Pattern Hit-and-Run for sampling efficiently on polytopes

Pattern Hit-and-Run (PHR) is a Markov chain Monte Carlo sampler for a target distribution that was originally designed for general sets embedded in a box. A specific set of interest to many applications is a polytope intersected with discrete or mixed continuous/discrete lattices. PHR requires an acceptance/rejection mechanism along a bidirectional walk to guarantee feasibility. We remove this inefficiency by utilizing the linearity of the constraints defining the polytope, so each iteration of PHR can be efficiently implemented even though the variables are allowed to be integer valued. Moreover, PHR converges to a uniform distribution in polynomial time for a class of discrete polytopes.     

Selective and periodic inventory routing problem for waste vegetable oil collection

We consider a biodiesel production company that collects waste vegetable oil from source points that generate waste in large amounts. The company uses the collected waste as raw material for biodiesel production. The manager of this company needs to decide which of the present source points to include in the collection program, which of them to visit on each day, which periodic routing schedule to repeat over an infinite horizon and how many vehicles to operate such that the total collection, inventory and purchasing costs are minimized while the production requirements and operational constraints are met. For this selective and periodic inventory routing problem, we propose two different formulations, compare them and apply the better performing one on a real-world problem with 36 scenarios. We generate lower bounds using a partial linear relaxation model, and observe that the solutions obtained through our model are within 3.28% of optimality on the average. Several insights regarding the customer selection, routing and purchasing decisions are acquired with sensitivity analysis.     

Cobalt(II)/(III) complexes bearing a tetradentate thiosemicarbazone: Synthesis,experimental and theoretical characterization,and electrochemical and antioxidant properties

New cobalt complexes, Co1 and Co2 , were synthesized starting from acetylacetone-S-methylthiosemicarbazone. The square planar cobalt(II) and octahedral cobalt(III) complexes were characterized by FT-IR, UV–visible, ¹H NMR, and X-ray diffraction spectroscopies and mass spectrometry. Frontier orbitals of the complexes were theoretically obtained to better understand the complex structures and intermolecular interactions. The electrochemical behaviors of Co1 and Co2 were investigated and the results were evaluated by comparing with each other and with similar published compounds to determine their possible usage in various electrochemical technologies, such as energy storage devices, electrocatalysts, and electrosensors. Metal-based oxidation at around 0 V and metal-based reduction at around −1.0 V indicated that these complexes are valuable for the proposed applications. By determining the trolox equivalent antioxidant capacity and the radical scavenging activity of the cobalt complexes, the compatibility between the antioxidant qualification, redox, and theoretical calculation results was discussed.     

4‐Amino‐3,5‐diethyl‐4H‐1,2,4‐triazole at 100 K: chains of edge‐fused R44(10) and R44(20) rings

The title compound, C₆H₁₂N₄, has four crystallographically independent molecules in the asymmetric unit. Intermolecular N—H...N hydrogen bonds involving amino groups and triazole N atoms form a three‐dimensional framework involving R₄⁴(10) and R₄⁴(20) rings. The hydrogen bonding is supported by weak C—H...π interactions.     

Synthesis of new boron complexes: application to transfer hydrogenation of acetophenone derivatives

Two new boron complexes were synthesized from N‐[3‐(methylmercapto)aniline]‐3,5‐di‐tert‐butylsalicylaldimine ( LH ) with boron reagent BPh₃ or BF₃.Et₂O. These boron complexes are stable and easily soluble in protic solvents such as ethanol (C₂H₅OH) but hardly soluble in nonprotic solvents such as chloroform (CHCl₃), dichloromethane (CH₂Cl₂) and tetrahydrofuran (THF). All new boron complexes have been fully characterized by both analytical and spectroscopic methods. The catalytic activities of complexes [LBPh₂], 2 , and [LBF₂], 3 , in the transfer hydrogenation of acetophenone derivatives were tested. Stable boron complexes were found to be efficient catalysts in the transfer hydrogenation of aromatic ketones in good conversions up to 99% in the presence of iso‐PrOH/KOH. Copyright © 2011 John Wiley & Sons, Ltd.     

Convex graph invariant relaxations for graph edit distance

Mathematical Programming - The edit distance between two graphs is a widely used measure of similarity that evaluates the smallest number of vertex and edge deletions/insertions required to...     

Reinforcing thermosets with crystallizable solvents

This study demonstrates an approach to generate reinforcement in thermosetting polymers through crystal growth of crystallizable solvents. Emphasis is to identify the reaction conditions, which lead to suitable reinforcement in selected compounds. Crystallization behavior and miscibility of dimethylsulfone (DMS) in diglycidylether of bisphenol‐A epoxy monomer was investigated. Small angle laser scattering and optical microscopy were utilized to monitor phase separation and crystallization of DMS at different isothermal conditions during the cure process. It is shown that DMS crystals grow anisotropically to form faceted geometries and demonstrate possible structures to anchor into the epoxy matrix. The growth mechanism and the agility of crystals are shown to be affected by the cure reaction as well as depth of supercooling. A completely cured sample with 15 wt % DMS shows a broad map of rich morphologies from nanoscale particles to uniformly distributed macroscale, discontinuous fiber‐like crystals generated only by altering the curing conditions. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 840–849, 2010     

An effective approach for numerical solution of linear and nonlinear singular boundary value problems

In this study, an effective approach is presented to obtain a numerical solution of linear and nonlinear singular boundary value problems. The proposed method is constructed by combining reproducing kernel and Legendre polynomials. Legendre basis functions are used to get the kernel function, and then the approximate solution is obtained as a finite series sum. Comparison of numerical results is made with the results obtained by other methods available in the literature. Furthermore, efficiency and accuracy of the method are demonstrated in tabulated results and plotted graphs. The numerical outcomes demonstrate that our method is very effective, applicable, and convenient.     

On the Singular Set of Free Interface in an Optimal Partition Problem

We study the singular set of free interface in an optimal partition problem for the Dirichlet eigenvalues. We prove that its upper (n − 2) -dimensional Minkowski content, and consequently its (n − 2) -dimensional Hausdorff measure, are locally finite. We also show that the singular set is countably (n − 2) -rectifiable; namely, it can be covered by countably many C¹ -manifolds of dimension (n − 2) , up to a set of (n − 2) -dimensional Hausdorff measure zero. Our results hold for optimal partitions on Riemannian manifolds and harmonic maps into homogeneous trees as well. © 2019 Wiley Periodicals, Inc.