Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

The structure of algebraic covariant derivative curvature tensors

We use the Nash embedding theorem to construct generators for the space of algebraic covariant derivative curvature tensors

Aluminide coatings for nickel base alloys

The metalliding process was used to aluminide IN-100 and TD NiCr. Aluminum was deposited over a broad range of deposition rates, with two types of coating structures resulting. Chromium, silicon, titanium and yttrium were also individually deposited simutaneously with aluminum on IN-100. None of these had a marked effect on the oxidation resistance of the aluminide coating. Porosity-free aluminide coatings with good oxidation resistance were formed on TD NiCr providing the aluminum concentration did not exceed 8 percent, the limit of solubility in the gamma phase

Generalized modularity matrices

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection

Control of Phomopsis Blight of Eastern Redcedar with Benomyl

Control of Phomopsis blight (P. juniperovora) of eastern redcedar (Juniperus virginiana) with benomyl was investigated using potted seedlings in a greenhouse. Benomyl sprays and drenches did not prevent infection. However, three pre-inoculation foliar sprays (600 ppm a.i.) applied at weekly intervals followed by three post-inoculation sprays gave significant control of disease progression. Benomyl drenches of 0, 6.5, 13, 40, 80, 160, 320 and 640 mg/liter pot resulted in significant blight control with the 40 to 640 mg treatments. Thin layer chromatography coupled with Penicillium bioassay determined that 3 μg of benomyl (MBC)/g plant tissue (fresh weight) was the minimal concentration necessary to limit disease progression. Fungitoxic activity was also determined biweekly in nursery grown 2-0 eastern redcedar receiving benomyl applications of 0.6 kg/ha biweekly, 1.4 kg/ha monthly, or 2.8 kg/ha every 6 weeks. Analysis for systemically transported benomyl (MBC) revealed concentrations to be less than the minimal amount necessary for disease control as indicated by the greenhouse experiments. However, the percentage of trees with pycnidia and the percentage of pycnidia with spores were both significantly lower in the benomyl treatments

Phytoremediation of Saline-Sodic Soils in East Central South Dakota Utilizing Perennial Grass Mixtures

Several decades of above average precipitation in South Dakota has increased the area of saline and sodic soils, which reduce crop yields and inhibit sensitive plant growth. Saline and sodic soils are difficult to remediate using traditional agricultural crops. Establishing salt tolerant perennial species may restore productivity to salt affected areas. Two perennial grass mixtures (mix 1: slender wheatgrass, beardless wildrye; mix 2: slender wheatgrass, western wheatgrass, green wheatgrass, creeping meadow foxtail) were dormant frost seeded along a topographic gradient in Clark Co., SD. Soils were Forman-Cresbard loam and a Cresbard-Cavour loam with surface electrical conductivity (EC1:1) that ranged from \u3c 0.5 to \u3e15 dS m-1 and sodium \u3c 400 to \u3e2500 ug g-1. Perennial grass and corn biomass, soil chemical properties, weed cover, and greenhouse gas emissions were quantified in two growing seasons (2018 and 2019). By 2019 perennial grass mixtures and corn reduced soil EC1:1 and sodium similarly. Slender wheatgrass was the dominant species in mix 1, comprising up to 65% of September 2018 total biomass (246-1705 kg ha-1) and 83% in 2019 (6400-9700 kg ha-1). AC Saltlander was the dominant species in mix 2 comprising up to 61% of 2018 total September biomass (604- 2646 kg ha-1) and 81% in July, 2019 (5853-10663 kg ha-1). In July, 2019 mix 1 and mix 2 saline plots had 16% and 3% weed cover (kochia/foxtail barley), respectively, compared to 75% in corn. Over a 7 d period in July, 2018 and 2019 non-fertilized barren saline soils emitted 2.09 and 4.89 g N2O-N ha-1 hr-1, respectively; and 611 and 324 g CO2-C ha-1 hr-1, respectively. During the same time period, grass vegetated non-saline soil emitted 0.38 and 0.46 g N2O-N ha-1 hr-1 in 2018 and 2019, respectively; and 1589 and 2538 g CO2-C ha-1 hr-1, respectively. Corn vegetated non-saline soil emitted 0.01 and 0.62 g N2O-N ha-1 hr-1 in 2018 and 2019, respectively; and 1821 and 1812 g CO2-C ha-1 hr-1, respectively. Urea application (224 kg-1 ha-1) increased CO2 emissions in all treatments both years from 19-155%, but increased N2O emissions by 102-704% in 2019 only. Simulated root exudates, plant residue decomposition, simulated root respiration, and barley growth increased greenhouse gas emissions compared with nontreated controls in laboratory studies on a saline Cresbard-Cavour loam. Growing barley plants reduced soil EC1:1 from 6.3 dS m-1 to 5.9 dS m-1 and reduced soil NO3- from 509 ug g-1 to 428 ug g-1 after 7 weeks and increased N2O-N and CO2-C flux by 224% and 244%, respectively, from baselines of 0.359 ug N2O-N kg-1 hr-1 and 206 ug CO2-C kg-1 hr-1. Revegetating salt affected soils with perennial grasses may reduce soil EC1:1, NO3-, Na, and weed cover and also may improve soil microbial activity and nutrient cycling