Simple Arithmetic Research Articles

UNCERTAINTY IN THE PERT’S CRITICAL PATH

In this paper, the problem of scheduling is addressed. Due to difficulties in scheduling projects, researchers and professionals have proposed a tremendous number of works aiming at finding the best method to accomplish this phase of any project, especially if the decision maker is facing the challenge of uncertain estimations. One of the most used families of techniques is discussed in this paper, namely the Fuzzy Program Evaluation and Review Technique techniques. This family of techniques is based mainly on using the classical Program Evaluation and Review Technique and the fuzzy set theory. This work presents a comparison between two interesting techniques used to tackle the problem of uncertainty, namely the Model for Project Scheduling with Fuzzy Precedence Links and the Centroid techniques. The first technique is based on the relationship strength between each two activities in order to resolve the problem of the critical path. The second technique is based on a very simple mathematical concept and arithmetic of fuzzy numbers to tackle the same problem. Based on the results of a numerical example, we noticed that the simplicity and inexpensiveness of the Centroid method beat the complicated and expensive characteristics of the Model for Project Scheduling with Fuzzy Precedence Links.

UNCERTAINTY IN THE PERT’S CRITICAL PATH

In this paper, the problem of scheduling is addressed. Due to difficulties in scheduling projects, researchers and professionals have proposed a tremendous number of works aiming at finding the best method to accomplish this phase of any project, especially if the decision maker is facing the challenge of uncertain estimations. One of the most used families of techniques is discussed in this paper, namely the Fuzzy Program Evaluation and Review Technique techniques. This family of techniques is based mainly on using the classical Program Evaluation and Review Technique and the fuzzy set theory. This work presents a comparison between two interesting techniques used to tackle the problem of uncertainty, namely the Model for Project Scheduling with Fuzzy Precedence Links and the Centroid techniques. The first technique is based on the relationship strength between each two activities in order to resolve the problem of the critical path. The second technique is based on a very simple mathematical concept and arithmetic of fuzzy numbers to tackle the same problem. Based on the results of a numerical example, we noticed that the simplicity and inexpensiveness of the Centroid method beat the complicated and expensive characteristics of the Model for Project Scheduling with Fuzzy Precedence Links. Article DOI: https://dx.doi.org/10.20319/mijst.2018.41.0109 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

The Turtleback Diagram for Conditional Probability

We elaborate on an alternative representation of conditional probability to the usual tree diagram. We term the representation `turtleback diagram' for its resemblance to the pattern on turtle shells. Adopting the set theoretic view of events and the sample space, the turtleback diagram uses elements from Venn diagrams---set intersection, complement and partition---for conditioning, with the additional notion that the area of a set indicates probability whereas the ratio of areas for conditional probability. Once parts of the diagram are drawn and properly labeled, the calculation of conditional probability involves only simple arithmetic on the area of relevant sets. We discuss turtleback diagrams in relation to other visual representations of conditional probability, and detail several scenarios in which turtleback diagrams prove useful. By the equivalence of recursive space partition and the tree, the turtleback diagram is seen to be equally expressive as the tree diagram for representing abstract concepts. We also provide empirical data on the use of turtleback diagrams with undergraduate students in elementary statistics or probability courses.

Education of physiology in nursing school: common issues and measures with pharmacology

Anatomy, physiology or pharmacology is the important subject in nursing education. Nursing education is established in a law since 1951. Although the law is revised many times according to social situation, the subjects like physiology have been positioned as a basic specialized subject in the law now. Physiology is educated at 1st grade in most nursing school. However, there are some problems in educating physiology. First, academic ability in nursing students tend to decline recently. For example, there are some students who cannot solve simple arithmetic. They cannot calculate how much volume (mL) they have to aspirate injection solution to the syringe, when a doctor orders an injection medicine. Thus, there are increasing number of students who are not good at calculation. Second, they do not learn the technical term exactly. There are many names of pharmaceutical drug they must learn in pharmacology, some of which have similar names of pharmaceutical drug. If students do not learn them exactly, there is the possibility of causing a medical accident. Third, students learn something or an events from restricted one side. Therefore, they cannot answer the question they are asked from a different point of view. Furthermore, student cannot relate the knowledge they have learned with other knowledge. It seems that it must be important to have students understand how to utilize the knowledge in physiology or pharmacology in nursing practice at an early stage.

The simple arithmetic of carbon pricing and stranded assets

A simple rule for the optimal global price of carbon is presented, which captures the geophysical, economic, and ethical drivers of climate policy as well as the effect of uncertainty about future growth of consumption. There is also a discussion of the optimal carbon budget and the amount of unburnable carbon and stranded fossil fuel reserves and a back-on-the-envelope expression are given for calculating these. It is also shown how one can derive the end of the carbon era and peak warming. This simple arithmetic for determining climate policy is meant to complement the simulations of large-scale integrated assessment model, and to give analytical understanding of the key determinants of climate policy. The simple rules perform very well in a full integrated assessment model. It is also shown how to take account of a 2 °C upper limit on global warming. Steady increases in energy efficiency do not affect the optimal price of carbon, but postpone the carbon-free era somewhat and if technical progress in renewables and economic growth are strong leads to substantially lower cumulative emissions and lower peak global warming.

The “sweet” effect: Comparative assessments of dietary sugars on cognitive performance

In recent years there has been increasing interest in studying cognitive effects associated with sugar consumption. Neuro-cognitive research has confirmed that glucose, as a main energy substrate for the brain, can momentarily benefit cognitive performances, particularly for memory functioning. However, there is still limited understanding of relative effects of other common sugars (e.g., fructose and sucrose) on cognitive performance. The present study tested in 49 people the effects of three common dietary sugars against a placebo sweetener (i.e., sucralose), on performance of three well-studied cognitive tasks – simple response time, arithmetic, and Stroop interference, all of which are suggested to rely on the prefrontal lobe. A double-blind, placebo-controlled, cross-over experimental design was used. Results revealed that ingestion of glucose and sucrose led to poorer performances on the assessed tasks as opposed to fructose and the placebo (p<0.05); these effects were particularly pronounced under the fasting condition in comparison to the non-fasting condition (p<0.001). Overall, these results indicate that cognitive effects of sugar are unlikely to be mediated by the perception of sweetness. Rather, the effects are mediated by glucose. Further research should systematically assess effects of dietary sugars on other cognitive domains, such as memory, to give further insights on general cognitive effects of sugar consumption.

Simple arithmetic: not so simple for highly math anxious individuals.

Fluency with simple arithmetic, typically achieved in early elementary school, is thought to be one of the building blocks of mathematical competence. Behavioral studies with adults indicate that math anxiety (feelings of tension or apprehension about math) is associated with poor performance on cognitively demanding math problems. However, it remains unclear whether there are fundamental differences in how high and low math anxious individuals approach overlearned simple arithmetic problems that are less reliant on cognitive control. The current study used functional magnetic resonance imaging to examine the neural correlates of simple arithmetic performance across high and low math anxious individuals. We implemented a partial least squares analysis, a data-driven, multivariate analysis method to measure distributed patterns of whole-brain activity associated with performance. Despite overall high simple arithmetic performance across high and low math anxious individuals, performance was differentially dependent on the fronto-parietal attentional network as a function of math anxiety. Specifically, low—compared to high—math anxious individuals perform better when they activate this network less—a potential indication of more automatic problem-solving. These findings suggest that low and high math anxious individuals approach even the most fundamental math problems differently.

Effect of monomer sequence distribution on the CO2-philicity of a well-defined ternary copolymer: Poly(vinyl acetate-co-vinyl butyrate-co-vinyl butyl ether)

The work aims to interpret the phase behavior of multi-polymers in super critical CO2 via a spatially dependent structural parameter, the monomer sequence distribution, rather than traditional statistical factors. Well-defined statistical copolymers based on three CO2-philic monomers, vinyl acetate, vinyl butyrate and vinyl butyl ether, were synthesized with reversible addition-fragmentation chain transfer free-radical polymerization by combining their kinetic behaviors and pairwise reactivity ratios into the Alfrey–Goldfinger–Skeist model. The corresponding cloud point pressures become nonlinear with the polymer composition and possess upper critical solution pressure behavior. Additionally, their diad and triad monomer sequence distributions were calculated by simple theoretical arithmetic. While analyzing the cloud point pressure measurements, we found that both the differences in composition and symmetrical structure of the monomer triads could impact the CO2-philicity of triads, which were close to the properties of the products, and thus, the variations in the triad sequence distribution could reasonably predict the phase behavior of the products.

Intraoperative direct cortical stimulation motor evoked potentials: Stimulus parameter recommendations based on rheobase and chronaxie

ObjectiveTo determine optimal interstimulus interval (ISI) and pulse duration (D) for direct cortical stimulation (DCS) motor evoked potentials (MEPs) based on rheobase and chronaxie derived with two techniques. MethodsIn 20 patients under propofol/remifentanil anesthesia, 5-pulse DCS thenar MEP rheobase and chronaxie with 2, 3, 4 and 5ms ISI were measured by linear regression of five charge thresholds at 0.05, 0.1, 0.2, 0.5 and 1msD, and estimated from two charge thresholds at 0.1 and 1msD using simple arithmetic. Optimal parameters were defined by minimum threshold energy: the ISI with lowest rheobase2×chronaxie, and D at its chronaxie. Near-optimal was defined as threshold energy <25% above minimum. ResultsThe optimal ISI was 3 or 4 (n=7 each), 2 (n=4), or 5ms (n=2), but only 4ms was always either optimal or near-optimal. The optimal D was ∼0.2 (n=12), ∼0.1 (n=7) or ∼0.3ms (n=1). Two-point estimates closely approximated five-point measurements. ConclusionsOptimal ISI/D varies, with 4ms/0.2ms being most consistently optimal or near-optimal. Two-point estimation is sufficiently accurate. SignificanceThe results endorse 4ms ISI and 0.2msD for general use. Two-point estimation could enable quick individual optimization.

The correlation and prediction of the temperature variation of infinite dilution activity coefficients of compounds in water

We list infinite dilution activity coefficients, γ∞, in water for 81 compounds from 273.15 to 373.15 K, and we use our linear free energy relationship to obtain equations for log γ∞ at 5 K intervals between 273.15 and 373.15 K. These equations, together with Abraham descriptors can then be used to calculate or predict the temperature variation of activity coefficient in water with an estimated error of 0.25–0.30 log unit. If an experimental value of log γ∞ is available at 298.15 K (or at any specific temperature) this can be used as a reference point to adjust our calculated values at any other temperature, leading to an estimated error for the temperature variation of around 0.1 log units. This procedure is especially useful in extrapolating limited data on log γ∞ over the entire range 273.15–373.15 K. The method requires no complicated software and calculations involve no more than simple arithmetic.

Hair Zinc: an Index for Zinc Status in Under-Five Children from Low-Income Communities in Kanam Area of North-Central Nigeria.

Nutritional deficiencies of trace elements are among the top ten causes of death in Sub Saharan Africa. In Kanam Local Government Area of Nigeria, the problem is compounded by high levels of poverty and illiteracy. Abnormally low hair zinc levels are important, sensitive diagnostic biochemical indices of Zinc deficiency. The purpose of this study is to assess the zinc status of children less than 5years in Kanam local government area, north-central Nigeria, by measuring the zinc level in hair samples collected from 44 under-5 children across the area. A household survey was made to assess the pattern and frequency of consumption of zinc-rich foods which was done by means of questionnaire. Hair samples were analysed for zinc content by the inductively coupled plasma-mass spectrophotometry (ICP-MS). The data were analysed statistically using the Student's t test, z test, and Pearson correlation, while questionnaire-captured data were analysed by simple arithmetic. The results of the analyses showed that the average hair zinc level was 74.35±48.05μg/g. This was below the normal range of 130-140μg/g, for children less than 5years. Based on the results, 86.36% have hair zinc level below the lower limit of the normal range of 130μg/g. Between the gender, boys have higher hair zinc content than girls. Data from the questionnaire showed that 53.45% of the population studied have poor/inadequate intake of zinc-rich foods of animal origin, a dietary behaviour reported to predispose to micronutrient deficiency, including zinc.

The Trouble with Keynesian Stimulus Spending

For more than 70 years, a strand of Keynesian thought has maintained that the cure for economic depressions is merely a matter of simple arithmetic. According to these Keynesians, the government need only increase spending by an amount equal to the ratio of the output gap to the fiscal multiplier. Moreover, these Keynesians assert that even wasteful government spending can be desirable because any spending is better than nothing. This simple Keynesian approach fails to account, however, for several significant sources of cost. In addition to the cost of waste inherent in government spending, financing that spending requires taxation, which entails an excess burden. Furthermore, the employment of even previously idle resources involves opportunity costs. In this paper, we subject Keynesian stimulus spending to a benefit-cost test that accounts for waste, labor disutility, capital consumption, and the excess burden of taxation. We calibrate our model by surveying the published estimates of key parameters, including the Keynesian fiscal multiplier. Our results indicate that stimulus spending can successfully generate net wealth, but generally only if the burden of waste is limited to no more than 20 to 30 percent of the overall size of the spending package.

Vulnerability of Elderly Women: Victim of Gender Discrimination

The life cycle of human being completes with the process of aging but we fail to realize this simple arithmetic of life and often consider our elders as a burden for us. They are compelled to compromise with their dignity and integrity and forced to live at the mercy of their own nearest and dearest. When we talk about elderly women their position is more appalling than their male counterpart due to this male chauvinism which tries to regulate every affair of the life of the people. Under the alibi of protection and security of women they are subjected to the violent gender discrimination and compelled to live and lead their life at the fingertips of a male. The women in especially in third world countries are considered as a tool of procreation of child and all her activities and qualities of life are relegated with the household course. Across the globe the male tendency is to regulate Women’s ownership and control of property, resources created by her own labor, education and information and even her reproductive abilities and sexualities with an intention to jeopardize and throttled down the rights of the women. Women bear this status till her last breath and hence, it is axiomatic that how vulnerable their position is.

The functional architectures of addition and subtraction: Network discovery using fMRI and DCM.

The neuronal mechanisms underlying arithmetic calculations are not well understood but the differences between mental addition and subtraction could be particularly revealing. Using fMRI and dynamic causal modeling (DCM), this study aimed to identify the distinct neuronal architectures engaged by the cognitive processes of simple addition and subtraction. Our results revealed significantly greater activation during subtraction in regions along the dorsal pathway, including the left inferior frontal gyrus (IFG), middle portion of dorsolateral prefrontal cortex (mDLPFC), and supplementary motor area (SMA), compared with addition. Subsequent analysis of the underlying changes in connectivity - with DCM - revealed a common circuit processing basic (numeric) attributes and the retrieval of arithmetic facts. However, DCM showed that addition was more likely to engage (numeric) retrieval-based circuits in the left hemisphere, while subtraction tended to draw on (magnitude) processing in bilateral parietal cortex, especially the right intraparietal sulcus (IPS). Our findings endorse previous hypotheses about the differences in strategic implementation, dominant hemisphere, and the neuronal circuits underlying addition and subtraction. Moreover, for simple arithmetic, our connectivity results suggest that subtraction calls on more complex processing than addition: auxiliary phonological, visual, and motor processes, for representing numbers, were engaged by subtraction, relative to addition. Hum Brain Mapp 38:3210-3225, 2017. © 2017 Wiley Periodicals, Inc.

Contribución de los Componentes de la Memoria de Trabajo a la Eficiencia en Aritmética Básica Durante la Edad Escola

Aunque existen múltiples evidencias respecto de la relación entre la memoria de trabajo (MT) y el rendimiento aritmético, los resultados aún son inconsistentes. El objetivo del presente estudio fue evaluar la contribución única de cada componente de la MT (bucle fonológico, agenda visuo-espacial y ejecutivo central) a la explicación de la varianza de la eficiencia en aritmética básica, durante diferentes momentos del desarrollo escolar. Se evaluaron 285 estudiantes (M edad: 9,58 años, DE = 1,79) de 5 establecimientos educacionales de Santiago y Chillán, Chile, con y sin dificultades en aritmética básica, a través de tareas de MT. Análisis de regresiones jerárquicas mostraron que los componentes de la MT tienen una contribución única a la varianza de la eficiencia en aritmética básica, pero esta varía durante el desarrollo escolar. Análisis de varianza mostraron diferencias en el funcionamiento de la MT entre estudiantes con y sin dificultades en aritmética, lo cual sugiere que el origen de estas dificultades podría estar muy asociado a la MT. Estos resultados tienen especial relevancia para explicar el desarrollo de la cognición numérica durante la edad escolar.

Quantifying non-specific interactions between flavour and food biomolecules.

The ways in which flavour molecules interact with proteins in foods have an impact on flavour and aroma and on the (in)stability of the proteins. There is a long history of analysing these interactions using a "specific binding model" that gives values for the number of molecules, n, bound to the proteins with a binding constant Kb. However, recent progress in molecular thermodynamics forced us to reconsider this approach. In addition, there are a number of methods for determining these values and it is not at all clear whether the various assumptions behind the various methods allow legitimate comparisons between techniques. By adopting an assumption-free molecular thermodynamics approach, Kirkwood-Buff theory, we find that we gain a welcome universality, simplicity and deep understanding of what is happening at the molecular level. Here we look at three different methods for examining flavour-protein interactions (vapour pressure, dialysis equilibrium and melting temperature changes), show how historical data can be re-cast into the universal language of Kirkwood-Buff and provide a free, open-source app that can both re-analyze historical data and be a platform for analyzing fresh data. In each case, the fundamental theory is described along with a pragmatic implementation accepting the realities of experimentation. One key insight is that the n and Kb parameters of the classical binding models can be turned directly, via simple arithmetic, into the Kirkwood-Buff integrals that accurately capture non-specific flavour-protein interactions.

Layout Symmetries: Quantification and Application to Cancel Nonlinear Process Gradients

This paper presents criteria, using simple integer arithmetic, to determine if a layout of a pair of devices broken into multiple, identical sections cancels the effect of nonlinear process gradients. These criteria allow quantification of 12 layout symmetries that can be leveraged to cancel specific process gradient components. “Dispersion,” the degree to which device segments are distributed throughout a layout, is also quantified in a simple and intuitive way, and used to identify which of multiple gradient canceling layouts is best. Techniques to construct maximally dispersive quadratic gradient canceling layouts with arbitrary numbers of rows and columns are presented.

Conceptual knowledge of arithmetic for Chinese- and Canadian-educated adults.

This study investigated whether Canadian- and Chinese-educated adults differ in their understanding of simple arithmetic concepts. Participants (n = 21 per group) solved 3-term addition and subtraction (e.g., 5 + 22 - 22 and 3 + 24 - 26) and multiplication and division (e.g., 2 × 28 ÷ 28 and 4 × 39 ÷ 13) problems. All problems could be solved more easily if conceptual knowledge of the relationship between the 2 operations in each problem was understood and applied. Accuracy, solution time, and immediately retrospective self-reports of problem-solving strategy data were collected. Participants also completed a timed arithmetic fluency task. Chinese-educated participants demonstrated stronger conceptual understanding of arithmetic on all problems and outperformed Canadian-educated participants on the fluency task. A cluster analysis revealed 4 groups of individuals: weak concept users, who rarely used conceptual knowledge to aid their problem solving; strong concept users, who almost exclusively used their conceptual knowledge to facilitate problem solving; addition and subtraction concept users, who frequently used conceptual knowledge except on difficult multiplication and division problems; and multiplication and division concept users, who frequently used conceptual knowledge except on difficult addition and subtraction problems. Chinese-educated participants were more likely to be in the strong concept clusters, and none were in the weak concept cluster, providing further evidence of stronger conceptual knowledge of arithmetic. These results demonstrate for the 1st time that there are strong cross-cultural differences in conceptual knowledge of simple arithmetic, even in adulthood. (PsycINFO Database Record

Risk of shear failure and extensional failure around over-stressed excavations in brittle rock

The authors investigate the failure modes surrounding over-stressed tunnels in rock. Three lines of investigation are employed: failure in over-stressed three-dimensional (3D) models of tunnels bored under 3D stress, failure modes in two-dimensional (2D) numerical simulations of 1000 m and 2000 m deep tunnels using FRACOD, both in intact rock and in rock masses with one or two joint sets, and finally, observations in TBM (tunnel boring machine) tunnels in hard and medium hard massive rocks. The reason for ‘stress-induced’ failure to initiate, when the assumed maximum tangential stress is approximately (0.4–0.5)σc (UCS, uniaxial compressive strength) in massive rock, is now known to be due to exceedance of a critical extensional strain which is generated by a Poisson's ratio effect. However, because similar ‘stress/strength’ failure limits are found in mining, nuclear waste research excavations, and deep road tunnels in Norway, one is easily misled into thinking of compressive stress induced failure. Because of this, the empirical SRF (stress reduction factor in the Q-system) is set to accelerate as the estimated ratio σθmax/σc >> 0.4. In mining, similar ‘stress/strength’ ratios are used to suggest depth of break-out. The reality behind the fracture initiation stress/strength ratio of ‘0.4’ is actually because of combinations of familiar tensile and compressive strength ratios (such as 10) with Poisson's ratio (say 0.25). We exceed the extensional strain limits and start to see acoustic emission (AE) when tangential stress σθ ≈ 0.4σc, due to simple arithmetic. The combination of 2D theoretical FRACOD models and actual tunnelling suggests frequent initiation of failure by ‘stable’ extensional strain fracturing, but propagation in ‘unstable’ and therefore dynamic shearing. In the case of very deep tunnels (and 3D physical simulations), compressive stresses may be too high for extensional strain fracturing, and shearing will dominate, both ahead of the face and following the face. When shallower, the concept of ‘extensional strain initiation but propagation’ in shear is suggested. The various failure modes are richly illustrated, and the inability of conventional continuum modelling is emphasized, unless cohesion weakening and friction mobilization at different strain levels are used to reach a pseudo state of yield, but still considering a continuum.

The obligatory activation of practiced complex multiplication facts and what it tells us about models of arithmetic processing

Three experiments were conducted in which adults practiced complex multiplication problems (e.g., 4 x 17). In Experiments 1 and 2, after practice participants completed a number-matching task in which two digits (cues) were followed by a single digit (probe) and had to determine whether the probe matched either of the cues. In simple arithmetic (e.g., 4 x 3), when the probe is the product of the cues (12), participants are slower/more error prone when determining whether there is a match. Results of Experiment 1 extended this effect to complex multiplication. In Experiment 2, participants practiced problems with the larger operand first (e.g., 17 x 4) or with the smaller operand first (e.g., 4 x 17). The number-matching interference effect from Experiment 1 was replicated, and was equal across the two groups whether cues were presented in their practiced or non-practiced order. Experiment 3 was conducted to determine if two additional simple multiplication effects, consistency and relatedness, could be documented for complex multiplication. After practice, in a verification task (4 x 13 = 56?) it was found that when presented answers shared a digit with the decade digit of the correct answer (consistency) or were a correct answer to another practiced problem (relatedness), participants rejected answers more slowly and/or less accurately. Together, findings from the three experiments support arithmetic models that posit that commuted pairs are not represented in long-term memory independently and that posit representations of two-digit multiplication answers are decomposed into decades and units during arithmetic processing.