We prove that the homotopy theory of $N_\infty$ operads is equivalent to a discrete operads, and we construct free associative operadic realizations every indexing system. This resolves conjecture Blumberg Hill in affirmative.

The vehicle routing problem with simultaneous pickup and delivery (VRPSPD) is a well-known combinatorial optimization problem which addresses provided service to a set of customers using a homogeneous fleet of capacitated vehicles. The objective is to minimize the distance traveled. The VRPSPD is an NP-hard combinatorial optimization problem. Therefore, practical large-scale instances of VR...

The UNIQUAC activity coefficient model is extended to predict solid-liquid equilibrium of isotactic crystalline poly (1-butene), iPBu-1, in different organic solvents. The UNIQUAC activity coefficient model used in this work is based on the concept of group contribution and consists of combinatorial, residual and free volume terms. To account for branching of atom groups in the monomer structur...

My half-century journey started from synthetic organic chemistry. During the first stage of my journey, my interest in stereochemistry was initiated through the investigation on the participation of steric effects in reactive intermediates, cylophanes, strained heterocycles, and organic compounds for photography. In chemoinformatics as the next stage of the journey, I proposed the concept of im...

The vehicle routing problem with simultaneous pickup and delivery (VRPSPD) is a well-known combinatorial optimization problem which addresses provided service to a set of customers using a homogeneous fleet of capacitated vehicles. The objective is to minimize the distance traveled. The VRPSPD is an NP-hard combinatorial optimization problem. Therefore, practical large-scale instances of VR...

A combinatorial auction is an auction where the bidders have the choice to bid on bundles of items. The WDP in combinatorial auctions is the problem of finding winning bids that maximize the auctioneer’s revenue under the constraint that each item can be allocated to at most one bidder. The WDP is known as an NP-hard problem with practical applications like electronic commerce, production manag...