Invertibility conditions for the nonlinear difference operator (\mathcal{D}x)(n) = x(n + 1) - f(x(n)) in the space l ∞(ℤ, ℝ)

We obtain necessary and sufficient conditions for the invertibility of the nonlinear difference operator $(\mathcal{D}x)(n) = x(n + 1) - f(x(n))$ , n ∈ ?, in the space of bounded two-sided number sequences. Here, f: ? → ? is a continuous function.     

On the invertibility of the operator \frac{d}{{dt}} + A in the space L 2 (ℝ, H)

We strengthen the assertion on the continuous invertibility of the operator in the space L ₂(ℝ, H), where H is a complex Hilbert space and A is a sectorial operator with spectrum in the right half-plane of ℂ. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 31–36, January–March, 2006.     

利用k=f(d_2╱d_1)的函数曲线图求弧形倒角轴段的柔度

刘先志同志在《几种弧形倒角变直径轴段的柔度或刚度的积分算法》一文中,曾就圆弧倒角过渡轴段、椭圆弧倒角过渡轴段及抛物线弧倒角过渡轴段用积分法推导出了它们的平均截面极惯性矩J_m和轴段柔度e的较精确的计算公式,这对研究内燃机轴系的     

Bäcklund transformations for the equation ∂2u/∂x1∂x1 + ∂2u/∂x2∂x2−f (u)

Bäcklund transformations for the equation ² u/x¹x ¹+ ²u/x ² x ²=f (u)here f is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition d ² f/du ²=f is sufficient for the existence of Bäcklund transformations for the equation of our interest. A special case of our results leads to the conclusion of Leibbrandt ^[1,2].     

Bézier curves in the modification of boundary integral equations (BIE) for potential boundary-values problems

The paper presents a modification of the classical boundary integral equation method (BIEM) for two-dimensional potential boundary values problems. The proposed modification consists in describing the boundary geometry by means of Bézier curves. As a result of this analytical modification of the BIEM, a new parametric integral equation system (PIES) was obtained. The kernels of these equations include the geometry of the boundary. This new PIES is no longer defined on the boundary, as in the case of the BIEM, but on the straight line for any given domain. The solution of the new PIES does not require a boundary discretization since it can be reduced merely to an approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained were compared with exact solutions.     

On the “bead,hoop and spring” (BHS) dynamical system

Here, we make the theoretical and numerical analysis of the non-linear equation describing the evolution of the “bead, hoop and spring” (BHS) dynamical system derived by Ochoa and Clavijo in (Eur. J. Phys. 27:1277–1288, 2006). In particular, we solve by standard techniques of non-linear physics an approximation of their equation neglecting the centrifugal effect before giving a more mathematical and exact treatment. The analogy with phase transitions is underlined. We point out the existence of finite-time singularities in the phase-space and we derive a criterion for possible oscillations.     

Uniqueness of positive radial solutions of △u+g(r)u+h(r)u p =0 in Rn

Positive radial solutions of a semilinear elliptic equation u+g(r)u+h(r)u ^p =0, where r=|x|, xR ⁿ , and p>1, are studied in balls with zero Dirichlet boundary condition. By means of a generalized Pohoaev identity which includes a real parameter, the uniqueness of the solution is established under quite general assumptions on g(r) and h(r). This result applies to Matukuma's equation and the scalar field equation and is shown to be sharp for these equations.     

On the Mechanism of Turbulent Coherent Structure(Ⅰ)──The Physical Model o

ＯＮＴＨＥＭＥＣＨＡＮＩＳＭＯＦＴＵＲＢＵＬＥＮＴＣＯＨＥＲＥＮＴＳＴＲＵＣＴＵＲＥ（Ｉ）──ＴＨＥＰＹＳＩＣＡＬＭＯＤＥＬＯＦＴＨＥＣＯＨＥＲＥＮＴＳＴＲＵＣＴＵＲＥＦＯＲＴＨＥＳＭＯＯＴＨＢＯＵＮＤＡＲＹＬＡＹＥＲＴｓａｉｓｈｕ－ｔａｎｇ（蔡树棠...     

ON THE SOLUTION OF NONLINEARTWOPOINT BOUNDARY VALUE PROBLEM──u" g(t.u) = f(t),u(0) = u(2π) = 0

I.IntroductionLetHbearealHilbertspace,XandYtwoclosedsubspacesofHsuchthatH=X$Y,T:H-HaC'mapping,n>1.Assumethatthereexisttwopositiveconstantsniland)liZsuchthatforVueH,Vx6X,VYey'Undertheconditions(l.1),(l.2)and(l.3),ManasevichprovedthatTisaC"diffeomorphismontoH'tl].ThepurposeofthispaperistoimprovetheaboveManasevich'shomeomQrphismtheorem,andthen,itisusedtoproveanexistenceanduniquenessresultforthenonlineartulopointboundaryvalueproblem11.ANonVariationalVersionofaMax-MinPrincipleToimprov…     

Group Classification of Equations of the Form y″ = f(x,y)

The problem of classification of ordinary differential equations of the form y = f(x,y) by admissible local Lie groups of transformations is solved. Standard equations are listed on the basis of the equivalence concept. The classes of equations admitting a oneparameter group and obtained from the standard equations by invariant extension are described.     

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(φ)=(1+k)sinφ/ 1+kcosφ.     

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(φ)=(1+k)sinφ/1+kcosφ.     

On the Solution of Elliptic Equation sum from k=0 to n (a_kΔ~kφ)=0 and Its Application in Mechanics

In this paper,the solution of elliptic equation(?)a_k△~kφ=0 is discussedin detail by the method of separation of variables in complex field.The ge-neral solution which can be used in the approximation to the boundary con-ditions of the practical problems is presented.Two practical examples inmechanics are given.     

On the stability of distorted laminar flow(III)—The nonlinear stability analysis of distorted parallel shear flow

Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the nonlinear stability behaviour of parallel shear flow, carries on stability calculation taking account of the perturbations of background turbulence noise under certain assumption, and obtains some results in accordance qualitatively with those of experiment for plane Poiseuille flow and pipe Poiseuille flow.The author thanks Prof. Zhou Heng sincerely for his kind offer of his computer program of the artificial neutrality method on the stability in subcritical range of plane Poiseuille flow.     

Spatiotemporal dynamics of lump solution to the (1 + 1)-dimensional Benjamin–Ono equation

Nonlinear Dynamics - This paper focuses on the finite-time synchronization problem for a kind of general complex networks with intrinsic time-varying delays and hybrid couplings (i.e., containing...