A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).     

Reconstruction of n-dimensional convex bodies from surface tensors

In this paper, we derive uniqueness and stability results for surface tensors. Further, we develop two algorithms that reconstruct shape of n-dimensional convex bodies. One algorithm requires knowledge of a finite number of surface tensors, whereas the other algorithm is based on noisy measurements of a finite number of harmonic intrinsic volumes. The derived stability results ensure consistency of the two algorithms. Examples that illustrate the feasibility of the algorithms are presented.     

Bounds for the fundamental solutions of elliptic and parabolic equations

It is shown that any elloptic or parabolic operator in nondivergence form with measurable coefficients has a global fundamental solution verifying certain pointwise bounds.     

Improved Bohr’s inequality for locally univalent harmonic mappings

We prove several improved versions of Bohr’s inequality for the harmonic mappings of the form $f=h+\overline{g}$, where $h$ is bounded by 1 and $\left|g^{\prime }\left(z\right)\right|\le \left|h^{\prime }\left(z\right)\right|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. (Kayumov and Ponnusamy, 2018) for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided.     

Factorization method and new potentials from the inverted oscillator

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.     

Mass‐Spectrometric Observation of Counter Anion Production in SU‐8 Exposed to UV Light and its Use for Dill C Parameter Determination

Photopolymerization is a phenomenon that is the basis of much of today's microfabrication technology and intense research is conducted to improve its control and the characteristics of end products for a variety of applications. The design of microscopic structures often relies on the accurate knowledge and modeling of photopolymer's behavior upon exposure, i.e. the Dill parameters, for each radiation species of interest and therefore the development of flexible characterization techniques is of great importance. SU‐8 is a popular compound that is representative of a whole class that relies on cationic polymerization, where an acid is obtained via photolysis of an onium salt during exposure. Here we report on the observation of SbF₆^? via laser desorption mass spectrometry on SU‐8 exposed to UV light at the wavelength of 365 nm and demonstrate that the yield of this counter‐anion as a function of exposure is consistent with the Dill C parameter value available in the literature. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 967–972     

Dahlberg's theorem in higher co-dimension

In 1977 the celebrated theorem of B. Dahlberg established that the harmonic measure is absolutely continuous with respect to the Hausdorff measure on a Lipschitz graph of dimension $n?1$ in ${\mathbb{R}}^n$, and later this result has been extended to more general non-tangentially accessible domains and beyond.In the present paper we prove the first analogue of Dahlberg's theorem in higher co-dimension, on a Lipschitz graph Γ of dimension d in ${\mathbb{R}}^n$, $d<n?1$, with a small Lipschitz constant. We construct a linear degenerate elliptic operator L such that the corresponding harmonic measure ${\omega }_L$ is absolutely continuous with respect to the Hausdorff measure on Γ. More generally, we provide sufficient conditions on the matrix of coefficients of L which guarantee the mutual absolute continuity of ${\omega }_L$ and the Hausdorff measure.     

Kurze Originalmitteilungen Ein neues Lanthan-140-Generatorsystem

Neben ihrer breiten Anwendung in der Nuklearmedizin gewinnen Radionuklidgeneratoren zunehmend auch für die verfahrensctechnische Forsehung Bedeutung. Es konnte gezeigt warden, daß die Generatorsysteme ⁹⁹Mo/^99mTe und ¹¹³Sn/^113mI für zahlreiche Untersuchungen von Transportund Mischvorgängen in technischen Anlagen genutzt warden könnea [1, 2].

Der Radionuklidgenerator ¹¹⁰Ba/¹¹⁰La hat für den Einsatz in der Technik günstigere Eigenschaftcn als die für die Nuklearmedizin entwickelten Generatoren. Insbesondere für die Untersuchung der Materialtransportvorgänge in Polykondensationsreaktoren der Chemiefaserindustrie hat sich ein Lanthan-140-Generator gut bewährt, der mit Tributylphosphat (gesättigt mit 13 N HN03) als Elutionsmittel arbeitet [3, 4].     

Non-local separable solutions of two interacting particles in a harmonic trap

We calculate the energy levels of two particles trapped in a harmonic potential. The actual two-body potential, assumed to be spherically symmetric, is replaced by a projective operator (non-local separable potential) to determine the energy levels in a closed form. This approach overcomes the limitations of the regularized Fermi pseudopotential when the characteristic length of the two-body interaction potential is of the order of the size of the harmonic trap. In addition, we recover the results obtained with the Fermi pseudopotential when the length of the interaction is much smaller than the size of the trap.