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.

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.

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.

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.

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.

Comparisons in finite element analysis of minimally invasive, locking,and non-locking plates systems used in treating calcaneal fractures of Sanders type Ⅱ and type Ⅲ

Background Calcaneal fractures are relatively common but complex,while the treatment of these fractures is still controversial.The objective of this study was to compare the biomechanical stability of minimally invasive,locking,and non-locking plating systems used for fixing Sanders type Ⅱ and type Ⅲ calcaneal fractures.Finite element analysis was used for comparing the three types of plating systems.This study helped in guiding the clinical management of calcaneal fractures.Methods The CT data acquired from a volunteer was used to construct a finite element model of calcaneus.The fracture lines were made according to Sanders type Ⅱ （A,B,C） and type Ⅲ （AB,AC,BC） and six calcaneal fractures models were constructed accordingly.Three fixation methods used in clinical treatment were simulated by design tools （minimally invasive plating with percutaneous screws,Y-size non-locking plating,and locking plating） and then fixed to these fracture models with the help of clinical principles.The single minimally invasive plating fixation was also tested to compare the function of percutaneous screws.Then,the neutral force was applied on established methods.The displacement and presses distribution condition in various plating models were analyzed and compared.Results The levels of displacement and compressive press on the bone around fixation or strains on plating were within the physiological limit,indicating that the three methods were suitable for application.Compared with the locked and unlocked plates,the minimally invasive plating caused a relatively lower displacement without the high stress in bone or fixation.The minimum stress in fixation was observed in locking plate as the distribution of stress was concentrated in the anterior part of locking plate.Conclusions The minimally invasive plating method could be a better alternative method in treating Sanders type Ⅱ and type Ⅲ calcaneal fractures.The observed stiffness of locking plate was not obviously stronger than unlocked plate.

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.

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.

On Ohtsuki's Invariants of Integral Homology 3-Spheres

We provide some more explicit formulae to facilitate the computation of Ohtsuki’s rational invariants λn of integral homology 3-spheres extracted from Reshetikhin-Turaev SU（2） quantum invari- ants. Several interesting consequences will follow from our computation of λ2. One of them says that λ2 is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that λ1 is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained from surgery on knots by using the Jones polynomial.

New procedure to generate multipliers in complex Neumann problem and effective Kohn algorithm

The purpose of this paper is threefold.(i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D'Angelo concerning the ineffectiveness of the latter.(ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations.(iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations.

L^p Boundedness of Marcinkiewicz Integrals with H^1 Kernels

We establish the L^p boundedness of Marcinkiewicz integral operators with kernels in theHardy space on a compact submanifold of finite type. Previously such boundedness properties were obtained when the submanifold is a sphere. Our result shows that what matters is not the symmetry, but a certain type of curvature property of the submanifold.