Estimates of the Best Approximation of Polynomials by Simple Partial Fractions

An asymptotics of the error of interpolation of real constants at Chebyshev nodes is obtained. Some well-known estimates of the best approximation by simple partial fractions (logarithmic derivatives of algebraic polynomials) of real constants in the closed interval [?1, 1] and complex constants in the unit disk are refined. As a consequence, new estimates of the best approximation of real polynomials on closed intervals of the real axis and of complex polynomials on arbitrary compact sets are obtained.

     

An adaptive multilevel wavelet framework for scale‐selective WENO reconstruction schemes

We put forth a dynamic computing framework for scale‐selective adaptation of weighted essential nonoscillatory (WENO) schemes for the simulation of hyperbolic conservation laws exhibiting strong discontinuities. A multilevel wavelet‐based multiresolution procedure, embedded in a conservative finite volume formulation, is used for a twofold purpose. (i) a dynamic grid adaptation of the solution field for redistributing grid points optimally (in some sense) according to the underlying flow structures, and (ii) a dynamic minimization of the in built artificial dissipation of WENO schemes. Taking advantage of the structure detection properties of this multiresolution algorithm, the nonlinear weights of the conventional WENO implementation are selectively modified to ensure lower dissipation in smoother areas. This modification is implemented through a linear transition from the fifth‐order upwind stencil at the coarsest regions of the adaptive grid to a fully nonlinear fifth‐order WENO scheme at areas of high irregularity. Therefore, our computing algorithm consists of a dynamic grid adaptation strategy, a scale‐selective state reconstruction, a conservative flux calculation, and a total variation diminishing Runge‐Kutta scheme for time advancement. Results are presented for canonical examples drawn from the inviscid Burgers, shallow water, Euler, and magnetohydrodynamic equations. Our findings represent a novel direction for providing a scale‐selective dissipation process without a compromise on shock capturing behavior for conservation laws, which would be a strong contender for dynamic implicit large eddy simulation approaches.     

Semigroup Classification and Gelfand–Shilov Classification of Systems of Partial Differential Equations

Mathematical Notes - Two approaches to systems of linear partial differential equations are considered: the traditional approach based on the generalized Fourier transform and the semigroup...     

New multifunctional heterobinuclear palladium (II) complexes based on organometallic dithiocarbazate ligands

In the research of new compounds with multifunctional applications, heterobinuclear palladium (II) complexes based on organometallic dithiocarbazates (DTCZs) have been isolated. The organometallic DTCZ ligands of the general formula [{(η⁵-C₅H₄)-CH=NNHC(S)SCH₃}]MLn [MLn = Re (CO)₃ ( 2a ); Mn (CO)₃ ( 2b ); FeCp ( 2c )] were prepared by the reaction between formyl organometallic precursors ( 1a−c ) with S-methyldithiocarbazate. Subsequently, a two-step reaction of 2a−c with: (i) K₂[PdCl₄] and (ii) PPh₃ yielded heterobinuclear complexes [Pd{MLn(η⁵-C₅H₄)-CH=NNHC(S)SCH₃}–(Cl)(PPh₃)] [MLn = Re (CO)₃ ( 3a ); Mn (CO)₃ ( 3b ); FeCp ( 3c )]. All compounds were characterized by conventional spectroscopic techniques (infrared spectroscopy, nuclear magnetic resonance spectroscopy, mass spectrometry and elemental analysis). In addition, the molecular structures of 2a , 2c and 3c were determined by single-crystal X-ray diffraction. The new palladium (II) complexes ( 3a−c ) were evaluated as antiproliferative agents against non-small cell lung cancer cells (H1299 cells). Complexes 3a and 3b containing cyrhetrenyl- and cymantrenyl-DTCZ ligands, respectively, were more active than their ferrocenyl analogue 3c . The activity was associated with the electron-withdrawing properties of the (η⁵-C₅H₄)M (CO)₃ moieties and their better lipophilicity than that of the ferrocenyl analogue. In addition, we studied the capacity of metalloligands ( 2a−c ) and palladium (II) complexes ( 3a−c ) to remove methylene blue in water under UV–visible light irradiation. The results established that the complexes showed moderate efficiency and were less active than their corresponding free ligands.     

NHC-Pd complex heterogenized on graphene oxide for cross-coupling reactions and supercapacitor applications

N-heterocyclic carbene (NHC)-palladium(II) complex (GO@NHC-Pd) was synthesized on graphene oxide (GO) support via a simple and cost-effective multistep approach. The spectroscopic, microscopic, thermal, and surface analyses of GO@NHC-Pd confirmed the successful formation of the catalyst. The investigation of catalytic activity showed that GO@NHC-Pd was very effective in Suzuki–Miyaura as well as Hiyama cross-coupling. Being heterogeneous in nature, GO@NHC-Pd was recovered after each reaction cycle easily and reused for up to nine and six cycles in Suzuki–Miyaura and Hiyama cross-coupling, respectively, without significant loss of activity. Further exploration of the supercapacitor performance of GO@NHC-Pd catalyst assembled in a two-electrode cell configuration shown a maximum attained capacitance of 105.26 F/g at a current density of 0.1 A/g with good cycling stability of 96.89% over 2,500 cycles.     

Dinuclear gold(I)-N-heterocyclic carbene complexes: Synthesis,characterization, and catalytic application for hydrohydrazidation of terminal alkynes

Dinuclear gold(I)-N-heterocyclic carbene complexes were developed for the hydrohydrazidation of terminal alkynes. The gold(I)-N-heterocyclic carbene complexes 2a-2b were synthesized in good yields from silver complexes synthesized in situ, which in turn were obtained from the corresponding imidazolium salts with Ag₂O in dichloromethane as a solvent. The new air-stable gold(I)-NHC complexes, 2a - 2b, were characterized using NMR spectroscopy, elemental analysis, infrared, and mass spectroscopy studies. The gold(I) complex 2a was characterized using X-ray crystallography. Bis-N-heterocyclic carbene–based gold(I) complexes 2a - 2b exhibited excellent catalytic activities for hydrohydrazidation of terminal alkynes yielding acylhydrazone derivatives. The working catalytic system can be used in gram-scale synthesis. In addition, the catalytic reaction mechanism of the hydrohydrazidation of terminal alkynes by gold(I)-NHC complex was studied in detail using density functional theory.     

Synthesis,molecular modeling,TD-DFT,antimicrobial, and in vitro therapeutic activity of new spherical nano-sized sulfonamide imine ligands and their zinc (II) and copper (II) complexes

A series of nanometer-sized spherical sulfonamide imine ligands HL ¹ -HL ⁵ and their copper and zinc complexes were synthesized and fully characterized based on elemental analyses, spectroscopic (UV/vis, FT-IR, NMR, EPR, SEM) studies, molar conductance and thermal analyses. Furthermore, computational studies of HL ¹ -HL ⁵ were carried out by the DFT/B3LYP method. TD-DFT, HOMO and LUMO energy values, chemical hardness, electronegativity, electrophilic index, softness, and other parameters were calculated. Screening against several pathogenic microorganisms indicated that HL ¹ exhibited high activity against the tested Gram-negative bacteria relative to other analogues and the inhibition activity is greater than the standard Gentamicin. Analogously, HL ² exhibited high potent activity against the tested Gram-positive bacteria. Copper complexes exhibited a higher potent activity than zinc analogues. Noteworthy, inhibition activity of [Cu ( L ³ )(OAc)] complex is higher than that of the standard Ampicillin. [Cu ( L ² )(OAc)] complex displayed a similar activity of the standard bactericides and fungicides in use. The complexes showed appreciated values of MIC against bacterial strains: B. subtilis (MIC = 0.4 μg / mL), E. coli and S. pneumonia (MIC = 1.95 μg / mL) and P. aeruginosa (MIC = 7.81 μg / mL). in vitro cytotoxic activities study proved that [Cu ( L ³ )(OAc)] complex exhibited appreciable activity versus (HEPG-2); IC₅₀ = 4.8 μg/ml, while [Cu( L ² )(OAc)] complex showed a high activity against (MCF-7); IC₅₀ = 6.2 μg/ml. These results could be considered as new findings of promising antitumor candidates for experimental chemotherapy.     

Partial control of delay-coordinate maps

Nonlinear Dynamics - Delay-coordinate maps have been widely used recently to study nonlinear dynamical systems, where there is only access to the time series of one of their variables. Here, we...     

New chalcone based liquid crystals with allylidene amino linking unit: Synthesis and characterization

In this study, the synthesis, structural characterization and mesomorphic properties of newly thirteen calamitic shaped compounds derived from allylidene amino chalcone and 4-n-alkoxy benzoyloxy benzoic acid. Comp.H₁ to H₃ exhibited nonliquid crystalline nature, while comp.H₄ to comp.H₁₈ displayed enantiotropical smectic C phase. Phase transition temperatures of present synthesised compounds were determined by optical polarising microscopy (POM), differential scanning calorimetric (DSC) and powder X-ray diffraction (PXRD) techniques. Thermal stabilities of smectic to isotropic phase are 150.0 °C and temperature range of mesophase is in decreasing order from comp.H₃ to comp.H₁₈ respectively. The presences of SmC phase are the type of broken fan and needle type in present synthesized series. It is also shown that presence of chalcone amino allylidene central linking group favors a calamitic liquid crystalline behaviour in molecules with lower member to higher member aliphatic side chain in alkoxy group (-OR).