Examination Timetabling: Algorithmic Strategies and Applications

Examination timetabling is an important operational problem in many schools, colleges and universities. The authors have developed a computerized examination timetabling system called EXAMINE. In this article several algorithmic strategies for this problem are investigated and compared. Computational results are reported on randomly generated problems and on some real problems.     

Upper bounds on the uniquely restricted chromatic index

Golumbic, Hirst, and Lewenstein define a matching in a simple, finite, and undirected graph to be uniquely restricted if no other matching covers exactly the same set of vertices. We consider uniquely restricted edge-colorings of , defined as partitions of its edge set into uniquely restricted matchings, and study the uniquely restricted chromatic index of , defined as the minimum number of uniquely restricted matchings required for such a partition. For every graph , where is the classical chromatic index, the acyclic chromatic index, and the strong chromatic index of . While Vizing's famous theorem states that is either the maximum degree of or , two famous open conjectures due to Alon, Sudakov, and Zaks, and to Erdős and Nešetřil concern upper bounds on and in terms of . Since is sandwiched between these two parameters, studying upper bounds in terms of is a natural problem. We show that with equality if and only if some component of is . If is connected, bipartite, and distinct from , and is at least , then, adapting Lovász's elegant proof of Brooks’ theorem, we show that . Our proofs are constructive and yield efficient algorithms to determine the corresponding edge-colorings.     

Diamagnetic susceptibility obtained from the six-vertex model and its implications for the high-temperature diamagnetic state of cuprate superconductors

We study the diamagnetism of the six-vertex model with the arrows as directed bond currents. To our knowledge, this is the first study of the diamagnetism of this model. A special version of this model, called the F model, describes the thermal disordering transition of an orbital antiferromagnet, known as d-density wave, a proposed state for the pseudogap phase of the high-T(c) cuprates. We find that the F model is strongly diamagnetic and the susceptibility may diverge in the high-temperature critical phase with power-law arrow correlations. These results may explain the surprising recent observation of a diverging low-field diamagnetic susceptibility seen in some optimally doped cuprates within the d-density wave model of the pseudogap phase.     

Proton-transfer reaction of 4-methyl 2,6-diformyl phenol in cyclodextrin nanocage

We report here on the steady-state and time-resolved fluorescence studies on proton-transfer (PT) reaction of 4-methyl 2,6-diformyl phenol (MFOH) in confined nanocavities in three solvents, dimethyl sulfoxide (DMSO), dimethyl formamide (DMF), and water. Though DMSO and DMF individually interact with MFOH in a similar fashion, their modes of interaction get significantly modified in the presence of cyclodextrin (CD) nanocages. In DMSO, in the ground state, the solvated molecular anion of MFOH forms 1:1 inclusion complex with beta- or gamma-CD and attains greater stability compared to the normal form. In DMF, the solvated molecular anion gets converted to the H-bonded complex within the CD cavity resulting in a 50-nm blue shift in the absorption spectra. In the excited state, the anionic species gets more stabilized in DMSO while in DMF it is significantly destabilized in the presence of CDs. However, in case of water, MFOH gets trapped inside the water cages so that the CDs fail to complex with it effectively. There are also no changes in the excited-state lifetimes in water in the presence of CDs, but in case of DMSO and DMF, because of restricted rotation of the formyl group within the CD cavity, the contribution of the shorter lifetime components reduce significantly increasing the larger components. Some theoretical calculations at the AM1 level of approximation have also been carried out to demonstrate how the dipolar nature of the solvent influences excited-state PT in confined media.     

Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs

We present subexponential parameterized algorithms on planar graphs for a family of problems of the following shape: given a graph, find a connected (induced) subgraph with bounded maximum degree and with maximum number of edges (or vertices). These problems are natural generalisations of the Longest Path problem. Our approach uses bidimensionality theory combined with novel dynamic programming techniques over branch decompositions of the input graph. These techniques can be applied to a more general family of problems that deal with finding connected subgraphs under certain degree constraints.     

Influence of ion–ion correlation on Na+ transport in Na2Ni2TeO6: molecular dynamics study

Molecular dynamics (MD) study of Na⁺ transport in Na₂Ni₂TeO₆ is performed systematically with varying strength of Na⁺–Na⁺ short range repulsions to understand the physical principle governing ion transport mechanism. Na⁺ diffusion is enhanced by nearly an order of magnitude with reduced Na⁺–Na⁺ short range repulsion within the studied range. A similar behavior is also observed in other systems, e.g., AgI and Na₂Zn₂TeO₆, where mobile ions are located closely. The Na⁺ ion occupancy in Na₂Ni₂TeO₆ shows a significant shift from Na1 to Na2 sites gaining some degree of correlation. The study also emphasizes how mobile ion size influences the ionic diffusion. The fresh insight such as microscopic migration pathways, energy barriers, and jumping mechanism of Na⁺ are derived from the study.     

A method of three-jet analysis ine + e − annihilation

For three-jet events ine ⁺ e ^? annihilation, a procedure is described to determine all three jet axes by minimizing the sum of squares of transverse momenta. Computations with this procedure show that at high energies the result is quite insensitive to missing particles, such as neurals.     

Synthesis of N-heterocycles via [4 + 3] cycloaddition of azomethine imine

Di, tri and tetra-nitrogen containing 7-membered heterocycles are the key building blocks for natural and medicinally active compounds. They are using as antidepressants, antiulcer, antibiotics, antiemetic and also used as herbicides and insecticides. These building blocks can be synthesized easily from [4 + 3] cycloadditon reaction of azomethine imine with the other suitable reacting partner. Research on this area is very much important as this area is not much explored till now. Hence, the synthetic literature survey towards the di-nitrogen containing heterocycles is paramount importance. Herein, we report numerous synthetic routes (metal catalyzed, metal free, asymmetric) of di-nitrogen containing 7-membered heterocycle through [4 + 3] cycloadditon reaction of the last 10 years (2011-2019).     

Electrophilic ruthenium(VI) nitrido complex containing Kläui's oxygen tripodal ligand

Treatment of [n-Bu4N][Ru(N)Cl4] with [AgL(OEt)] (L(OEt)- = [(eta5-C5H5)Co{P(O)(OEt)2}3]-) afforded the ruthenium(VI) nitrido complex [L(OEt)Ru(N)Cl2] (1), which reacted with PPh3 to give the ruthenium(IV) phosphiniminato complex [L(OEt)Ru(NPPh3)Cl2] (2). The cyclic voltammogram of 2 displays the RuIV/III couple at ca. 0 V vs ferrocenium/ferrocene. Treatment of 1 with Me3NO afforded [LOEtRu(NO)Cl2] (3), which reacted with Ag(OTf) (OTf- = triflate) to give the chloro-bridged tetranuclear ruthenium/silver complex [L(OEt)Ru(NO)Cl2]2[Ag(OTf)]2 (4). Treatment of 1 with Na2S2O3 gave the thionitrosyl complex [L(OEt)Ru(NS)Cl2] (5). The solid-state structures of 1-4 have been established by X-ray crystallography.     

Unprecedented chemical transformation of benzaldehyde semicarbazone mediated by osmium

para-Nitrobenzaldehyde semicarbazone (O(2)N(para)-C(6)H(4)C(H)=N-NH-CO-NH(2)) undergoes unprecedented chemical transformation during its reaction with [Os(PPh(3))(2)(CO)(2)(HCOO)(2)] in different alcoholic (R'OH, R' = CH(2)CH(2)OCH(3), CH(2)CH(3), CH(2)CH(2)CH(3), and CH(2)CH(2)CH(2)CH(3)) solvents whereby the NH(2) group of the semicarbazone ligand is displaced by a OR' group provided by the solvents. The transformed semicarbazone ligand binds to osmium as a bidentate N,O-donor forming five-membered chelate ring to afford complexes of type [Os(PPh(3))(2)(CO)(H)(L-OR')], where L-OR' refers to the transformed semicarbazone ligand. Structure of the [Os(PPh(3))(2)(CO)(H)(L-OCH(2)CH(2)OCH(3))] complex has been determined by X-ray crystallography. All the [Os(PPh(3))(2)(CO)(H)(L-OR')] complexes are diamagnetic and show characteristic (1)H NMR signals. They also show intense absorptions in the visible and ultraviolet region. Cyclic voltammetry on the complexes shows an irreversible oxidative response within 0.69-0.88 V versus SCE.