ROUGH MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this article, certain Marcinkiewicz integral operators associated to surfaces of revolution on product domains were studied. The Lp boundedness for these operators are established under some rather weak conditions on kernels. The main results essentially improve and extend some known results.

L^p Bounds for the Commutators of Rough Singular Integrals Associated with Surfaces of Revolution

In this paper, we establish the L^p （R-n＋1） boundedness for the commutators of singular integrals associated to surfaces of revolution, { （t,Ф （ ｜ t｜ ） ）： t ∈R^n }, with rough kernels Ω∈ L（IogL）^2（sn^-1）, if Ф（｜t｜） = ｜t｜.

L^p BOUNDS FOR SINGULAR INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION ON PRODUCT DOMAINS

In this paper, the authors establish Lp boundedness for several classes of multiple singular integrals along surfaces of revolution with kernels satisfying rather weak size condition. The results of the corresponding maximal truncated singular integrals are also obtained. The main results essentially improve and extend some known results.

Oscillatory Strongly Singular Integral Associated to the Convex Surfaces of Revolution

Here we consider the following strongly singular integral TΩ,γ,α,βf（x,t）=∫R^ne^i｜y｜^-βΩ（y/｜y｜）/｜y｜^n＋af（x-y,t-γ（｜y｜））dy, where Ω∈L^p（S^n-1）,p〉1,n〉1,α〉0 and γis convex on （0,∞）.We prove that there exists A（p,n） 〉 0 such that if β 〉 A（p,n） （1 ＋α）, then TΩ,γ,α,β is bounded from L^2 （R^n＋1） to itself and the constant is independent of γ Furthermore,when Ω∈ C^∞ （S^n-1 ）, we will show that TΩ,γ,α,β is bounded from L^2 （R^n＋l） to itself only if β〉 2α and the constant is independent of γ.

Surfaces of Revolution in Minkowski 3-Space Satisfying F （G） = k（G ＋ C）

In this paper, we investigate the surfaces of revolution under the condition FIl（G） = k（G ＋ C）, where r11 is one of the Christoffel-like operators, G is the Gauss map of the surface, k is a non-constant function and C is a constant vector in Minkowski 3-space.

Triebel-Lizorkin space boundedness of rough singular integrals associated to surfaces of revolution

We consider the boundedness of the rough singular integral operator T_（？,ψ,h） along a surface of revolution on the Triebel-Lizorkin space F^α_（ p,q）（R^n） for Ω ∈ H^1（（S^n-1）） and Ω ∈ Llog^＋L（S^n-1） ∪_1

On Quadratric Rotational Curved Surface

In this paper,a deterministic theorem is proposed for quadratic rotational curved surface.The relationship between invariants for quadratic rotational curved surface is established.In addition we give each type of equitions for rotational curved surface using the invariant.

Small symmetrical deformation and stress analysis of catenary shells of revolution

The catenary shells of revolution are widely used in church constructions due to their unique mechanics'features.To have a better understanding of the deformation and stress of the catenary shells of revolution,we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations.Numerical simulations are carried out based on both Reissner-Meissner(R-M)mixed formulations and displacement formulations.Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter c,and reveal that the mechanics of the catenary shells of revolution has some advantages over the spherical shell for some loadings.Two complete codes in Maple are provided.

Factors Affecting Small Axial Cooling Fan Performance

Many factors such as outer diameter, hub ratio, blade numbers, shape and stagger angle affect the performance of small cooling fans. A small cooling fan was simulated using CFD software for three blade stagger angles （30.5°, 37.5°, 44.5°）and obtained the internal flow field and the static characteristics. Research indicated that the stagger angle has an obvious effect on the static characteristics of a fan. For flow rates below 0.0104 mVs, total pressure is the greatest when the stagger angle is 37.5°; flow rates higher than 0.0104 m^3/s, the total pressure is greatest when the stagger angle is 44.5° For the same flow rates, the velocity at inlet of pressure surface increases with in- creasing stagger angle, but the change of velocity on the suction surface is very small. For one model, vortices and the speed of revolution surfaces decrease with tip clearance increasing. But for other three models, increasing the stagger angle, the vortex intensity and speed of revolution surfaces at same height tip clearance increases, simultaneously, the position of vortex offset from the top of the rotor blade to the suction surface.

Existence and uniqueness for variational problem from progressive lens design

We study a functional modelling the progressive lens design,which is a combination of Willmore functional and total Gauss curvature.First,we prove the existence for the minimizers of this class of functionals among the class of revolution surfaces rotated by the curves y=f(x)about the x-axis.Then,choosing such a minimiser as background surfaces to approximate the functional by a quadratic functional,we prove the existence and uniqueness of the solution to the Euler-Lagrange equation for the quadratic functionals.Our results not only provide a strictly mathematical proof for numerical methods,but also give a more reasonable and more extensive choice for the background surfaces.