Position Formula Research Articles

Serial execution Josephus problem

In this paper, we will study a generalized version of Josephus where a serial execution occurs at each iteration and give a non-recursive formula for the initial positions of survivors.

Generalized Storage–Yield–Reliability Relationships for Analysing Shopping Centre Rainwater Harvesting Systems

The objective of this study was to develop guidelines for analysing rainwater harvesting (RWH) systems of shopping centres in South Africa. A model consisting of three dimensionless relationships relating rainwater supply and demand to storage capacity, yield and reliability was formulated. Data from daily simulation of potential RWH systems of 19 shopping were used to obtain the relationships. The simulations revealed within-year storage behaviour with considerable variation of annual yield. By applying the Weibull plotting position formula, yield–reliability relationships were derived. The aim to maximize yield and reliability whilst minimizing storage identified Pareto-optimal combinations of the three variables and these combinations were used to develop two dimensionless relationships. An additional relationship based on the dependence of the slope of the yield–reliability plots on yield was formulated to enable analysis of hydrologically non-optimal systems. Verification tests using four RWH systems obtained results that matched those from simulation and the model could therefore be applied for RWH feasibility analysis and preliminary design. This study highlights the need to incorporate inter-annual variability in RWH analysis and shows how reliability can be used to quantify this. This study further demonstrates how reliability can be fully integrated into regression relationships for generalized RWH analysis.

REGIONAL RAINFALL FREQUENCY ANALYSIS FOR SAMARAHAN RIVER BASIN

In planning to mitigate flood, it is essential for engineers to determine the magnitude and frequency of rainfall. The rainfall frequency and magnitude can be determined by rainfall frequency analysis. This study analyzes the regional rainfall frequency of the Samarahan River basin. There are 12 rainfall stations over the 508km2 of basin area, of which 11 are included in this study. The rainfall frequency analyses of each individual station in Samarahan River basin are conducted using Gumbel distribution and Weibull plotting position formulas. The curves that are close to each other are grouped into the same region. Other factors such as topography, station elevation, type of rainfall distribution and isohyet are also considered in determining the region. Subsequently, a regional rainfall frequency map of Samarahan River basin is established. The findings show that Samarahan River basin can be divided into three homogenous regions. In comparison to previous research, there are changes in grouping the rainfall stations selected into regions. These changes may be due to different years of data used and number of rainfall stations selected since the data is limited. Dissimilar outcomes may also be caused by other factors such as nature change over time. This research updates the rainfall analysis of the Samarahan River basin using more adequate data compared to previous research.

Effects of sample size on estimation of rainfall extremes at high temperatures

Abstract. High precipitation quantiles tend to rise with temperature, following the so-called Clausius–Clapeyron (CC) scaling. It is often reported that the CC-scaling relation breaks down and even reverts for very high temperatures. In our study, we investigate this reversal using observational climate data from 142 stations across Germany. One of the suggested meteorological explanations for the breakdown is limited moisture supply. Here we argue that, instead, it could simply originate from undersampling. As rainfall frequency generally decreases with higher temperatures, rainfall intensities as dictated by CC scaling are less likely to be recorded than for moderate temperatures. Empirical quantiles are conventionally estimated from order statistics via various forms of plotting position formulas. They have in common that their largest representable return period is given by the sample size. In small samples, high quantiles are underestimated accordingly. The small-sample effect is weaker, or disappears completely, when using parametric quantile estimates from a generalized Pareto distribution (GPD) fitted with L moments. For those, we obtain quantiles of rainfall intensities that continue to rise with temperature.

X-ray focusing properties of doubly bent crystals

The focusing properties of several bent crystal geometries, including the newly introduced Pestehe & Askari general point-focusing system [Pestehe & Askari Germi (2012),Opt. Soc. Am. A,29, 68–77; Pestehe & Askari Germi (2012),J. Appl. Cryst.45, 890–901], on an arbitrarily positioned detector plane are investigated and illustrated. The properties of the focal points and the generated images are theoretically related to the local, ℓ, and directional, γ, positions of the detector plane for a given position of a point source on the Rowland circle. A general relation is derived for the detector positioning to obtain a specially focused image. This formula for the polar position of the detector plane, given by the two ℓ and γ variables, enables the exact determination of the system astigmatism and the exact calculation of the sagittal and meridional image positions for the spectrometer under study. The astigmatisms of the above-mentioned bent crystal geometries have been studied, and their sagittal and meridional focal positions and characteristics have been obtained and are illustrated. It is also shown that there is a possibility of designing a spectrometer to focus rays from a linear source onto a point on the Rowland circle.

Statistical Analysis of 30 Years Rainfall Data: A Case Study

Rainfall is a prime input for various engineering design such as hydraulic structures, bridges and culverts, canals, storm water sewer and road drainage system. The detailed statistical analysis of each region is essential to estimate the relevant input value for design and analysis of engineering structures and also for crop planning. A rain gauge station located closely in Trichy district is selected for statistical analysis where agriculture is the prime occupation. The daily rainfall data for a period of 30 years is used to understand normal rainfall, deficit rainfall, Excess rainfall and Seasonal rainfall of the selected circle headquarters. Further various plotting position formulae available is used to evaluate return period of monthly, seasonally and annual rainfall. This analysis will provide useful information for water resources planner, farmers and urban engineers to assess the availability of water and create the storage accordingly. The mean, standard deviation and coefficient of variation of monthly and annual rainfall was calculated to check the rainfall variability. From the calculated results, the rainfall pattern is found to be erratic. The best fit probability distribution was identified based on the minimum deviation between actual and estimated values. The scientific results and the analysis paved the way to determine the proper onset and withdrawal of monsoon results which were used for land preparation and sowing.

Sense making in the context of algebraic activities

This article concerns student sense making in the context of algebraic activities. We present a case in which a pair of middle-school students attempts to make sense of a previously obtained by them position formula for a particular numerical sequence. The exploration of the sequence occurred in the context of two-month-long student research project. The data were collected from the students’ drafts, audiotaped meetings of the students with the teacher and a follow-up interview. The data analysis was aimed at identification and characterization of the algebraic activities in which the students were engaged and the processes involved in the students’ sense-making quest. We found that sense-making process consisted of a sequence of generational and transformational algebraic activities in the overarching context of a global, meta-level activity, long-term problem solving. In this sense-making process, the students: (1) formulated and justified claims; (2) made generalizations, (3) found the mechanisms behind the algebraic objects (i.e., answered why-questions); and (4) established coherence among the explored objects. The findings are summarized as a suggestion for a four component decomposition of algebraic sense making.

Comparative analysis of predictive methods for drought durations: a case of monthly and annual streamflow droughts in Atlantic Canada

ABSTRACTMethods based on the recursive probability, the extreme number theorem, and Markov chain (MC) concepts were applied to predict drought lengths (duration) on the standardized (termed as standardized hydrological index, SHI) sequences of monthly and annual river flows from Atlantic Canada. Results of the study indicated that the MC-based method is the most efficient, reliable and versatile method for predicting drought durations followed by the extreme-number-based method. The recursive-probability-based method was found to be computationally intensive and less efficient, although it provided a powerful means for calibrating the empirical plotting position formula needed in the MC-based method. The Weibull plotting position formula turned out to be a suitable measure of the exceedance probability in MC methodology for predicting drought lengths in Atlantic Canada. Based on results, it can be inferred that the MC-based method can be extended to MC2 and higher-order chains for predicting drought lengths on SHI sequences. The predictive capability of the extreme-number-theorem-based method is limited only to independent or weakly first-order persistent SHI sequences.EDITOR D. KoutsoyiannisASSOCIATE EDITOR Q. Zhang

Flood-risk assessment in urban environment by geospatial approach: a case study of Ambala City, India

Looking at land use and functional structure characteristics, floods in urban environment are costlier and difficult to manage than in rural environment. In India, flooding is an inevitable problem for several cities. In the state of Haryana, Ambala City has a long history of serious flooding problem. Based on primary as well as secondary data, the present study attempts to examine the natural and anthropogenic causes of flooding on catchment and city scale. Geographic Information System (GIS)-based flood-risk modeling and consequences of flooding are presented for the selected most critical zone. Based on the past 21-year maximum discharge data of the Tangri River, flood probability is calculated for a 2-, 5-, 10-, and 20-year return period using Weibull’s plotting position formula, and the likely maximum discharge of 500, 1000, 1200, and 1500 m3, respectively, is used for the prediction of flood extent using Hydraulic Engineering Center-River Analysis System (HEC-RAS) software. Flood depth is calculated by employing spatial interpolation method using observed flood depth samples. Model result revealed that the flood inundation areas are 690, 1135, 1530, and 2300 ha, respectively, and accordingly likely impact on land use and population are assessed. The modeled 5-year return flood extents were validated using the observed data of the latest flood event in July 2010, including remote sensing imagery and field survey. Hence, in order to mitigate adverse impact of flooding in urban environment, such output can be used by urban local bodies, town planners, and policy makers to support decision-making in risk-sensitive land use planning by integrating climate change scenarios.

Confinement-induced resonances in ultracold atom-ion systems

We investigate confinement-induced resonances in a system composed by a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region -- from the "long-wavelength" limit to the opposite case when the typical length scale of the atom-ion polarisation potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the "long-wavelength and zero-energy" limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semi-analytic formula for the resonance position in the "long-wavelength and zero-energy" limit and we investigate numerically how the position of the resonance is affected by a finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi one dimensional atomic quantum gas.

Three-pile Sharing Nim and the quadratic time winning strategy

We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing them, topping up on a smaller pile provided that the destination pile does not have more tokens than the source pile after the move. We discover a situation in which each column of two-dimensional array of Sprague–Grundy values is a palindrome. We establish a formula for P-positions by which winning moves can be computed in quadratic time. We prove a formula for positions whose Sprague–Grundy values are 1 and estimate the distribution of those positions whose nim-values are g. We discuss the periodicity of nim-sequences that seem to be bounded.

Modified Firefly Algorithm based controller design for integrating and unstable delay processes

In this paper, Modified Firefly Algorithm has been used for optimizing the controller parameters of Smith predictor structure. The proposed algorithm modifies the position formula of the standard Firefly Algorithm in order to achieve faster convergence rate. Performance criteria Integral Square Error (ISE) is optimized using this optimization technique. Simulation results show high performance for Modified Firefly Algorithm as compared to conventional Firefly Algorithm in terms of convergence rate. Integrating and unstable delay processes are taken as examples to indicate the performance of the proposed method.

Predicting return periods of hydrological droughts using the Pearson 3 distribution: a case from rivers in the Canadian prairies

The standardized series of monthly and weekly flow sequences, referred to as standardized hydrological index (SHI) series, from five rivers in the Canadian prairies were subjected to return period (Tr) analysis of drought length (L). The SHI series were truncated at drought probability levels q ranging from 0.5 to 0.05 with the intention of deducing drought events and corresponding drought lengths. The values of L were fitted to the Pearson 3, the gamma (2-parameter), the exponential (1-parameter), the Weibull 3 and the Weibull (2-parameter) probability density functions (pdfs). A priori assignment of one week or one month for the location parameter in the Pearson 3 pdf proved logical and also facilitated the rapid estimation of other parameters using either the method of moments or the method of maximum likelihood. The Pearson 3 turns out to be the most suitable pdf to describe and to estimate return periods of drought lengths. At the monthly and weekly time scales, it was inferred that the sample size (T, months or weeks) of SHI series could be treated equivalent to the return period of the largest recorded drought length. At the annual time scale, however, the sample size (T, years) should be modified using either the Hazen or the Gringorten plotting position formula to reflect the actual return period of the largest recorded drought length in years.Editor D. Koutsoyiannis; Associate editor E. Gargouri

Development of an unbiased plotting position formula considering the coefficient of skewness for the generalized logistic distribution

Summary This study considered the plotting position formula with a coefficient of skewness for the generalized logistic distribution. For the development of the plotting position formula, the theoretical reduced variates were derived with consideration of the shape parameter of the generalized logistic distribution. The parameters of the plotting position formula were estimated using genetic algorithms. The accuracy of derived plotting position formula was examined using the error values between the theoretical and the calculated reduced variates from the derived and existing formulas. The error values from the derived plotting position formula were smaller than those from the existing formulas for - 0.30 ⩽ β - 0.05 and + 0.05 β ⩽ + 0.30 . For - 0.05 ⩽ β ⩽ + 0.05 , the error values from Gringorten’s plotting position formula were smaller than those of other methods, but the differences were notably small, i.e., 0.0001–0.0008. As a result, the derived plotting position formula could be applied to the generalized logistic distribution with a shape parameter range of - 0.30 ⩽ β ⩽ + 0.30 . In addition, the theoretical reduced variate shows a straighter line for sample data plotted on probability paper. And then, the coefficients of determination by the derived plotting position formula were higher than those by Gringorten’s one for applied annual maximum rainfall data in Korea. Therefore, more reliable quantiles can be estimated using the derived plotting position formula.

Positional accommodative intraocular lens power error induced by the estimation of the corneal power and the effective lens position.

Purpose:To evaluate the predictability of the refractive correction achieved with a positional accommodating intraocular lenses (IOL) and to develop a potential optimization of it by minimizing the error associated with the keratometric estimation of the corneal power and by developing a predictive formula for the effective lens position (ELP).Materials and Methods:Clinical data from 25 eyes of 14 patients (age range, 52–77 years) and undergoing cataract surgery with implantation of the accommodating IOL Crystalens HD (Bausch and Lomb) were retrospectively reviewed. In all cases, the calculation of an adjusted IOL power (PIOLadj) based on Gaussian optics considering the residual refractive error was done using a variable keratometric index value (nkadj) for corneal power estimation with and without using an estimation algorithm for ELP obtained by multiple regression analysis (ELPadj). PIOLadj was compared to the real IOL power implanted (PIOLReal, calculated with the SRK-T formula) and also to the values estimated by the Haigis, HofferQ, and Holladay I formulas.Results:No statistically significant differences were found between PIOLReal and PIOLadj when ELPadj was used (P = 0.10), with a range of agreement between calculations of 1.23 D. In contrast, PIOLReal was significantly higher when compared to PIOLadj without using ELPadj and also compared to the values estimated by the other formulas.Conclusions:Predictable refractive outcomes can be obtained with the accommodating IOL Crystalens HD using a variable keratometric index for corneal power estimation and by estimating ELP with an algorithm dependent on anatomical factors and age.

Evaluating Methods to Predict Streamflow at Ungauged Sites Using Regional Flow Duration Curves: A Case Study

Precise information on streamflows is of major importance for planning and monitoring of water resources schemes related to hydro power, water supply, irrigation, flood control, and for maintaining ecosystem. Engineers encounter challenges when streamflow data are either unavailable or inadequate at target locations. To address these challenges, there have been efforts to develop methodologies that facilitate prediction of streamflow at ungauged sites. Conventionally, time intensive and data exhaustive rainfall-runoff models are used to arrive at streamflow at ungauged sites. Most recent studies show improved methods based on regionalization using Flow Duration Curves (FDCs). A FDC is a graphical representation of streamflow variability, which is a plot between streamflow values and their corresponding exceedance probabilities that are determined using a plotting position formula. It provides information on the percentage of time any specified magnitude of streamflow is equaled or exceeded. The present study assesses the effectiveness of two methods to predict streamflow at ungauged sites by application to catchments in Mahanadi river basin, India. The methods considered are (i) Regional flow duration curve method, and (ii) Area Ratio method. The first method involves (a) the development of regression relationships between percentile flows and attributes of catchments in the study area, (b) use of the relationships to construct regional FDC for the ungauged site, and (c) use of a spatial interpolation technique to decode information in FDC to construct streamflow time series for the ungauged site. Area ratio method is conventionally used to transfer streamflow related information from gauged sites to ungauged sites. Attributes that have been considered for the analysis include variables representing hydrology, climatology, topography, land-use/land-cover and soil properties corresponding to catchments in the study area. Effectiveness of the presented methods is assessed using jack knife cross-validation. Conclusions based on the study are presented and discussed.

Probabilistic assessment of the rainwater harvesting potential of schools in South Africa

Abstract. In comparison to other sources of water supply, rainwater harvesting (RWH) has the typical advantages of being cheaper and easier to operate and maintain. This study aimed at assessing the hydrologic rainwater harvesting potential of rural schools in South Africa by obtaining RWH storage capacity (level of supply) reliability relationships of representative schools. Thirty-two schools located in three rural areas that have varied rainfall characteristics were selected for the analysis. For each school, a daily time-step behaviour analysis of the rainwater harvesting system with a specified storage was carried out for a period of 101 years (over which rainfall data was available) and the number of days that the school’s daily water demand was met in each year obtained. Using the Weibull plotting position formula, the expected number of days that the demand can be met per year was then obtained for 85, 90 and 95 % reliability. For the two summer rainfall regions where a large proportion of rain falls during school holidays, the expected number of days of supply per year improved up to a storage capacity of 25 m3. For the winter rainfall region where the rainfall periods and school learning times have more co-incidence, a tank volume of 5 m3 obtained similar supply levels as larger capacities. At 90 % reliability, the supply levels for different schools in the summer rainfall area with a mean annual precipitation (MAP) of 800–1000 mm/year ranged from 60 to 120 days per year, while the summer rainfall region with a lower MAP (500–600 mm) gave supply levels ranging from 40 to 70 days per year. The winter rainfall area had a MAP of 500–600 mm and obtained supply levels ranging from 60 to 80 days at 90 % reliability.

Optimized Rationalize Security and Efficient Data Gathering in Wireless Sensor Networks

Wireless reprogramming during a wireless detector network (WSN) is that the method of propagating a replacement code image or relevant commands to detector nodes. As a WSN is sometimes deployed in hostile environments, secure reprogramming is and can continue to be a significant concern. Whereas all existing insecure/secure reprogramming protocols square measure supported the centralized approach, it\'s necessary to support distributed reprogramming during which multiple licensed network users will at the same time and directly reprogram detector nodes while not involving the bottom station. Terribly recently, a novel secure rationalize and distributed reprogramming protocol named SRDRP has been planned, that is that the initial work of its kind. However, during this paper, we have a tendency to establish associate inherent style weakness within the increased signature verification of SRDRP associated demonstrate that it\'s at risk of associate impersonation attack by that an resister will simply impersonate any licensed user to hold out reprogramming. Later on, we have a tendency to propose a straightforward modification to mend the known security drawback while not losing any options of SRDRP. Our experimental results demonstrate that it\'s able to eliminate the planning weakness by adding one-B redundant information which the execution time of the prompt answer during a 1.6-GHz laptop personal computer is not any quite one ms. Therefore, our answer is possible and secure for real-world applications. Moreover, we have a tendency to show that, so as to additional improve the safety and potency of SRDRP; any higher established identity-based position formula will be directly utilized in SRDRP. Supported implementation results, we have a tendency to demonstrate potency improvement over the initial SRDRP.

Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia

Parametric method of flood frequency analysis (FFA) involves fitting of a probability distribution to the observed flood data at the site of interest. When record length at a given site is relatively longer and flood data exhibits skewness, a distribution having more than three parameters is often used in FFA such as log-Pearson type 3 distribution. This paper examines the suitability of a five-parameter Wakeby distribution for the annual maximum flood data in eastern Australia. We adopt a Monte Carlo simulation technique to select an appropriate plotting position formula and to derive a probability plot correlation coefficient (PPCC) test statistic for Wakeby distribution. The Weibull plotting position formula has been found to be the most appropriate for the Wakeby distribution. Regression equations for the PPCC tests statistics associated with the Wakeby distribution for different levels of significance have been derived. Furthermore, a power study to estimate the rejection rate associated with the derived PPCC test statistics has been undertaken. Finally, an application using annual maximum flood series data from 91 catchments in eastern Australia has been presented. Results show that the developed regression equations can be used with a high degree of confidence to test whether the Wakeby distribution fits the annual maximum flood series data at a given station. The methodology developed in this paper can be adapted to other probability distributions and to other study areas. Copyright © 2014 John Wiley & Sons, Ltd.

X-ray multiple diffraction of ZnO substrates and heteroepitaxial thin films

We investigate Umweganregung reflections (X-ray multiple reflections) for , (00.3), and (00.5) for a number of wurtzite structure ZnO samples, namely various bulk crystals (substrates), two ZnO thin films and a ZnO:Mg thin film, grown by pulsed laser deposition on a-plane sapphire. Using a low divergence setup, we achieve a high angular resolution of 0.1 or better. We derive an analytical formula for peak positions as a function of wavelength and the lattice parameters a and c. The three investigated ZnO substrates exhibit all expected (kinematically allowed) reflections for Cu Kα1, Kα2, and Kβ. A lineshape analysis of the multiple reflection peaks shows that the width of certain reflections is determined by the spectral linewidth of the exciting copper lines. The thin films exhibit only slight broadening of the peaks but disappearance of several reflections. The a lattice constant can be determined from the azimuthal peak positions. Umweganregung scan for () of a hydrothermally grown ZnO substrate, excited with Cu Kα1 radiation. The pattern is symmetric with respect to zero angle representing the (10.0) azimuth.