Group Analysis of Nonlinear Fin Equations

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of truly nonlinear equations for the class under consideration. Nonclassical symmetries of the fin equations are discussed. Adduced results amend and essentially generalize recent works on the subject [M. Pakdemirli and A.Z. Sahin, Appl. Math. Lett., 2006, V.19, 378-384; A.H. Bokhari, A.H. Kara and F.D. Zaman, Appl. Math. Lett., 2006, V.19, 1356-1340].Comment: 6 page

The Toda lattice is super-integrable

We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the use of some special action--angle coordinates introduced by Moser to solve the equations of motion.Comment: 8 page

Solution-processed, low voltage tantalum-based memristive switches

In this letter, preliminary results showing the memristive behavior of tantalum/tantalum oxide/platinum devices on glass substrates are reported. The ultra-thin (d < 10 nm) tantalum oxide films were obtained using solution-based anodic oxidation (anodization) of Ta in citric acid. The devices were tested using standard ReRAM characterization tests from ±0.5 V to ±5 V and showed a promising memristive behavior. The memristive switches show an almost 80-times change in resistance between the ON and OFF states

a two stage calibration for detection of leakage hotspots in a real water distribution network

Abstract The paper presents a two-stage approach for solving a calibration-based problem for the ultimate purpose of detecting leakage hotspots. This is compared with a one-stage approach. A Genetic Algorithm is used to solve optimization problems of searching for calibration parameters values, while minimizing the differences between observations and model predictions. The approach takes into account suspect valves with unknown status, as well as pipes with incorrect roughness values and nodal leakage. The methodology also takes advantage of a new approach to reducing solution search space size for the optimisation problems. These problems are then solved for different leakage scenarios. Artificial calibration data are generated by means of hydraulic modelling employed to mimic planned hydrant discharges during a low demand period, combined with step tests. The case study demonstrates the improved leakage detection and model calibration of the two-stage calibration approach relative to the one-stage approach, which considers all calibration parameters together. This can result in a useful practical network operation tool

Treated Wastewater and Nitrate Transport Beneath Irrigated Fields near Dodge City, Kansas

Use of secondary-treated municipal wastewater for crop irrigation south of Dodge City, Kansas, where the soils are mainly of silty clay loam texture, has raised a concern that it has resulted in high nitrate-nitrogen concentrations (10-50 mg/kg) in the soil and deeper vadose zone, and also in the underlying deep (20-45 m) ground water. The goal of this field-monitoring project was to assess how and under what circumstances nitrogen (N) nutrients under cultivated corn that is irrigated with this treated wastewater can reach the deep ground water of the underlying High Plains aquifer, and what can realistically be done to minimize this problem. We collected 15.2-m-deep cores for physical and chemical properties characterization; installed neutron moisture-probe access tubes and suction lysimeters for periodic measurements; sampled area monitoring, irrigation, and domestic wells; performed dye-tracer experiments to examine soil preferential-flow processes through macropores; and obtained climatic, crop, irrigation, and N-application rate records. These data and additional information were used in the comprehensive Root Zone Water Quality Model (RZWQM2) to identify key parameters and processes that influence N losses in the study area. We demonstrated that nitrate-N transport processes result in significant accumulations of N in the thick vadose zone. We also showed that nitrate-N in the underlying ground water is increasing with time and that the source of the nitrate is from the wastewater applications. RZWQM2 simulations indicated that macropore flow is generated particularly during heavy rainfall events, but during our 2005-06 simulations the total macropore flow was only about 3% of precipitation for one of two investigated sites, whereas it was more than 13% for the other site. Our calibrated model for the two wastewater-irrigated study sites indicated that reducing current levels of corn N fertilization by half or more to the level of 170 kg/ha substantially increases N-use efficiency and achieves near-maximum crop yield. Combining such measures with a crop rotation that includes alfalfa should further reduce the amounts of residual N in the soil, as indicated in one of the study sites that had alfalfa in past crop rotations

Dexamethasone Administration in Mice Leads to Less Body Weight Gain over Time, Lower Serum Glucose, and Higher Insulin Levels Independently of NRF2.

Glucocorticoids are used widely on a long-term basis in autoimmune and inflammatory diseases. Their adverse effects include the development of hyperglycemia and osteoporosis, whose molecular mechanisms have been only partially studied in preclinical models. Both these glucocorticoid-induced pathologies have been shown to be mediated at least in part by oxidative stress. The transcription factor nuclear erythroid factor 2-like 2 (NRF2) is a central regulator of antioxidant and cytoprotective responses. Thus, we hypothesized that NRF2 may play a role in glucocorticoid-induced metabolic disease and osteoporosis. To this end, WT and Nrf2 knockout (Nrf2KO) mice of both genders were treated with 2 mg/kg dexamethasone or vehicle 3 times per week for 13 weeks. Dexamethasone treatment led to less weight gain during the treatment period without affecting food consumption, as well as to lower glucose levels and high insulin levels compared to vehicle-treated mice. Dexamethasone also reduced cortical bone volume and density. All these effects of dexamethasone were similar between male and female mice, as well as between WT and Nrf2KO mice. Hepatic NRF2 signaling and gluconeogenic gene expression were not affected by dexamethasone. A 2-day dexamethasone treatment was also sufficient to increase insulin levels without affecting body weight and glucose levels. Hence, dexamethasone induces hyperinsulinemia, which potentially leads to decreased glucose levels, as well as osteoporosis, both independently of NRF2

The type 2 cannabinoid receptor regulates susceptibility to osteoarthritis in mice

SummaryObjectiveCannabinoid receptors and their ligands have been implicated in the regulation of various physiological processes but their role in osteoarthritis has not been investigated. The aim of this study was to evaluate the role of the type 2 cannabinoid receptor (Cnr2) in regulating susceptibility to osteoarthritis in mice.MethodsWe analysed the severity of knee osteoarthritis as assessed by the Osteoarthritis Research Society International (OARSI) scoring system in mice with targeted deletion of Cnr2 (Cnr2−/−) and wild type (WT) littermates. Studies were conducted in mice subjected to surgical destabilisation of the medial meniscus (DMM) and in those with spontaneous age-related osteoarthritis (OA).ResultsOsteoarthritis was more severe following DMM in the medial compartment of the knee in Cnr2−/− compared with WT mice (mean ± sem score = 4.9 ± 0.5 vs 3.6 ± 0.3; P = 0.017). Treatment of WT mice with the CB2-selective agonist HU308 following DMM reduced the severity of OA in the whole joint (HU308 = 8.4 ± 0.2 vs vehicle = 10.4 ± 0.6; P = 0.007). Spontaneous age related osteoarthritis was also more severe in the medial compartment of the knee in 12-month old Cnr2−/− mice compared with WT (5.6 ± 0.5 vs 3.5 ± 0.3, P = 0.008). Cultured articular chondrocytes from Cnr2−/− mice produced less proteoglycans in vitro than wild type chondrocytes.ConclusionThese studies demonstrate that the Cnr2 pathway plays a role in the pathophysiology of osteoarthritis in mice and shows that pharmacological activation of CB2 has a protective effect. Further studies of the role of cannabinoid receptors in the pathogenesis of osteoarthritis in man are warranted

JZL184, a monoacylglycerol lipase inhibitor, induces bone loss in a multiple myeloma model of immunocompetent mice

Multiple myeloma (MM) patients develop osteolysis characterised by excessive osteoclastic bone destruction and lack of osteoblast bone formation. Pharmacological manipulation of monoacylglycerol lipase (MAGL), an enzyme responsible for the degradation of the endocannabinoid 2-arachidonoyl glycerol (2-AG), reduced skeletal tumour burden and osteolysis associated with osteosarcoma and advanced breast and prostate cancers. MM and hematopoietic, immune and bone marrow cells express high levels of type 2 cannabinoid receptor and osteoblasts secrete 2-AG. However, the effects of MAGL manipulation on MM have not been investigated. Here, we report that treatment of pre-osteoclasts with non-cytotoxic concentrations of JZL184, a verified MAGL inhibitor, enhanced MM- and RANKL-induced osteoclast formation and size in vitro. Exposure of osteoblasts to JZL184 in the presence of MM cell-derived factors reduced osteoblast growth but had no effect on the ability of these cells to mature or form bone nodules. In vivo, administration of JZL184 induced a modest, yet significant, bone loss at both trabecular and cortical compartments of long bones of immunocompetent mice inoculated with the syngeneic 5TGM1-GFP MM cells. Notably, JZL184 failed to inhibit the in vitro growth of a panel of mouse and human MM cell lines, or reduce tumour burden in mice. Thus, MAGL inhibitors such as JZL184 can exacerbate MM-induced bone loss

Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.Comment: 25 page

Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

The application of the Gardner method for generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely B\"acklund transformations and initial conservation laws, follow from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for generation of symmetries is developed and applied to discrete KdV. It can also be applied to all the other ABS equations