Generalized symmetries of an N=1 supersymmetric Boiti–Leon–Manna–Pempinelli system

The formal series symmetry approach （FSSA）, a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the N = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely f（t）. Some interesting special cases of symmetry algebras are commutativity of higher order generalized symmetries. many generalized symmetries with an arbitrary function presented, including a limit case f（t） = 1 related to the

INVARIANT SUBSPACES AND GENERALIZED FUNCTIONAL SEPARABLE SOLUTIONS TO THE TWO-COMPONENT b-FAMILY SYSTEM

Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.

Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic potential vorticity equation

By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including the modified KP （mKP） equation, standard KP equation and cylindrical KP （cKP） equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.

In-pit coal mine personnel uniqueness detection technology based on personnel positioning and face recognition

Since the coal mine in-pit personnel positioning system neither can effectively achieve the function to detect the uniqueness of in-pit coal-mine personnel nor can identify and eliminate violations in attendance management such as multiple cards for one person, and swiping one's cards by others in China at present. Therefore, the research introduces a uniqueness detection system and method for in-pit coal-mine personnel integrated into the in-pit coal mine personnel positioning system, establishing a system mode based on face recognition + recognition of personnel positioning card + release by automatic detection. Aiming at the facts that the in-pit personnel are wearing helmets and faces are prone to be stained during the face recognition, the study proposes the ideas that pre-process face images using the 2D-wavelet-transformation-based Mallat algorithm and extracts three face features: miner light, eyes and mouths, using the generalized symmetry transformation-based algorithm. This research carried out test with 40 clean face images with no helmets and 40 lightly-stained face images, and then compared with results with the one using the face feature extraction method based on grey-scale transformation and edge detection. The results show that the method described in the paper can detect accurately face features in the above-mentioned two cases, and the accuracy to detect face features is 97.5% in the case of wearing helmets and lightly-stained faces.

Constructing(2+1)-dimensional N=1 supersymmetric integrable systems from the Hirota formalism in the superspace

The N = 1 supersymmetric extensions of two integrable systems,a special negative Kadomtsev–Petviashvili（NKP）system and a（2＋1）-dimensional modified Korteweg–de Vries（MKd V） system,are constructed from the Hirota formalism in the superspace.The integrability of both systems in the sense of possessing infinitely many generalized symmetries are confirmed by extending the formal series symmetry approach to the supersymmetric framework.It is found that both systems admit a generalization of W∞type algebra and a Kac-Moody–Virasoro type subalgebra.Interestingly,the first one of the positive flow of the supersymmetric NKP system is another N = 1 supersymmetric extension of the（2＋1）-dimensional MKd V system.Based on our work,a hypothesis is put forward on a series of（2＋1）-dimensional supersymmetric integrable systems.It is hoped that our work may develop a straightforward way to obtain supersymmetric integrable systems in high dimensions.

The derivative-dependent functional variable separation for the evolution equations

This paper studies variable separation of the evolution equations via the generalized conditional symmetry. To illustrate, we classify the extended nonlinear wave equation utt = A（u, ux）uxx＋B（u, ux, ut） which admits the derivative- dependent functional separable solutions （DDFSSs）. We also extend the concept of the DDFSS to cover other variable separation approaches.

THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS

For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem.

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.

Diagonal reflection symmetries and universal four-zero texture

In this paper,we consider a set of new symmetries in the SM:diagonal reflection symmetries Rm_(u,v)^(*),R=m_(u,v),m_(d,e)^(*)=mde with R=diag(-1,1,1).These generalized CP symmetries predict the Majorana phases to beα_(2.3)/2-0π/2.Realization of diagonal reflection symmetries implies a broken chiral U(1)po symmetry only for the first generation.The axion scale is suggested to be(θ_(u,d))~△GuT√m_(u,dm_(c,s))/v-10^(12)[GeV].By combining the symmetries with the four-zero texture,the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well.This scheme predicts the normal hierarchy,the Dirac phase ocp≈203°,and|ml|≈2.5 or 6.2[meV].In this scheme,the type-I seesaw mechanism and a given neutrino Yukawa matrix Y_(y)completely determine the structure of the right-handed neutrino mass M_(R).A u-y unification predicts the mass eigenvalues to be(M_(RI),M_(R2),M_(R3))=(O(10^(5)).O(10^(9)),O(10^(14))[Gev].

Realization of photonic p-orbital higher-order topological insulators

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals.Despite tremendous efforts in engineering synthetic cold-atom,as well as electronic and photonic lattices to explore orbital physics,thus far high orbitals in an important class of materials,namely,higher-order topological insulators(HOTIs),have not been realized.Here,we demonstrate p-orbital corner states in a photonic HOTI,unveiling their underlying topological invariant,symmetry protection,and nonlinearity-induced dynamical rotation.In a Kagome-type HOTI,we find that the topological protection of p-orbital corner states demands an orbital-hopping symmetry in addition to generalized chiral symmetry.Due to orbital hybridization,nontrivial topology of the p-orbital HOTI is“hidden”if bulk polarization is used as the topological invariant,but well manifested by the generalized winding number.Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher-band topology applicable to a broad spectrum of systems.