Interpolation in the semiplane by generalized canonical products

The problem of the interpolation of functions, analytic in the upper semiplane, of type not greater than normal, and of given order, is considered. Necessary and sufficient conditions for its solvability are obtained.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 45, pp. 84–96, 1986.     

Hydrophilization of Magnetic Nanoparticles with Modified Alternating Copolymers. Part 1: The Influence of the Grafting

Iron oxide nanoparticles (NPs) with a diameter 21.6 nm were coated with poly(maleic acid-alt-1-octadecene) (PMAcOD) modified with grafted 5,000 Da poly(ethyelene glycol) (PEG) or short ethylene glycol (EG) tails. The coating procedure utilizes hydrophobic interactions of octadecene and oleic acid tails, while the hydrolysis of maleic anhydride moieties as well as the presence of hydrophilic PEG (EG) tails allows the NP hydrophilicity. The success of the NP coating was found to be independent of the degree of grafting which was varied between 20 and 80% of the -MacOD-units, but depended on the length of the grafted tail. The NP coating and hydrophilization did not occur when the modified copolymer contained 750 Da PEG tails independently of the grafting degree. To explain this phenomenon the micellization of the modified PMAcOD copolymers in water was analyzed by small angle x-ray scattering (SAXS). The PMAcOD molecules with the grafted 750 Da PEG tails form compact non-interacting disk-like micelles, whose stability apparently allows for no interactions with the NP hydrophobic shells. The PMAcOD containing the 5,000 Da PEG and EG tails form much larger aggregates capable of an efficient coating of the NPs. The coated NPs were characterized using transmission electron microscopy, dynamic light scattering, ζ-potential measurements, and thermal gravimetry analysis. The latter method demonstrated that the presence of long PEG tails in modified PMAcOD allows the attachment of fewer macromolecules (by a factor of ~20) compared to the case of non-modified or EG modified PMAcOD, emphasizing the importance of PEG tails in NP hydrophilization. The NPs coated with PMAcOD modified with 60% (towards all -MAcOD- units) of the 5,000 PEG tails bear a significant negative charge and display good stability in buffers. Such NPs can be useful as magnetic cores for virus-like particle formation.     

Extremal Problems in the Class of Delta-Subharmonic Functions of Finite Order in a Half-Plane

We obtain exact lower bounds of the upper limits of ratios of the Nevanlinna characteristics of a delta-subharmonic function in the upper half-plane.     

Transformation formulas for pseudo-characters of braid groups

We develop the theory of pseudo-characters of braid groups. We study a special family of operators between spaces of pseudo-characters of braid groups and describe techniques for obtaining new pseudo-characters of braid groups from known ones. A number of general results on the structure of the space of pseudo-characters is obtained. Bibliography: 12 titles.     

Optimal workforce assignment to operations of a paced assembly line

We study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation’s processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data.