Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection

We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.     

Inverse Operators, q-Fractional Integrals, and q-Bernoulli Polynomials

We introduce operators of q-fractional integration through inverses of the Askey–Wilson operator and use them to introduce a q-fractional calculus. We establish the semigroup property for fractional integrals and fractional derivatives. We study properties of the kernel of q-fractional integral and show how they give rise to a q-analogue of Bernoulli polynomials, which are now polynomials of two variables, x and y. As q→1 the polynomials become polynomials in x−y, a convolution kernel in one variable. We also evaluate explicitly a related kernel of a right inverse of the Askey–Wilson operator on an L² space weighted by the weight function of the Askey–Wilson polynomials.     

On sieved orthogonal polynomials. VIII. Sieved associated Pollaczek polynomials

We study a general orthogonal polynomial set which includes the sieved associated ultraspherical and the sieved Pollaczek polynomials. This we get by letting q approach a root of unity in the recurrence relation and the generating functions of the associated q-ultraspherical and the Pollaczek polynomials. We find the weight functions with respect to which these polynomials are orthogonal and determine the asymptotic behavior of these polynomials on and off their interval of orthogonality.     

Synthesis of 1,3,4-thiadiazole, 1,3,4-thiadiazine, 1,3,6-thiadiazepane and quinoxaline derivatives from symmetrical dithiobiureas and thioureidoethylthiourea derivatives

Reactions of N,N;-disubstituted hydrazinecarbothioamides 8a-c and substituted thioureidoethylthioureas 9a-c with 2,3,5,6-tetrachloro-1,4-benzoquinone (chloranil, 10a) and 2,3,5,6-tetrabromo-1,4-benzoquinone (bromanil, 10b) to form N,N;-disubstituted [1,3,4]thiadiazole-2,5-diamines 11a-c, 6,7-dichloro-3-substituted amino-1H-benzo[1,3,4]- thiadiazine-5,8-diones 12a-c, 2,3,7,8-tetrahalothianthrene-1,4,6,9-tetraones 13a,b, 5,6,8- trihalo-7-oxo-3,7-dihydro-2H-quinoxaline-1-carbothioic acid substituted amides 14a-c, 15a-c and 7-substituted imino-[1,3,6]thiadiazepane-3-thiones 16a-c are reported. Rationales for the observed conversions are presented.     

Electro-adsorption of polyethyleneimine on the anion exchange membrane: Application to the nitrate removal from loaded solutions

Anion exchange membrane has been modified by fixation of polyethyleneimine. The modification has been carried out aiming to achieve a separation of anions according to their hydration radii and their sizes. The performances of the modified membranes were compared with the unmodified one by applying Donnan dialysis of nitrate ion using Cl⁻ in the strip compartment. The transfer of nitrate ions in the presence of chloride was enhanced by using immersion modified membrane. The presence of a thin layer of PEI on the strip side of the membrane improves Cl⁻ transference, by creating a chemical potential difference which increases the transfer.     

New reaction of ethenetetracarbonitrile with N-arylisoindolines

N-Arylisoindolines 1a-i react with ethenetetracarbonitrile 2 in aerated benzene by formation of [3-(2-aryl-3-dicyanomethylene-2,3-dihydro-1H-isoindol-1-ylidene)-2-aryl-2,3-dihydro-1H-isoindol-1-ylidene]propanedinitriles 8a-i (20-36%), N-aryl-3-dicyanomethylene-isoindol-2-ones 9a-i (15-21%) and N-arylphthalimides 10a-i (4-9%) as well as 1,1,2,2-tetracyanoethane 11 (35-55%). The structure of 8d has been unambiguously confirmed by a single crystal X-ray structure analysis. A rationale for the formation of products 8-11 is presented.     

Methyl imidazo[1,2-b]pyridazine-2-carbamates and related compounds as potential antifilarial agents

A series of imidazo[1,2-b]pyridazines have been synthesized for antifilarial evaluation. The compounds prepared include methyl 6-benzoylimidazo[1,2-b]pyridazine-2-carbamate ( 12 ), 6-benzoyl-2-t-butylimidazo[1,2-b]pyridazine ( 13 ), methyl 6-(4-fluorobenzoyl)imidazo[1,2-b]pyridazine-2-carbamate ( 14 ), and methyl 6-(2-thienylcarbonylcarbonyl)imidazo[1,2-b]pyridazine-2-carbamate ( 15 ) which are aza analogs of the anthelmintic agents mebendazole, flubendazole and nocadazole. In addition, the preparation of a series of 2-t-butylimidazo[1,2-b]-pyridazine-6-carboxylic acid derivatives is described. Electrophilic bromination and iodination substitutions of 2-t-butyl-6-methylimidazo[1,2-b]pyridazine afforded 3-halo derivatives. Methyl 6-(4-fluorobenzoyl)pyridazine-3-carbamate was also prepared for antifilarial evaluation. None of these compounds possessed significant antifilarial activity against Brugia pahangi or Acanthocheilonema viteae infections in jirds.     

A cluster of many small holes with negative imaginary surface impedances may generate a negative refraction index

We deal with the scattering of an acoustic medium modeled by an index of refraction n varying in a bounded region Ω of and equal to unity outside Ω. This region is perforated with an extremely large number of small holes D_m's of maximum radius a, a << 1, modeled by surface impedance functions. Precisely, we are in the regime described by the number of holes of the order M:=O(a^{β ? 2}), the minimum distance between the holes is d ～ a^t, and the surface impedance functions of the form λ_m～λ_m,0a^?β with β > 0 and λ_m,0 being constants and eventually complex numbers. Under some natural conditions on the parameters β,t, and λ_m,0, we characterize the equivalent medium generating approximately the same scattered waves as the original perforated acoustic medium. We give an explicit error estimate between the scattered waves generated by the perforated medium and the equivalent one, respectively, as a→0. As applications of these results, we discuss the following findings:

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Ultrafast Click Chemistry with Fluorosydnones

We report the synthesis and reactivity of 4‐fluorosydnones, a unique class of mesoionic dipoles displaying exquisite reactivity towards both copper‐catalyzed and strain‐promoted cycloaddition reactions with alkynes. Synthetic access to these new mesoionic compounds was granted by electrophilic fluorination of σ‐sydnone Pd^II precursors in the presence of Selectfluor. Their reactions with terminal and cyclic alkynes were found to proceed very rapidly and selectively, affording 5‐fluoro‐1,4‐pyrazoles with bimolecular rate constants up to 10⁴ m ^?1 s^?1, surpassing those documented in the literature with cycloalkynes. Kinetic studies were carried out to unravel the mechanism of the reaction, and the value of 4‐fluorosydnones was further highlighted by successful radiolabeling with [¹⁸F]Selectfluor.