FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE

Let M be a smooth pseudoconvex hypersurface in ℂ^(n+1) whose Levi form has at most one degenerate eigenvalue. For any tangent vector field L of type (1, 0), we prove the equality of the commutator type and the Levi form type associated to L. We also show that the regular contact type, the commutator type and the Levi form type of the real hypersurface are the same.

The Hausdorff Dimension and Hausdorff Measure of Full Parry Measure Subset of Finite Type

All the full Parry measure subsets of a given subshift of finite type determined by an irreducible 0-1 matrix have the same Hausdorrf dimension and Hausdorff measure which coincide with those of the set of finite type.

Finite Type Non-Minimal Submanifolds

The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.

L^(2)Schrödinger Maximal Estimates Associated with Finite Type Phases in R^(2)

In this paper,we establish Schrödinger maximal estimates associated with the finite type phaseФ(ξ_(1),ξ_(2)):=ξ_(1)^(m)+ξ_(2)^(m),where m≥4 is an even number.Following[12],we prove an L2 fractal restriction estimate associated with the surface{(ξ_(1),ξ_(2),Ф(ξ_(1),ξ_(2))):(ξ_(1),ξ_(2)∈[0,]^(2)}as the main result,which also gives results on the average Fourier decay of fractal measures associated with these surfaces.The key ingredients of the proof include the rescaling technique from[16],Bourgain-Demeter’sℓ^(2)decoupling inequality,the reduction of dimension arguments from[17]and induction on scales.We notice that our Theorem 1.1 has some similarities with the results in[8].However,their results do not cover ours.Their arguments depend on the positive definiteness of the Hessian matrix of the phase function,while our phase functions are degenerate.

Local symmetries of finite type hypersurfaces in C^2 Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.

l^(2) Decoupling for Certain Surfaces of Finite Type in R^(3)

In this article,we establish an 2 decoupling inequality for the surface F_(4)^(2):={(ξ1,ξ2,ξ_(1)^(4)+ξ_(2)^(4)):(ξ1,ξ2)∈[0,1]^(2)}associated with the decomposition adapted to finite type geometry from our previous work[Li,Z.,Miao,C.,Zheng,J.:A restriction estimate for a certain surface of finite type in R^(3).J.Fourier Anal.Appl.,27(4),Paper No.63,24 pp.(2021)].The key ingredients of the proof include the so-called generalized rescaling technique,an l^(2) decoupling inequality for the surfaces{(ξ1,ξ2,φ1(ξ1)+ξ42):(ξ1,ξ2)∈[0,1]^(2)}with φ1 being non-degenerate,reduction of dimension arguments and induction on scales.

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the hausdorff meausre fo the sets of finite type of the one-sided symbolic space are given

Area integral,Littlewood-Paley g-function and BMOA on convex domains of finite type

Let Ω be a smoothly bounded convex domain of finite type in Cn,Ω be the boundary of Ω, S α(f) and g(f) be the area integral and Littlewood-Paley g-function on Ω,respectively. If f ∈ BMOA,then S α(f) < ∞ a.e. on Ω,and there exists a constant C such that Sα(f) ‖*≤ C ‖f‖*. The same result also holds for g(f).

Topological Entropy of a Class of Subshifts of Finite Type

In this paper, we construct a special class of subshifts of finite type. By studying the spectral radius of the transfer matrix associated with the subshift of finite type, we obtain an estimation of its topological entropy. Interestingly, we find that the topological entropy of this class of subshifts of finite type converges monotonically to log（n ＋ 1） （a constant only depends on the structure of the transfer matrices） as the increasing of the order of the transfer matrices.

A New Proof of Superclose of a Crouzeix-Raviart Type Finite Element for Second Order Elliptic Equation

In this paper, a new proof of superclose of a Crouzeix-Raviart type finite element is given for second order elliptic boundary value problem by Bramble-Hilbert lemma on anisotropic meshes.

Superconvergence of nonconforming finite element penalty scheme for Stokes problem using L^2 projection method

A modified penalty scheme is discussed for solving the Stokes problem with the Crouzeix-Raviart type nonconforming linear triangular finite element. By the L^2 projection method, the superconvergence results for the velocity and pressure are obtained with a penalty parameter larger than that of the classical penalty scheme. The numerical experiments are carried out to confirm the theoretical results.

Remarks on the Veronese Generating Submanifolds in Minkoski Space

In this paper,the minimal conjecture on the Veronese Generating submanifolds in S(1)5 is generalized to minmal submanifolds in Sm. Two classes of the Generating submanifolds of spherical minimal submanifolds in Minkowski space are respectively space-like Minimal submanifolds of Hyperbolic space and pseudo-Rie-mannian Minimal submanifolds of pseudo-Riemannian sphere and they are of 1-type submanifolds in Minkowski space is proved.

A Note on P-chaos Implies Distributional Chaos and Chaos in the Sense of Devaney with Positive Topological Entropy

In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.

On Two Conjectures Concerning the Veronese Generating submanifolds

The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.

ANISOTROPIC CROUZEIX-RAVIART TYPE NONCONFORMING FINITE ELEMENT METHODS TO VARIATIONAL INEQUALITY PROBLEM WITH DISPLACEMENT OBSTACLE

In this paper, anisotropic Crouzeix-Raviart type nonconforming finite element meth- ods are considered for solving the second order variational inequality with displacement obstacle. The convergence analysis is presented and the optimal order error estimates are obtained under the hypothesis of the finite length of the free boundary. Numerical results are provided to illustrate the correctness of theoretical analysis.

Rate decline analysis of multiple fractured horizontal well in shale reservoir with triple continuum

Multiple fractured horizontal well(MFHW) is widely applied in the development of shale gas. To investigate the gas flow characteristics in shale, based on a new dual mechanism triple continuum model, an analytical solution for MFHW surrounded by stimulated reservoir volume(SRV) was presented. Pressure and pressure derivative curves were used to identify the characteristics of flow regimes in shale. Blasingame type curves were established to evaluate the effects of sensitive parameters on rate decline curves, which indicates that the whole flow regimes could be divided into transient flow, feeding flow, and pseudo steady state flow. In feeding flow regime, the production of gas well is gradually fed by adsorbed gases in sub matrix, and free gases in matrix. The proportion of different gas sources to well production is determined by such parameters as storability ratios of triple continuum, transmissibility coefficients controlled by dual flow mechanism and fracture conductivity.

A Conjecture on Veronese Generating Submanifolds

In this paper,the higher dimensional conjecture on Veronese generating subman-ifolds proposed by Prof. SUN Zhen-zu is generalized to Pseudo-Euclidean Space L1(m+1), it is proved that in the higher dimentional Lorentz Space L1(m+1), the generating submanifolds of an n dimentional submanifold of Pseudo-Riemannian unit sphere S1m is an n+1 dimentional minimal submanifold of S1(m+1) in L1(m+2) and is of 1-type in L1(m+2).

The Projective Cover of the Trivial Representation for a Finite Group of Lie Type in Defining Characteristic

We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.

Some Characterizations of Algebras of Finite Representation Type

Let A be a finite dimensional, connected, basic algebra over an algebraically closed field. We prove that A is of finite representation type if and only if there is a natural number m such that rad^m（End（M）） = 0, for any indecomposable A-modules M. This gives a partial answer to one of problems posed by Skowrofiski.

Bounding Topology via Geometry,A-Simple Fundamental Groups

We call a group A-simple,if it has no non-trivial normal abelian subgroup.We will present finiteness results in controlled topology via geometry on manifolds whose fundamental groups are A-simple.