Isometric embeddings into Heisenberg groups

We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not necessarily sub-Riemannian. We show that if all infinite geodesics in the target are straight lines, then such an embedding must be a homogeneous homomorphism. We discuss a necessary and certain sufficient conditions for the target space to have this ‘geodesic linearity property’, and we provide various examples.     

On structure-preserving connections

In this paper we find the formula of connections under which an almost complex structure is covariantly constant. These types of connections on anti-Kähler–Codazzi manifolds are described. Also, twin metric-preserving connections are analyzed for quasi-Kähler manifolds. Finally, anti-Hermitian Chern connections are investigated.     

Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Nonlinear vibrations of circular cylindrical shells with thermal effects: an experimental study

Nonlinear Dynamics - The nonlinear dynamics of a polymeric cylindrical shell carrying a top mass under axial harmonic excitation are experimentally investigated; the tests have been carried out in...     

Bis-amino methylation for the synthesis of spiro-fused piperidines using iron(III) trifluroacetate in aqueous micellar medium

An environmentally benign, multicomponent integrated chemical process has been developed for the synthesis of 3,5-dispirosubstituted piperidines by cyclo-condensation reaction of amines, formaldehyde, and dimedone using iron(III) trifluroacetate [Fe(F₃CCO₂)₃] Lewis acid in aqueous micellar medium at ambient temperature (25–30 °C). The heterogeneous solid acid catalyst conveniently promotes this double amino methylation reaction in which six molecules condense in one pot to form six new covalent bonds. The synthesized 3,5-dispirosubstituted piperidines have been screened for their in vitro antibacterial activity using agar well method. Many of these compounds showed satisfactory antibacterial activity as compared to standard drugs against all the bacteria tested.