On the relative strengths of fragments of collection

Let $\mathbf{M}$ be the basic set theory that consists of the axioms of extensionality, emptyset, pair, union, powerset, infinity, transitive containment, $\Delta_0$-separation and set foundation. This paper studies the relative strength of set theories obtained by adding fragments of the set-theoretic collection scheme to $\mathbf{M}$. We focus on two common parameterisations of collection: $\Pi_n$-collection, which is the usual collection scheme restricted to $\Pi_n$-formulae, and strong $\Pi_n$-collection, which is equivalent to $\Pi_n$-collection plus $\Sigma_{n+1}$-separation. The main result of this paper shows that for all $n \geq 1$, (1) $\mathbf{M}+\Pi_{n+1}\textrm{-collection}+\Sigma_{n+2}\textrm{-induction on } \omega$ proves the consistency of Zermelo Set Theory plus $\Pi_{n}$-collection, (2) the theory $\mathbf{M}+\Pi_{n+1}\textrm{-collection}$ is $\Pi_{n+3}$-conservative over the theory $\mathbf{M}+\textrm{strong }\Pi_n \textrm{-collection}$. It is also shown that (2) holds for $n=0$ when the Axiom of Choice is included in the base theory. The final section indicates how the proofs of (1) and (2) can be modified to obtain analogues of these results for theories obtained by adding fragments of collection to a base theory (Kripke-Platek Set Theory with Infinity and $V=L$) that does not include the powerset axiom.Comment: 22 page

Study of component technologies for fuel cell on-site integrated energy system. Volume 2: Appendices

This data base catalogue was compiled in order to facilitate the analysis of various on site integrated energy system with fuel cell power plants. The catalogue is divided into two sections. The first characterizes individual components in terms of their performance profiles as a function of design parameters. The second characterizes total heating and cooling systems in terms of energy output as a function of input and control variables. The integrated fuel cell systems diagrams and the computer analysis of systems are included as well as the cash flows series for baseline systems

Partial normalizations of coxeter arrangements and discriminants

We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin’s Frobenius manifold structure which is lifted (without unit) to the space of the arrangement. We also describe an independent approach to these structures via duality of maximal Cohen–Macaulay fractional ideals. In the process, we find 3rd order differential relations for the basic invariants of the Coxeter group. Finally, we show that our partial normalizations give rise to new free divisors

Study of component technologies for fuel cell on-site integrated energy systems

Heating, ventilation and air conditioning equipment are integrated with three types of fuel cells. System design and computer simulations are developed to utilize the thermal energy discharge of the fuel in the most cost effective manner. The fuel provides all of the electric needs and a loss of load probability analysis is used to ensure adequate power plant reliability. Equipment cost is estimated for each of the systems analyzed. A levelized annual cost reflecting owning and operating costs including the cost of money was used to select the most promising integrated system configurations. Cash flows are presented for the most promising 16 systems. Several systems for the 96 unit apartment complex (a retail store was also studied) were cost competitive with both gas and electric based conventional systems. Thermal storage is shown to be beneficial and the optimum absorption chiller sizing (waste heat recovery) in connection with electric chillers are developed. Battery storage was analyzed since the system is not electric grid connected. Advanced absorption chillers were analyzed as well. Recommendations covering financing, technical development, and policy issues are given to accelerate the commercialization of the fuel cell for on-site power generation in buildings

Use of the metastatic breast cancer progression (MBC-P) questionnaire to assess the value of progression-free survival for women with metastatic breast cancer.

While overall survival (OS) has historically been the primary endpoint for clinical trials in oncology, progression-free survival (PFS) has gained acceptance as a valuable surrogate endpoint. However, there are no known published reports about the value of PFS from the patient's perspective. We developed a questionnaire that included items regarding quality of life (QoL) and the importance of different treatment outcomes and presented hypothetical scenarios for which respondents were asked to indicate their preferences concerning treatments as they relate to PFS. 282 women with metastatic breast cancer (MBC), ranging in age from 21 to 80 years completed an online version of this questionnaire. The majority of women (66 %) had been diagnosed with MBC within the previous 3 years and 56 % had been told their MBC had progressed. When asked to rank five treatment characteristics from most important to least important, respondents ranked "extending PFS" as the second most important treatment outcome after OS. When presented with a hypothetical scenario of two women receiving different treatments, respondents preferred the treatment that resulted in longer PFS (16 vs. 12 months), even when OS and side effects were assumed to be equal. Specifically, when asked to consider which woman within the hypothetical scenario had better QoL, physical functioning, and emotional well-being, respondents more often chose the woman who experienced longer PFS (QoL: 40 vs. 6 %; physical functioning: 32 vs. 8 %; emotional well-being: 58 vs. 6 %) compared to the woman within the hypothetical scenario who had a shorter time of progression. Respondents rated their own QoL highest after being told their MBC was responding to treatment (mean score 76.6) versus after the initial diagnosis of breast cancer and MBC (68.5 and 60.3). These findings suggest that extending PFS is an important treatment outcome and, from a patient perspective, improves overall QoL, physical functioning, and emotional well-being

Electron-magnon scattering in elementary ferromagnets from first principles: lifetime broadening and band anomalies

We study the electron-magnon scattering in bulk Fe, Co, and Ni within the framework of many-body perturbation theory implemented in the full-potential linearized augmented-plane-wave method. To this end, a $\mathbf{k}$-dependent self-energy ($GT$ self-energy) describing the scattering of electrons and magnons is constructed from the solution of a Bethe-Salpeter equation for the two-particle (electron-hole) Green function, in which single-particle Stoner and collective spin-wave excitations (magnons) are treated on the same footing. Partial self-consistency is achieved by the alignment of the chemical potentials. The resulting renormalized electronic band structures exhibit strong spin-dependent lifetime effects close to the Fermi energy, which are strongest in Fe. The renormalization can give rise to a loss of quasiparticle character close to the Fermi energy, which we attribute to electron scattering with spatially extended spin waves. This scattering is also responsible for dispersion anomalies in conduction bands of iron and for the formation of satellite bands in nickel. Furthermore, we find a band anomaly at a binding energy of 1.5~eV in iron, which results from a coupling of the quasihole with single-particle excitations that form a peak in the Stoner continuum. This band anomaly was recently observed in photoemission experiments. On the theory side, we show that the contribution of the Goldstone mode to the $GT$ self-energy is expected to (nearly) vanish in the long-wavelength limit. We also present an in-depth discussion about the possible violation of causality when an incomplete subset of self-energy diagrams is chosen

A universal scaling law for the evolution of granular gases

Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. This clustering transition is important for a number of problems ranging from geophysics to cosmology. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier--Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system's Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of $\mathcal{O}(1)$. Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters

Definable orthogonality classes in accessible categories are small

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Levy hierarchy. For example, the statement that, for a class S of morphisms in a locally presentable category C of structures, the orthogonal class of objects is a small-orthogonality class (hence reflective) is provable in ZFC if S is \Sigma_1, while it follows from the existence of a proper class of supercompact cardinals if S is \Sigma_2, and from the existence of a proper class of what we call C(n)-extendible cardinals if S is \Sigma_{n+2} for n bigger than or equal to 1. These cardinals form a new hierarchy, and we show that Vopenka's principle is equivalent to the existence of C(n)-extendible cardinals for all n. As a consequence, we prove that the existence of cohomological localizations of simplicial sets, a long-standing open problem in algebraic topology, is implied by the existence of arbitrarily large supercompact cardinals. This result follows from the fact that cohomology equivalences are \Sigma_2. In contrast with this fact, homology equivalences are \Sigma_1, from which it follows (as is well known) that the existence of homological localizations is provable in ZFC.Comment: 38 pages; some results have been improved and former inaccuracies have been correcte