Sub-200 fs microjoule pulses from a monolithic linear fiber CPA system

An all-fiber-integrated linear chirped-pulse amplifier system generating microjoule pulse energies is reported. It is seeded by an all-fiber dissipative-soliton laser and incorporates a newly developed fiber stretcher, whose dispersive properties match that of the grating compressor. Pulse durations of 189 fs with energies of 2.2 μJ were achieved after compression. The average power was 9.8 W at the repetition rate of 4.5 MHz.     

Magnetic resonance studies of laryngeal tumors implanted in nude mice: effect of treatment with bleomycin and electroporation

Recently, a new type of cancer treatment has been introduced that combines pulsed electric fields (PEF) with anticancer drugs. The proposed mode of action is that PEF create transient pores in the membranes which allow entry of drugs into the cells. This method increases cytotoxicity of some anticancer drugs like bleomycin (BLM) by 2-3 orders of magnitude, which, in turn, reduces systemic drug dosage without decreasing efficacy. In the present study, magnetic resonance imaging (MRI) was used to determine changes in apparent water self-diffusion coefficients (ADC) and spin-lattice (T(1)) and spin-spin (T(2)) relaxation times that occur in an animal laryngeal tumor (HEp-2 cells) model with BLM delivered by PEF. A Bruker 14 Tesla (600 MHz) wide-bore spectrometer with micro-imaging capability was used to generate all the data. Mice carrying approximately 8 mm tumors were treated with several combinations of drug and PEF. All measurements were made on tumor samples excised from mice 24 and 48 hours after treatment with (i) saline, intratumor injection (i.t.), (ii) BLM, i.t., (iii) saline with PEF, and (iv) BLM, i.t., followed by PEF. Although T(1) does not differ between the controls (i, ii, and iii) and full treatment (iv) 6.72 +/- 0.20 s vs. 6.31 +/- 1.7 s, T(2) for (iv) at 24 hours is significantly different from the controls 52.4 +/- 0.91 ms vs. 46.5 +/- 1.54 ms. T(2) differences between treatment and controls disappear at 48 hours. ADC increases significantly from 24 to 48 hours (7.31 +/- 0.16 x 10(-6) to 8.28 +/- 0.28 x 10(-6) cm(2)/sec, p = 0.05). Longer T(2) values may reflect early apoptosis and tumor death when the tumor is structurally less dense. Higher ADC's, associated with the periphery of the tumors and the central region, may indicate loose structural organization and necrosis resulting from the combination treatment.     

Solitons in geometric potentials

We show that the geometrically induced potential existing in undulated slab waveguides dramatically affects the properties of solitons. In particular, whereas solitons residing in the potential maxima do not feature power thresholds and are stable, their counterparts residing in the potential minima are unstable and may exhibit a power threshold for their existence. Additionally, the geometric potential is shown to support stable multipole solitons that cannot be supported by straight waveguides. Finally, the geometric potential results in the appearance of the effective barriers that prevent transverse soliton motion.     

Morse theory for periodic solutions of hamiltonian systems and the maslov index

In this paper we prove Morse type inequalities for the contractible 1-periodic solutions of time dependent Hamiltonian differential equations on those compact symplectic manifolds M for which the symplectic form and the first Chern class of the tangent bundle vanish over π₂ (M). The proof is based on a version of infinite dimensional Morse theory which is due to Floer. The key point is an index theorem for the Fredholm operator which plays a central role in Floer homology. The index formula involves the Maslov index of nondegenerate contractible periodic solutions. This Maslov index plays the same role as the Morse index of a nondegenerate critical point does in finite dimensional Morse theory. We shall use this connection between Floer homology and Maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every 1-periodic solution has at least one Floquet multiplier which is not equal to 1.     

Singly generated planar algebras of small dimension, Part II

We classified in Bisch and Jones (Duke Math. J. 101 (2000) 41) all spherical C∗-planar algebras generated by a non-trivial 2-box subject to the condition that the dimension of N′∩M₂ is ?12. We showed that they are given by the Fuss-Catalan systems discovered in Bisch and Jones (Invent. Math. 128 (1997) 89) and one exceptional planar algebra. In the present paper, we extend these results and show that there is only one spherical C∗-planar algebra generated by a single non-trivial 2-box if the dimension of N′∩M₂ is 13. It is given by the standard invariant of the crossed product subfactor , where D₅ denotes the dihedral group with 10 elements.     

The Steiner ratio of several discrete metric spaces

Steiner's Problem is the “Problem of shortest connectivity”, that means, given a finite set of points in a metric space (X,ρ), search for a network interconnecting these points with minimal length. This shortest network must be a tree and is called a Steiner Minimal Tree (SMT). It may contain vertices different from the points which are to be connected. Such points are called Steiner points. If we do not allow Steiner points, that means, we only connect certain pairs of the given points, we get a tree which is called a Minimum Spanning Tree (MST). Steiner's Problem is very hard as well in combinatorial as in computational sense, but, on the other hand, the determination of an MST is simple. Consequently, we are interested in the greatest lower bound for the ratio between the lengths of these both trees:

which is called the Steiner ratio (of (X,ρ)). We look for estimates and exact values for the Steiner ratio in several discrete metric spaces. Particularly, we determine the Steiner ratio for spaces of words, and we estimate the Steiner ratio for specific graphs.     

Image guide couplers with dielectric coupling elements and radiation reduction

Directional couplers in image guide technique for millimeter-wave circuits are discussed, and steps to improve their properties are demonstrated. The simple two-line-9 dB coupler with periodical coupling is compared to a design with an intermediate dielectric coupling element to reduce the frequency dependence. Radiation from the waveguide bends can be reduced significantly by inserting absorber materials at critical points. Experimental results for a-3 dB coupler are also given.     

Image guide couplers with isotropic and anisotropic coupling elements

Among other waveguide elements directional couplers are required in integrated millimeterwave circuits in image guide technique. Hereby an I-guide is used which consists of a dielectric slab between two conducting plates on which the electric field is perpendicularily. Flat coupling behaviour and better isolation can be reached by use of a dielectric coupling element and absorber materials. Thereby the frequency dependence is reduced significantly. Further the coupling can be steered by an additional premagnetized ferrite slab. In this way switched couplers can be realized.     

Perfect imaging through a disordered waveguide lattice

It is experimentally demonstrated that perfect imaging is possible in disordered wave guiding media, provided that the disorder is off-diagonal, i.e., that only the spacing varies randomly between the otherwise identical lattice sites. On-diagonal disorder or Kerr nonlinearity destroys the imaging.     

Systematic investigations of anthocyanin–metal interactions by Raman spectroscopy

The FT‐Raman spectra of the chloride salts of pelargonidin‐3‐glucoside, cyanidin‐3‐glucoside and delphinidin‐3‐glucoside, their structures at pH 5.0 and their interaction with aluminium and ferric ions are presented for the first time and discussed with regard to their spectroscopic response. Two marker bands at approximately 1510 and 1330/1350 cm⁻¹ and one band at approximately 1330/1350 cm⁻¹ were identified being characteristic for the formation of ferric and aluminium chelates, respectively, of cyanidin‐3‐glucoside and delphinidin‐3‐glucoside. In contrast, pelargonidin‐3‐glucoside, exhibiting one single hydroxyl group in the B‐ring, did not form metal chelates, which could be clearly demonstrated by missing marker bands. The formation of anthocyanin–metal chelates was also verified in model systems containing commercial sugar beet pectin and a pectic polysaccharide fraction isolated thereof, respectively. In addition, the absence of anthocyanin–metal chelates in systems prepared with citrate buffer was confirmed, and the effects of low and high methoxylated citrus pectins on chelate formation were studied. Copyright © 2012 John Wiley & Sons, Ltd.