Kantorovich-type inequalities and the measures of inefficiency of the glse

In this paper we introduce some Kantorovich inequalities for the Euclidean norm of a matrix, that is, the upper bounds to (X'B ^–1 X) ^–1 X'B ^–1 AB ^–1 X(X'B ^–1X)^–1 X' BX(X'AX) ^–1 X'CX² are given, where A²=trace (A'A). In terms of these inequalities the upper bounds to the three measures of inefficiency of the generalized least squares estimator (GLSE) in general Gauss-Markov models are also established.Project supported partially by the Third World Academy of Sciences under contract TWASRG 87-46 and by the National Natural Science Foundation.     

Layered petroleum reservoirs with cross-flows

Studied is a cylindrical reservoir consisting of three layers: a water-containing bottom layer, and two oil-containing top layers from whose upper layer oil is produced. For its solution, a corrected version of the finite Hankel transform for Neumann-Neumann boundary conditions was used together with numerical inversion of the Laplace transform. The effects of the water zone on the unsteady state pressure in the reservoir were evaluated at distances away from the well and at the well-bore itself. We found that the vertical pressure drop increases gradually with time and is more significant in the vicinity of the well-bore. For constant production and at any time t, smaller reservoirs experience higher pressure drops than larger ones. For the reservoir investigated, we found that for nondimensional time t _Dw <10⁴ the presence of a second fluid (water) has no effect on the pressure drop. Of all the formation and fluid properties investigated, porosity has the largest effect on pressure.Nomenclature c ₁, c ₂ Oil and water compressibilities, vol/vol/atm, vol/vol/psi - h Height of water zone from bottom of reservoir, cm, ft - h _D h/r _w , non-dimensional - H Height of reservoir, cm, ft - H _D H/r _w, non-dimensional - J ₀, J ₁ Bessel functions of the first kind, zero and first-order - K _r2, K _r1 Oil and water zones, horizontal permeabilities, darcies, md - K _z2, K _z1 Oil and water zones, vertical permeabilities, darcies, md - k ₁ n=1, 2, 3... - k ₂ n=1, 2, 3... - k _1,0 - k _2,0 - p(r, z, t) P(r, z, 0)–P(r, z, t), atm, psi - P(r, z, t) Pressure at any layer in the reservoir, atm, psi - P(r, z, 0) Initial pressure at any layer in the reservoir, atm, psi - P _D , non-dimensional - q Constant production rate of well, cc/sec, barrels/day - r Radius of reservoir, cm, ft - r _D r/r _w , non-dimensional - r _e Drainage radius, cm, ft - r _eD re/r _w , non-dimensional - r _w Well-bore radius, cm, ft - t Time, sec, hr - _Dw (k _r2 t)/( _{2 2} c ₂ r _w ² ), non-dimensional - Y ₀, Y ₁ Bessel functions of the second kind, zero and first-order - z Distance z measured vertically upward from bottom of reservoir, cm, ft - Z _D z/r _w , non-dimensional - z ₁ Height of the bottom of the producing layer, cm, ft - z _1D z ₁/r _w , non-dimensional - z ₂ Height of the top of the producing layer, cm, ft - z _2,D z ₂/r _w , non-dimensional - _n nth positive root of equation (18) - ₁ k _z1/k _r1, non-dimensional - ₂ k _z2/k _r2, non-dimensional - _{1 1 1} c ₁/k _r1, hydraulic diffusivity of layer I - _{2 2 2} c ₂/k _r2, hydraulic diffusivity of layers II and III - ₂, ₁ Viscosity of oil and water, cp, cp - _{n n} /r _w , l/cm, l/ft - ₂, ₁ Porosity of oil and water-filled zones, fraction - ( ₁/ ₂) (k _z2/k _z1), non-dimensional     

Essay on gravitation: Present-time variation of Newton's gravitational constant in superstring theories

Superstring theories provide an appropriate framework for studying the time variation of fundamental coupling constants. The present time variation of coupling constants in Superstring theories with currently favorable internal backgrounds critically depends on the shape of the potential for the size of internal space. If the potential is almost flat, as in perturbation theory to all orders, the present value of ¦/G¦ for Newton's gravitational constant is calculable and estimated to be 1×10^–11±1yr^–1, which is just at the edge of the present observational bound for/G. If the potential has a minimum with finite curvature due to unknown nonperturbative effects,/G will become unobservably small. The improvement of the measurement of/G of 1 or 2 orders of magnitude would discriminate between the two situations. Problems with the time variation of other coupling constants are also discussed.This essay received the fourth award from the Gravity Research Foundation for the year 1987-Ed.     

在DBU存在下酞菁锰配合物的合成及溶剂影响

在强有机碱１，８－二氮杂双环［５，４，０］十一－７烯（简称ＤＢＵ）存在下，ＭｎＣｌ２与邻二氰基苯在某些二元醇溶剂中可高效合成Ｍｎ（Ⅱ）Ｐｃ（Ｐｃ表示酞菁），同时研究了不同溶剂对合成产物的物种及产率的影响和不同氧化态锰的酞菁配合物在一些醇溶剂中的互变现象