Scaling by 5 on a 1/4-Cantor Measure

Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L^2(\mu), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB (\Gamma) is the original Jorgensen-Pedersen ONB for the Cantor measure (\mu) and the other ONB is is 5\Gamma. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.Comment: 34 page

Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. In this paper, we focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the theory of existential Presburger Arithmetic with divisibility (PAD). Since PAD is decidable, we get a decision procedure for quadratic words equations with length constraints for which the associated counter system is \emph{flat} (i.e., all nodes belong to at most one cycle). We show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, together with length constraints. Decidability holds when the constraints are additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page

Droplet based microfluidic fabrication of designer microparticles for encapsulation applications

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Microfluidic fabrication of polymeric core-shell microspheres for controlled release applications

Footnote in article: Paper submitted as part of the 3rd European Conference on Microfluidics ... 2012We report a facile and robust microfluidic method to fabricate polymeric core-shell microspheres as delivery vehicles for biomedical applications. The characteristics of core-shell microspheres can be precisely and easily tuned by manipulating the microfluidic double emulsion templates. The addition of a shell can significantly improve the versatility as well as functionality of these microspheres as delivery vehicles. We demonstrate that the nature of the shell material plays an important role in the properties of the core-shell delivery vehicles. The release kinetics is significantly influenced by the material of the shell and other characteristics such as the thickness. For example, by adding a poly(lactic-co-glycolic acid) (PLGA) shell to an alginate core, the encapsulation efficiency is enhanced and undesired leakage of hydrophilic actives is prevented. By contrast, adding an alginate shell to PLGA core can lead to a reduction of the initial release rate, thus extending the release period of hydrophobic actives. Microfluidic fabrication enables the generation of precisely controlled core-shell microspheres with a narrow size distribution, which enables the investigation of the relationship between the release kinetics of these microspheres and their characteristics. The approach of using core-shell particles as delivery vehicles creates new opportunities to customize the release kinetics of active ingredients. © 2013 AIP Publishing LLC.published_or_final_versio

Non-ancient solution of the Ricci flow

For any complete noncompact K$\ddot{a}$hler manifold with nonnegative and bounded holomorphic bisectional curvature,we provide the necessary and sufficient condition for non-ancient solution to the Ricci flow in this paper.Comment: seven pages, latex fil

Revision of the derivation of stellar rates from experiment and impact on Eu s-process contributions

The final, definitive version of this paper has been published in Journal of Physics: Conference Series, 665(1), January 5, 2016, and is available on line at doi: 10.1088/1742-6596/665/1/012024 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing LtdA new, general formalism to include experimental data in revised stellar rates is discussed, containing revised uncertainties. Application to the s-process shows that the actual uncertainties in the neutron capture rates can be larger than would be expected from the experimental errors alone. As a specific example for how astrophysical conclusions can depend on the approach selected to derive stellar rates, the 151Eu/(151Eu+153 Eu) abundance ratio from AGB star models is presented. Finally, a recommended workflow for the derivation of stellar rates from experiment is laid out.Peer reviewe

An inhomogeneous toy-model of the quantum gravity with explicitly evolvable observables

An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt equation and the "particle on a sphere" type of the gauge condition is suggested. In the quantization scheme considered, the "problem of time" is solved by building of the quasi-Heisenberg operators acting in a space of solutions of the Wheeler-DeWitt equation and the normalization of the wave function corresponds to the Klein-Gordon type. To analyze the physical consequences of the scheme, a (1+1)-dimensional background space is considered for which a classical solution is found and quantized. The obtained estimations show the way to solution of the cosmological constant problem, which consists in compensation of the zero-point oscillations of the matter fields by the quantum oscillations of the scale factor. Along with such a compensation, a slow global evolution of a background corresponding to an universe expansion exists.Comment: 18 page

Inspection of Computed Tomography (CT) Data and Finite Element (FE) Simulation of Additive Manufactured (AM) Components

This is the author accepted manuscript. The final version is available from the publisherOne of the challenges of working with Additive Manufactured (AM) metal parts involves checking accuracy and reliability before production. Techniques used Computed Tomography (CT) scans, 3D image processing, and Finite Element (FE) simulation help detect problems prior to costly faults. A workflow has been developed by Synopsys, ANSYS, North Star Imaging, and the University of Pittsburgh to streamline this often-complex process, with applications to analyzing metal AM-produced lightweight brackets and a component from Moog, Inc. Software like Synopsys Simpleware™ is used to generate robust models from 3D scans of AM parts to compare original CAD models with ‘as-built’ geometries, and to export a FE mesh for simulation in ANSYS. This method enables identification of design deviations early in the design process, and how their impact might be tackled prior to production. For the Moog application, unexpected defects were identified for aerospace parts to inform future design iteration