A new class of conformable spectral observers for signal reconstruction

In this work, the design of spectral observers for signal reconstruction based on Kalman filters is performed and evaluated. The conformable derivative and the beta‐derivative were used to design the Kalman filters. Both derivatives satisfy the same formulas of the classical derivation, eg, the chain rule. The derivative order, the Ricatti equation parameters, and the observers tuning parameters were optimized using an optimization algorithm based on the bat's echolocation behavior (Bat algorithm). The simulation results showed the advantages of using the proposed observers for the signal reconstruction.     

Multicomponent one-pot synthesis of (dihydro-1H-benzo[d]imidazole) phosphonate

Abstract

We present a multicomponent reaction strategy to synthesize a (dihydro-1H-benzo[d]imidazole)phosphonate family of compounds, using benzimidazoles, diethyl chlorophosphate and aliphatic amines as starting reactants. Giving its simplicity, our procedure involves reaction times of only few hours and avoid the usage of any catalyst agent. All the newly synthesized compounds were characterized by Nuclear Magnetic Resonance spectroscopy (¹H, ¹³C and ³¹P) and mass spectrometry by the DART method.     

Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology

In the present paper, an optimal control problem constrained by the tridomain equations in electrocardiology is investigated. The state equations consisting in a coupled reaction–diffusion system modeling the propagation of the intracellular and extracellular electrical potentials, and ionic currents, are extended to further consider the effect of an external bathing medium. The existence and uniqueness of solution for the tridomain problem and the related control problem is assessed, and the primal and dual problems are discretized using a finite volume method which is proved to converge to the corresponding weak solution. In order to illustrate the control of the electrophysiological dynamics, we present some preliminary numerical experiments using an efficient implementation of the proposed scheme.     

Synthesis of pentabromopseudilin and other arylpyrrole derivatives via Heck arylations

Pentrabromopseudilin and other 2 and 3-arylpyrrole derivatives were synthesized through the Heck–Matsuda reaction involving endocyclic enecarbamates and N-protected 3-pyrrolines, respectively. The overall processes permitted an easy and efficient access to these structural motifs present in several bioactive compounds. Attempts to synthesize the compound isopentabromopseudilin led to a tribromo aryl maleimide. We hypothesize that this latter compound is the putative product arising from the unusual thermal instability of isopentabromopseudilin.     

Cytotoxic and NF-κB inhibitory sesquiterpene lactones from Piptocoma rufescens

Six new (1-6) and eight known germacranolide-type sesquiterpene lactones, along with several known phenylpropanol coumarates and methylated flavonoids, were isolated from the leaves of Piptocoma rufescens, collected in the Dominican Republic. The new compounds were identified by analysis of their spectroscopic data, with the molecular structure of 3 being established by single-crystal X-ray diffraction. The absolute configurations of the sesquiterpene lactones isolated were determined from their CD and NOESY NMR spectra, together with the analysis of Mosher ester reactions. Bioassay screening results showed the majority of the sesquiterpene lactones isolated (1-13) to be highly cytotoxic toward the HT-29 human colon cancer cell line, with the most potent compound being 15-deoxygoyazensolide (10, IC(50), 0.26 μM). In addition, several of the sesquiterpene lactones exhibited NF-κB (p65) inhibitory activity.     

Definable nilpotent and soluble envelopes in groups without the independence property

We prove that in a group without the independence property a nilpotent subgroup is always contained in a definable nilpotent subgroup of the same nilpotency class. The analogue for the soluble case is also shown when the subgroup is normal in the ambient group.     

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.     

The Coordination Behaviour of the Peroxodisulfate Anion with Group XII Metal Ions: [Zn(H2O)(C12H8N2)2(S2O8)]·H2O and Related Compounds

Abstract  

The title compound is monomeric with a Zn(II) hexacoordinated center. The coordination sphere is formed by four nitrogens from two phenanthroline molecules, one oxygen from a monodentate peroxodisulfate ion, and one oxygen from a water molecule. A non-coordinated water molecule completes the formula with an important role in the stabilization of the structure through the formation of two O_HW–H···O_pds bridges (acting as a donor) and one O_CW–H···O_HW bridge where it is an acceptor group (HW: hydration water; pds: peroxodisulfato; CW: coordinated water). The compound is triclinic, space group P-1 with a = 8.763 (3) ?, b = 9.068 (3) ?, c = 17.531 (6) ?, α = 96.48 (2)°, β = 103.94 (3)°, γ = 104.57 (3)°, V = 1286.0 (7) ?³ and Z = 2. The structure was solved by direct methods with a conventional R (on F) = 0.050 for 4534 reflections with Fo > 4σ(Fo). The compound is isomorphous with the Cd analogue (in Harvey et al. Aust J Chem 54:307, 2001). An eventual dependence of conformation and coordination mode of the peroxodisulfate anion on the ancillary organic ligand taking part in the coordination compounds analyzed is discussed.