Vertex Cover Gets Faster and Harder on Low Degree Graphs

The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637(k) n(O(1)).

Role of degree of saturation in denitrification of unsaturated sand specimens

Nitrate contamination of groundwater arises from anthropogenic activities, such as, fertilizer and animal manure applications and infiltration of wastewater/leachates. During migration of wastewater and leachates, the vadose zone (zone residing above the groundwater table), is considered to facilitate microbial denitrification. Particle voids in vadose zone are deficient in dissolved oxygen as the voids are partially filled by water and the remainder by air. Discontinuities in liquid phase would also restrict oxygen diffusion and therefore facilitate denitrification in the vadose/unsaturated soil zone. The degree of saturation of soil specimen (S (r)) quantifies the relative volume of voids filled with air and water. Unsaturated specimens have S (r) values ranging between 0 and 100 %. Earlier studies from naturally occurring nitrate losses in groundwater aquifers in Mulbagal town, Kolar District, Karnataka, showed that the sub-surface soils composed of residually derived sandy soil; hence, natural sand was chosen in the laboratory denitrification experiments. With a view to understand the role of vadose zone in denitrification process, experiments are performed with unsaturated sand specimens (S (r) = 73-90 %) whose pore water was spiked with nitrate and ethanol solutions. Experimental results revealed 73 % S (r) specimen facilitates nitrate reduction to 45 mg/L in relatively short durations of 5.5-7.5 h using the available natural organic matter (0.41 % on mass basis of sand); consequently, ethanol addition did not impact rate of denitrification. However, at higher S (r) values of 81 and 90 %, extraneous ethanol addition (C/N = 0.5-3) was needed to accelerate the denitrification rates.

Influence of initial degree of saturation on swell pressures of compacted Barmer bentonite specimens

Densely compacted bentonite or bentonite-sand mixture has been identified as suitable buffer in deep geological repositories as its exceptionally high swelling capacity enables tight contact between the waste canister and surrounding rock. The degree of saturation of the compacted bentonite buffer can increase upon ingress of groundwater from the surrounding rock mass or decrease from evaporation due to high temperature (50-210 degrees C) derived from the waste canister. Available studies indicate that the influence of initial moisture content or degree of saturation on the swell pressure or swell potential of compacted bentonites is unclear. Some studies suggest that initial degree of saturation has an influence, while others suggest that it does not have bearing on the swell pressure of compacted bentonites. This paper examines the influence of initial degree of saturation in montmorillonite voids (termed,S-r,S-MF) on swell pressure of compacted Barmer bentonite-sand mixtures (dry density range: 1.4-2 Mg/m(3)) from micro-structural considerations. The experimental results bring out that, constant dry density specimens that developed similar number of hydration layers upon wetting developed comparable swell pressures and were unaffected by variations in initial S-r,S-MF values. Comparatively, constant dry density specimens that developed dis-similar number of hydration layers upon wetting established different swell pressures and were responsive to variations in initial S-r,S-MF. (C) 2015 Elsevier Ltd. All rights reserved.

SEPARATION DIMENSION OF BOUNDED DEGREE GRAPHS

The separation dimension of a graph G is the smallest natural number k for which the vertices of G can be embedded in R-k such that any pair of disjoint edges in G can be separated by a hyperplane normal to one of the axes. Equivalently, it is the smallest possible cardinality of a family F of total orders of the vertices of G such that for any two disjoint edges of G, there exists at least one total order in F in which all the vertices in one edge precede those in the other. In general, the maximum separation dimension of a graph on n vertices is Theta(log n). In this article, we focus on bounded degree graphs and show that the separation dimension of a graph with maximum degree d is at most 2(9) (log*d)d. We also demonstrate that the above bound is nearly tight by showing that, for every d, almost all d-regular graphs have separation dimension at least d/2]

MODELING AND SIMULATION OF A THREE-WHEELED MOBILE ROBOT ON UNEVEN TERRAINS WITH TWO-DEGREE-OF-FREEDOM SUSPENSION MECHANISMS

A wheeled mobile robot (WMR) will move on an uneven terrain without slip if its torus-shaped wheels tilt in a lateral direction. An independent two degree-of-freedom (DOF) suspension is required to maintain contact with uneven terrain and for lateral tilting. This article deals with the modeling and simulation of a three-wheeled mobile robot with torus-shaped wheels and four novel two-DOF suspension mechanism concepts. Simulations are performed on an uneven terrain for three representative pathsa straight line, a circular, and an S'-shaped path. Simulations show that a novel concept using double four-bar mechanism performs better than the other three concepts.

Three-degree-of-freedom Parallel Manipulator to Track the Sun for Concentrated Solar Power Systems

In concentrated solar power(CSP) generating stations, incident solar energy is reflected from a large number of mirrors or heliostats to a faraway receiver. In typical CSP installations, the mirror needs to be moved about two axes independently using two actuators in series with the mirror effectively mounted at a single point. A three degree-of-freedom parallel manipulator, namely the 3-RPS parallel manipulator, is proposed to track the sun. The proposed 3-RPS parallel manipulator supports the load of the mirror, structure and wind loading at three points resulting in less deflection, and thus a much larger mirror can be moved with the required tracking accuracy and without increasing the weight of the support structure. The kinematics equations to determine motion of the actuated prismatic joints in the 3-RPS parallel manipulator such that the sun's rays are reflected on to a stationary receiver are developed. Using finite element analysis, it is shown that for same sized mirror, wind loading and maximum deflection requirement, the weight of the support structure is between 15% and 60% less with the 3-RPS parallel manipulator when compared to azimuth-elevation or the target-aligned configurations.

A mobile robot with a two-degree-of-freedom suspension for traversing uneven terrain with minimal slip: Modeling, simulation and experiments

It is known in literature that a wheeled mobile robot (WMR) with fixed length axle will slip on an uneven terrain. One way to avoid wheel slip is to use a torus-shaped wheel with lateral tilt capability which allows the distance between the wheel-ground contact points to change even with a fixed length axle. Such an arrangement needs a two degree-of-freedom (DOF) suspension for the vertical and lateral tilting motion of the wheel. In this paper modeling, simulation, design and experimentation with a three-wheeled mobile robot, with torus-shaped wheels and a novel two DOF suspension allowing independent lateral tilt and vertical motion, is presented. The suspension is based on a four-bar mechanism and is called the double four-bar (D4Bar) suspension. Numerical simulations show that the three-wheeled mobile robot can traverse uneven terrain with low wheel slip. Experiments with a prototype three-wheeled mobile robot moving on a constructed uneven terrain along a straight line, a circular arc and a path representing a lane change, also illustrate the low slip capability of the three-wheeled mobile robot with the D4Bar suspension. (C) 2015 Elsevier Ltd. All rights reserved.

In-situ synthesized poly(vinyl butyral)/MMT-clay nanocomposites: The role of degree of acetalization and clay content on thermal, mechanical and permeability properties of PVB matrix

Poly(vinyl butyral) - MMT clay nanocomposites were synthesized in situ with three different degrees of acetalization and with varying clay content for each vinyl butyral polymer ratio. The clay nano-platelet galleries were expanded, as determined by X-ray diffraction and TEM analysis. The glass transition temperature of the polymer nanocomposites were found to be similar to 56 degrees C and similar to 52 degrees C for the neat polymer and the 4% clay loaded samples, respectively. The 4 wt% clay loaded film showed higher strength and low strain to failure. The dynamic mechanical analysis also confirmed the improved stability of the matrix. The matrix with 0.5 butyral to alcohol ratio for 4 wt% clay exhibited good water vapor transmission compared to all other compositions. The encapsulated devices with 2.5 and 4 wt% clay loaded films increases the device life time and the efficiencies of these films were 50% higher than their encapsulated pristine polymer films. (C) 2015 Elsevier Ltd. All rights reserved.

Lower Bounds for Sums of Powers of Low Degree Univariates

We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Omega(root d/t) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.

Identification of type and degree of railway ballast fouling using ground coupled GPR antennas

GPR is widely used for ballast fouling identification, however, there are no robust guidelines to find the degree and type of fouling quantitatively. In this study, GPR studies were carried out on model and actual railway tracks using three ground coupled antennas and considering three fouling materials. Three ground coupled antennas viz., 100 MHz, 500 MHz and 800 MHz antennas were used for the initial survey and it was found that the 800 MHz ground coupled antenna is an optimum one to get quality results. Three major fouling materials viz., screened/broken ballast, coal and iron ore were used to construct prototype model sections, which were 1/2 of the actual Indian broad-gauge railway track. A separate model section has been created for each degree and type of fouling and GPR surveys were carried out. GPR study shows that increasing the fouling content results in a decrease in the Electromagnetic Wave (EMW) velocity and an increase in the dielectric constant. EMW velocity of ballast fouled with screened ballast was found to be more than coal fouled ballast and iron ore fouled ballast at any degree of fouling and EMW velocity of iron ore fouled ballast was found to be less than coal and screen ballast fouled ballast. Dielectric constant of iron ore fouled ballast was found to be higher than coal and screen ballast fouled ballast for all degrees of fouling. Average slope of the trend line of screen ballast fouled section is low (25.6 degrees), coal fouled ballast is medium (27.8 degrees) and iron ore fouled ballast is high (47.6 degrees). (C) 2016 Elsevier B.V. All rights reserved.

Style and the “Idea” of the sophist after Plato : the impact of form typology on sophistic teaching and writing on interdisciplinary scholarly work

Resumen: Después de la primera sofística, los sofistas actuaron entre el resto de los pensadores del Mediterráneo como un grupo definido. Dado que hay muchos ejemplos que muestran que los sofistas ejercían sus prácticas y que también eran personas comprometidas en otras actividades, vamos a examinar aquí diversos casos de semejanzas y diferencias entre ellos y otros grupos de pensadores. Nuestras tres preguntas fundamentales son: qué, cómo y por qué los sofistas escribían y enseñaban. Intentaremos responder haciendo un análisis diacrónico de las principales formas y géneros de escritura que produjeron (qué). El cómo lo responderemos en su desenvolvimiento como una actividad comunicativa más allá de las fronteras de las disciplinas de la época. El por qué tendrá su respuesta al enfatizar la necesidad de la actividad de los sofistas en la socialización de la época y en la educación de la antigüedad. Al aseverar que el estilo era la idea de los sofistas, ponemos la noción de idea en Platón en el contexto de idea derivado de los sofistas contemporáneos a él y de los sofistas posteriores (segunda sofística) y centramos el foco en la función de visualidad expresada en su concepto de idea desde las obras sofísticas más tempranas en la época de Platón hasta las contribuciones posteriores.

The degree of predictability of earthquakes in several regions of China: statistical analysis of historical data

The stress release model, a stochastic version of the elastic-rebound theory, is applied to the historical earthquake data from three strong earthquake-prone regions of China, including North China, Southwest China, and the Taiwan seismic regions. The results show that the seismicity along a plate boundary (Taiwan) is more active than in intraplate regions (North and Southwest China). The degree of predictability or regularity of seismic events in these seismic regions, based on both the Akaike information criterion (AIC) and fitted sensitivity parameters, follows the order Taiwan, Southwest China, and North China, which is further identified by numerical simulations. (c) 2004 Elsevier Ltd. All rights reserved.

Joan Robinson Was Almost Right: Output under Third-Degree Price Discrimination

In this paper, we show that in order for third-degree price discrimination to increase total output, the demands of the strong markets should be, as conjectured by Robinson (1933), more concave than the demands of the weak markets. By making the distinction between adjusted concavity of the inverse demand and adjusted concavity of the direct demand, we are able to state necessary conditions and sufficient conditions for third-degree price discrimination to increase total output.