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Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica

Concurrent implementation of the Crank-Nicolson method for heat transfer analysis

To exploit the significant gains in computing speed provided by Multiple Instruction Multiple Data (MIMD) computers, concurrent methods for practical problems need to be investigated and test problems implemented on actual hardware. One such problem class is heat transfer analysis which is important in many aerospace applications. This paper compares the efficiency of two alternate implementations of heat transfer analysis on an experimental MIMD computer called the Finite Element Machine (FEM). The implicit Crank-Nicolson method is used to solve concurrently the heat transfer equations by both iterative and direct methods. Comparison of actual timing results achieved for the two methods and their significance relative to more complex problems are discussed

Implications of non-feasible transformations among icosahedral hh orbitals

The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of the Coulomb energies for the icosahedral configurations $h^N$ based on the sequence $O(5) \supset S_6 \supset S_5 \supset I$ can be brought to bear on Racah's classic theory for the atomic d shell based on $SO(5) \supset SO_L(3) \supset I$. Among the elements of $S_6$ is the kaleidoscope operator ${\cal K}$ that rotates the weight space of SO(5) by $\pi/2$. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figur

ALARP and the risk management of civil unmanned aircraft systems

Key to the continued growth of the civil Unmanned Aircraft System (UAS) aviation sector is the devel- opment of a regulatory framework that will provide assurances in the management of the risks associated with their operation. Decisions in relation the evalu- ation and treatment of aviation risks need to be made in accordance with the As Low As Reasonably Prac- ticable (ALARP) framework. There are a number of concerns in relation to the application of the ALARP framework to new technologies. This paper explores these concerns with respect to the risk management of civil UAS. A review of the ALARP frameworks de ned by the International Civil Aviation Organization (ICAO), the Civil Aviation Safety Authority (Australia), the Civil Aviation Authority (United Kingdom) and by the UK Health and Safety Executive is presented. This review identi ed subtle di erences that can have a signi cant impact on how ALARP frameworks would be applied to UAS. A number of inconsistencies in the frameworks were also identi ed. These issues aside, it was found that a conceptual application of an ALARP framework can be made. However, sig- ni cant diculties were identi ed in the substantia- tion of a framework. In particular, the quanti cation of the decision criteria for UAS, the handling of un- certainty, and the identi cation, characterisation and representation of societal concerns within a frame- work. Guidance as to how the dimensions of societal concern and levels of risk can be jointly considered within an ALARP framework could not be identi ed within the literature. For new technologies such asUAS, these dimensions can be as signi cant a factor in decision-making as that of the quanti ed measures of the risk. Due to these de ciencies, there are signif- icant diculties in the application and substantiation of an ALARP framework to the risk management of new technologies such as UAS

Hyperinsulinism-hyperammonaemia syndrome: novel mutations in the GLUD1 gene and genotype-phenotype correlations

Background: Activating mutations in the GLUD1 gene (which encodes for the intra-mitochondrial enzyme glutamate dehydrogenase, GDH) cause the hyperinsulinism–hyperammonaemia (HI/HA) syndrome. Patients present with HA and leucine-sensitive hypoglycaemia. GDH is regulated by another intra-mitochondrial enzyme sirtuin 4 (SIRT4). Sirt4 knockout mice demonstrate activation of GDH with increased amino acid-stimulated insulin secretion. Objectives: To study the genotype–phenotype correlations in patients with GLUD1 mutations. To report the phenotype and functional analysis of a novel mutation (P436L) in the GLUD1 gene associated with the absence of HA. Patients and methods: Twenty patients with HI from 16 families had mutational analysis of the GLUD1 gene in view of HA (n=19) or leucine sensitivity (n=1). Patients negative for a GLUD1 mutation had sequence analysis of the SIRT4 gene. Functional analysis of the novel P436L GLUD1 mutation was performed. Results: Heterozygous missense mutations were detected in 15 patients with HI/HA, 2 of which are novel (N410D and D451V). In addition, a patient with a normal serum ammonia concentration (21 µmol/l) was heterozygous for a novel missense mutation P436L. Functional analysis of this mutation confirms that it is associated with a loss of GTP inhibition. Seizure disorder was common (43%) in our cohort of patients with a GLUD1 mutation. No mutations in the SIRT4 gene were identified. Conclusion: Patients with HI due to mutations in the GLUD1 gene may have normal serum ammonia concentrations. Hence, GLUD1 mutational analysis may be indicated in patients with leucine sensitivity; even in the absence of HA. A high frequency of epilepsy (43%) was observed in our patients with GLUD1 mutations

KELT-23Ab: A Hot Jupiter Transiting a Near-solar Twin Close to the TESS and JWST Continuous Viewing Zones

We announce the discovery of KELT-23Ab, a hot Jupiter transiting the relatively bright (V = 10.3) star BD+66 911 (TYC 4187-996-1), and characterize the system using follow-up photometry and spectroscopy. A global fit to the system yields host-star properties of T_(eff)=5900±49K, M∗=0.945^(+0.060)_(−0.054)M⊙, R∗=0.995±0.015R⊙, L∗=1.082^(+0.051)_(−0.048)L⊙, logg∗=4.418^(+0.026)_(−0.025) (cgs), and [Fe/H]=−0.105±0.077. KELT-23Ab is a hot Jupiter with a mass of MP=0.938^(+0.045)_(−0.042)M_J, radius of R_P=1.322±0.025RJ, and density of ρ_P=0.504^(+0.038)_(−0.035) g cm^(−3). Intense insolation flux from the star has likely caused KELT-23Ab to become inflated. The time of inferior conjunction is T_0=2458149.40776±0.00091 BJD_(TDB) and the orbital period is P=2.255353^(+0.000031)_(−0.00003) days. There is strong evidence that KELT-23A is a member of a long-period binary star system with a less luminous companion, and due to tidal interactions, the planet is likely to spiral into its host within roughly a gigayear. This system has one of the highest positive ecliptic latitudes of all transiting planet hosts known to date, placing it near the Transiting Planet Survey Satellite and James Webb Space Telescope continuous viewing zones. Thus we expect it to be an excellent candidate for long-term monitoring and follow up with these facilities

Grothendieck groups and a categorification of additive invariants

A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general categorical set-up we introduce a generalized relative Grothendieck group from a cospan of functors of categories and also consider a categorification of additive invariants on objects. As an example, we obtain a general theory of characteristic homology classes of singular varieties.Comment: 27 pages, to appear in International J. Mathematic

Heisenberg antiferromagnet on the square lattice for S>=1

Theoretical predictions of a semiclassical method - the pure-quantum self-consistent harmonic approximation - for the correlation length and staggered susceptibility of the Heisenberg antiferromagnet on the square lattice (2DQHAF) agree very well with recent quantum Monte Carlo data for S=1, as well as with experimental data for the S=5/2 compounds Rb2MnF4 and KFeF4. The theory is parameter-free and can be used to estimate the exchange coupling: for KFeF4 we find J=2.33 +- 0.33 meV, matching with previous determinations. On this basis, the adequacy of the quantum nonlinear sigma model approach in describing the 2DQHAF when S>=1 is discussed.Comment: 4 pages RevTeX file with 5 figures included by psfi