Clifford algebra and the propagation of Kähler spinors

The Kähler equation for an inhomogeneous differential form is analyzed in some detail and expressed in a set of coordinates called Riemann normal coordinates. A class of solutions to the Kähler spinors is constructed. It is shown how we can perturbatively decouple the Kähler equation and write its solution as a sum of spinors by considering the isomorphism between Clifford and the total matrix algebras.     

New relation formula for generating functions

Periodica Mathematica Hungarica - In this paper, we develop a new relation between certain types of generating functions using formal algorithmic methods. As an application, we give a relation...     

Generalized harmonic numbers,Jacobi numbers and a Hankel determinant evaluation

In this paper we will introduce a sequence of complex numbers that are called the Jacobi numbers. This sequence generalizes in a natural way several sequences that are known in the literature, such as Catalan numbers, central binomial numbers, generalized catalan numbers, the coefficient of the Hilbert matrix and others. Subsequently, using a study of the polynomial of Jacobi, we give an evaluation of the Hankel determinants that associated with the sequence of Jacobi numbers. Finally, by finding a relationship between the Jacobi numbers and generalized harmonic numbers, we determine the evaluation of the Hankel determinants that are associated with generalized harmonic numbers.     

The centroid of the zeroes of a polynomial via certain Laguerre-type operators

In this paper, we present several properties of the centroid of the zeroes of a polynomial. As an illustration, we apply these results to the d-orthogonal polynomials. Finally, we provide the relationship between different centroids of a general monic polynomial and its image under a certain Laguerre–type operator.     

Expanding the carbo‐Benzene Chemical Space for Electron‐Accepting Ability: Trifluorotolyl/Tertiobutyl Substitution Balance

With the view to altering the lipophilicity and electron accepting ability of the tetraphenyl‐carbo‐benzene scaffold, peripheral fluorination of the C₁₈ ring through aromatic linkers was envisaged from the C₁₈Ph₆ and o‐^tBu₂C₁₈Ph₄ references, by replacement of two Ph substituents with two p‐CF₃‐C₆H₄ counterparts (^FTol). The synthesis relied on a [8+10] macrocyclization involving a common bis(trifluorotolyl)‐tetraynedione, followed by reductive aromatization of the resulting [6]pericyclynediols. While p‐^FTol₂C₁₈Ph₄ proved to be hardly tractable due to an extremely low solubility, p‐^FTol₂‐o‐^tBu₂C₁₈Ph₂ could be extensively studied by X‐ray crystallography, NMR and UV/Vis spectroscopy, voltammetry, STM imaging of monolayers, and AFM imaging of binary films with P3HT or PC₇₁BM fabricated by spin‐coating for organic photovoltaic cells and J?V curve measurement thereof. The electronic and polarity properties are correlated with moderate but consistent electron‐withdrawing effects of the CF₃ groups, in agreement with the DFT‐calculated frontier orbitals and multipole moments. The results provide guidelines for optimization of fluorinated carbo‐benzene targets.     

Cosmological solutions of the Einstein-KÄhler field equations in Robertson-Walker backgrounds

We examine in detail a class of cosmological solutions to the coupled Einstein-KÄhler field equations in space-time geometries described by the Friedmann-Robertson-Walker metric. We consider the massive cases of the KÄhler equation for generating these solutions.     

Solution of the Dirac equation in plane wave metric backgrounds

We present a new solution of the Dirac equation in the background of a plane wave metric. We examine the relation between sections of the exterior and Clifford bundles of a (pseudo-)Riemannian manifold. A spinor calculus is established and used to investigate a new solution of the Dirac equation lying in a minimal left ideal characterized by a certain idempotent projector.