A New Lower Bound on the Maximum Number of Satisfied Clauses in Max-SAT and its Algorithmic Applications

A pair of unit clauses is called conflicting if it is of the form $(x)$, $(\bar{x})$. A CNF formula is unit-conflict free (UCF) if it contains no pair of conflicting unit clauses. Lieberherr and Specker (J. ACM 28, 1981) showed that for each UCF CNF formula with $m$ clauses we can simultaneously satisfy at least \pp m clauses, where \pp =(\sqrt{5}-1)/2. We improve the Lieberherr-Specker bound by showing that for each UCF CNF formula $F$ with $m$ clauses we can find, in polynomial time, a subformula $F'$ with $m'$ clauses such that we can simultaneously satisfy at least \pp m+(1-\pp)m'+(2-3\pp)n"/2 clauses (in $F$), where $n"$ is the number of variables in $F$ which are not in $F'$. We consider two parameterized versions of MAX-SAT, where the parameter is the number of satisfied clauses above the bounds $m/2$ and $m(\sqrt{5}-1)/2$. The former bound is tight for general formulas, and the later is tight for UCF formulas. Mahajan and Raman (J. Algorithms 31, 1999) showed that every instance of the first parameterized problem can be transformed, in polynomial time, into an equivalent one with at most $6k+3$ variables and $10k$ clauses. We improve this to $4k$ variables and $(2\sqrt{5}+4)k$ clauses. Mahajan and Raman conjectured that the second parameterized problem is fixed-parameter tractable (FPT). We show that the problem is indeed FPT by describing a polynomial-time algorithm that transforms any problem instance into an equivalent one with at most $(7+3\sqrt{5})k$ variables. Our results are obtained using our improvement of the Lieberherr-Specker bound above

Nonlinear Modulation of Multi-Dimensional Lattice Waves

The equations governing weakly nonlinear modulations of $N$-dimensional lattices are considered using a quasi-discrete multiple-scale approach. It is found that the evolution of a short wave packet for a lattice system with cubic and quartic interatomic potentials is governed by generalized Davey-Stewartson (GDS) equations, which include mean motion induced by the oscillatory wave packet through cubic interatomic interaction. The GDS equations derived here are more general than those known in the theory of water waves because of the anisotropy inherent in lattices. Generalized Kadomtsev-Petviashvili equations describing the evolution of long wavelength acoustic modes in two and three dimensional lattices are also presented. Then the modulational instability of a $N$-dimensional Stokes lattice wave is discussed based on the $N$-dimensional GDS equations obtained. Finally, the one- and two-soliton solutions of two-dimensional GDS equations are provided by means of Hirota's bilinear transformation method.Comment: Submitted to PR

Winglet design for vertical axis wind turbines based on a design of experiment and CFD approach

Vertical axis wind turbines (VAWTs) have been attracting an increasing attention in recent years because of their potential for effectively using wind energy. The tip vortices from the VAWT blades have a negative impact on the power efficiency. Since a winglet has been proved to be effective in decreasing the tip vortex in the aerospace field, this paper numerically studies the aerodynamic effect of appending a winglet on the blade of a VAWT. Based on the theoretical motion pattern of the VAWT blade, this paper simplifies the three-dimensional full-scale rotor simulation to a one-blade oscillating problem in order to reduce the computational cost. The full rotor model simulation is also used in validating the result. The numerical approach has been validated by the experimental data that is available in the open literature. Six parameters are applied in defining the configuration of the winglet. The orthogonal experimental design (OED) approach is adopted in this paper to determine the significance of the design parameters that affect the rotor’s power coefficient. The OED results show that the twist angle of the winglet is the most significant factor that affects the winglet’s performance. A range analysis of the OED results produces an optimal variable arrangement in the current scope, and the winglet’s performance in this variable arrangement is compared with the blade without a winglet. For the single blade study, the comparison result shows that the optimal winglet can decrease the tip vortices and improve the blade’s power performance by up to 31% at a tip speed ratio of 2.29. However, for the full VAWT case, the relative enhancement in the power coefficient is about 10.5, 6.7, and 10.0% for TSRs of 1.85, 2.29, and 2.52, respectively. The winglet assists in maintain the pressure difference between the two sides of the blade, thus weakening the tip vortex and improving the aerodynamic efficiency of the surface near the blade tip

Impacts of Global Solid Biofuel Stove Emissions on Ambient Air Quality and Human Health

Global solid biofuel stove emissions strongly impact air quality, climate change, and human health. However, investigations of the impacts of global solid biofuel stove emissions on human health associated with PM2.5 (particulate matter with aerodynamic diameter ≤2.5 μm) and ozone (O3) are limited. Here, we quantify the impacts of global solid biofuel stove emissions on ambient PM2.5 and O3 air quality and the associated human health effects for the year 2010, using the Community Atmosphere Model coupled with Chemistry version 5.3. Annual mean surface PM2.5 concentrations from global solid biofuel stove emissions averaged over 2006-2010 are up to 23.1 μg m-3, with large impacts found over China, India, sub-Saharan Africa, and eastern and central Europe. For surface O3 impacts, we find that global solid biofuel stove emissions lead to increases in surface O3 concentrations by up to 5.7 ppbv for China, India, and sub-Saharan Africa, and negligible impacts or reductions of up to 0.5 ppbv for the US, Europe, and parts of South America. Global solid biofuel stove emissions for the year 2010 contribute to 382,000 [95% confidence interval (95CI): 349,000-409,000] annual premature deaths associated with PM2.5 and O3 exposure, with the corresponding years of life lost as 8.10 million years (95CI: 7.38-8.70 million years). Our study highlights air quality and human health benefits of mitigating emissions from the global solid biofuel stove sector, especially over populous regions of low-income and middle-income countries, through promoting clean household energy programs for the residential energy supply

Baryon Tri-local Interpolating Fields

We systematically investigate tri-local (non-local) three-quark baryon fields with U_L(2)*U_R(2) chiral symmetry, according to their Lorentz and isospin (flavor) group representations. We note that they can also be called as "nucleon wave functions" due to this full non-locality. We study their chiral transformation properties and find all the possible chiral multiplets consisting J=1/2 and J=3/2 baryon fields. We find that the axial coupling constant |g_A| = 5/3 is only for nucleon fields belonging to the chiral representation (1/2,1)+(1,1/2) which contains both nucleon fields and Delta fields. Moreover, all the nucleon fields belonging to this representation have |g_A| = 5/3.Comment: 8 pages, 3 tables, accepted by EPJ

Self-Organized Criticality and Stock Market Dynamics: an Empirical Study

The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that the market is in a self-organized critical state (SOC). A wavelet transform method is used in order to separate high activity periods, related to the avalanches of sandpile models, from quiescent. A statistical analysis of the filtered data show a power law behaviour in the avalanche size, duration and laminar times. The memory process, implied by the power law distribution, of the laminar times is not consistent with classical conservative models for self-organized criticality. We argue that a ``near-SOC'' state or a time dependence in the driver, which may be chaotic, can explain this behaviour.Comment: 16 pages, 13 figures. In press: Physica

Noncommutative Dipole Field Theories And Unitarity

We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.Comment: typos corrected, more details added in Sec 5, version to appear in JHE

Observational constraints on holographic dark energy with varying gravitational constant

We use observational data from Type Ia Supernovae (SN), Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB) and observational Hubble data (OHD), and the Markov Chain Monte Carlo (MCMC) method, to constrain the cosmological scenario of holographic dark energy with varying gravitational constant. We consider both flat and non-flat background geometry, and we present the corresponding constraints and contour-plots of the model parameters. We conclude that the scenario is compatible with observations. In 1$\sigma$ we find $\Omega_{\Lambda0}=0.72^{+0.03}_{-0.03}$, $\Omega_{k0}=-0.0013^{+0.0130}_{-0.0040}$, $c=0.80^{+0.19}_{-0.14}$ and $\Delta_G\equiv G'/G=-0.0025^{+0.0080}_{-0.0050}$, while for the present value of the dark energy equation-of-state parameter we obtain $w_0=-1.04^{+0.15}_{-0.20}$.Comment: 12 pages, 2 figures, version published in JCA

Continuous twin screw rheo-extrusion of an AZ91D magnesium alloy

© The Minerals, Metals & Materials Society and ASM International 2012The twin screw rheo-extrusion (TSRE) is designed to take advantage of the nondendritc microstructure and thixotropic characterization of semisolid-metal slurries and produce simple metal profiles directly from melts. The extrusion equipment consists of a rotor-stator high shear slurry maker, a twin screw extruder, and a die assembly. The process is continuous and has a potential for significantly saving energy, manufacturing cost, and enhancing efficiency. The present investigation was carried out to study the process performance for processing rods of an AZ91D magnesium alloy and the microstructure evolution during processing. The semisolid slurry prepared by the process was characterized by uniformly distributed nondendritic granular primary phase particles. AZ91D rods with uniform and fine microstructures and moderate mechanical properties were produced. For the given slurry making parameters, decreasing extrusion temperature was found to improve microstructures and properties. The mechanisms of particle granulation and refinement and the effect of processing parameters on process performance and thermal management are discussed. © 2012 The Minerals, Metals & Materials Society and ASM International.EPSRC (UK) and Rautomead Lt