Interval total colorings of graphs

A total coloring of a graph $G$ is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. An \emph{interval total $t$-coloring} of a graph $G$ is a total coloring of $G$ with colors $1,2,\...,t$ such that at least one vertex or edge of $G$ is colored by $i$, $i=1,2,\...,t$, and the edges incident to each vertex $v$ together with $v$ are colored by $d_{G}(v)+1$ consecutive colors, where $d_{G}(v)$ is the degree of the vertex $v$ in $G$. In this paper we investigate some properties of interval total colorings. We also determine exact values of the least and the greatest possible number of colors in such colorings for some classes of graphs.Comment: 23 pages, 1 figur

All Stable Characteristic Classes of Homological Vector Fields

An odd vector field $Q$ on a supermanifold $M$ is called homological, if $Q^2=0$. The operator of Lie derivative $L_Q$ makes the algebra of smooth tensor fields on $M$ into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator $L_Q$ and are represented by $Q$-invariant tensors made up of the homological vector field and a symmetric connection on $M$ by means of tensor operations.Comment: 17 pages, references and comments adde

Graph complexes in deformation quantization

Kontsevich's formality theorem and the consequent star-product formula rely on the construction of an $L_\infty$-morphism between the DGLA of polyvector fields and the DGLA of polydifferential operators. This construction uses a version of graphical calculus. In this article we present the details of this graphical calculus with emphasis on its algebraic features. It is a morphism of differential graded Lie algebras between the Kontsevich DGLA of admissible graphs and the Chevalley-Eilenberg DGLA of linear homomorphisms between polyvector fields and polydifferential operators. Kontsevich's proof of the formality morphism is reexamined in this light and an algebraic framework for discussing the tree-level reduction of Kontsevich's star-product is described.Comment: 39 pages; 3 eps figures; uses Xy-pic. Final version. Details added, mainly concerning the tree-level approximation. Typos corrected. An abridged version will appear in Lett. Math. Phy

A Review of Disintegration Mechanisms and Measurement Techniques

Pharmaceutical solid dosage forms (tablets or capsules) are the predominant form to administer active pharmaceutical ingredients (APIs) to the patient. Tablets are typically powder compacts consisting of several different excipients in addition to the API. Excipients are added to a formulation in order to achieve the desired fill weight of a dosage form, to improve the processability or to affect the drug release behaviour in the body. These complex porous systems undergo different mechanisms when they come in contact with physiological fluids. The performance of a drug is primarily influenced by the disintegration and dissolution behaviour of the powder compact. The disintegration process is specifically critical for immediate-release dosage forms. Its mechanisms and the factors impacting disintegration are discussed and methods used to study the disintegration in-situ are presented. This review further summarises mathematical models used to simulate disintegration phenomena and to predict drug release kinetics.We would like to acknowledge the U.K. Engineering and Physical Sciences Research Council (EPSRC) for funding (EP/L019922/1)

Investigating the influence of a powder compact's geometry on its pore structure and optical properties using terahertz spectroscopy

In this study, terahertz time domain spectroscopy (THz-TDS) is used to analyze how the geometry of a compact affects its pore structure (pore shape and orientation). By using flat-faced and biconvex compacts, it was evident from our analysis that pores tend to assume specific shapes and orientations based on the compact's geometry and this was found to significantly affect the extracted optical properties of samples prepared by mixing a material with polyethylene (PE) as diluent and subsequent compaction. However, such sensitivity to the pore properties opens a number of industrial applications such as for quality testing of pharmaceutical tablets. A comparison made between the PE based compacts and a set of pharmaceutical tablets prepared from the same formulation has revealed that flatfaced and biconvex compacts possess different pore geometries and hence different optical properties

A quantitative comparison of in-line coating thickness distributions obtained from a pharmaceutical tablet mixing process using discrete element method and terahertz pulsed imaging

The application of terahertz pulsed imaging (TPI) in the in-line configuration to monitor the coating thickness distribution of pharmaceutical tablets has the potential to improve the performance and quality of the spray coating process. In this study, an in-line TPI method is used to measure coating thickness distributions on pre-coated tablets during mixing in a rotating pan, and compared with results obtained numerically using the discrete element method (DEM) combined with a ray-tracing technique. The hit rates (i.e. the number of successful coating thickness measurements per minute) obtained from both terahertz in-line experiments and the DEM/ray-tracing simulations are in good agreement, and both increase with the number of baffles in the mixing pan. We demonstrate that the coating thickness variability as determined from the ray-traced data and the terahertz in-line measurements represents mainly the intra-tablet variability due to relatively uniform mean coating thickness across tablets. The mean coating thickness of the ray-traced data from the numerical simulations agrees well with the mean coating thickness as determined by the off-line TPI measurements. The mean coating thickness of in-line TPI measurements is slightly higher than that of off-line measurements. This discrepancy can be corrected based on the cap-to-band surface area ratio of the tablet and the cap-to-band sampling ratio obtained from ray-tracing simulations: the corrected mean coating thickness of the in-line TPI measurements shows a better agreement with that of off-line measurements

Fluid mixing from below in unconformity-related hydrothermal ore deposits

This research was partly funded by German Research Foundation (DFG) grant BO 1776/8 and was carried out within the framework of DGMK (German Society for Petroleum and Coal Science and Technology) project 718, funded by the companies ExxonMobil Production Deutschland GmbH, GDF SUEZ E&P Deutschland GmbH, RWE Dea AG, and Wintershall Holding GmbH. Assistance by Simone Kaulfuss, Gabi Stoschek, Sara Ladenburger, Mathias Burisch, and Bernd Steinhilber with sample preparation and crush-leach analyses is gratefully acknowledged. We thank Steve Cox and two anonymous reviewers for their critical comments.Peer reviewedPostprin

The homotopy theory of simplicial props

The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher props," we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.Comment: Final version, to appear in Israel J. Mat

Review of sensing technologies for measuring powder density variations during pharmaceutical solid dosage form manufacturing

Oral solid dosage forms, the most widely used pharmaceutical products, are typically manufactured through a series of processes that transform a blend of drug and excipient particles into a densified product with consistent quality attributes. While the densification of powder during processing is crucial and directly impacts the quality of the drug product, there is still scarcity of non-destructive and fast sensor systems that provide access to the powder density at critical process stages. This review discusses methods for monitoring density variations of particulate matter by describing their principles and presenting application examples. The techniques discussed range from common in-line methods such as near-infrared spectroscopy, acoustic emission and ultrasonic methods as well as techniques with potential to be more frequently applied in a pharmaceutical manufacturing line, i.e., terahertz spectroscopy and imaging, microwave technique, electrical tomography and X-ray based methods. This review also compares these techniques in terms of measurement and data processing time, resolution and its ability to be integrated in a process