The Dirichlet problem for a Monge-Ampère equation corresponding to a nonnegative, possible degenerate cohomology class on a Kähler manifold with boundary is studied. C1,α estimates away from a divisor are obtained, by combining techniques of Blocki, Tsuji, Yau, and pluripotential theory. In particular, C1,α geodesic rays in the space of Kähler potentials are constructed for each test configurat...

Studies of the amidase activity ofextracts of various animal tissues have been reported in earlier papers (Bray, James, Ryman & Thorpe, 1948; Bray, James, Raffan, Ryman & Thorpe, 1949a; Bray, Thorpe & Wood, 1949c; Bray, James, Thorpe, Wasdell & Wood, 1949 b). The present paper records further observations, including the behaviour of the enzyme towards some saturated long-chain and w-phenylsubst...

We prove the existence of a solution of a free boundary problem for the transonic small-disturbance equation. The free boundary is the position of a transonic shock dividing two regions of smooth flow. Assuming inviscid, irrotational flow, as modeled by the transonic small-disturbance equation, the equation is hyperbolic upstream where the flow is supersonic, and elliptic in the downstream subs...

In this paper, we study the solution of nonlinear equation ⊗♦c1u(x) = f (x, L♦c1u(x)) where ⊗♦c1 is the product of the Otimes operator and Diamond operator where c1 is positive constants, k is a positive integer, p + q = n, n is the dimension of the Euclidean space Rn, for x = (x1, x2, . . . , xn) ∈ Rn,u(x) is an unknown function and f (x, .L♦c1u(x)) is a given function. It was found that the e...

Low-density lipoprotein cholesterol (LDL-C) is frequently estimated using the empirical Friedewald equation. We compared the accuracy of the novel equation named as the 180-cell method (180-c), which estimates LDL-C using a stratification approach, to those of 9 previously suggested formulas, including the Friedewald equation.We compared the accuracy of 10 equations by calculating intraclass co...

In this paper we investigate the continuity of maps solutions of optimal transportation problems. These maps are expressed through the gradient of a potential for which we establish C1 and C1,α regularity. Our results hold assuming a condition on the cost function (condition A3 below), that was the one used for C2 a priori estimates in [5]. The optimal potential will solve a Monge-Ampère equati...

The lower critical field H(c1) for highly underdoped YBa2Cu3O(6+x) with T(c) between 8.9 and 22 K has been determined by measurements of magnetization M(H) curves with applied field parallel to the c axis. H(c1) is linear in temperatures below about 0.6T(c), and H(c1)(0) is proportional to T(1.64+/-0.04)(c), clearly violating the proportionality between rho(s)(0) and T(c). Moreover, the slope -...

Abstract We report the application of Pd(II)-catalyzed, directing-group-aided C–H arylation/alkylation tactics to functionalize pyrene core, especially, relatively inaccessible C2 and K-region C10 positions core augmentation library derivatives with C1,C2- C1,C10-disubstituted motifs. The Pd(II)-catalyzed β-C–H C2-position pyrene-1-carboxamide possessing an 8-aminoquinoline directing group yiel...