A Family of Three Living Buddhas

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A FAMILY OF BERNSTEIN QUASI-INTERPOLANTS ON[0,1]

Suppose that we want to approximate fC[0,1]by polynomials in P_n,using only its values on X_n={i/n,0≤i≤n}.This can be done by the Lagrange interpolant L_n f or the classical Bernstein polynomial B_n f.But,when n tends to infinity,L_n f does not converge to f in general and the convergence of B_n f to fis very slow.We define a family of operators B^(k)_n, n≥k,which are intermediate ones between B(0)_n=B^(1)_n=B_n and B^(n)_n=L_n,and we study some of their properties.In particular,we prove a Voronovskaja-type theorem which asserts that B^(k)_n f-f=0(n^(-[(k+2)/2))for f sufficiently regular. Moreover,B(k)_n f uses only values of B_n f and its derivaties and can be computed by De Casteljau or subdivision algorithms.

A FAMILY OF MODAL METHODS FOR COMPUTING EIGENVECTOR DERIVATIVES WITH REPEATED ROOTS

A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgun's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods.

Identification of a LMNA (c.646C>T) variant by whole-exome sequencing in combination with a dilated cardiomyopathy (DCM) related gene filter in a family with familiar DCM

Dilated cardiomyopathy（DCM）is characterized by the dilated heart chambers and reduced systolic function in the absence of specific aetiology[1].Approximately one third of DCM cases are hereditary.In recent years,DCM concomitant with arrhythmias and sudden death resulting from gene mutation has been widely

A Family of the Exponential Attractors and the Inertial Manifolds for a Class of Generalized Kirchhoff Equations

In this paper, we studied a family of the exponential attractors and the inertial manifolds for a class of generalized Kirchhoff-type equations with strong dissipation term. After making appropriate assumptions for Kirchhoff stress term and nonlinear term, the existence of exponential attractor is obtained by proving the discrete squeezing property of the equation, then according to Hadamard’s graph transformation method, the spectral interval condition is proved to be true, therefore, the existence of a family of the inertial manifolds for the equation is obtained.

The Family of Exponential Attractors and Inertial Manifolds for a Generalized Nonlinear Kirchhoff Equations

In this paper, we study the long-time behavior of a class of generalized nonlinear Kichhoff equation under the condition of n dimension. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup related to the initial-boundary value problem are proved, and then the existence of its exponential attractor is obtained. By extending the space E0 to Ek, a family of the exponential attractors of the initial-boundary value problem is obtained. In the second part, we consider the long-time behavior for a system of generalized Kirchhoff type with strong damping terms. Using the Hadamard graph transformation method, we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectrum interval condition.

A Family of Exponential Attractors and Inertial Manifolds for a Class of Higher Order Kirchhoff Equations

In this paper, the global dynamics of a class of higher order nonlinear Kirchhoff equations under n-dimensional conditions is studied. Firstly, the Lipschitz property and squeezing property of the nonlinear semigroup associated with the initial boundary value problem are proved, and the existence of a family of exponential attractors is obtained. Then, by constructing the corresponding graph norm, the condition of a spectral interval is established when N is sufficiently large. Finally, the existence of the family of inertial manifolds is obtained.

A Family of the Random Attractors for a Class of Generalized Kirchhoff-Type Equations

In this paper, we studied the existence of a family of the random attractor for a class of generalized Kirchhoff-type equations with a strong dissipation term. Firstly, according to Ornstein-Uhlenbeck process, we transformed the equation into a stochastic equation with random variables and multiplicative white noise. Secondly, we proved the existence of a bounded random absorbing set. Finally, by using the isomorphic mapping method and the compact embedding theorem, we get the stochastic dynamical system with a family of random attractors.

A Family of the Inertial Manifolds for a Class of Generalized Kirchhoff-Type Coupled Equations

The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under the corresponding hypothetical conditions, according to the Hadamard graph transformation method, obtain the equivalent norm in space , and we obtain the existence of a family of the inertial manifolds while such equations satisfy the spectral interval condition.

A Family of Dancers

AS the last strains of music from Swan Lake faded, ballerina Yu Chuanya returned to stage in joburg Theater from the wings to take a bow. She was joined by other dancers from China, South Africa, Cuba and the United States, It was April 17, the open- ing night of the current season, and the first joint performance was greeted with rapturous applause, The collaboration between the Liaoning Ballet and Joburg Ballet companies in a new production of the classic Swan Lake was the first of its kind. Their 21 performances in South Africa gave audiences the first opportunity to watch such an eclectic group of danc- ers on stage in a single production,

Yunnan,A Family of Many Nationalities

All in all,Governor He is full of confidence about the future of Yun-nan."Total elimination of poverty and common prosperity for all一this is our goal.To do that,we are carrying out all sorts of new expan-sion programs,such as the develop-ment of the Lancang River Basin in the center of the province and that of the Jinsha River Basin in the north.We're promoting border trade in the southwest,increasing econo-mic exchange and cooperation with Southeast Asia,and even reactivat-ing the Southerm Silk Road.

Global Attractors and Their Dimension Estimates for a Class of Generalized Kirchhoff Equations

In this paper, we studied the long-time properties of solutions of generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for the nonlinear source term g (u) and Kirchhoff stress term M (s) in the equation, and the existence and uniqueness of the solution are proved by using uniform prior estimates of time and Galerkin’s finite element method. Then, abounded absorption set B0k is obtained by prior estimation, and the Rellich-kondrachov’s compact embedding theorem is used to prove that the solution semigroup S (t) generated by the equation has a family of the global attractor Ak in the phase space . Finally, linearize the equation and verify that the semigroups are Frechet diifferentiable on Ek. Then, the upper boundary estimation of the Hausdorff dimension and Fractal dimension of a family of the global attractor Ak was obtained.

The Need for a Family

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A Family for Abandoned Pets

ＡＦａｍｉｌｙｆｏｒＡｂａｎｄｏｎｅｄＰｅｔｓＰｅｔｓａｓｋｆｏｒｓｏｌｉｔｔｌｅ，ｙｅｔｇｉｖｅｓｏｍｕｃｈＢｙｓｔａｆｆｒｅｐｏｒｔｅｒＹＩＬＩＷＨＥＮｆｏｒｍｅｒＵＳＰｒｅｓｉ－ｄｅｎｔＦｒａｎｋｌｉｎＤ．Ｒｏｏ－ｓｅｖｅｌｔｗａｓｂｕｒｉｅｄ...

Shrinking Projection Methods for a Family of Quasi-φ-Strict Asymptotically Pseudo-Contractions in Banach Spaces

The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property （K）. The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.

ON THE INVARIANT FOR A FAMILY OF DEFORMED HALLEY METHODS

In this paper, an invariant determined by a function used to guarantee the convergence of all members with l ≤ k in the family of deformed Halley iterative methods for solving nonlinear equation in complex field is given. Results include some known ones as this special cases. We get not only the error estimates of the iterative sequences {zn,l} but also those of f(zn,l) for all l ≤ k.