.It emphasizes on how and why the various methods are introduced to solve several important conjectures for higher genus Gromov-Witten invariants of Calabi-Yau quintics.

Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

Hojman Exact Invariants and Adiabatic Invariants of Hamilton System

The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetryis studied,and Hojman adiabatic invariants of Hamilton system are obtained.An example is given to illustrate theapplication of the results.

Classification of Four-Qubit States by Means of a Stochastic Local Operation and the Classical Communication Invariant

It is a recent observation that entanglement classification for qubits is closely related to stochastic local operations and classical communication(SLOCC)invariants.Verstraete et al.[Phys.Rev.A 65(2002)052112]showed that for pure states of four qubits there are nine different degenerate SLOCC entanglement classes.Li et al.[Phys.Rev.A 76(2007)052311]showed that there are at least 28 distinct true SLOCC entanglement classes for four qubits by means of the SLOCC invariant and semi-invariant.We give 16 different entanglement classes for four qubits by means of basic SLOCC invariants.

Joint Invariants and Joint Differential Invariants of Some Transformation Groups

The theory of moving frames developed by Peter J Olver and M Fels has impor-tant applications to geometry, classical invariant theory. We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.

DS环的Morita invariant性

证明了关于左 DS环的几个结果 :1 )若对 R的中心幂等元 e,有 e Re和 (1 -e) R(1 -e)都是左 DS环 ,则 R是左 DS环 ;2 ) R是左 DS环当且仅当全矩阵环 Mn(R)是左 DS环 ;3 )左 DS环是 Moritainvariant;4) R是左 DS环当且仅当 R是左 MC2环且极小内射左 R-模的同态像是极小内射左 R-模 .

MBIUS INVARIANT GRADIENT AND LITTLE α-BLOCH FUNCTIONS

In this paper, the authors get the characterizations of the integral and Car-leson type measure both associated with the invariant gradient for little a-Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended.

Mucosal-associated invariant T cells in hepatitis B virus-related liver failure

BACKGROUND Liver failure has high mortality and poor prognosis,and establishing new reliable markers for predicting its prognosis is necessary.Mucosal-associated invariant T(MAIT)cells are a novel population of innate-like lymphocytes involved in inflammatory liver disease,and their potential role in liver failure remains unclear.AIM To investigate alteration of circulating MAIT cells and assess its prognostic value in patients with hepatitis B virus(HBV)-related liver failure.METHODS We recruited 55 patients with HBV-related liver failure,48 patients with chronic hepatitis B and 40 healthy controls(HCs)from Nantong Third People’s Hospital Affiliated to Nantong University.Peripheral blood mononuclear cells were isolated,and the percentage and number of circulating MAIT cells were detected by flow cytometry.Plasma levels of interleukin(IL)-7,IL-12p70,IL-18 and interferon-αwere measured by Luminex assay.RESULTS Circulating MAIT cells were significantly decreased in HBV-related liver failure patients(percentage:2.00±1.22 vs 5.19±1.27%,P<0.0001;number:5.47±4.93 vs 84.43±19.59,P<0.0001)compared with HCs.More importantly,there was a significant reduction of MAIT cells in patients with middle/late-stage compared with early-stage liver failure.Circulating MAIT cells partially recovered after disease improvement,both in percentage(4.01±1.21 vs 2.04±0.95%,P<0.0001)and in cell count(17.24±8.56 vs 7.41±4.99,P<0.0001).The proportion(2.29±1.01 vs 1.58±1.38%,P<0.05)and number(7.30±5.70 vs 2.94±1.47,P<0.001)of circulating MAIT cells were significantly higher in the survival group than in the dead/liver transplantation group,and the Kaplan–Meier curve showed that lower expression of circulating MAIT cells(both percentage and cell count)predicted poor overall survival(P<0.01).Also,the levels of IL-12(20.26±5.42 pg/mL vs 17.76±2.79 pg/mL,P=0.01)and IL-18(1470.05±1525.38 pg/mL vs 362.99±109.64 pg/mL,P<0.0001)were dramatically increased in HBV-related liver failure patients compared with HCs.CONCLUSION Circulating MAIT cells may play an important role in the process of HBV-related liver failure and can be an important prognostic marker.

PERTURBATION OF SYMMETRIES OF BIRKHOFF SYSTEM AND ADIABATIC INVARIANTS

The perturbation of symmetries of the free Birkhoff system undersmall excitation is discussed.The concept of high-order adiabatic invariant is pre-sented,and the form of adiabatic invariants and the conditions for their existence aregiven.Then these results are generalized to the constrained Birkhoff system.Oneexample is presented to illustrate these results.

Perturbation to Noether Quasi-Symmetry and Adiabatic Invariants for Nonholonomic Systems on Time Scales

Perturbation to Noether quasi-symmetry and adiabatic invariants for the nonholonomic system on time scales are studied. Firstly, some properties of time scale calculus are reviewed. Secondly, the differential equations of motion for the nonholonomic system on time scales, Noether quasi-symmetry and conserved quantity are given. Thirdly, perturbation to Noether quasi-symmetry and adiabatic invariants, which are the main results of this paper, are investigated. The main results are achieved by two steps, the first step is to obtain adiabatic invariants without transforming the time, and the next is to obtain adiabatic invariants under the infinitesimal transformations of both the time and the coordinates. And in the end, an example is given to illustrate the methods and results.

Conserved quantities and adiabatic invariants of fractional Birkhoffian system of Herglotz type

In order to further study the dynamical behavior of nonconservative systems,we study the conserved quantities and the adiabatic invariants of fractional Brikhoffian systems with four kinds of different fractional derivatives based on Herglotz differential variational principle.Firstly,the conserved quantities of Herglotz type for the fractional Brikhoffian systems based on Riemann-Liouville derivatives and their existence conditions are established by using the fractional Pfaff-Birkhoff-d Alembert principle of Herglotz type.Secondly,the effects of small perturbations on fractional Birkhoffian systems are studied,the conditions for the existence of adiabatic invariants for the Birkhoffian systems of Herglotz type based on Riemann-Liouville derivatives are established,and the adiabatic invariants of Herglotz type are obtained.Thirdly,the conserved quantities and adiabatic invariants for the fractional Birkhoffian systems of Herglotz type under other three kinds of fractional derivatives are established,namely Caputo derivative,Riesz-Riemann-Liouville derivative and Riesz-Caputo derivative.Finally,an example is given to illustrate the application of the results.

Mucosal-associated invariant T cells from induced pluripotent stem cells:A novel approach for modeling human diseases

Mice have frequently been used to model human diseases involving immune dysregulation such as autoimmune and inflammatory diseases.These models help elucidatethe mechanisms underlying the disease and in the development of novel therapies.However,if mice are deficient in certain cells and/or effectors associated with human diseases,how can their functions be investigated in this species?Mucosal-associated invariant T(MAIT)cells,a novel innate-like T cell family member,are a good example.MAIT cells are abundant in humans but scarce in laboratory mice.MAIT cells harbor an invariant T cell receptor and recognize nonpeptidic antigens vitamin B2metabolites from bacteria and yeasts.Recent studies have shown that MAIT cells play a pivotal role in human diseases such as bacterial infections and autoimmune and inflammatory diseases.MAIT cells possess granulysin,a human-specific effector molecule,but granulysin and its homologue are absent in mice.Furthermore,MAIT cells show poor proliferation in vitro.To overcome these problems and further our knowledge of MAIT cells,we have established a method to expand MAIT cells via induced pluripotent stem cells(iP SCs).In this review,we describe recent advances in the field of MAIT cell research and our approach for human disease modeling with iP SCderived MAIT cells.

Incorporating mucosal-associated invariant T cells into the pathogenesis of chronic liver disease

Mucosal-associated invariant T(MAIT)cells have been described in liver and nonliver diseases,and they have been ascribed antimicrobial,immune regulatory,protective,and pathogenic roles.The goals of this review are to describe their biological properties,indicate their involvement in chronic liver disease,and encourage investigations that clarify their actions and therapeutic implications.English abstracts were identified in PubMed by multiple search terms,and bibliographies were developed.MAIT cells are activated by restricted non-peptides of limited diversity and by multiple inflammatory cytokines.Diverse pro-inflammatory,anti-inflammatory,and immune regulatory cytokines are released;infected cells are eliminated;and memory cells emerge.Circulating MAIT cells are hyper-activated,immune exhausted,dysfunctional,and depleted in chronic liver disease.This phenotype lacks disease-specificity,and it does not predict the biological effects.MAIT cells have presumed protective actions in chronic viral hepatitis,alcoholic hepatitis,non-alcoholic fatty liver disease,primary sclerosing cholangitis,and decompensated cirrhosis.They have pathogenic and pro-fibrotic actions in autoimmune hepatitis and mixed actions in primary biliary cholangitis.Local factors in the hepatic microenvironment(cytokines,bile acids,gut-derived bacterial antigens,and metabolic by-products)may modulate their response in individual diseases.Investigational manipulations of function are warranted to establish an association with disease severity and outcome.In conclusion,MAIT cells constitute a disease-nonspecific,immune response to chronic liver inflammation and infection.Their pathological role has been deduced from their deficiencies during active liver disease,and future investigations must clarify this role,link it to outcome,and explore therapeutic interventions.