A constructive approach to examination timetabling based on adaptive decomposition and ordering

In this study, we investigate an adaptive decomposition and ordering strategy that automatically divides examinations into difficult and easy sets for constructing an examination timetable. The examinations in the difficult set are considered to be hard to place and hence are listed before the ones in the easy set in the construction process. Moreover, the examinations within each set are ordered using different strategies based on graph colouring heuristics. Initially, the examinations are placed into the easy set. During the construction process, examinations that cannot be scheduled are identified as the ones causing infeasibility and are moved forward in the difficult set to ensure earlier assignment in subsequent attempts. On the other hand, the examinations that can be scheduled remain in the easy set. Within the easy set, a new subset called the boundary set is introduced to accommodate shuffling strategies to change the given ordering of examinations. The proposed approach, which incorporates different ordering and shuffling strategies, is explored on the Carter benchmark problems. The empirical results show that the performance of our algorithm is broadly comparable to existing constructive approaches.     

PHA-L lectin and carbohydrate relationship: conjugation with CdSe/CdS nanoparticles, radiolabeling and in vitro affinities on MCF-7 cells

This research aims to investigate the interaction between phytohemagglutinin-L (PHA-L) and sialic acid, which is abundant on the breast cancer cell (MCF-7) surface and displays monosaccharide characteristics, by experimental and computational methods. Experimentally, CdSe/CdS nanoparticles (QDs) were synthesized; PHA-L was conjugated with QDs and labeled with ¹²⁵I. Radiolabeling yield was found to be 97 ± 1.2 %. Afterwards, in vitro bioaffinities of radiolabeled PHA-L conjugated QDs have been investigated on MCF-7 cells and it has been observed that the cell incorporation increased with time. The results indicated that ¹²⁵I labeled QD-PHA-L conjugates represent significant affinity on MCF-7 cells. In the second step of the study, the crystal structure of carbohydrate interaction surface of PHA-L was extracted from the crystal structure of PHA-L. The interactions between this surface and sialic acid were calculated by computational tools. These calculations revealed specific interactions between PHA-L and sialic acid. Semi-empirical methods, PM3 and AM1, were used in these calculations. Significant outcomes have been obtained from the experimental and computational studies and these results demonstrated that PHA-L may be an effective agent for imagining MCF-7 cells.     

A Frustrated Phosphane–Borane Lewis Pair and Hydrogen: A Kinetics Study

The energy profile of a frustrated Lewis pair (FLP) dihydrogen splitting system was determined by a combined experimental kinetic and DFT study. A trimethylene‐bridged phosphane–borane FLP was converted into its endothermic H₂‐cleavage product by sequential H⁺/H^? addition. The system could be handled at low temperature, and the kinetics of the H₂ elimination were determined to give a rate constant of k_HH,exp(299 K)=(2.87±0.1)×10^?4 s^?1 in solution. The primary kinetic isotope effects were determined; for example, (k_HH/k_DD)_exp=3.19. The system was accurately analyzed by DFT calculations.     

Green’s Functional for Higher-Order Ordinary Differential Equations with General Nonlocal Conditions and Variable Principal Coefficient

Ukrainian Mathematical Journal - The method of Green’s functional is a little-known technique for the construction of fundamental solutions to linear ordinary differential equations (ODE)...     

The Radical Formula for Noncommutative Rings

Ukrainian Mathematical Journal - We determine some classes of left modules satisfying the radical formula in a noncommutative ring. We also show that, under a certain condition, a finitely...     

Re-Evaluation of a Fulvene-Based Self-Replicating Diels–Alder Reaction System

We re-evaluate our claim of a high diastereoselectivity in the self-relicating Diels–Alder reaction between maleimide 1 and fulvene 3 . It was shown that the system has a diastereoselectivity of 1.8:1 for NN-4 : NX-4 , which is contrary to the 16:1 ratio claimed by Dieckmann et al. The analysis of ¹H NMR monitoring of the reaction revealed that both replicators show sigmoidal growth which is typical for auto-catalytic systems.     

Correction to: Characterization of essential oil from Matricaria sevanensis by microwave-assisted distillation

Journal of Thermal Analysis and Calorimetry - In the original publication of the article, peak numbers were not given in figure 4. The corrected figure 4 is given below.     

Restricted Modules and Conjectures for Modules of Constant Jordan Type

We introduce the class of restricted k[A]-modules and p ^t -Jordan types for a finite abelian p-group A of exponent at least p ^t and a field k of characteristic p. For these modules, we generalize several theorems by Benson, verify a generalization of conjectures stated by Suslin and Rickard giving constraints on Jordan types for modules of constant Jordan type when t is 1. We state conjectures giving constraints on p ^t -Jordan types and show that many p ^t -Jordan types are realizable.