Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel

Let $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = \sum_{k=0}^N (-1)^k T_k(u) e^{-k\partial_u}$ whose coefficients $T_k(u): M \to M$ are the XXX transfer matrices associated with $M$. We show that the difference equation $Df = 0$ for an $M$-valued function $f$ has a basis of solutions consisting of quasi-exponentials. We prove the same for the universal differential operator $D = \sum_{k=0}^N (-1)^k S_k(u) \partial_u^{N-k}$ whose coefficients $S_k(u) : M \to M$ are the Gaudin transfer matrices associated with the tensor product $M$ of finite-dimensional polynomial evaluation $gl_N[x]$-modules.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

060. Provider

A family devotion based on trusting in God the Father to meet our daily needs.https://scholar.csl.edu/tabletalk/1068/thumbnail.jp

Fasc. 060

https://digitalcommons.kennesaw.edu/chmprojectarchive/1059/thumbnail.jp

Apollo-Soyuz pamphlet no. 8: Zero-g technology

The behavior of liquids in zero gravity environments is discussed with emphasis on foams, wetting, and wicks. A multipurpose electric furnace (MA-010) for the high temperature processing of metals and salts in zero-g is described. Experiments discussed include: monolectic and synthetic alloys (MA-041); multiple material melting point (MA-150); zero-g processing of metals (MA-070); surface tension induced convection (MA-041); halide eutectic growth; interface markings in crystals (MA-060); crystal growth from the vapor phase (MA-085); and photography of crystal growth (MA-028)

Discriminating cool-water from warm-water carbonates and their diagenetic environments using element geochemistry: the Oligocene Tikorangi Formation (Taranaki Basin) and the dolomite effect

Fields portrayed within bivariate element plots have been used to distinguish between carbonates formed in warm- (tropical) water and cool- (temperate) water depositional settings. Here, element concentrations (Ca, Mg, Sr, Na, Fe, and Mn) have been determined for the carbonate fraction of bulk samples from the late Oligocene Tikorangi Formation, a subsurface, mixed dolomite-calcite, cool-water limestone sequence in Taranaki Basin, New Zealand. While the occurrence of dolomite is rare in New Zealand Cenozoic carbonates, and in cool-water carbonates more generally, the dolomite in the Tikorangi carbonates is shown to have a dramatic effect on the "traditional" positioning of cool-water limestone fields within bivariate element plots. Rare undolomitised, wholly calcitic carbonate samples in the Tikorangi Formation have the following average composition: Mg 2800 ppm; Ca 319 100 ppm; Na 800 ppm; Fe 6300 ppm; Sr 2400 ppm; and Mn 300 ppm. Tikorangi Formation dolomite-rich samples (>15% dolomite) have average values of: Mg 53 400 ppm; Ca 290 400 ppm; Na 4700 ppm; Fe 28 100 ppm; Sr 5400 ppm; and Mn 500 ppm. Element-element plots for dolomite-bearing samples show elevated Mg, Na, and Sr values compared with most other low-Mg calcite New Zealand Cenozoic limestones. The increased trace element contents are directly attributable to the trace element-enriched nature of the burial-derived dolomites, termed here the "dolomite effect". Fe levels in the Tikorangi Formation carbonates far exceed both modern and ancient cool-water and warm-water analogues, while Sr values are also higher than those in modern Tasmanian cool-water carbonates, and approach modern Bahaman warm-water carbonate values. Trace element data used in conjunction with more traditional petrographic data have aided in the diagenetic interpretation of the carbonate-dominated Tikorangi sequence. The geochemical results have been particularly useful for providing more definitive evidence for deep burial dolomitisation of the deposits under the influence of marine-modified pore fluids

POSSIBILITIES OF INITIAL ESTIMATION AND FURTHER VALIDATION OF INSIDE CONTROL RISK

The approach option of the theme of this essay had in mind the distinguished importance of the objective of inside control regarding the segmentation with maximum exigency of the risks which can disadvantageously influence the fulfillment of the entity objectives. We considered essential the use of adequate procedures regarding the estimation and documentary validation of inside control risk. Regarding the initial estimation we analyzed the phases that are justified to be followed (four) and the proper steps which are followed (ten), starting with the assessment of audit objectives on types of operations and ending with reporting to the competent institutions. Regarding initial risk validation we examined the subsequent circumstances of this operation which are influencing the forecasted risk level, like: adjourning of control mechanisms applications, the apparition of new legal procedures, the alterations of the entity’s politics, etc.critical; inside control, initial risk estimation, subsequent risk validation, risk estimation procedure.

Recycling and the Environment: a Comparative Review Between Mineral-based Plastics and Bioplastics

Since their conception in the 1950s, mineral-based plastics have completely revolutionised our society with production reaching record highs year upon year. This cheap, and durable material has seen usage across a plethora of diverse industries and products, replacing traditional materials such as metals and wood. However, our reliance on mineral-based plastics has led to their improper disposal across the global, affecting our environments and ecosystems. As a response, different methods have been developed to help dispose of the large amounts of plastic waste produced, such as incineration or dumping in landfill sites, but these methods are not without their drawbacks including release of toxic substances into the air and leachate into the soil and waters respectively. Consequently, much interest is generated and channelled in recent years to the introduction of several types of biopolymers. These include plastics based on cellulosic esters, starch derivatives, polyhydroxybutyrate and polylactic acid. These biopolymers have been viewed as a suitable replacement for mineral-based plastics, and their production a good strategy towards sustainable development as they are mainly composed of biocompounds such as starch, cellulose and sugars. This short review article provides an overview as to whether biopolymers can rival mineral-based plastics considering properties such as mechanical strength, Young’s modulus and crystallinity and could they be regarded as a suitable material to reduce our reliance on mineral-based plastics, whilst simultaneously reducing non-renewable energy consumption and carbon dioxide emissions