Single Straight Line Research Articles

Mechanical properties and drug release of venlafaxine HCl solid mini matrices prepared by hot-melt extrusion and hot or ambient compression

Objective/significance: To elucidate the role of plasticizers in different mini matrices and correlate mechanical properties with drug release.Methods: Cylindrical pellets were prepared by hot-melt extrusion (HME) and mini tablets by hot (HC) and ambient compression (AC). Venlafaxine HCl was the model drug, Eudragit® RSPO the matrix former and citric acid or Lutrol® F127 the plasticizers. The matrices were characterized for morphology, crystallinity, and mechanical properties. The influence of plasticizer’s type and content on the extrusion pressure (Pe) during HME and ejection during tableting was examined and the mechanical properties were correlated with drug release parameters.Results: Resistance to extrusion and tablet ejection force were reduced by Lutrol® F127 which also produced softer and weaker pellets with faster release, but harder and stronger HC tablets with slower release. HME pellets showed greater tensile strength (T) and 100 times slower release than tablets. Pe correlated with T and resistance to deformation of the corresponding pellets (r2 = 0.963 and 0.945). For both HME and HC matrices the decrease of drug release with T followed a single straight line (r2 = 0.990) and for HME the diffusion coefficient (De) and retreat rate constant (kb) decreased linearly with T (r2 = 0.934 and 0.972).Conclusions: Lutrol® F127 and citric acid are efficient plasticizers and Lutrol® F127 is a thermal binder/lubricant in HC compression. The different bonding mechanisms of the matrices were reflected in the mechanical strength and drug release. Relationships established between T and drug release parameters for HME and HC matrices may be useful during formulation work.

A PRELIMINARY WORK ON LAYOUT SLAM FOR RECONSTRUCTION OF INDOOR CORRIDOR ENVIRONMENTS

Abstract. We propose a real time indoor corridor layout estimation method based on visual Simultaneous Localization and Mapping (SLAM). The proposed method adopts the Manhattan World Assumption at indoor spaces and uses the detected single image straight line segments and their corresponding orthogonal vanishing points to improve the feature matching scheme in the adopted visual SLAM system. Using the proposed real time indoor corridor layout estimation method, the system is able to build an online sparse map of structural corner point features. The challenges presented by abrupt camera rotation in the 3D space are successfully handled through matching vanishing directions of consecutive video frames on the Gaussian sphere. Using the single image based indoor layout features for initializing the system, permitted the proposed method to perform real time layout estimation and camera localization in indoor corridor areas. For layout structural corner points matching, we adopted features which are invariant under scale, translation, and rotation. We proposed a new feature matching cost function which considers both local and global context information. The cost function consists of a unary term, which measures pixel to pixel orientation differences of the matched corners, and a binary term, which measures the amount of angle differences between directly connected layout corner features. We have performed the experiments on real scenes at York University campus buildings and the available RAWSEEDS dataset. The incoming results depict that the proposed method robustly performs along with producing very limited position and orientation errors.

LONG-TERM OUTCOMES AND INCIDENCE OF RECURRENCE OF NEOVASCULARIZATION IN TREATED EXUDATIVE AGE-RELATED MACULAR DEGENERATION.

To assess the long-term visual outcome and incidence of recurrence of neovascular age-related macular degeneration (NAMD) treated with intravitreal anti-VEGF injections (IVAI). One hundred and thirty-two consecutive eyes treated with IVAI for NAMD based on an as-needed regimen with a follow-up ≥5 years (mean 7.55, range 5-9.67) were retrospectively reviewed. Main outcome measures included visual acuity, yearly number of IVAI, and occurrence of a long-term remission, defined as no recurrence of NAMD for ≥12 consecutive months. Mean baseline visual acuity was 20/100. Mean final visual acuity change was -3.41 letters. Mean overall IVAI number was 22.8 ± 17.4 (range 2-71), decreasing from 4.6 during Year 1 to 2.21 during Year 8. A significant positive correlation was found between the number of IVAI during the first year of treatment and the overall number of IVAI during 5 years, 6 years, 7 years, or 8 years follow-up (r = 0.67-0.70, P <0.0001). Long-term remission occurred at least once in 83/132 eyes (63%) and was associated with a better visual outcome (-1.04 vs. -7.43 letters, P = 0.034). Incidence of yearly remission of NAMD increased from 28% during Year 2 to 59% during Year 8, fitting along a single straight line (+5.231%/year, R = 0.9511). The incidence of recurrence of treated NAMD decreases slowly but steadily during follow-up. The number of years of follow-up is the main factor to assess the proportion of treated eyes at remission at a given moment. Incidence of recurrence of neovascularization during year 1 and length of follow-up are significant factors when tailoring an optimal long-term follow-up regimen.

Metal inhibition on the reactivity of manganese dioxide toward organic contaminant oxidation in relation to metal adsorption and ionic potential

Coexisting metal ions may significantly inhibit the oxidative reactivity of manganese oxides toward organic contaminants in metal-organic multi-pollutant waters. While the metal inhibition on the oxidation of organic contaminants by manganese oxides has previously been reported, the extent of the inhibition in relation to metal properties has not been established. Six alkali, alkaline, and transition metals, as well as two testing metals were evaluated for their abilities to inhibit the reactivity of birnessite. Regardless of the pathways of phenol and diuron oxidation (polymerization vs. breakdown), the extent of metal inhibition depended mainly on the metal itself and its concentration. The observed metal inhibition efficiency followed the order of Mn2+ > Co2+ > Cu2+ > Al3+ > Mg2+ > K+, consistent with metal adsorption on birnessite. The first-order organic oxidation rate constant (kobs) was linearly negatively correlated with metal adsorption (qe) on birnessite. These observations demonstrated that the metal inhibition efficiency was determined by metal adsorption on birnessite. The slopes of the kobs-qe varied among metals and followed the order of K+ > Ca2+ > Mg2+ > Mn2+ > Cd2+ > Co2+ > Cu2+ > Al3+. These slopes defined intrinsic inhibitory abilities of metals. As metals were adsorbed hydrated on birnessite, the intrinsic inhibitory ability was significantly linearly correlated with ionic potentials of metals, leading to a single straight line. Metals with multiple d electrons in the outermost orbit with polarizing energy that promotes hydrolysis sat slightly below the line, and vice versa.

A Material-Balance Equation for Stress-Sensitive Shale-Gas-Condensate Reservoirs

Summary During the last few years, production of liquid hydrocarbons has been reported from the gas-condensate window of the Eagle Ford, Barnett, Niobrara, and Marcellus shale plays in the US. This paper presents a new material-balance equation (MBE) for estimation of original gas in place (OGIP) and original condensate in place (OCIP) in shale-gas-condensate reservoirs. This material-balance methodology allows estimating the critical time for implementing gas injection in those cases in which condensate buildup represents a problem. In addition, the proposed MBE considers the effects of free, adsorbed, and dissolved gas-condensate production, and also takes into account the stress-dependency of porosity and permeability. An extension of the methodology is implemented for estimating the optimum time for hydraulically refracturing shale-condensate reservoirs. The new MBE applies to shale-gas-condensate reservoirs by incorporating a two-phase gas-deviation factor (Z2) and total cumulative gas production (Gpt) that includes both gas and condensate. If a crossplot of P/Z2 (pressure/Z2) vs. Gpt is prepared for a conventional gas-condensate reservoir, a single straight line is obtained. However, when the single-phase gas-compressibility factor (Z) is used, a deviation from the linear behavior is observed after the reservoir pressure falls below the gas dewpoint. This methodology is applied in this study to unconventional shale-gas condensate. Because there are three characteristic stages of production in a shale-gas reservoir (production of free, adsorbed, and dissolved gas), the location of the aforementioned deviation will provide a hint of the production stage that will be affected by condensate buildup. For example, if the deviation point is in the region where production of free gas is predominant, then the production caused by desorption mechanisms will be negatively affected because condensation will have already occurred in the reservoir, resulting in reduction of effective permeability to gas. This methodology then allows estimating the critical time for implementing gas injection on the basis of the total cumulative gas production. The method also permits estimating the optimum time for refracturing. The refracturing can be of a normal size for a given shale (similar to the original fracturing job), or it can be a superfrac job. Results are presented as crossplots of (1) P/Z2 vs. Gpt, (2) Gpt vs. time, and (3) gas rate vs. time. It is concluded that estimation of the critical time for implementing gas injection is useful for improving the performance of those shale-gas-condensate reservoirs in which condensate buildup represents a threat that can negatively affect the gas-production rate. The novelty of this work resides on the fact that the combined effect of free, adsorbed, and dissolved gas-production mechanisms on stress-sensitive shale-gas-condensate reservoirs had not been considered previously in the literature for estimation of OGIP, OCIP, and reservoir performance with an analytical MBE. The inclusion of gas injection and refracturing had not been considered either.

Hydrodynamic lubricating characteristics of water flooded single screw compressors based on two types of meshing pair profile

Reliability of the traditional single screw compressor (SSC) is poor since its discharge capacity decreases sharply. This is because that the lubrication between the screw and the gate-rotor meshing pair is poor, which leads to a rapid abrasion of the meshing pair. In this paper, a simulation model is established to analyze the lubrication problem of the meshing pair in the SSC. Based on the traditional single straight line enveloped meshing pair profile and the new proposed multi-columns-enveloped meshing pair profile, the hydrodynamic lubricating characteristics of the water-flooded single screw compressor are investigated. Results show that the water film can keep the gate-rotor tooth from contacting the screw thread flank during the meshing process in the optimized multi-columns-enveloped meshing pair, but the water film cannot keep the gate-rotor tooth from contacting the screw thread flank during the meshing process in the single straight line enveloped meshing pair. A prototype of the water flooded SSC with the optimized multi-columns-enveloped meshing pair was developed and has passed a 2000-h endurance test without discharge capacity reduction.

Jet Flight Patterns of Linear Shaped Charges

A typical jet flight pattern of linear shaped charges (LSCs) is studied, and analytical expressions are built for two important parameters of the angle of liner collapse line φ and jet projection angle ω. In order to simplify the nonlinear nature of the liner collapse behavior of LSCs, important assumptions are made, including (1) a constant jet projection velocity at the given standoff distance and (2) the liner collapse occurs in a steady-state fashion, generating a single straight collapse line during the detonation. Based on the assumptions, analytical expressions are derived and the result is compared with side-view images of LSC jet flight to evaluate accuracy and applicability. The analytical approach delivers reasonable accuracy in a given range and is applicable to a short range of standoff distances.

A Novel Monolithic MILP Framework for Lot-Sizing and Scheduling of Multiproduct Treelike Pipeline Networks

Detailed scheduling of long-distance multiproduct pipelines has received growing attention in the past few years. It helps the planner to reduce the number of pump and segment switches between active and idle conditions to obtain savings on pump operating and maintenance costs. Most contributions on the detailed scheduling of multiproduct pipelines concern networks with a single straight line. Large-scale pipeline networks, however, usually have a treelike configuration, featuring a mainline and several secondary lines, transporting smaller volumes of refined petroleum products over shorter distances. This work addresses the scheduling of a multiproduct treelike pipeline through a continuous-time mixed integer linear programming (MILP) model that allows the execution of simultaneous deliveries from a unique refinery to multiple downstream terminals so as to get a substantial increase in transportation capacity. Contrary to previous contributions on treelike pipeline systems, the new model solves batch siz...

Two-point gauge invariant quark Green's functions with polygonal phase factor lines

Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-Nc limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions.

Corrective Self Defence Training Unit using sensing of Kinect Maps

In the sports fields and technology, the accuracy of an athlete can never be monitored with 100% accuracy with naked eyes. Moves that are done by an athlete or a sports person in the game such as his stride length and the stride frequency cannot be easily seen by a person and hence, detection and correction of the minute mistakes that are being made are overlooked. For instance, while doing push-ups a person‟s head, neck, waist and ankle should be in a single straight line. In this paper, we discuss a sports training system which uses Microsoft Kinect for motion sensing. The infrared depth stream translates the presence of a user in real world, into digital space by tracking his/her joint coordinates. As per our empirical studies, Kinect maps the x,y and z coordinates of 20 primary joints of the body. This data forms the basis of our calculations as elaborated in the literature. This work gives a basis of how movements and postures may be corrected by the use of sensors like Kinect in an effective and efficient manner. General Terms Kinect, Motion Sensing, Sports, Training, Sports Training, Gestures, HMM.

Possible number systems

Number systems-such as the natural numbers, integers, rationals, reals, or complex numbers-play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people's concept of a number system by asking them whether "number lines" of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms' ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).

On the 1/f noise in the UV solar spectral irradiance

A major shortcoming of many climate studies on long-range dependence is the inference of long-term memory from climate data without considering that the power-law scaling needs to be established and a simple exponential decay of the autocorrelation function has to be rejected (Efstathiou and Varotsos 2010; Maraun et al. 2004; Varotsos 2005a; Varotsos and Kirk-Davidoff 2006; Varotsos et al. 2003a, b, 2005, 2006, 2007, 2008, 2009, 2013). Very recently, Varotsos et al. (2013), studying the highresolution observations of the spectral solar incident flux (SIF) reaching the ground and the top of the atmosphere, concluded that SIF versus ultraviolet wavelengths (WL) exhibit 1/f-type power-law correlations. This result was based on the slope (i.e., 1.02±0.02) of the log–log plot of the root mean square fluctuation function Fd(τ) of SIF versus the WL segment size τ, after the application of the detrended fluctuation analysis (DFA). However, the reader of the paper by Varotsos et al. (2013) may argue that the afore-mentioned power-law scaling should be established by employing the two criteria suggested by Maraun et al. (2004), notably the rejection of the exponential decay of the autocorrelation function and the constancy of “local slopes” in a certain range towards the low frequencies. In this respect, we herewith plot the profile of the power spectral density (i.e., the distribution of the variance over frequency) versus logτ for the detrended SIF-WL data set (depicted in Fig. 1a). This plot shows that in a WL scale range from logτ≈0.3 (given that the measurement step is 0.05, the value of τ≈10×0.05≈0.1 nm) to maximally logτ≈1.46 (τ≈10×0.05≈1.4 nm), the power spectral density is better fitted exponentially, while for larger scales, it turns into an algebraically (power-law) fit (i.e., satisfying thus the first criterion of Maraun et al. (2004) for the rejection of the exponential fit). On the other hand, we apply the method of local slopes, suggested by Maraun et al. (2004), in order to examine the establishment of the 1/f noise in the UV solar spectral irradiance. Since the single straight line of the DFA plot for the detrended SIF-WL data set that established in the whole range of scales may be biased, we evaluate the local slopes of logFd(τ) versus logτ detecting for constancy in a sufficient range. Along these lines, we first fit a straight line to logFd(τ) versus logτ within a specific window of WL scale range. This window is then shifted successively over all calculated scales τ. At this point, it should be noted that Maraun et al. (2004) state verbatim: “Choosing the optimal window size, one has to trade bias for variance: For small windows, the bias is small, but the variability renders the interpretation difficult, whereas for large windows, the variance is reduced at the cost of a biased estimate of a.” Figure 1b illustrates the local slope a versus logτ for two different window sizes. In addition, we compute the standard deviations, sa, of each estimated local slope over all the scales, along with the error bounds of each local slope a, defined as a±1.96⋅sa. Inspection of Fig. 1b shows that for small scales, the variance of the local slopes is low, while for large scales, the variance is increased with a values reaching to a constant threshold (a≈0.92) at a range that coincides with that in Fig. 1a, where the power-law behavior prevails (establishing thus the long-range dependence). Similar results were obtained by considering other windows. C. A. Varotsos (*) :M. N. Efstathiou :C. Tzanis Climate Research Group, Division of Environmental Physics and Meteorology, Faculty of Physics, University of Athens, University Campus Bldg. Phys. V, Athens 15784, Greece e-mail: covar@phys.uoa.gr

Comparison of three methods of cervical measurement in the first trimester: single‐line, two‐line, and tracing

To compare three methods of cervical length measurements using ultrasound in the first trimester: single-line, two-line, and tracing. Images appropriate for cervical length measurements were obtained using transvaginal ultrasound between 11 + 0 and 13 + 6 weeks' gestation. The cervix was measured on stored images using three methods: a single straight line, two segments (two-line method), and by tracing the distance along the cervical canal. Results were compared for intraoperator repeatability and interoperator variability. The degree of the cervical curvature was measured. The mean cervical measurement using the single-line measurement was 32.8 (SD 4.4) mm. The mean cervical length was essentially the same using the two-line and tracing measurement: 34.4 (SD 4.7) mm and 34.5 (SD 4.7) mm, respectively. Both intra- and interoperator agreement was high. The degree of curvature of the cervical canal was variable, with a resultant variability in the difference between the single straight line measurement and the other two types of measurement. Using stored images, each of the measurement techniques is highly reproducible. Both the two-line and the tracing methods yield larger measurements than the single-line technique. Therefore, it appears that in select cases the straight line measurement significantly underestimates the actual cervical length.

An EIRP Measurement Method for Base-Station Antennas Using Field Strengths Measured along a Single Straight Line

We describe an EIRP measurement technique for a base-station antenna. The proposed method especially can be applied to the base-station antenna installed in real environments. Fresnel region measurement method is an optimal technique to avoid the far-field multipath interference, and, furthermore, it could shorten the measurement time. For detecting only the field strengths along a single straight line, we also propose a simple phase-retrieval method. For verification, a simulation and experiment have been performed. An anechoic chamber was utilized in this paper before the real environment test with the outdoor measurement system. The transformed far-field pattern and EIRP agree closely with the reference data within a valid angle. The proposed method can be applied for the EIRPin situmeasurements without moving a vehicle loading the EIRP measurement apparatus.

Contrast sensitivity of pattern transient VEP components: Contribution from M and P pathways.

The purpose of this study was to compare contrast sensitivity estimated from transient visual evoked potentials (VEPs) elicited by achromatic pattern-reversal and pattern-onset/offset modes. The stimuli were 2-cpd, achromatic horizontal gratings presented either as a 1 Hz pattern reversal or a 300 ms onset/700 ms offset stimulus. Contrast thresholds were estimated by linear regression to amplitudes of VEP components vs. the logarithm of the stimulus contrasts, and these regressions were extrapolated to the zero amplitude level. Contrast sensitivity was defined as the inverse of contrast threshold. For pattern reversal, the relation between the P100 amplitude and log of the stimulus contrast was best described by two separate linear regressions. For the N135 component, a single straight line was sufficient. In the case of pattern onset/offset for both the C1 and C2 components, single straight lines described their amplitude vs. log contrast relations in the medium-to-low contrast range. Some saturation was observed for C2 components. The contrast sensitivity estimated from the low-contrast limb of the P100, from the N135, and from the C2 were all similar but higher than those obtained from the high-contrast limb of the P100 and C1 data, which were also similar to each other. With 2 cpd stimuli, a mechanism possibly driven by the M pathway appeared to contribute to the P100 component at medium-to-low contrasts and to the N135 and C2 components at all contrast levels, whereas another mechanism, possibly driven by the P and M pathways, appeared to contribute to the P100 component at high contrast and C1 component at all contrast levels.

Analysis of an Active Fault Geometry Using Satellite Sensor and DEM Data: Gazik&amp;#246;y-Saros Segment (NAFZ), Turkey

In this study, Landsat 5 Thematic Mapper (TM) and SPOT HRV Panchromatic data were analysed to determine the geometry of an active fault segment (the Ganos segment) in Gazikoy-Saros region, west of Marmara Sea, Turkey. Gazikoy-Saros/Ganos segment is a part of North Anatolian Fault Zone (NAFZ). North-Anatolian fault is considered to be one of the most important active strike-slip faults in the world. Thus far in relevant researches based on Gazikoy-Saros segment a single straight fault line representation is used on the fault descriptive geological maps. This study, with the aid of enhanced remotely sensed data aims to reveal the linear details of the NAFZ fault segment, which subsequently were superposed with a Digital Elevation Model (DEM) data. Respectively, using these data the surface geometry expression of Gazikoy-Saros fault segment was detailed and remapped. According to the results of the analysis two small releasing steps were identified on this segment. The first one is situated between Mürseli and Güzelkoy villages, and the second one is between Mürseli and Yorguc villages. In addition to this, it is found that the fault strike bends approximately 7° further to in south-eastern (SE) direction between Yenikoy and Sofular villages. This angular change was defined with the advantage of multi-angular viewing capability of the multi-satellite sensors and DEM data. The newly generated surface geometry expression of Ganos segment was compared with Global Positioning System (GPS) velocity vectors.

Straight contact lines on a soft, incompressible solid

The deformation of a soft substrate by a straight contact line is calculated, and the result applied to a static rivulet between two parallel contact lines. The substrate is supposed to be incompressible (Stokes-like description of elasticity), and having a non-zero surface tension, that eventually differs depending on whether its surface is dry or wet. For a single straight line separating two domains with the same substrate surface tension, the ridge profile is shown to be very close to that of Shanahan and de Gennes, but shifts from the contact line of a distance equal to the elastocapillary length built upon substrate surface tension and shear modulus. As a result, the divergence near contact line disappears and is replaced by a balance of surface tensions at the contact line (Neumann equilibrium), though the profile remains nearly logarithmic. In the rivulet case, using the previous solution as a Green function allows one to calculate analytically the geometry of the distorted substrate, and in particular its slope on each side (wet and dry) of the contact lines. These two slopes are shown to be nearly proportional to the inverse of substrate surface tensions, though the respective weight of each side (wet and dry) in the final expressions is difficult to establish because of the linear nature of standard elasticity. A simple argument combining Neumann and Young equations is however provided to overcome this limitation. The result may have surprising implications for the modelling of hysteresis on systems having both plastic and elastic properties, as initiated long ago by Extrand and Kumagai.

Relating Compressive Strength to Heat Release in Mortars

Conventionally, isothermal calorimetry and ASTM C186 heat of hydration results are reported on the basis of heat per mass of cement (powder), with typical units being Joules per gram (of cement), for example. Given that it is the filling of porosity with hydration products that is chiefly responsible for strength development in cement-based materials, there might be merit in instead reporting these results in terms of the unit volume of (initial) water. This paper examines a database of well over 200 mortar mixtures to investigate the relationship between heat release and mortar cube compressive strength development. For reasonably low water-to-cementitious-materials ratios (w/cm) (w/cm < 0.43), a single universal straight line relationship with some scatter is obtained. Based on numerous experimental data sets and the accompanying theoretical computations, the effects of the w/cm, sand volume fraction, cement chemical composition, sulfate content, cement fineness, incorporation of a high range water reducing admixture, and curing conditions on this universal relationship are all considered. Fifty data points from the Cement and Concrete Reference Laboratory proficiency sample program were analyzed in order to develop a linear relationship between ASTM C109 mortar cube compressive strengths and ASTM C186 heats of hydration at 7 d and 28 d. The application of this relationship for virtual testing is also evaluated. In this case, computer simulations would be employed to predict the heat of hydration versus time for a particular cement, and the developed equations would be employed to convert this heat release to a strength prediction at the age(s) of interest. In general, it appears that these relationships can be used to predict mortar cube compressive strengths based on measured heats of hydration, within about ±10 % of the experimentally measured strengths. A preliminary analysis of a single dataset for concretes with and without limestone replacement for cement indicates that the linear relationship between strength and heat release likely holds for concretes as well as for mortars.

New variations of the maximum coverage facility location problem

Consider a competitive facility location scenario where, given a set U of n users and a set F of m facilities in the plane, the objective is to place a new facility in an appropriate place such that the number of users served by the new facility is maximized. Here users and facilities are considered as points in the plane, and each user takes service from its nearest facility, where the distance between a pair of points is measured in either L1 or L2 or L∞ metric. This problem is also known as the maximum coverage (MaxCov) problem. In this paper, we will consider the k-MaxCov problem, where the objective is to place k (⩾1) new facilities such that the total number of users served by these k new facilities is maximized. We begin by proposing an O(nlogn) time algorithm for the k-MaxCov problem, when the existing facilities are all located on a single straight line and the new facilities are also restricted to lie on the same line. We then study the 2-MaxCov problem in the plane, and propose an O(n2) time and space algorithm in the L1 and L∞ metrics. In the L2 metric, we solve the 2-MaxCov problem in the plane in O(n3logn) time and O(n2logn) space. Finally, we consider the 2-Farthest-MaxCov problem, where a user is served by its farthest facility, and propose an algorithm that runs in O(nlogn) time, in all the three metrics.

City Shape and the Fractality of Street Patterns

City Shape and the Fractality of Street Patterns This paper discusses, first, the concepts of fractals and power laws in relation to the street patterns of the city of Dundee, East Scotland and, second, the results of the measurement of 6,004 street segments in the city. The trends of the street segments are presented through rose diagrams and show that there are two main street trends in the city: one is parallel with the coast, the other is roughly perpendicular to the coast. It is clear that the coastline largely regulates the street trend, because both the main street trends change along the city so as to be nearly coast-perpendicular and coast-parallel everywhere. The lengths of the street segments follow power laws. When presented on log-log plots, however, the result is not a single straight line but two straight lines. At the break in line slope, the fractal dimension changes from 0.88 to 2.20. The change occurs at the step length of about 100 m, indicating that the short streets belong to a population that is different from that of the longer streets.