Harmonic maps with fixed singular sets

Suppose Ω is a smooth domain in R^m,N is a compact smooth Riemannian manifold, andZ is a fixed compact subset of Ω having finite (m − 3)-dimensional Minkowski content (e.g.,Z ism − 3 rectifiable). We consider various spaces of harmonic mapsu: Ω →N that have a singular setZ and controlled behavior nearZ. We study the structure of such spacesH and questions of existence, uniqueness, stability, and minimality under perturbation. In caseZ = 0,H is a Banach manifold locally diffeomorphic to a submanifold of the product of the boundary data space with a finite-dimensional space of Jacobi fields with controlled singular behavior. In this smooth case, the projection ofu εH tou |ϖΩ is Fredholm of index 0. R. H.’s research partially supported by the National Science Foundation.     

The exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket

The authors rigorously prove that the exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket is

Energy-filtered XPEEM with NanoESCA using synchrotron and laboratory X-ray sources: Principles and first demonstrated results

The importance of energy filtering in PEEM-based imaging methods has been shown in recent years with the availability of powerful instruments. A new instrument, the NanoESCA, combines a fully electrostatic PEEM column and an aberration corrected double hemispherical analyser as energy filter. This paper reports on recently demonstrated XPEEM results using the first commercially available NanoESCA instrument operated with both synchrotron soft X-rays and monochromatic laboratory Al Kα radiation. The implementation of elemental and bonding-state specific imaging is shown with both excitation sources. The presently achieved (but not yet ultimate) lateral resolutions on energy filtered core-level images are 150 nm with a large synchrotron spot and below 1 μm with a focused laboratory source. To date this is the unique example of laboratory XPEEM core-level imaging.     

K9和石英玻璃基片上Au膜真空紫外反射特性研究

采用离子束溅射法,分别在经过不同前期清洗方法处理过的K9及石英玻璃光学基片上,选择不同的镀膜参量,镀制了多种厚度的Au膜。对镀制的Au膜在真空紫外波段较宽波长范围内的反射率进行了连续测量。测试结果表明:辅助离子源的使用方式、Au膜厚度对反射镜的反射率有重大影响。基片材料、镀前基片表面清洗工艺等对反射率也有一定影响。采用镀前离子轰击,可显著提高Au膜反射率及膜与基底的粘合力;获得最高反射率时的最佳膜厚与基片材料、镀膜工艺密切相关。对经过离子清洗的石英基片,膜厚在30 nm左右反射率最高;比较而言,石英基片可获得更高的反射率;辅助离子源的使用还显著影响获得最高反射率时对应的最佳膜厚值,且对K9基片的影响更显著。     

Strong electric field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential

We consider the Schrödinger operator with electric potential V, which decays at infinity, and magnetic potential A. We study the asymptotic behaviour for large values of the electric field coupling constant of the eigenvalues situated under the essential-spectrum lower bound. We concentrate on the cases of rapidly decaying V (e.g. V L ^m/2( ^m ) for m 3) and arbitrary A, or slowly decaying V (i.e. V(x |x|^– , (0,2), as |x| ) and magnetic potentials A corresponding to constant magnetic fields B = curl A.Partially supported by the Ministry of Culture, Science and Education under Grant No. 52.     

SDiff(2) Toda equation — Hierarchy,Tau function,and symmetries

A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda equation, is shown to have a Lax formalism and an infinite hierarchy of higher flows. The Lax formalism is very similar to the case of the self-dual vacuum Einstein equation and its hyper-Kähler version, however now based upon a symplectic structure on a cylinderS ¹×R. An analogue of the Toda lattice tau function is introduced. The existence of hidden SDiff(2) symmetries are derived from a Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function turn out to have commutator anomalies, hence give a representation of a central extension of the SDiff(2) algebra.     

New cw far infrared molecular lasers from ClO2, HCCF,FCN, CH3NC,CH3F,and propynal

Many new laser lines between 100 μm and 1 mm have been detected by optically pumping several polyatomic molecules with C¹⁶O₂ and C¹⁸O₂ lasers. Tentative assignment of the lasing transitions has been possible in some cases.     

Multivariate optimization and comparison between conventional extraction (CE) and ultrasonic-assisted extraction (UAE) of carotenoid extraction from cashew apple

Carotenoids are an essential component of cashew and can be used in pharmaceuticals, cosmetics, natural pigment, food additives, among other applications. The present work focuses on optimizing and comparing conventional and ultrasound-assisted extraction methods. Every optimization step took place with a 1:1 (w:w) mixture of yellow and red cashew apples lyophilized and ground in a cryogenic mill. A Simplex-centroid design was applied for both methods, and the solvents acetone, methanol, ethanol, and petroleum ether were evaluated. After choosing the extractor solvent, a central composite design was applied to optimize the sample mass (59–201 mg) and extraction time (6–34 min). The optimum conditions for the extractor solvent were 38% acetone, 30% ethanol, and 32% petroleum ether for CE and a mixture of 44% acetone and 56% methanol for UAE. The best experimental conditions for UAE were a sonication time of 19 min and a sample mass of 153 mg, while the CE was 23 min and 136 mg. Comparing red and yellow cashews, red cashews showed a higher carotenoid content in both methodologies. The UAE methodology was ca. 21% faster, presented a more straightforward composition of extracting solution, showed an average yield of superior carotenoid content in all samples compared to CE. Therefore, UAE has demonstrated a simple, efficient, fast, low-cost adjustment methodology and a reliable alternative for other applications involving these bioactive compounds in the studied or similar matrix.     

Nuklearpharmaka — Ihre Entwicklung,Präparation und Anwendungsmöglichkeiten

Radioaktiv markierte Präparate haben in denletzten Jahren in schnell zunehmendem Maße Eingang in die klinische Medizin gefunden. Sie sind beieiner Reihe von Indikationen schon jetzt außerordentlich wertvolle Hilfsmittel bei der Diagnose, besonders bei der Prüfung von Organfunktionen.     

Präparation polykristalliner LiF-Speicherphosphore für die Thermolumineszenzdosimetrie

Zur Ausbildung eines intensiven Glowmaximums der Thermolumineszenz bei 200°C wurden eine Vielzahl von Kationen auf ihre Aktivatorwirkung gegenüber LiF untersucht. Als günstige Aktivatoren erwiesen sich bei der Herstellung des LiF mitgefällte Mg-, Ca- und Ti-Spuren. Die Eigenscaften der präparierten Phosphore werden mit den Analysenergebnissen verglichen und diskutiert.