A Randomized Algorithm for 3-SAT

In this work we propose and analyze a simple randomized algorithm to find a satisfiable assignment for a Boolean formula in conjunctive normal form (CNF) having at most 3 literals in every clause. Given a k-CNF formula phi on n variables, and alpha in{0,1}^n that satisfies phi, a clause of phi is critical if exactly one literal of that clause is satisfied under assignment alpha. Paturi et. al. (Chicago Journal of Theoretical Computer Science 1999) proposed a simple randomized algorithm (PPZ) for k-SAT for which success probability increases with the number of critical clauses (with respect to a fixed satisfiable solution of the input formula). Here, we first describe another simple randomized algorithm DEL which performs better if the number of critical clauses are less (with respect to a fixed satisfiable solution of the input formula). Subsequently, we combine these two simple algorithms such that the success probability of the combined algorithm is maximum of the success probabilities of PPZ and DEL on every input instance. We show that when the average number of clauses per variable that appear as unique true literal in one or more critical clauses in phi is between 1 and 1.9317, combined algorithm performs better than the PPZ algorithm

Switching of ferroelectric liquid crystal doped with cetyltrimethylammonium bromide-assisted CdS nanostructures

Large scale high yield cadmium sulfide (CdS) nanowires with uniform diameter were synthesized using a rapid and simple solvo-chemical and hydrothermal route assisted by the surfactant cetyltrimethylammonium bromide (CTAB). Unique CdS nanowires of different morphologies could be selectively produced by only varying the concentration of CTAB in the reaction system with cadmium acetate, sulfur powder and ethylenediamine. We obtained CdS nanowires with diameters of 64–65 nm and lengths of up to several micrometers. A comparative study of the optical properties of ferroelectric liquid crystal (FLC) Felix-017/100 doped with 1% of CdS nanowires was performed. Response times of the order of from 160 to 180 μs, rotational viscosities of the order of from 5000 to 3000 mN s m−2 and polarizations of the order of from 10 to 70 nC cm−2 were measured. We also observed an anti-ferroelectric to ferroelectric transition for CdS doped FLC instead of the ferroelectric to paraelectric transition for pure FLC

Utilizing Reduced Graphene Oxide-Iron Nanoparticles Composite to Enhance and Accelerate the Removal of Methyl Blue Organic Dye in Wastewater

In this work, a nano-composite is used to remove dye from wastewater of different industries. For this purpose, thesynthesis of a magnetic 1:1 composite made of iron nanoparticles (NPs) using reduced graphene oxide is a novel techniqueand tested for Methyl Blue (MB) dye adsorption from aqueous solution. In this study Fe nanoparticles in reduced Graphenecomposite (FGOC) has been prepared using Graphene Oxide (GO). X-ray diffraction, FTIR spectroscopy and Ramanspectroscopy, are used to identify the structures. Many methods have been developed for MB removal in wastewater. One ofthe most popular methods is adsorption because it is simple and high-efficiency, and the adsorbent is crucial. It reached amaximum MB adsorption at pH 7. The kinetic study indicated that the adsorption of MB process was fitted well to thequasi-first-order and quasi-second-order kinetic models. The isotherm study revealed that the MB adsorption process obeyedthe Langmuir and Freundlich adsorption Isotherms models. The GO adding content and absorption conditions on the methylblue removal efficiencies were investigated. This adsorbent is easily recovered by an external magnetic field from thetreated wastewater and has high reusability

Unsteady nonlinear magnetohydrodynamic micropolar transport phenomena with hall and ion-slip current effects : numerical study

Unsteady viscous two-dimensional magnetohydrodynamic micropolar flow, heat and mass transfer from an infinite vertical surface with Hall and Ion-slip currents is investigated theoretically and numerically. The simulation presented is motivated by electro-conductive polymer (ECP) materials processing in which multiple electromagnetic effects arise. The primitive boundary layer conservation equations are transformed into a non-similar system of coupled non-dimensional momentum, angular momentum, energy and concentration equations, with appropriate boundary conditions. The resulting two-point boundary value problem is solved numerically by an exceptionally stable and welltested implicit finite difference technique. A stability analysis is included for restrictions of the implicit finite difference method (FDM) employed. Validation with a Galerkin finite element method (FEM) technique is included. The influence of various parameters is presented graphically on primary and secondary shear stress, Nusselt number, Sherwood number and wall couple stress. Secondary (cross flow) shear stress is strongly enhanced with greater magnetic parameter (Hartmann number) and micropolar wall couple stress is also weakl y enhanced for small time values with Hartmann number. Increasing thermo-diffusive Soret number suppresses both Nusselt and Sherwood numbers whereas it elevates both primary and secondary shear stress and at larger time values also increases the couple stress. Secondary shear stress is strongly boosted with Hall parameter. Ion slip effect induces a weak modification in primary and secondary shear stress distributions. The present study is relevant to electroconductive non-Newtonian (magnetic polymer) materials processing systems

On Exponential Time Algorithm for k-SAT

Abstract. In this work we present and analyze a simple algorithm for finding satisfying assignments of k-CNF (Boolean formulae in conjunctive normal form with at most k literals per clause). Our work is motivated by a simple question: Are there any structural property of the k-CNF which could help us to understand if a formula accepts isolated assignment? And can we deterministically find such isolated assignment if formula has one? In this work we show such a property exists in almost all non-trivial k-CNF formula, and we call it rigidity of a clause. Informally, rigidity of a clause can be defined to be how well connected a clause is to other clauses having same literals. If we satisfy a rigid clause for most of its literals then some of the variables are forced to take fixed values. Since, we can force such property and still get a satisfiable assignment; we save some of the decision paths in the algorithm and reduce its time complexity. Our main lemma shows that the number of branches in a depth n decision tree for k-CNF will be at least 2 n

Photoactivated TiO₂ Nanocomposite Delays the Postharvest Ripening Phenomenon through Ethylene Metabolism and Related Physiological Changes in <i>Capsicum</i> Fruit

Capsicum is one of the most perishable fruit which undergo rapid loss of commercial value during postharvest storage. In this experiment our aim is to evaluate the effect of photoactivated TiO2 nano-particle complexed with chitosan or TiO2-nanocomposite (TiO2-NC) on extension self-life of Capsicum fruit and its effect on related morphological, physiological and molecular attributes at room temperature (25 °C). Initially, TiO2-NC coated fruits recorded superior maintenance of total soluble solids accumulation along with retention of firmness, cellular integrity, hydration, color etc. On the extended period of storage, fruit recorded a lower bioaccumulation of TiO2 in comparison to metallic silver over the control. On the level of gene expression for ethylene biosynthetic and signaling the TiO2-NC had more regulation, however, discretely to moderate the ripening. Thus, ACC synthase and oxidase recorded a significantly better downregulation as studied from fruit pulp under TiO2-NC than silver. On the signaling path, the transcripts for CaETR1 and CaETR2 were less abundant in fruit under both the treatment when studied against control for 7 d. The reactive oxygen species (ROS) was also correlated to retard the oxidative lysis of polyamine oxidation by diamine and polyamine oxidase activity. The gene expression for hydrolytic activity as non-specific esterase had corroborated the development of essential oil constituents with few of those recorded in significant abundance. Therefore, TiO2-NC would be reliable to induce those metabolites modulating ripening behavior in favor of delayed ripening. From gas chromatography-mass spectrometry (GC-MS) analysis profile of all tested essential oil constituents suggesting positive impact of TiO2-NC on shelf-life extension of Capsicum fruit. Our results indicated the potentiality of TiO2-NC in postharvest storage those may connect ethylene signaling and ROS metabolism in suppression of specific ripening attributes