Accretive sets and differential equations in Banach spaces

This paper is concerned with global solutions of the initial value problem (1)du/dt +Au∋0,u(0)=x whereA is a (nonlinear) accretive set in a Banach spaceX. We show that various approximation processes converge to the solution (whenever it exists). In particular we obtain an exponential formula for the solutions of (1). AssumingX* is uniformly convex, we also prove the existence of a solution under weaker assumptions ofA than those made by previous authors (F. Browder, T. Kato). Results obtained at the Courant Institute of Mathematical Sciences, New York University, with the National Science Foundation, Grant NSF-GP-11600.     

Decay widths of lowest massive Regge excitations of open strings

With the advent of the LHC there is widespread interest in the discovery potential for physics beyond the standard model. In TeV-scale open string theory, the new physics can be manifest in the excitation and decay of new resonant structures, corresponding to Regge recurrences of standard model particles. An essential input for the prediction of invariant mass spectra of the decay products (which could serve to identify the resonance as a string excitation) are the partial and total widths of the decay products. We present a parameter-free calculation of these widths for the first Regge recurrence of the SU(3)$\mathit{SU}(3)$ gluon octet, of the U(1)$U(1)$ gauge boson which accompanies gluons in D-brane constructions, and of the quark triplet.     

A new concept of reduced measure for nonlinear elliptic equations

We study the existence of solutions of the nonlinear problem

(i)$?\mathrm{\Delta }u+g(u)=\mu \text{in}\Omega \text{,}u=0\text{on}?\Omega \text{,}$

where μ is a Radon measure and $g:\mathbb{R}\to \mathbb{R}$ is a nondecreasing continuous function with $g(t)=0$, $?t?0$. Given g, Eq. (i) need not have a solution for every measure μ, and we say that μ is a good measure if (i) admits a solution. We show that for every μ there exists a largest good measure ${\mu }^{*}?\mu$. This reduced measure${\mu }^{*}$ has a number of remarkable properties. To cite this article: H. Brezis et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Total syntheses of Yingzhaosu A and of its C(14)-epimer including the first evaluation of their antimalarial and cytotoxic activities

[reaction: see text] The molecular structure of the naturally occurring antimalarial agent yingzhaosu A (1) is characterized by a 2,3-dioxabicyclo[3.3.1]nonane system (3a), an allylic alcohol, a homoallylic alcohol, and five stereogenic centers. Herein we report on the total synthesis of yingzhaosu A (1) in eight steps and 7.3% overall yield starting from (S)-limonene (12). To maximize efficacy, the bridged bicyclic endoperoxide molecular core was constructed by a multicomponent free-radical domino reaction in which five bonds are formed in a single operation. In addition, reaction protocols that are compatible with the sensitivity of the peroxide function to strong basic and nucleophilic reagents as well as to reducing agents were employed. An intriguing step involved the selective hydrogenation of a carbon-carbon double bond in the presence of a peroxide and an aldehyde function to give aldehyde peroxide 7. The two major synthons (aldehydoperoxide 7 and its complementary five-carbon atom unit 35) were linked through a Mukaiyama aldol reaction followed by in situ dehydration under mild buffered basic conditions. The carbonyl group in the resulting peroxidic enone 39 was stereoselectively reduced with either R-CBS catalyst (42b) to give, after in situ desilylation, yingzhaosu A (1) or with S-CBS catalyst (42a) its C(14)-epimer 40. The first quantitative in vitro and in vivo data for the antimalarial activity of yingzhaosu A (1) and its C(14)-epimer 40 are reported. The C(14)-epiyingzhaosu A (40) exhibits potent cytotoxic activity against the KB nasal-pharyngeal cancer cell line in vitro.     

Matrix and fissure water movement through unsaturated calcareous sandstone

Evaluation of pollution endangering groundwater resources beneath fractured sediments may be achieved by estimating the transport rates and recharge amounts of both the matrix and the fissure components. This study examines the transport of water by matrix and fissure flow in the unsaturated zone using environmental tritium as a natural tracer. A 35-year record of tritium concentration along 40 m calcareous sandstone column was reconstructed. It was found that on the average, 40 mm yr¹ (8% of the yearly rain) percolated downward through the matrix pores at a velocity of 1.1 m yr¹. An additional amount of more than 20 mm yr¹ (more 4% of the rains) percolated rapidly through fissure network. These field data fit and support the model proposed by Wang and Narashimham (1985) that the bulk of the water movement under unsaturated conditions occurs through interconnected pores in the matrix.     

Equations d’evolution du second ordre associees a des operateurs monotones

This paper extends some recent results of V. Barbu. It is concerned with bounded solutions of the problem:u″∈Au, u′(0)∈ϖj(u(0)−a) whereA is a maximal monotone operator in a Hilbert spaceH, a∈D(A) andj is a strictly convex l.s.c. function fromH to [0,+∞]. An existence and uniqueness theorem for this problem is proved. Takingj to be the indicator function of a pointu ₀∈D(A), one obtains a bounded solutionu(t) of the initial value problem:u″∈Au, u(0)=u ₀. Denotingu(t)=S _1/2(t)u₀ one obtains a semi-group of contractions onD(A). The generator of this semigroup is denoted byA _1/2. Further properties ofS _1/2(t) andA _1/2 are studied.      

The Thomas-Fermi-von Weizsäcker theory of atoms and molecules

We place the Thomas-Fermi-von Weizsäcker model of atoms on a firm mathematical footing. We prove existence and uniqueness of solutions of the Thomas-Fermi-von Weizsäcker equation as well as the fact that they minimize the Thomas-Fermi-von Weizsäcker energy functional. Moreover, we prove the existence of binding for two very dissimilar atoms in the frame of this model.on leave from Universidad de Chile, Santiago, ChileResearch supported by U. S. National Science Foundation under Grants MCS78-20455 (R. B.), PHY-7825390 A 01 (H. B. and E. L.), and Army Research Grant DAH 29-78-6-0127 (H. B.)