Impact of the tip radius on the lateral resolution in piezoresponse force microscopy

We present a quantitative investigation of the impact of tip radius as well as sample type and thickness on the lateral resolution in piezoresponse force microscopy (PFM) investigating bulk single crystals. The observed linear dependence of the width of the domain wall on the tip radius as well as the independence of the lateral resolution on the specific crystal-type are validated by a simple theoretical model. Using a Ti-Pt-coated tip with a nominal radius of 15 nm the so far highest lateral resolution in bulk crystals of only 17 nm was obtained

On the three-space-problem and the lifting of bounded sets,

We exhibit a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two really different possibilities of defining the notion of a dual Fréchet space. If in a Three-spaceproblem the corresponding quotient map is assumed to lift bounded sets, we obtain partial positive answers. Finally, we give this property of lifting bounded sets a special treatment

Multi-slice ptychographic tomography

Ptychography is a form of Coherent Diffractive Imaging, where diffraction patterns are processed by iterative algorithms to recover an image of a specimen. Although mostly applied in two dimensions, ptychography can be extended to produce three dimensional images in two ways: via multi-slice ptychography or ptychographic tomography. Ptychographic tomography relies on 2D ptychography to supply projections to conventional tomographic algorithms, whilst multi-slice ptychography uses the redundancy in ptychographic data to split the reconstruction into a series of axial slices. Whilst multi-slice ptychography can handle multiple-scattering thick specimens and has a much smaller data requirement than ptychographic tomography, its depth resolution is relatively poor. Here we propose an imaging modality that combines the benefits of the two approaches, enabling isotropic 3D resolution imaging of thick specimens with a small number of angular measurements. Optical experiments validate our proposed method

A three-dimensional view of structural changes caused by deactivation of fluid catalytic cracking catalysts

Since its commercial introduction three-quarters of a century ago, fluid catalytic cracking has been one of the most important conversion processes in the petroleum industry. In this process, porous composites composed of zeolite and clay crack the heavy fractions in crude oil into transportation fuel and petrochemical feedstocks. Yet, over time the catalytic activity of these composite particles decreases. Here, we report on ptychographic tomography, diffraction, and fluorescence tomography, as well as electron microscopy measurements, which elucidate the structural changes that lead to catalyst deactivation. In combination, these measurements reveal zeolite amorphization and distinct structural changes on the particle exterior as the driving forces behind catalyst deactivation. Amorphization of zeolites, in particular, close to the particle exterior, results in a reduction of catalytic capacity. A concretion of the outermost particle layer into a dense amorphous silica–alumina shell further reduces the mass transport to the active sites within the composite

On the continuous Cesàro operator in certain function spaces

“The final publication is available at Springer via http://dx.doi.org/10.1007/s11117-014-0321-5"Various properties of the (continuous) Cesàro operator C, acting on Banach and Fréchet spaces of continuous functions and L p-spaces, are investigated. For instance, the spectrum and point spectrum of C are completely determined and a study of certain dynamics of C is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of C acting in the various spaces is identified.The research of the first two authors was partially supported by the projects MTM2010-15200 and GVA Prometeo II/2013/013 (Spain). The second author gratefully acknowledges the support of the Alexander von Humboldt Foundation.Albanese, AA.; Bonet Solves, JA.; Ricker, WJ. (2015). On the continuous Cesàro operator in certain function spaces. Positivity. 19:659-679. https://doi.org/10.1007/s11117-014-0321-5S65967919Albanese, A.A.: Primary products of Banach spaces. Arch. Math. 66, 397–405 (1996)Albanese, A.A.: On subspaces of the spaces $$L^p_{\rm loc}$$ L loc p and of their strong duals. Math. Nachr. 197, 5–18 (1999)Albanese, A.A., Moscatelli, V.B.: Complemented subspaces of sums and products of copies of $$L^1 [0,1]$$ L 1 [ 0 , 1 ] . Rev. Mat. Univ. Complut. Madr. 9, 275–287 (1996)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34, 401–436 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: On mean ergodic operators. In: Curbera, G.P. (eds.) Vector Measures, Integration and Related Topics. Operator Theory: Advances and Applications, vol. 201, pp. 1–20. Birkhäuser, Basel (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: $$C_0$$ C 0 -semigroups and mean ergodic operators in a class of Fréchet spaces. J. Math. Anal. Appl. 365, 142–157 (2010)Albanese, A.A., Bonet, J., Ricker, W.J.: Convergence of arithmetic means of operators in Fréchet spaces. J. Math. Anal. Appl. 401, 160–173 (2013)Bayart, F., Matheron, E.: Dynamics of linear operators. Cambridge Tracts in Mathematics, vol. 179. Cambridge University Press, Cambridge (2009)Bellenot, S.F., Dubinsky, E.: Fréchet spaces with nuclear Köthe quotients. Trans. Am. Math. Soc. 273, 579–594 (1982)Bonet, J., Frerick, L., Peris, A., Wengenroth, J.: Transitive and hypercyclic operators on locally convex spaces. Bull. Lond. Math. Soc. 37, 254–264 (2005)Boyd, D.W.: The spectrum of the Cesàro operator. Acta Sci. Math. (Szeged) 29, 31–34 (1968)Brown, A., Halmos, P.R., Shields, A.L.: Cesàro operators. Acta Sci. Math. (Szeged) 26, 125–137 (1965)Dierolf, S., Zarnadze, D.N.: A note on strictly regular Fréchet spaces. Arch. Math. 42, 549–556 (1984)Dunford, N., Schwartz, J.T.: Linear Operators I: General Theory (2nd Printing). Wiley-Interscience, New York (1964)Galaz Fontes, F., Solís, F.J.: Iterating the Cesàro operators. Proc. Am. Math. Soc. 136, 2147–2153 (2008)Galaz Fontes, F., Ruiz-Aguilar, R.W.: Grados de ciclicidad de los operadores de Cesàro–Hardy. Misc. Mat. 57, 103–117 (2013)González, M., León-Saavedra, F.: Cyclic behaviour of the Cesàro operator on $$L_2(0,+\infty )$$ L 2 ( 0 , + ∞ ) . Proc. Am. Math. Soc. 137, 2049–2055 (2009)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear chaos. In: Universitext. Springer, London (2011)Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. In: Reprint of the 1952 Edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988)Krengel, U.: Ergodic theorems. In: De Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter Co., Berlin (1985)Leibowitz, G.M.: Spectra of finite range Cesàro operators. Acta Sci. Math. (Szeged) 35, 27–28 (1973)Leibowitz, G.M.: The Cesàro operators and their generalizations: examples in infinite-dimensional linear analysis. Am. Math. Mon. 80, 654–661 (1973)León-Saavedra, F., Piqueras-Lerena, A., Seoane-Sepúlveda, J.B.: Orbits of Cesàro type operators. Math. Nachr. 282, 764–773 (2009)Lin, M.: On the uniform ergodic theorem. Proc. Am. Math. Soc. 43, 337–340 (1974)Meise, R., Vogt, D.: Introduction to functional analysis. In: Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press; Oxford University Press, New York (1997)Metafune, G., Moscatelli, V.B.: Quojections and prequojections. In: Terzioğlu, T. (ed.) Advances in the Theory of Fréchet spaces. NATO ASI Series, vol. 287, pp. 235–254. Kluwer Academic Publishers, Dordrecht (1989)Moscatelli, V.B.: Fréchet spaces without norms and without bases. Bull. Lond. Math. Soc. 12, 63–66 (1980)Piszczek, K.: Quasi-reflexive Fréchet spaces and mean ergodicity. J. Math. Anal. Appl. 361, 224–233 (2010)Piszczek, K.: Barrelled spaces and mean ergodicity. Rev R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 104, 5–11 (2010)Yosida, K.: Functional Analysis, 6th edn. Springer, Berlin (1980

Three-Dimensional X-ray Observation of Atmospheric Biological Samples by Linear-Array Scanning-Electron Generation X-ray Microscope System

Recently, we developed a soft X-ray microscope called the scanning-electron generation X-ray microscope (SGXM), which consists of a simple X-ray detection system that detects X-rays emitted from the interaction between a scanning electron beam (EB) and the thin film of the sample mount. We present herein a three-dimensional (3D) X-ray detection system that is based on the SGXM technology and designed for studying atmospheric biological samples. This 3D X-ray detection system contains a linear X-ray photodiode (PD) array. The specimens are placed under a CuZn-coated Si3N4 thin film, which is attached to an atmospheric sample holder. Multiple tilt X-ray images of the samples are detected simultaneously by the linear array of X-ray PDs, and the 3D structure is calculated by a new 3D reconstruction method that uses a simulated-annealing algorithm. The resulting 3D models clearly reveal the inner structure of the bacterium. In addition, the proposed method can easily be used for diverse samples in a broad range of scientific fields

On Ultrabarrelled Spaces, their Group Analogs and Baire Spaces

Let E and F be topological vector spaces and let G and Y be topological abelian groups. We say that E is sequentially barrelled with respect to F if every sequence (un)n∈N of continuous linear maps from E to F which converges pointwise to zero is equicontinuous. We say that G is barrelled with respect to F if every set H of continuous homomorphisms from G to F, for which the set H(x) is bounded in F for every x∈E, is equicontinuous. Finally, we say that G is g-barrelled with respect to Y if every H⊆CHom(G,Y) which is compact in the product topology of YG is equicontinuous. We prove that - a barrelled normed space may not be sequentially barrelled with respect to a complete metrizable locally bounded topological vector space, - a topological group which is a Baire space is barrelled with respect to any topological vector space, - a topological group which is a Namioka space is g-barrelled with respect to any metrizable topological group, - a protodiscrete topological abelian group which is a Baire space may not be g-barrelled (with respect to R/Z)

Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging

Diffractive imaging, in which image-forming optics are replaced by an inverse computation using scattered intensity data, could, in principle, realize wavelength-scale resolution in a transmission electron microscope. However, to date all implementations of this approach have suffered from various experimental restrictions. Here we demonstrate a form of diffractive imaging that unshackles the image formation process from the constraints of electron optics, improving resolution over that of the lens used by a factor of five and showing for the first time that it is possible to recover the complex exit wave (in modulus and phase) at atomic resolution, over an unlimited field of view, using low-energy (30 keV) electrons. Our method, called electron ptychography, has no fundamental experimental boundaries: further development of this proof-of-principle could revolutionize sub-atomic scale transmission imaging

Lensless X-ray imaging in reflection geometry

Lensless X-ray imaging techniques such as coherent diffraction imaging and ptychography, and Fourier transform holography can provide time-resolved, diffraction-limited images. Nearly all examples of these techniques have focused on transmission geometry, restricting the samples and reciprocal spaces that can be investigated. We report a lensless X-ray technique developed for imaging in Bragg and small-angle scattering geometries, which may also find application in transmission geometries. We demonstrate this by imaging a nanofabricated pseudorandom binary structure in small-angle reflection geometry. The technique can be used with extended objects, places no restriction on sample size, and requires no additional sample masking. The realization of X-ray lensless imaging in reflection geometry opens up the possibility of single-shot imaging of surfaces in thin films, buried interfaces in magnetic multilayers, organic photovoltaic and field-effect transistor devices, or Bragg planes in a single crystal