A multi-frequency inverse source problem

This paper is concerned with an inverse source problem that determines the source from measurements of the radiated fields away at multiple frequencies. Rigorous stability estimates are established when the background medium is homogeneous. It is shown that the ill-posedness of the inverse problem decreases as the frequency increases. Under some regularity assumptions on the source function, it is further proven that by increasing the frequency, the logarithmic stability converts to a linear one for the inverse source problem.     

Authentication schemes from actions on graphs, groups, or rings

We propose a couple of general ways of constructing authentication schemes from actions of a semigroup on a set, without exploiting any specific algebraic properties of the set acted upon. Then we give several concrete realizations of this general idea, and in particular, we describe several authentication schemes with long-term private keys where forgery (a.k.a. impersonation) is NP-hard. Computationally hard problems that can be employed in these realizations include the Graph Colorability problem, the Diophantine problem, and many others.     

Asymptotic behaviour of nonlocal reaction-diffusion equations

The existence of a global attractor in L²(Ω) is established for a reaction-diffusion equation on a bounded domain Ω in R^d with Dirichlet boundary conditions, where the reaction term contains an operator F:L²(Ω)→L²(Ω) which is nonlocal and possibly nonlinear. Existence of weak solutions is established, but uniqueness is not required. Compactness of the multivalued flow is obtained via estimates obtained from limits of Galerkin approximations. In contrast with the usual situation, these limits apply for all and not just for almost all time instants.     

Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods

This paper is devoted to the numerical simulation of two-dimensional stationary Bingham fluid flow by semismooth Newton methods. We analyze the modeling variational inequality of the second kind, considering both Dirichlet and stress-free boundary conditions. A family of Tikhonov regularized problems is proposed and the convergence of the regularized solutions to the original one is verified. By using Fenchel’s duality, optimality systems which characterize the original and regularized solutions are obtained. The regularized optimality systems are discretized using a finite element method with (cross-grid P₁)-Q₀ elements for the velocity and pressure, respectively. A semismooth Newton algorithm is proposed in order to solve the discretized optimality systems. Using an additional relaxation, a descent direction is constructed from each semismooth Newton iteration. Local superlinear convergence of the method is also proved. Finally, we perform numerical experiments in order to investigate the behavior and efficiency of the method.     

Reciprocal relations between cyclotomic fields

We describe a reciprocity relation between the prime ideal factorization, and related properties, of certain cyclotomic integers of the type ?n(c−ζm) in the cyclotomic field of the m-th roots of unity and that of the symmetrical elements ?m(c−ζn) in the cyclotomic field of the n-th roots. Here m and n are two positive integers, ?n is the n-th cyclotomic polynomial, ζm a primitive m-th root of unity, and c a rational integer. In particular, one of these integers is a prime element in one cyclotomic field if and only if its symmetrical counterpart is prime in the other cyclotomic field. More properties are also established for the special class of pairs of cyclotomic integers q(1−ζp)−1 and p(1−ζq)−1, where p and q are prime numbers.     

Progress of the intense positron beam project EPOS

EPOS (the ELBE POsitron Source) is a running project to build an intense, bunched positron beam for materials research. It makes use of the bunched electron beam of the ELBE radiation source (Electron Linac with high Brilliance and low Emittance) at the Research Centre Dresden-Rossendorf (40 MeV, 1 mA). ELBE has unique timing properties, the bunch length is <5 ps and the repetition time is 77 ns. In contrast to other Linacs made for Free Electron Lasers (e.g., TTF at DESY, Hamburg), ELBE can be operated in full cw-mode, i.e., with an uninterrupted sequence of bunches. The article continues an earlier publication. It concentrates on details of the timing system and describes issues of radiation protection.     

Theoretical investigation into coordination and selectivity of uranyl-unilateral benzotriazole salophens (X = O/S) for R/S-triadimefons

The design of new uranyl-ligands (uranyl-Ls) is of great significance for the separation and utilization of uranium. In this paper, the triazole group was introduced into uranyl-salophen (uranyl-S) to form new asymmetric uranyl-unilateral benzotriazole salophen (uranyl-UBS); we further replaced two oxygen atoms of uranyl-UBS with two sulfur atoms to generate uranyl-unilateral benzotriazole thio-salophen (uranyl-UBTS) as a new receptor. Then, we comprehensively explored coordination models of uranyl-UBS and uranyl-UBTS with R/S-triadimefons (R/S-TDFs) enantiomers as the guests using density functional theory calculations at the B3LYP//RECP/6-311G** level; we then investigated enantioselectivity recognition of the new receptors to the guests R/S-TDFs. The results indicated that the uranium atoms of the receptors uranyl-S, uranyl-UBS and uranyl-UBTS could coordinate with the carbonyl oxygens in guests R/S-TDFs to form complexes of guest-receptors R/S-TDFs-uranyl-Ls that exhibited two stable V-shaped structures with quite different properties. It was found that the coordination ability to the guests R/S-TDFs is uranyl-UBTS > uranyl-UBS > uranyl-S, while the enantioselectivity for the guests is uranyl-UBTS > uranyl-S > uranyl-UBS and, when the receptor is the same, R-TDF has stronger coordination ability than S-TDF. These results provide information and theoretical supports for the experiments of asymmetric uranyl-UBS with R/S-TDFs, and produce a reference for further exploring the coordination characteristics of asymmetric uranyl-salophen with the triazole derivatives.     

A Micellar Mitotane Formulation with High Drug‐Loading and Solubility: Physico‐Chemical Characterization and Cytotoxicity Studies in 2D and 3D In Vitro Tumor Models

Adrenocortical carcinoma (ACC) is a rare tumor and prognosis is overall poor but heterogeneous. Mitotane (MT) has been used for treatment of ACC for decades, either alone or in combination with cytotoxic chemotherapy. Even at doses up to 6 g per day, more than half of the patients do not achieve targeted plasma concentration (14–20 mg L^?1) even after many months of treatment due to low water solubility, bioavailability, and unfavorable pharmacokinetic profile. Here a novel MT nanoformulation with very high MT concentrations in physiological aqueous media is reported. The MT‐loaded nanoformulations are characterized by Fourier transform infrared spectroscopy, differential scanning calorimetry, and powder X‐ray diffraction which confirms the amorphous nature of the drug. The polymer itself does not show any cytotoxicity in adrenal and liver cell lines. By using the ACC model cell line NCI‐H295 both in monolayers and tumor cell spheroids, micellar MT is demonstrated to exhibit comparable efficacy to its ethanol solution. It is postulated that this formulation will be suitable for i.v. application and rapid attainment of therapeutic plasma concentrations. In conclusion, the micellar formulation is considered a promising tool to alleviate major drawbacks of current MT treatment while retaining bioactivity toward ACC in vitro.     

Invariants de classes : exemples de non-annulation en dimension supérieure

The so-called class-invariant homomorphism ψ measures the Galois module structure of torsors—under a finite flat group scheme G—which lie in the image of a coboundary map associated to an isogeny between (Néron models of) abelian varieties with kernel G. When the varieties are elliptic curves with semi-stable reduction and the order of G is coprime to 6, it is known that the homomorphism ψ vanishes on torsion points. In this paper, using Weil restrictions of elliptic curves, we give the construction, for any prime number p > 2, of an abelian variety A of dimension p endowed with an isogeny (with kernel μ _p ) whose coboundary map is surjective. In the case when A has rank zero and the p-part of the Picard group of the base is non-trivial, we obtain examples where ψ does not vanish on torsion points.

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Résumé  Le class-invariant homomorphism permet de mesurer la structure galoisienne des torseurs—sous un schéma en groupes fini et plat G—qui sont dans l’image du cobord associé à une isogénie, de noyau G, entre des (modèles de Néron de) variétés abéliennes. Quand les variétés sont des courbes elliptiques à réduction semi-stable et que l’ordre de G est premier à 6, on sait que cet homomorphisme s’annule sur les points de torsion. Dans cet article, en nous servant de restrictions de Weil de courbes elliptiques, nous construisons, pour tout nombre premier p > 2, une variété abélienne A de dimension p munie d’une isogénie (de noyau μ _p ) dont le cobord est surjectif. Si A est de rang nul, et si la p-partie du groupe de Picard de la base est non triviale, nous obtenons ainsi un exemple où le class-invariant homomorphism ne s’annule pas sur les points de torsion.

     

有偏总体的极差控制图

根据加权标准差方法建立有偏总体的极差控制图,它基于有偏总体来计算对应于正态分布的控制图常数,根据样本数据的偏度来计算上下控制限,对于总体是对称分布,该控制图退化为标准的休哈特控制图.最后,用蒙特卡洛方法给出了改进的控制图常数.