Singular values of fractional integral operators: A unification of theorems of Hille, Tamarkin, and Chang

AbstractWe obtain upper bounds on the singular values of fractional integral operators of the form Lα · = ∝0x(x − y)x − 1Γ(α) · dy under the constraint α > 0. These bounds are employed to extend various results obtained over the last half century on the rate of decrease of eigenvalues and singular values of much more general integral operators. Apart from one relatively difficult theorem of Hardy and Littlewood (Math. Z., 27 (1928), 565–606) the devices used are quite simple. They involve no complex variable arguments

Investigation into the limits of perturbation theory at low Q^2 using HERA deep inelastic scattering data

A phenomenological study of the final combined HERA data on inclusive deep inelastic scattering (DIS) has been performed. The data are presented and investigated for a kinematic range extending from values of the four-momentum transfer, $Q^2$, above 10$^4$ GeV$^2$ down to the lowest values observable at HERA of $Q^2$ = 0.045 GeV$^2$ and Bjorken $x$, $x_{\rm Bj}$ = 6 $\cdot$ 10$^{-7}$. The data are well described by fits based on perturbative quantum chromodynamics (QCD) using collinear factorisation and evolution of the parton densities encompassed in the DGLAP formalism from the highest $Q^2$ down to $Q^2$ of a few GeV$^2$. The Regge formalism can describe the data up to $Q^2 \approx$ 0.65 GeV$^2$. The complete data set can be described by a new fit using the ALLM parameterisation. The region between the Regge and the perturbative QCD regimes is of particular interest.Comment: 38 pages, 13 figure

Imagining the Future of Science in America: Scenarios to Spark Conversation

In early 2020, Intertidal Agency began a project to understand the challenges and opportunities facing groups supporting scientists, scientific research, and science-based policy in the US. We found a broad interest in creating new narratives about the role of science in society. Through a series of interviews and discussion sessions we created a framework of four scenarios designed to foster conversations about the future of science in the US. In the next decade, who gets to do science, where and how is science done, and what purpose does science serve

Chitosan/β-glycerophosphate in situ gelling mucoadhesive systems for intravesical delivery of mitomycin-C

The development of mucoadhesive in situ gelling formulations for intravesical application may improve the therapeutic outcomes of bladder cancer patients. In this work, chitosan/β-glycerophosphate (CHIGP) thermosensitive formulations have been prepared using three different chitosan grades (62, 124 and 370 kDa). Their ability to form in situ gelling systems triggered by changes in temperature upon administration to urinary bladder were evaluated using vial inversion and rheological methods. Texture analysis was used to study their mucoadhesive properties as well as syringeability through the urethral catheter. The retention of CHIGP formulations, with fluorescein sodium as the model drug, was studied on porcine urinary bladder mucosa ex vivo using the flow-through technique and fluorescent microscopy. CHIGP formulations containing mitomycin-C were prepared and drug release was studied using in vitro dialysis method. It was established that the molecular weight of chitosan influenced the thermogelling, mucoadhesive and drug release behaviour of the in situ gelling delivery systems. Formulations prepared from chitosan with greatest molecular weight (370 kDa) were found to be the most promising for intravesical application due to their superior gelling properties and in vitro retention in the bladder

Methacrylated chitosan as a polymer with enhanced mucoadhesive properties for transmucosal drug delivery

Chitosan is a cationic polysaccharide that exhibits mucoadhesive properties which allow it to adhere to mucosal tissues. In this work, we explored chemical modification of chitosan through its reaction with methacrylic anhydride to synthesise methacrylated derivative with the aim to improve its mucoadhesive properties. The reaction products were characterised using 1H NMR, FTIR and UV–Vis spectroscopy. 1H NMR and ninhydrin test were used to quantify the degree of methacrylation of chitosan. Turbidimetric analysis of the effect of pH on aqueous solubility of the polymers revealed that the highly methacrylated derivative remained turbid and its turbidity did not change from pH 3 to 9. However, solutions of native chitosan and its derivative with low methacrylation remained transparent at pH 6.5 and exhibited a rapid increase in turbidity at pH > 6.5. The mucoadhesive properties of chitosan and its methacrylated derivatives were evaluated using flow-through method combined with fluorescent microscopy with fluorescein sodium as a model drug. The retention of these polymers was evaluated on porcine bladder mucosa in vitro. The methacrylated derivatives exhibited greater ability to retain fluorescein sodium on the bladder mucosa compared to the parent chitosan. Toxicological studies using MTT assay with UMUC3 bladder cells show no significant differences in toxicity between chitosan and its methacrylated derivatives suggesting good biocompatibility of these novel mucoadhesive polymers

Synthesis and evaluation of boronated chitosan as a mucoadhesive polymer for intravesical drug delivery

This work reports the synthesis of boronated chitosan by reacting it with 4-carboxyphenylboronic acid to improve its mucoadhesive properties. Three products with differing extent of boronate conjugation were synthesised and characterised using 1H NMR, FT-IR and UV-Vis spectroscopy and the potential of these polymers to extend the residence time of loaded model drug in the bladder was investigated. 1H NMR and ninhydrin test were used to evaluate the extent of chitosan modification. Mucoadhesive properties were evaluated using ex vivo flow-through technique on porcine bladder mucosal tissue combined with fluorescent microscopy, where fluorescein sodium was used as a model drug. The mucoadhesive properties of these polymers on porcine bladder mucosa were also studied using tensile test. There was good correlation in the mucoadhesive profiles of the polymers using the flow through and tensile techniques. The degree of chitosan modification had a remarkable influence on their mucoadhesive behaviour and greater mucoadhesion was observed with increased degree of boronation. These chitosan derivatives have the potential as intravesical drug delivery systems to improve bladder therapy

"Boring formal methods" or "Sherlock Holmes deduction methods"?

This paper provides an overview of common challenges in teaching of logic and formal methods to Computer Science and IT students. We discuss our experiences from the course IN3050: Applied Logic in Engineering, introduced as a "logic for everybody" elective course at at TU Munich, Germany, to engage pupils studying Computer Science, IT and engineering subjects on Bachelor and Master levels. Our goal was to overcome the bias that logic and formal methods are not only very complicated but also very boring to study and to apply. In this paper, we present the core structure of the course, provide examples of exercises and evaluate the course based on the students' surveys.Comment: Preprint. Accepted to the Software Technologies: Applications and Foundations (STAF 2016). Final version published by Springer International Publishing AG. arXiv admin note: substantial text overlap with arXiv:1602.0517