The flat model structure on

Given a cotorsion pair in an abelian category with enough objects and enough objects, we define two cotorsion pairs in the category of unbounded chain complexes. We see that these two cotorsion pairs are related in a nice way when is hereditary. We then show that both of these induced cotorsion pairs are complete when is the ``flat' cotorsion pair of -modules. This proves the flat cover conjecture for (possibly unbounded) chain complexes and also gives us a new ``flat' model category structure on . In the last section we use the theory of model categories to show that we can define using a flat resolution of and a cotorsion coresolution of .

     

An example in the theory of -operators

-operators are a generalization in the context of well-boundedness of normal operators on Hilbert space. It was shown by Doust and Walden that compact -operators have a representation as a conditionally convergent sum reminiscent of the spectral representations for compact normal operators. In this representation, the eigenvalues must be taken in a particular order to ensure convergence of the sum. Here we show that one cannot replace the ordering given by Doust and Walden by the more natural one suggested in their paper.

     

Short-Channel Effect Limitations on High-Frequency Operation of AlGaN/GaN HEMTs for T-Gate Devices

AlGaN/GaN high-electron mobility transistors (HEMTs) were fabricated on SiC substrates with epitaxial layers grown by multiple suppliers and methods. Devices with gate lengths varying from 0.50 to 0.09 mum were fabricated on each sample. We demonstrate the impact of varying the gate lengths and show that the unity current gain frequency response (f_T) is limited by short-channel effects for all samples measured. We present an empirically based physical model that can predict the expected extrinsic f_T for many combinations of gate length and commonly used barrier layer thickness (t_bar) on silicon nitride passivated T-gated AlGaN/GaN HEMTs. The result is that even typical high-aspect-ratio (gate length to barrier thickness) devices show device performance limitations due to short-channel effects. We present the design tradeoffs and show the parameter space required to achieve optimal frequency performance for GaN technology. These design rules differ from the traditional GaAs technology by requiring a significantly higher aspect ratio to mitigate the short-channel effects.     

The synthesis and reactivity of polysilylacetylenes: Diels—Alder reactions to give bis (silyl) benzenes

Six bis(silyl)acetylenes (XMe²Si? C?C? SiMe₂X) with the following varied silicon substituents X were prepared: 1 (Me, Me); 2 (H, H); 3 (C1, H); 4 (CI, CI); 5 (MeO, H); 6 (MeO, MeO). While 1 and 2 may be prepared by the reaction of dilithio- or bis(bromomagnesium)-acetylide with the appropriate chlorosilane, similar reactions designed to give 3–6 yielded oligomers, XMe₂Si? (? C?C? SiMe₂)_n? X, 7, X=CI, MeO, as the major products, indicating that the acetylenic functionality on silicon activates the chlorosilane towards nucleophilic substitution. Compounds 3 and 4 were prepared by free radical chlorination of 2. Methanolysis of 3 and 4 gave quantitative yields of 5 and 6 respectively. Compounds 1–6 undergo a Diels–Alder reaction with α-pyrone to produce, after loss of carbon dioxide, bis(silyl)-substituted benzene derivatives. The order of reactivity has been determined to be: 4=6>3=5>1>2, indicating that chloro or alkoxy substituents favor the cycloaddition with 2- pyrone. The adducts formed by compounds 3–6 undergo an unusually facile hydrolysis or elimination to give 1,1,3,3-tetramethyl-1,3-disila-2-oxaindane.     

Evolving access networks: a European perspective

The diversity of telecommunications markets and access network infrastructure among the countries of Europe is a complicating factor in the development of effective standards for Europe's future access networks. The need for evolving access networks to make efficient use of a wide variety of existing infrastructure may at times conflict with the long-term requirement for a stable platform of self-consistent standards which allow future-proof evolution. In light of these constraints, the authors summarize progress made in the European Telecommunications Standards Institute (ETSI) toward standards for future access networks     

Spectroscopic analysis and kinetics of intermolecular hydrogen bond formation in poly‐pyridobisimidazole (M5) fiber

Poly‐pyridobisimiazole (M5) single filaments subjected to varying degrees of heat treatment have been analyzed using Fourier Transform Infrared (FTIR) microspectroscopy in transmission mode to detect changes in the state of intermolecular hydrogen bonding as a function of fiber annealing conditions. The FTIR absorbance bands associated with hydrogen bonding in M5 fiber have been identified, and the integrated molar absorption coefficients for the bands of interest have been determined experimentally, which allows to quantify the concentration of N? H vibration groups hydrogen‐bonded (H‐bonded) to water molecules, and the concentration of N? H vibration groups H‐bonded to adjacent polymer chains in the fiber. A dual mechanism kinetic rate expression is used to describe intermolecular H‐bond formation in M5 fiber as a function of annealing conditions, from which an activation energy for H‐bond formation of 14.8 kJ/mol is obtained. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1809–1824, 2009     

Using phase-type models to cost stroke patient care across health,social and community services

Stroke disease places a heavy burden on society, incurring long periods of time in hospital and community care, and associated costs. Also stroke is a highly complex disease with diverse outcomes and multiple strategies for therapy and care. Previously a modeling framework has been developed which clusters patients into classes with respect to their length of stay (LOS) in hospital. Phase-type models were then used to describe patient flows for each cluster. Also multiple outcomes, such as discharge to normal residence, nursing home, or death can be permitted. We here add costs to this model and obtain the Moment Generating Function for the total cost of a system consisting of multiple transient phase-type classes with multiple absorbing states. This system represents different classes of patients in different hospital and community services states. Based on stroke patients’ data from the Belfast City Hospital, various scenarios are explored with a focus on comparing the cost of thrombolysis treatment under different regimes. The overall modeling framework characterizes the behavior of stroke patient populations, with a focus on integrated system-wide costing and planning, encompassing hospital and community services. Within this general framework we have developed models which take account of patient heterogeneity and multiple care options. Such complex strategies depend crucially on developing a deep engagement with the health care professionals and underpinning the models with detailed patient-specific data.     

Monodromy and K-theory of Schubert curves via generalized jeu de taquin

We establish a combinatorial connection between the real geometry and the K-theory of complex Schubert curves \(S(\lambda _\bullet )\), which are one-dimensional Schubert problems defined with respect to flags osculating the rational normal curve. In Levinson (One-dimensional Schubert problems with respect to osculating flags, 2016, doi: 10.4153/CJM-2015-061-1), it was shown that the real geometry of these curves is described by the orbits of a map \(\omega \) on skew tableaux, defined as the commutator of jeu de taquin rectification and promotion. In particular, the real locus of the Schubert curve is naturally a covering space of \({\mathbb {RP}}^1\), with \(\omega \) as the monodromy operator. We provide a fast, local algorithm for computing \(\omega \) without rectifying the skew tableau and show that certain steps in our algorithm are in bijective correspondence with Pechenik and Yong’s genomic tableaux (Pechenik and Yong in Genomic tableaux, 2016. arXiv:1603.08490), which enumerate the K-theoretic Littlewood–Richardson coefficient associated to the Schubert curve. We then give purely combinatorial proofs of several numerical results involving the K-theory and real geometry of \(S(\lambda _\bullet )\).     

Model structures on exact categories

We define model structures on exact categories, which we call exact model structures. We look at the relationship between these model structures and cotorsion pairs on the exact category. In particular, when the underlying category is weakly idempotent complete, we get Hovey’s one-to-one correspondence between model structures and complete cotorsion pairs. We classify the right and the left homotopy relation in terms of the cotorsion pairs and look at examples of exact model structures. In particular, we see that given any hereditary abelian model category, the full subcategories of cofibrant, fibrant and cofibrant-fibrant subobjects each has natural exact model structures equivalent to the original model structure. These model structures each has interesting characteristics. For example, the cofibrant-fibrant subobjects form a Frobenius category, whose stable category is the same as the homotopy category of its model structure.