Triangulable locally nilpotent derivations in dimension three

In this paper we give an algorithm to recognize triangulable locally nilpotent derivations in dimension three. In case the given derivation is triangulable, our method produces a coordinate system in which it exhibits a triangular form.     

Reliable root detection with the qd-algorithm: When Bernoulli,Hadamard and Rutishauser cooperate

When using Rutishauser's qd-algorithm for the determination of the roots of a polynomial (originally the poles of a meromorphic function), or for related problems, conditions have been formulated for the interpretation of the computed q- and e-values. For a correct interpretation, the so-called critical indices play a crucial role. They index a column of e-values that tends to zero because of a jump in modulus among the poles. For more than 50 years the qd-algorithm in exact arithmetic was considered to be fully understood. In this presentation we push the detailed theoretical investigation of the qd-algorithm even further and we present a new aspect that seems to have been overlooked. We indicate a new element that makes a column of e-values tend to zero, namely a jump in multiplicity among equidistant poles. This result is obtained by combining the qd-algorithm with a deflation technique, and hence mainly relying on Bernoulli's method and Hadamard's formally orthogonal polynomials. Our results round up the theoretical analysis of the qd-algorithm as formulated in its original form, and are of importance in a variety of practical applications as outlined in the introduction.     

Avoiding breakdown in the CGS algorithm

The conjugate gradient squared algorithm can suffer of similar breakdowns as Lanczos type methods for the same reason that is the non-existence of some formal orthogonal polynomials. Thus curing such breakdowns is possible by jumping over these non-existing polynomials and using only those of them which exist. The technique used is similar to that employed for avoiding breakdowns in Lanczos type methods. The implementation of these new methods is discussed. Numerical examples are given.     

Intelligent Online Monitoring of Rolling Bearing: Diagnosis and Prognosis

This paper suggests a new method to predict the Remaining Useful Life (RUL) of rolling bearings based on Long Short Term Memory (LSTM), in order to obtain the degradation condition of the rolling bearings and realize the predictive maintenance. The approach is divided into three parts: the first part is the clustering to detect the damage state by the density-based spatial clustering of applications with noise. The second one is the health indicator construction which could give a better reflection of the bearing degradation tendency and is selected as the input for the prediction model. In the third part of the RUL prediction, the LSTM approach is employed to improve the accuracy of the prediction. The rationale of this work is to combine the two methods—the density-based spatial clustering of applications with noise and LSTM—to identify the abnormal state in rolling bearings, then estimate the RUL. The suggested method is confirmed by experimental data of bearing life cycle, and the RUL prediction results of the model LSTM are compared with the nonlinear au-regressive model with exogenous input model. In addition, the constructed health indicator is compared with the spectral kurtosis feature. The results demonstrated that the suggested method is more appropriate than the nonlinear au-regressive model with exogenous input model for the prediction of bearing RUL.     

PELDOR Spectroscopy Distance Fingerprinting of the Octameric Outer‐Membrane Protein Wza from Escherichia coli.

Distance fingerprinting : Pulsed electron–electron double resonance spectroscopy (PELDOR) is applied to the octameric membrane protein complex Wza of E. coli. The data yielded a detailed distance fingerprint of its periplasmic region that compares favorably to the crystal structure. These results provide the foundation to study conformation changes from interaction with partner proteins.

     

EPR Spectroscopy of a Family of CrIII7MII (M = Cd,Zn, Mn,Ni) “Wheels”: Studies of Isostructural Compounds with Different Spin Ground States

Spinning wheels : The presented highly resolved multifrequency continuous wave EPR spectra (e.g., see figure) of the heterooctametalic “wheels” Cr₇M provide rare examples of high nuclearity polymetallic systems where detailed information on the spin‐Hamiltonian parameters of the ground and excited spin states is observed.

     

Crystal structure, vibrational spectra and thermal decomposition of a new tetrazinc(II) dipyrophosphate decahydrate, Zn4(P2O7)2 < eqid1 > ?10H2O

A new zinc(II) pyrophosphate, Zn₄(P₂O₇)₂ < eqid1 > 10H₂O, has been synthesized and characterized by single-crystal X-ray diffraction [orthorhombic space group Pnma, with unit cell parameters of a = 9.1508(2) A, b = 25.5271(5) Å, c = 8.3574(2) Å, Z = 4]. All the pyrophosphate anions show nonlinear P–O–P bonds with an average angle of 126.5. The framework of this new pyrophosphate is made up of packed layers of ZnO₆ octahedra connected by double-tetrahedra P₂O₇ groups and a layer of Zn(H₂O)₆ units. The [P₂O₇]^4– anions adopt a bent, near-staggered conformation. The absence of coincidences for the majority of the IR and Raman bands is in accord with the centrosymmetric structure of the material. The vibrational spectra have been interpreted in part on the basis of factor group effects. The structural changes occurring during heating have been investigated by TG-DSC, powder X-ray diffraction, and IR and Raman spectroscopy. When Zn₄(P₂O₇)₂ 10H₂O is gradually heated, it decomposes and -Zn₂P₂O₇ is formed at 481C. On further heating, -Zn₂P₂O₇ is transformed into -Zn₂P₂O₇ at 750C. The conversion between the and -Zn2P2O7 forms is irreversible and, on cooling -Zn2P2O7 to room temperature, it reverts back to -Zn2P2O7. The crystal structure of the new zinc(II) pyrophosphate material is compared with the known structures of the related anhydrous products -, -, and -Zn2P2O7.     

Opuntia dillenii (Ker Gawl.) Haw., Seeds Oil Antidiabetic Potential Using In Vivo,In Vitro,In Situ,and Ex Vivo Approaches to Reveal Its Underlying Mechanism of Action

Opuntia dillenii Ker Gawl. is one of the medicinal plants used for the prevention and treatment of diabetes mellitus (DM) in Morocco. This study aims to investigate the antihyperglycemic effect of Opuntia dillenii seed oil (ODSO), its mechanism of action, and any hypoglycemic risk and toxic effects. The antihyperglycemic effect was assessed using the OGTT test in normal and streptozotocin (STZ)-diabetic rats. The mechanisms of action were explored by studying the effect of ODSO on the intestinal absorption of d-glucose using the intestinal in situ single-pass perfusion technique. An Ussing chamber was used to explore the effects of ODSO on intestinal sodium-glucose cotransporter 1 (SGLT1). Additionally, ODSO’s effect on carbohydrate degrading enzymes, pancreatic α-amylase, and intestinal α-glucosidase was evaluated in vitro and in vivo using STZ-diabetic rats. The acute toxicity test on mice was performed, along with a single-dose hypoglycemic effect test. The results showed that ODSO significantly attenuated the postprandial hyperglycemia in normal and STZ-diabetic rats. Indeed, ODSO significantly decreased the intestinal d-glucose absorption in situ. The ex vivo test (Ussing chamber) showed that the ODSO significantly blocks the SGLT1 (IC₅₀ = 60.24 µg/mL). Moreover, ODSO indu\ced a significant inhibition of intestinal α-glucosidase (IC₅₀ = 278 ± 0.01 µg/mL) and pancreatic α-amylase (IC₅₀ = 0.81 ± 0.09 mg/mL) in vitro. A significant decrease of postprandial hyperglycemia was observed in sucrose/starch-loaded normal and STZ-diabetic ODSO-treated rats. On the other hand, ODSO had no risk of hypoglycemia on the basal glucose levels in normal rats. Therefore, no toxic effect was observed in ODSO-treated mice up to 7 mL/kg. The results of this study suggest that ODSO could be suitable as an antidiabetic functional food.     

Exploration of the effects of chloride ions on the analysis of polar compounds at low concentrations by hydrophilic interaction liquid chromatography coupled to a charged aerosol detector: Application to tromethamine

In this study, we discuss the origin of the slightly increased response of the charged aerosol detector when low-concentration polar drugs formulated with sodium chloride are analyzed by hydrophilic interaction liquid chromatography coupled to the charged aerosol detector. In the case of tromethamine mixed with saline solutions, we investigated several levels including the mobile phase, sample matrix, and detection. We show that the analysis of the rich-salted sample results in both interactions with the mobile phase modifiers and the stationary phase during the run time. With 150 mM NaCl as a compounding solution, a slight increase in the tromethamine peak area was observed (<5.5%). Our study suggests that chloride ions in excess sequentially interact firstly with the counterions from the organic modifiers and secondly with the analyte via the stationary phase and the contribution of hydrophilic interaction liquid chromatography retention mechanisms. Because of these effects, the hydrophilic interaction liquid chromatography-charged aerosol detector analysis of drugs in saline solutions requires particular attention, and a correction factor for quantitative purposes that accounts for formulation ions remains appropriate.