The Structure of Residuated Lattices

A residuated lattice is an ordered algebraic structure [formula] such that is a lattice, is a monoid, and \ and / are binary operations for which the equivalences [formula] hold for all a,b,c ∈ L. It is helpful to think of the last two operations as left and right division and thus the equivalences can be seen as dividing on the right by b and dividing on the left by a. The class of all residuated lattices is denoted by ℛℒ The study of such objects originated in the context of the theory of ring ideals in the 1930s. The collection of all two-sided ideals of a ring forms a lattice upon which one can impose a natural monoid structure making this object into a residuated lattice. Such ideas were investigated by Morgan Ward and R. P. Dilworth in a series of important papers [15, 16, 45–48] and also by Krull in [33]. Since that time, there has been substantial research regarding some specific classes of residuated structures, see for example [1, 9, 26] and [38], but we believe that this is the first time that a general structural theory has been established for the class ℛℒ as a whole. In particular, we develop the notion of a normal subalgebra and show that ℛℒ is an ideal variety in the sense that it is an equational class in which congruences correspond to normal subalgebras in the same way that ring congruences correspond to ring ideals. As an application of the general theory, we produce an equational basis for the important subvariety ℛℒ[sup C] that is generated by all residuated chains. In the process, we find that this subclass has some remarkable structural properties that we believe could lead to some important decomposition theorems for its finite members (along the lines of the decompositions provided in [27]

Larra bicolor Fabricius (Hymenoptera: Crabronidae): its distribution throughout Florida

We document the presence of Larra bicolor Fabricius (Hymenoptera: Crabronidae) in 46 of Florida's 67 counties. The species is represented by two stocks. The first (released in 1981) originated in Pará, Brazil, but was obtained from Puerto Rico, and became established in Broward County in southern Florida. The second (released in 1988) originated in Santa Cruz de la Sierra, Bolivia, and became established in Alachua County in northern Florida. The Bolivian stock, aided by additional satellite releases from Alachua County, is now widely distributed. The species probably occupies all counties in central and northern Florida, but may yet be absent from some southern counties. Introduction was made for classical biological control of invasive mole crickets

Polar type density of states in non-unitary odd-parity superconducting states of gap with point nodes

It is shown that the density of states (DOS) proportional to the excitation energy, the so-called polar like DOS, can arise in the odd-parity states with the superconducting gap vanishing at points even if the spin-orbit interaction for Cooper pairing is strong enough. Such gap stuructures are realized in the non-unitary states, F_{1u}(1,i,0), F_{1u}(1,varepsilon,varepsilon^{2}), and F_{2u}(1,i,0), classified by Volovik and Gorkov, Sov. Phys.-JETP Vol.61 (1985) 843. This is due to the fact that the gap vanishes in quadratic manner around the point on the Fermi surface. It is also shown that the region of quadratic energy dependence of DOS, in the state F_{2u}(1,varepsilon,varepsilon^{2}), is restricted in very small energy region making it difficult to distinguish from the polar-like DOS.Comment: 5 pages, 3 figures, submitted to J. Phys.: Condens. Matter Lette

Many-body position operator in lattice fermionic systems with periodic boundary conditions

A total position operator $X$ in the position representation is derived for lattice fermionic systems with periodic boundary conditions. The operator is shown to be Hermitian, the generator of translations in momentum space, and its time derivative is shown to correspond to the total current operator in a periodic system. The operator is such that its moments can be calculated up to any order. To demonstrate its utility finite size scaling is applied to the Brinkman-Rice transition as well as metallic and insulating Gutzwiller wavefunctions.Comment: to appear in Journal of Physics A: Mathematical and General (reference will be added later

Tissue Damage and Nutritive Value of Warm-Season Grasses Following a Freeze

Bahiagrass (Paspalum notatum Flugge) is a major forage for livestock in the subtropics of the U.S.A. However, it is subject to freeze damage with minimal winter regrowth, and is generally considered a poor grass for stockpiling due to poor quality of the residue. Bahiagrass genotypes have been found showing a range of leaf freezing tolerance in the in the field (-30 C) (Blount et al., 2001). Other C4 grasses have been reported to have genotype-specific tolerances to below-freezing temperatures ranging from -3 to -100 C (Sakai & Larcher, 1987). This research was begun to try to understand the processes that take place following freeze injury to bahiagrass. Three grasses native to the Midwest, big bluestem (Andropogon gerardii Vitman cv Alamo), Indiangrass (Sorghastrum nutans (L.) Nash cv Lometa), and switchgrass (Panicum virgatum L. cv Kaw) and commonly used for stockpiling were used for comparison

Un-LINQed: Spontaneous extrusion of newer generation implantable loop recorders

BACKGROUND: Insertable cardiac monitors (ICMs) are often used for long-term monitoring of cardiac rhythm. The Medtronic\u27s LINQ Reveal ™ is a new generation wireless, automated, and patient responsive subcutaneous ECG monitoring device. Despite several advantages to its small size we have noted an unusually high incidence of extrusion at our center. METHODS: & Results: We conducted a retrospective case analysis to review Reveal LINQs implanted at our center. All devices were inserted using the provided insertion tools. Patients with extruded devices were identified and details regarding the site and technique of insertion, incision closure, use of peri-operative antibiotics, and follow-up details were collected. 81 patients underwent 85 Reveal LINQ implants at a tertiary care University Hospital referral center. The most common reason for implant was suspected arrhythmia with or without structural heart disease or unexplained syncope. There were 4 spontaneous extrusions occurring within 7-24 days after insertion with an incidence rate of 4.7%. One extruded device was anchored to subcutaneous tissue, and no pocket/device infections or hematomas were noted. CONCLUSIONS: Device migration and erosion through skin are important potential adverse events for the Reveal LINQ implantable loop recorder. This study reports an unexpectedly high rate of extrusion without infection. The authors suggest that the depth of the incision is the main factor impacting extrusions. Larger studies are recommended, however, and a proposed measure to avoid spontaneous extrusion is the design of a longer manufacturer\u27s blade in order to increase the depth of the incision and insertion

Tilting instability and other anomalies in the flux-lattice in some magnetic superconductors

The flux-line lattice in the compound $ErNi_2B_2C$, which has a tendency to ferromagnetic order in the a-b plane is studied with external magnetic field direction close to the c-axis. We show the existence of an instability where the direction of flux-lines spontaneously tilts away from that of the applied field near the onset of ferromagnetic order. The enhanced fluctuations in the flux lattice and the square flux lattice recently observed are explained and further experiments suggested.Comment: 12 pages, Latex file, no figur

Measures of oxidative state are primarily driven by extrinsic factors in a long-distance migrant

This is the author accepted manuscript. The final version is available from the Royal Society via the DOI in this recordData accessibility: Data are available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.j4k3t6f/1 [20].Oxidative stress is a likely consequence of hard physical exertion and thus a potential mediator of life-history trade-offs in migratory animals. However, little is known about the relative importance of intrinsic and extrinsic stressors on the oxidative state of individuals in wild populations. We quantified the relationships between air temperature, sex, body condition and three markers of oxidative state (malondialdehyde, superoxide dismutase and total antioxidant capacity) across hundreds of individuals of a long-distance migrant (the brent goose Branta bernicla hrota) during wintering and spring staging. We found that air temperature and migratory stage were the strongest predictors of oxidative state. This emphasizes the importance of extrinsic factors in regulating the oxidative state of migrating birds, with differential effects across the migration. The significance of abiotic effects demonstrates an additional mechanism by which changing climates may affect migratory costs.European Commissio

2D superconductivity with strong spin-orbit interaction

We consider superconductivity confined at a two-dimensional interface with a strong surface spin-orbit (Rashba) interaction. Some peculiar properties of this system are investigated. In particular, we show that an in-plane Zeeman field can induce a supercurrent flow.Comment: latex, 1 figure in ep

Transport and the Order Parameter of Superconducting UPt3

We calculate the ultrasonic absorption and the thermal conductivity in the superconducting state of UPt$_{3}$ as functions of temperature and direction of propagation and polarization. Two leading candidates for the superconducting order parameter are considered: the $E_{1g}$ and $E_{2u}$ representations. Both can fit the data except for the ultrasonic absorption in the $A$ phase. To do that, it is necessary to suppose that the system has only a single domain, and that must be chosen as the most favorable one. However, the $E_{2u}$ theory requires fine-tuning of parameters to fit the low temperature thermal conductivity. Thus, transport data favor the $E_{1g}$ theory. Measurements of the thermal conductivity as a function of pressure at low temperature could help to further distinguish the two theories.Comment: 7 pages, 4 figure