Solving structured nonsmooth convex optimization with complexity $$\mathcal {O}(\varepsilon ^{-1/2})$$

This paper describes an algorithm for solving structured nonsmooth convex optimization problems using the optimal subgradient algorithm (OSGA), which is a first-order method with the complexity \(\mathcal {O}(\varepsilon ^{-2})\) for Lipschitz continuous nonsmooth problems and \(\mathcal {O}(\varepsilon ^{-1/2})\) for smooth problems with Lipschitz continuous gradient. If the nonsmoothness of the problem is manifested in a structured way, we reformulate the problem so that it can be solved efficiently by a new setup of OSGA (called OSGA-V) with the complexity \(\mathcal {O}(\varepsilon ^{-1/2})\). Further, to solve the reformulated problem, we equip OSGA-O with an appropriate prox-function for which the OSGA-O subproblem can be solved either in a closed form or by a simple iterative scheme, which decreases the computational cost of applying the algorithm for large-scale problems. We show that applying the new scheme is feasible for many problems arising in applications. Some numerical results are reported confirming the theoretical foundations.     

A computation study on an integrated alternating direction method of multipliers for large scale optimization

The alternating direction method of multipliers (ADMM) has recently received a lot of attention especially due to its capability to harness the power of the new parallel and distributed computing environments. However, ADMM could be notoriously slow especially if the penalty parameter, assigned to the augmented term in the objective function, is not properly chosen. This paper aims to accelerate ADMM by integrating that with the Barzilai–Borwein gradient method and an acceleration technique known as line search. Line search accelerates an iterative method by performing a one-dimensional search along the line segment connecting two successive iterations. We pay a special attention to the large-scale nonnegative least squares problems, and our experiments using real datasets indicate that the integration not only accelerate ADMM but also robustifies that against the penalty parameter.     

On the limitations of classical benchmark functions for evaluating robustness of evolutionary algorithms

Although evolutionary algorithms (EAs) have some operators which let them explore the whole search domain, still they get trapped in local minima when multimodality of the objective function is increased. To improve the performance of EAs, many optimization techniques or operators have been introduced in recent years. However, it seems that these modified versions exploit some special properties of the classical multimodal benchmark functions, some of which have been noted in previous research and solutions to eliminate them have been proposed.In this article, we show that quite symmetric behavior of the available multimodal test functions is another example of these special properties which can be exploited by some EAs such as covariance matrix adaptation evolution strategy (CMA-ES). This method, based on its invariance properties and good optimization results for available unimodal and multimodal benchmark functions, is considered as a robust and efficient method. However, as far as black box optimization problems are considered, no special trend in the behavior of the objective function can be assumed; consequently this symmetry limits the generalization of optimization results from available multimodal benchmark functions to real world problems. To improve the performance of CMA-ES, the Elite search sub-algorithm is introduced and implemented in the basic algorithm. Importance and effect of this modification is illustrated experimentally by dissolving some test problems in the end.     

A DFT study of carbon monoxide adsorption on a Si4 nano-cluster

Using the gradient-corrected hybrid density functional method of Predew, Burke, and Ernzerhof (PBEPBE) and the new hybrid meta-density functional method of Truhlar (MPW1B95), the geometry, adsorption energy, vibrational frequency, and charge distribution of carbon monoxide adsorption on a Si₄ nano-cluster has been studied. Taking into account spin multicipility in the calculations, a new stable structure of CO absorbed on the Si₄ cluster has been found, in addition to the previously reported structures. Exhaustive vibrational frequency analysis of optimized structures shows that some of the formerly reported structures have imaginary vibrational frequencies and are not proper stable structures. Thus, they do not represent real local energy minima. Also, CO vibrational frequency analysis shows that a significant change of vibrational frequency in the stable structures occurs.     

Sonochemical synthesis of silver vanadium oxide micro/nanorods: Solvent and surfactant effects

In this investigation, a facile sonochemical route has been developed for the preparation of silver vanadium oxide (SVO) micro/nanorods by using silver salicylate and ammonium metavanadate as silver and vanadate precursor, respectively. Here, silver salicylate, [Ag(HSal)], is introduced as a new silver precursor to fabricate AgVO₃ nanorods. The effect of numerous solvents and surfactants on the morphology and sonochemical formation mechanism of AgVO₃ nanorods was studied. AgVO₃ nanorods were characterized by SEM and TEM images, XRD patterns, FT-IR, XPS, and EDS spectroscopy. SEM, TEM, and XRD results showed that AgO nanoparticles were formed onto AgVO₃ nanorods in the presence of ethanol, cyclohexanol, dimethylsulfoxide (DMSO), and acetone. By using polyethylene glycol (PEG-6000) and N,N-dimethylformamide (DMF) as organic additives, the thickness of AgVO₃ nanorods decreased.     

Residual stress delaying phase transformation in Y-TZP bio-restorations

Engineering favorable residual stress for the complex geometry of bi-layer porcelain-zirconia crowns potentially prevents crack initiation and improves the mechanical performance and lifetime of the dental restoration. In addition to external load, the stress field depends on initial residual stress before loading. Residual stress is the result of factors such as the thermal expansion mismatch of layers and compliance anisotropy of zirconia grains in the process of sintering and cooling. Stress induced phase transformation in zirconia extensively relaxes the residual stress and changes the stress state. The objective of this study is to investigate the coupling between tetragonal to monoclinic phase transformations and residual stress. Residual stress, on the surface of the sectioned single load to failure crown, at 23 points starting from the pure tetragonal and ending at a fully monoclinic region were measured using the micro X-ray diffraction sin² ψ method. An important observation is the significant range in measured residual stress from a compressive stress of ?400?MPa up to tensile stress of 400?MPa and up to 100% tetragonal to monoclinic phase transformation.     

Spectral Studies On Some 2-Quinolones

Spectral properties of some 2-Quinolones were investigate-ed. IR and ¹H NMR were applied to characterize the ligands. The hydrogen bond property is of important parameter for controlling the behaviour of the compounds. The N[sbnd]H, O[sbnd]H, C[dbnd]O, C[sbnd]H, and C[sbnd]N fundamental functional groups are characterized. The electronic transitions are assigned. The data are explained on the basis of molecular structure and substituents effects. The acid-base equilibria and the phenomena of tautomerism for these compounds are explained and discussed. The acid exponents (pK_OH, and pK_NH) are evaluated.     

Weyl’s Law and Connes’ Trace Theorem for Noncommutative Two Tori

We prove the analogue of Weyl’s law for a noncommutative Riemannian manifold, namely the noncommutative two torus ${\mathbb{T}_{\theta}^{2}}$ equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is achieved by studying the asymptotic distribution of the eigenvalues of the perturbed Laplacian on ${\mathbb{T}_{\theta}^{2}}$ . We also prove the analogue of Connes’ trace theorem by showing that the Dixmier trace and a noncommutative residue coincide on pseudodifferential operators of order ?2 on ${\mathbb{T}_{\theta}^{2}}$ .     

An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates

An analytical solution based on a new exact closed form procedure is presented for free vibration analysis of stepped circular and annular FG plates via first order shear deformation plate theory of Mindlin. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. Based on the domain decomposition technique, five highly coupled governing partial differential equations of motion for freely vibrating FG plates were exactly solved by introducing the new potential functions as well as using the method of separation of variables. Several comparison studies were presented by those reported in the literature and the FEM analysis, for various thickness values and combinations of stepped thickness variations of circular/annular FG plates to demonstrate highly stability and accuracy of present exact procedure. The effect of the geometrical and material plate parameters such as step thickness ratios, step locations and the power law index on the natural frequencies of FG plates is investigated.     

Quasi Co-Hopfian Modules and Applications

We carry out an extensive study of modules M _R with the property that M/f(M) is singular for all injective endomorphisms f of M. Such modules called “quasi co-Hopfian”, generalize co-Hopfian modules. It is shown that a ring R is semisimple if and only if every quasi co-Hopfian R-module is co-Hopfian. Every module contains a unique largest fully invariant quasi co-Hopfian submodule. This submodule is determined for some modules including the semisimple ones. Over right nonsingular rings several equivalent conditions to being quasi co-Hopfian are given. Modules with all submodules quasi co-Hopfian are called “completely quasi co-Hopfian” (cqcH). Over right nonsingular rings and over certain right Noetherian rings, it is proved that every finite reduced rank module is cqcH. For a right nonsingular ring which is right semi-Artinian (resp. right FBN) the class of cqcH modules is the same as the class of finite reduced rank modules if and only if there are only finitely many isomorphism classes of nonsingular R-modules which are simple (resp. indecomposable injective).