Equational spectrum of Hilbert varieties

We prove that an equational class of Hilbert algebras cannot be defined by a single equation. In particular Hilbert algebras and implication algebras are not one-based. Also, we use a seminal theorem of Alfred Tarski in equational logic to characterize the set of cardinalities of all finite irredundant bases of the varieties of Hilbert algebras, implication algebras and commutative BCK algebras: all these varieties can be defined by independent bases of n elements, for each n > 1.      

Structures and redox characteristics of electron-deficient vanadyl phthalocyanines

The first single-crystal X-ray structures of substituted vanadyl phthalocyanine materials reveal the high-valence vanadium ions (denoted as V(IV)), whose coordination by a highly electron-deficient ligand is facilitated by an axial oxo group. The metal center of the hydrophilic V═O core, encapsulated in F-rich hydrophobic pockets, reaches a coordination number of 6 by binding an additional H(2)O that, in turn, hydrogen-bonds with ketones, resulting in solvent-induced variable solid-state architectures. Fluoroalkyl (R(f)) ligand substituents hinder π-π stacking interactions and favor ordered long-range packing, as well as the facile formation of film materials that exhibit high thermal stability and oxidation resistance. Reversible redox chemistry and spectroscopic studies in both solution and the solid-state indicate single-site isolation in both phases and an R(f)-induced propensity for electron uptake and inhibition of electron loss. Repeated redox cycles reorganize the thin films to accommodate Li(+) ions and facilitate their migration. The facile reduction, combined with high stability and ease of sublimation imparted by the R(f) scaffold that suppresses oxidations, recommends the new materials for sensors, color displays, electronic materials, and redox catalysts, as well as other applications.     

Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions with regular rotating event horizon. For corresponding parameterizations, the metrics and connections define Finsler–Einstein geometries modeled on tangent bundles, or on nonholonomic (pseudo) Riemannian manifolds. In general, there are vacuum nonholonomic gravitational configurations which can not be generated in the limit of zero cosmological constant.     

Fractional nonholonomic Ricci flows

We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman’s functionals and derived the corresponding fractional evolution (Hamilton’s) equations. We apply in fractional calculus the nonlinear connection formalism originally elaborated in Finsler geometry and generalizations and recently applied to classical and quantum gravity theories. There are also analyzed the fractional operators for the entropy and fundamental thermodynamic values.     

Energy dissipation characteristics of particle sloshing in a rotating cylinder

A study on the energy dissipation characteristics of granular materials flowing/sloshing in a rotating container is presented here. The objective is to develop a configuration for control of excessive structural oscillations, similar to those of tuned vibration absorbers and tuned sloshing absorbers. The effectiveness of energy dissipation through granular flow is primarily determined experimentally. A computational model is developed to understand the flow behavior and energy dissipation in this system. A promising kinematic match of the particle behavior is demonstrated between the numerical predictions and the experimental observations. The use of the granular flow in a rotating drum for vibration control is being investigated for the first time.     

Yang-mills fields and gauge gravity on generalized Lagrange and Finsler spaces

Locally anisotropic gauge theories for semisimple and nonsemisimple groups are examined. A gauge approach to generalized Lagrange gravity based on local linear and affine structural groups is proposed.     

Complexation to Fe(II), Ni(II), and Zn(II) of multidentate ligands resulting from condensation of 2-pyridinecarboxaldehyde with alpha,omega-triamines: selective imidazolidine/hexahydropyrimidine ring opening revisited

The condensation reaction between 2-pyridinecarboxaldehyde and diethylenetriamine, 3-[(2-aminoethyl)amino]propylamine, and 3,3'-iminobis(propylamine) in a 2:1 molar ratio yields ligands that may be isolated exclusively in the dissymmetric (cyclic) isomeric forms L(A), L(B)/L(B*), and L(C). The template effect of a metal center (Fe(II), Ni(II), and Zn(II)) results in the ring opening of L(C) including one hexahydropyrimidine ring and one (long) propylene bridge. The resulting symmetric bis-Schiff base isomeric form L(C') is stabilized through pentacoordination, yielding [Fe(II)L(C')(NCS)](NCS) (3), [Ni(II)L(C')(NCS)](NCS) (6), and [Zn(II)L(C')(NCS)](NCS) (9). The same metal centers are too bulky to exert a template effect on L(A) including one imidazolidine ring and one (short) ethylene bridge. L(A) acts as a tetradentate ligand yielding [Fe(II)L(A)(NCS)2] (1), [Ni(II)L(A)(NCS)2] (4), and [Zn(II)L(A)(NCS)2] (7). The template effect of the metal center is selective toward the ligand L(B)/L(B*) including a hexahydropyrimidine (imidazolidine) ring and the shorter ethylene (longer propylene) bridge. The Fe(II) cation is small enough to exert a template effect, resulting in the ring opening of L(B)/L(B*). The resulting bis-Schiff base L(B') is stabilized through pentacoordination, yielding [Fe(II)L(B')(NCS)](NCS) (2). Ni(II) is too bulky to promote the ring opening of L(B)/L(B*): L(B) acts as a tetradentate ligand, yielding [Ni(II)L(B)(NCS)2] (5) (the L(B*) isomer is totally converted to L(B)). The coordinative requirements and stereochemical preference of the bulkier Zn(II) cation allow neither the ring opening of L(B)/L(B*) nor the tetracoordination of L(B) or L(B*) but stabilize the novel tetradentate dissymmetric form L(B degrees) in [Zn(II)L(B degrees)(NCS)2].H2O (8) (L(B degrees) results from MeOH addition across the imine bond of L(B)). Density functional theory calculations performed for Ni(II) and Zn(II) complexes of the L(B)/L(B*)/L(B degrees) set of ligands allowed one to compare the relative stabilities of all possible isomers, showing that the most stable ones correspond to those experimentally obtained: isomerization, or methanol addition across the imine bond, of the tetradentate ligand depends on the relative stabilities of all possible isomeric complexes.     

A 2D coordination polymer assembled from a nickel(II) tetraazamacrocyclic cation and 4,4′‐(dimethylsilanediyl)diphthalate(3–) linker

The preformed nickel(II) complex of the 14‐membered macrocyclic ligand 1,4,8,11‐tetraazacyclotetradecane (cyclam, L), when treated with 4,4′‐(dimethylsilanediyl)diphthalic acid (H₄A) in a DMF/H₂O mixture (4:1 v/v) under heating, leads to [Ni(L)]₃(HA)₂·3DMF ( I·DMF ). Redissolution of this compound in a DMF/H₂O/MeOH mixture (4:1:30 v/v/v) with mild acidification under gentle heating results in the formation of a similar compound but containing water and methanol molecules of crystallization, [Ni(L)]₃(HA)₂·5H₂O·2MeOH ( II·H₂O ). At lower temperature and concentration of reactants and longer reaction time, single crystals of composition {[{Ni(L)}₃(HA)₂]·4CH₃OH}_n ( II·MeOH ) were isolated. Single‐crystal X‐ray diffraction analysis of this compound, which, according to PXRD is isostructural with II·H₂O but different from I·DMF , revealed its two‐dimensional (2D) polymeric structure, i.e. poly[[bis{μ₃‐4‐[(4‐carboxy‐3‐carboxylatophenyl)dimethylsilyl]benzene‐1,2‐dicarboxylato‐κ³O¹:O²:O^3′}tris(1,4,8,11‐tetraazacyclotetradecane‐κ⁴N)trinickel(II)] methanol tetrasolvate], {[Ni₃(C₁₈H₁₃O₈Si)₂(C₁₀H₂₄N₄)₃]·4CH₃OH}_n. It is built up of the monoprotonated tricarboxylate HA^3? ligand coordinated in a monodentate manner in the axial positions of two crystallographically independent Ni^II cations, one of which is located on a crystallographic inversion centre. Both metal ions adopt a slightly tetragonally elongated trans‐N₄O₂ octahedral geometry. The compound has a lamellar structure with polymeric layers oriented parallel to the (10) plane, which are in turn linked via hydrogen bonds involving protonated carboxylic acid groups of the ligand. Bulk compounds I·DMF and II·H₂O were characterized by FT–IR and diffuse reflectance spectroscopy and thermogravimetry, which provide evidence of their structural differences.     

Boolean transformations with unique fixed points

We determine the Boolean transformations F: B ⁿ → B ⁿ which have unique fixed points.