Samples of biological tissue are modelled as inhomogeneous fluids with density ?(X) and sound speed c(x) at point x. The samples are contained in the sphere |x| ? δ and it is assumed that ?(x) ? ?0 = 1 and c(x) ? c0 = 1 for |x| ? δ, and |γn(x)| ? 1 and |?γ?(x)| ? 1 where γ?(x) = ?(x) ? 1 and γn(x) = c?2(x) ? 1. The samples are insonified by plane pulses s(x · θ0 – t) where x = |θ0| = 1 and the scattered pulse is shown to have the form |x|?1es(|x| – t, θ, θ0) in the far field, where x = |x| θ. The response es(τ, θ, θ0) is measurable. The goal of the work is to construct the sample parameters γn and γ? from es(τ, θ, θ0) for suitable choiches of s, θ and θ0. In the limiting case of constant density: γ?(x)? 0 it is shown that Where δ represents the Dirac δ and S2 is the unit sphere |θ| = 1. Analogous formulas, based on two sets of measurements, are derived for the case of variable c(x) and ?(x). 相似文献
Let Γ be a distance-regular graph of diameterd≥3. For each vertexx of Γ, letT(x) denote the Terwilliger algebra for Γ with respect tox. An irreducibleT(x)-moduleW is said to bethin if dimEi*(x)W≤1 for 0≤i≤d, whereEi*(x) is theith dual idempotent for Γ with respect tox. The graph Γ isthin if for each vertexx of Γ, every irreducibleT(x)-module is thin. Aregular generalized quadrangle is a bipartite distance-regular graph with girth 8 and diameter 4. Our main results are as follows: Theorem.Let Γ=(X,R) be a distance-regular graph with diameter d≥3 and valency k≥3. Then the following are equivalent:
Γis a regular generalized quadrangle.
Γis thin and c3=1.
Corollary.Let Γ=(X,R) be a thin distance-regular graph with diameter d≥3 and valency k≥3. Then Γ has girth 3, 4, 6, or 8. Then girth of Γ is 8 exactly when Γ is a regular generalized quadrangle. 相似文献
In this paper we study the scattering of acoustic waves by an obstacle ??. We establish the following relation between the scattering kernel S(s, θ, ω) and the support function h?? of the obstacle: The right endpoint of the support of S(s, θ, ω) as function of s is h??(θ-ω); h?? is defined by For Dirichlet boundary condition the result is proved in full generality, for Neumann condition only for backscattering, i.e., for θ = -ω. Since the convex hull of ?? can be recovered from knowledge of h??, the above result may be useful in reconstructing ?? from scattering data. 相似文献
Generalized Hopf formulas are provided for minimax (viscosity) solutions of Hamilton–Jacobi equations of the form Vt + H(t, DxV) = 0 and Vt + H(t, V, DxV) = 0 with the boundary condition V(T, x) = (x), where is a convex function. The bounds within which these formulas apply are elucidated. 相似文献
We consider the equation of mixed type (k(y) ? 0 whenever y ? 0) in a region G which is bounded by the curves: A piecewise smooth curve Γ lying in the half-plane y > 0 which intersects the line y = 0 at the points A(-1, 0) and B(0, 0). For y < 0 by a piecewise smooth curve Γ through A which meets the characteristic of (1) issued from B at the point P and the curve Γ which consists of the portion PB of the characteristic through B. We obtain sufficient conditions for the uniqueness of the solution of the problem L[u] = f, dnu: = k(y)uxdy – uydx|γ0 = = Ψ(s) for a “general” function k(y), when r(x, y) is not necessarily zero and Γ1 is of a more general form then in the papers of V. P. Egorov [6], [7]. 相似文献
We are interested in finding the velocity distribution at the wings of an aeroplane. Within the scope of a three — dimensional linear theory we analyse a model which is formulated as a mixed screen boundary value problem for the Helmholtz equation (Δ +k2)Φ = 0 in ?3\s where Φ denotes the perturbation velocity potential, induced by the presence of the wings and s :=L UW with the projection L of the wings onto the (x,y)- plane and the wake W. Not all Cauchy data are given explicitly on L, respectively W. These missing Cauchy data depend on the wing circulation Γ· Γ has to be fixed by the Kutta–Joukovskii condition: Λ Φ should be finite near the trailing edge xt of L. To fulfil this condition in a way that all appearing terms can be defined mathematically exactly and belong to spaces which are physically meaningful, we propose to fix Γ by the condition of vanishing stress intensity factors of Φ near xt up to a certain order such that ΛΦ|xt ?W2?(xt)? L2(xt),?>0. In the two–dimensional case, and if L is the left half–plane in ?2, we have an explicit formula to calculate Γ and we can control the regularity of Γ and Φ. 相似文献
We prove a theorem giving conditions under which a discrete-time dynamical system as (xt,yt) = (f;(xt – 1, yt – 1), g(xt – 1, yt – 1)) can be reconstructed from a scalar valued time series (t)t, which depends only on xt where t = (xt). This theorem allows us to use the delay-coordinate method in this setting. 相似文献
We formulate a continuous function FR×HH, where H is a separable Hilbert space such that the Cauchy problem. x(t)=F(t, x(t)), x(t0)=x0 has no solution in any neighborhood of the point t0, no matter what t0 R and x0 H are considered.Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 467–477, March, 1974.In conclusion, the author thanks O. G. Smolyanov and V. I. Averbukh for their constant interest and for a number of useful remarks. 相似文献
The problem is as follows: How to describe graphically the set T(1)(Γ) where $T(1)(z) = \int_\Gamma {\tfrac{{d\mu (\zeta )}} {{\zeta - z}}} $ and Γ = Γθ is the Von Koch curve, θ ∈ (0, π/4)? In this paper we give some expression permitting us to compute Tθ(1)(z) for each z ∈ Γ to within an arbitrary ? > 0. Also we provide an estimate for the error. 相似文献
Let the real functionsK(x) andL(x) be such thatM(x)=K(x)+iL(x)=eixg(x), whereg(x) is infinitely differentiable for all largex and is non-oscillatory at infinity. We develop an efficient automatic quadrature procedure for numerically computing the integrals
aK(t)f(t) and
aL(t)f(t)dt, where the functionf(t) is smooth and nonoscillatory at infinity. One such example for which we also provide numerical results is that for whichK(x)=J(x) andL(x)=Y(x), whereJ(x) andY(x) are the Bessel functions of order . The procedure involves the use of an automatic scheme for Fourier integrals and the modified W-transformation which is used for computing oscillatory infinite integrals. 相似文献