Consistency requirements and pattern methods in cost sharing problems with technological cooperation

Using the discrete cost sharing model with technological cooperation, we investigate the implications of the requirement that demand manipulations must not affect the agents’ shares. In a context where the enforcing authority cannot prevent agents (who seek to reduce their cost shares) from splitting or merging their demands, the cost sharing methods used must make such artifices unprofitable. The paper introduces a family of rules that are immune to these demand manipulations, the pattern methods. Our main result is the characterization of these methods using the above requirement. For each one of these methods, the associated pattern indicates how to combine the technologies in order to meet the agents’ demands. Within this family, two rules stand out: the public Aumann–Shapley rule, which never rewards technological cooperation; and the private Aumann–Shapley rule, which always rewards technology providers. Fairness requirements imposing natural bounds (for the technological rent) allow to further differentiate these two rules.     

Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.     

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.     

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.