Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions

Image space analysis is a new tool for studying scalar and vector constrained extremum problems as well as generalized systems. In the last decades, the introduction of image space analysis has shown that the image space associated with the given problem provides a natural environment for the Lagrange theory of multipliers and that separation arguments turn out to be a fundamental mathematical tool for explaining, developing and improving such a theory. This work, with its 3 parts, aims at contributing to describe the state-of-the-art of image space analysis for constrained optimization and to stress that it allows us to unify and generalize the several topics of optimization. In this 1st part, after a short introduction of such an analysis, necessary and sufficient optimality conditions are treated. Duality and penalization are the contents of the 2nd part. The 3rd part deals with generalized systems, in particular, variational inequalities and Ky Fan inequalities. Some further developments are discussed in all the parts.     

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.     

Biocatalytic Feedback-Controlled Non-Newtonian Fluids

Non-Newtonian fluids are ubiquitous in daily life and industrial applications. Herein, we report an intelligent fluidic system integrating two distinct non-Newtonian rheological properties mediated by an autocatalytic enzyme reaction. Associative polyelectrolytes bearing a small amount of ionic and alkyl groups are engineered: by carefully balancing the charge density and the hydrophobic effect, the polymer solutions demonstrate a unique shear thickening property at low pH while shear thinning at high pH. The urea-urease clock reaction is utilized to program a feedback-induced pH change, leading to a strong upturn of the nonlinear viscoelastic properties. As long as the chemical fuel is supplied, two distinct non-Newtonian states can be achieved with a tunable lifetime span. As a proof of concept, we demonstrate how the physical energy-driven nonequilibrium properties can be manipulated by a chemical-fueled process.     

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.