Rational Periodic Points of the Quadratic Function Q c (x) = x 2 + c

1994 ◽  
Vol 101 (4) ◽  
pp. 318 ◽  
Author(s):  
Ralph Walde ◽  
Paula Russo
Keyword(s):  
Quadratic Function ◽  
Periodic Points

Optimal Inventory Policies for Price and Time Sensitive Demand under Advertisement

2020 ◽  
Vol 13 ◽  
Author(s):  
Nita Shah ◽  
Ekta Patel ◽  
Kavita Rabari
Keyword(s):  
Cycle Time ◽  
Quadratic Function ◽  
Solution Procedure ◽  
Vital Role ◽  
Optimal Number ◽  
Deteriorating Items ◽  
Marginal Effect ◽  
Selling Price ◽  
Total Profit ◽  
Back Order

Aims: This article analyzes an inventory system for deteriorating items. The demand is quadratic function of time and is dependent on time, price and advertisement. Shortages are allowed and partially backlogged. Background: Demand and pricing are the two most crucial factors in inventory policy for any business to be successful. In today’s era of competitive circumstances, any product is promoted through advertisement, which plays a vital role in changing the demand pattern among the community. The marketing and demonstration of an item by time-to-time with fashionable advertisements through well-known media such as TV, radio, newspaper, magazine, etc. However, this idea is not always true for some goods like wheat, vegetables, fruits, food grains, medicines and other perishable goods due to their deteriorating nature and this in turn decreases demand for such goods. Deterioration may define as decay, damage, spoilage, evaporation, obsolescence, pilferage. Hence, deterioration effect is a major part in inventory control theory. So in this article demand rate is considered to be a function of selling price, time and occurrence of advertisement instantaneously. Objective: A solution procedure is obtained to find optimal number of price changes and optimal selling price to maximize the total profit. Method: Classical Optimization. Result: From the sensitivity analysis table, it can be seen that the optimal profit is highly sensible to advertisement coefficient and purchase cost. With an increment in rate of deterioration, selling price decreases. Scale demand has reasonable effect on cycle time and selling price. When the value of increase, the cycle length and profit goes on decreasing. Growth in profit is observed if we increase parameter b, higher will be the profit. Price elasticity is sensible parameter with respect to selling price. If backlogging rate increases, the profit will decreases. The inventory parameters holding cost, back order cost and lost sale cost have marginal effect on total profit. Conclusion: In this article, an inventory model is proposed for deteriorating items with variable demand depends upon the advertisement, selling price of the item and time. Shortages are allowed and partially backlogged and backlogging rate depends on the waiting time for the next replenishment. From this article, we can conclude that the parameters are insensible with respect to optimal profit, cycle time and selling price and rest of the parameters have practical output on total profit.

Examining the Temporal Dynamics of Anxiety and Depressive Symptoms During a Therapist-Supported, Smartphone-Based Intervention for Major Depression (Preprint)

2020 ◽  
Author(s):  
Santiago Allende ◽  
Valerie Forman-Hoffman ◽  
Philippe Goldin
Keyword(s):  
Depressive Symptoms ◽  
Temporal Relationship ◽  
Temporal Dynamics ◽  
Digital Health ◽  
Quadratic Function ◽  
Depression Symptoms ◽  
Symptoms Of Depression ◽  
Effect Model ◽  
End Of Treatment ◽  
Highly Correlated

UNSTRUCTURED Background: Anxiety and depression symptoms are highly correlated in adults with depression; however, little is known about their interaction and temporal dynamics of change during treatment. Thus, the primary aim of this study was to examine the temporal dynamics of anxiety and depressive symptoms during a 12-week therapist-supported, smartphone-delivered digital health intervention for symptoms of depression and anxiety, the Meru Health Program (MHP). Method: A total of 290 participants from the MHP were included in the present analyses (age Mean = 39.64, SD = 10.25 years; 79% female; 54% self-reported psychotropic medication use). A variance components model was used to examine whether (1) reporting greater anxiety during the current week relative to anxiety reported in other weeks would be associated with greater reporting of depressive symptoms during the current week, while a time-varying effect model was used to examine whether, (2) consistent with findings reported by Wright et al. (2014), the temporal relationship between anxiety and depressive symptoms during the intervention would be expressed as a quadratic function marked by a weak association at baseline, followed by an increase to a peak before demonstrating a negligible decrease until the end of treatment. Results: In support of hypothesis 1, we found that reporting greater anxiety symptoms during the current week relative to other weeks was associated with greater depressive symptoms during the current week. Contrary to hypothesis 2, the temporal relationship between anxiety and depressive symptoms evidenced a recurring pattern, with the association increasing during the initial weeks, decreasing during mid-treatment and sharply increasing toward the end of treatment. Conclusions: The present findings demonstrate that anxiety and depressive symptoms overlap and fluctuate in concert during a smartphone-based intervention for anxiety and depressive symptoms. The present findings may warrant more refined intervention strategies specifically tailored to co-occurring patterns of change in symptoms.

Pengembangan Media Pembelajaran Interaktif Berdasarkan Teori Apos pada Materi Fungsi Kuadrat

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10
Author(s):  
Arie Gusman ◽  
Kamid Kamid ◽  
Syamsurizal Syamsurizal
Keyword(s):  
Learning Theory ◽  
Teaching And Learning ◽  
Quadratic Function ◽  
Test Group ◽  
Quadratic Functions ◽  
High School Mathematics ◽  
Constructivist Learning Theory ◽  
Average Value ◽  
Long Time ◽  
Action Process

Learning quadratic functions that had been performed by the majority of vocational school and high school mathematics teacher in Kuala Tungkal is still using conventional learning media. The use of conventional learning media is experiencing a lot of obstacles, such as: a fairly long time in describing the graph function, especially when analyzing some quadratic function graphs with various characteristics. APOS is one of the constructivist learning theory which states that students learn through several stages, namely: action – process – object – schema. And to integrate into media APOS writer adapting ADDIE development model. The effectiveness of the use of media-based learning theory APOS seen from the student activity sheet can be concluded more increased activity of students in the learning process. Study of the test results, students were able to meet the completeness criteria stipulated minimum is 75. With an average value of learning outcomes, namely 87.14. It can be seen from the students' responses on a test group of small and large groups where it is concluded that researchers develop learning media can be categorized as good / interesting in the teaching and learning of mathematics.

scholarly journals On monotonicity and search strategies in face-based copositivity detection algorithms

2021 ◽  
Author(s):  
B. G.-Tóth ◽  
E. M. T. Hendrix ◽  
L. G. Casado
Keyword(s):  
Research Question ◽  
Quadratic Function ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Matrix Methods ◽  
Detection Algorithms ◽  
Standard Simplex ◽  
Mathematical Properties ◽  
The Face ◽  
Spatial Branch And Bound

AbstractOver the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the relative interior minima of the standard quadratic program (StQP) and monotonicity. We derive several theoretical properties related to convexity and monotonicity of the standard quadratic function over faces of the standard simplex. We illustrate with numerical instances up to 28 dimensions the use of monotonicity in face-based algorithms. The question is what traversal through the face graph of the standard simplex is more appropriate for which matrix instance; top down or bottom up approaches. This depends on the level of the face graph where the minimum of StQP can be found, which is related to the density of the so-called convexity graph.

scholarly journals A Pneumatic Generator Based on Gas-Liquid Reversible Transition for Soft Robots

Actuators ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 103
Author(s):  
Guolong Zhang ◽  
Guilin Yang ◽  
Yimin Deng ◽  
Tianjiang Zheng ◽  
Zaojun Fang ◽  
...  
Keyword(s):  
Smart Materials ◽  
Load Capacity ◽  
Angular Displacement ◽  
Quadratic Function ◽  
Air Cooling ◽  
Soft Robots ◽  
Reversible Transformation ◽  
Exponential Term ◽  
Reversible Transition ◽  
Gas Volume

The soft robots actuated by pressure, cables, thermal, electrosorption, combustion and smart materials are usually faced with the problems of poor portability, noise, weak load capacity, small deformation and high driving voltages. In this paper, a novel pneumatic generator for soft robots based on the gas-liquid reversible transition is proposed, which has the advantages of large output force, easy deformation, strong load capacity and high flexibility. The pressure of the pneumatic generator surges or drops flexibly through the reversible transformation between liquid and gas phase, making the soft actuator stretch or contract regularly, without external motors, compressors and pressure-regulating components. The gas-liquid reversible-transition actuation process is modeled to analyze its working mechanism and characteristics. The pressure during the pressurization stage increases linearly with a rate regulated by the heating power and gas volume. It decreases exponentially with the exponential term as a quadratic function of time at the fast depressurization stage, while with the exponential term as a linear function of time at the slow depressurization stage. The drop rate can be adjusted by changing the gas volume and cooling conditions. Furthermore, effectiveness has been verified through experiments of the prototype. The pressure reaches 25 bar with a rising rate of +3.935 bar/s when 5 mL weak electrolyte solution is heated at 800 W, and the maximum depressurization rate in air cooling is –3.796 bar/s. The soft finger actuated by the pneumatic generator can bend with an angular displacement of 67.5°. The proposed pneumatic generator shows great potential to be used for the structure, driving and sensing integration of artificial muscles.

scholarly journals Mathematical pattern of Kessler psychological distress distribution in the general population of the U.S. and Japan

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Shinichiro Tomitaka ◽  
Toshiaki A. Furukawa
Keyword(s):  
United States ◽  
General Population ◽  
National Survey ◽  
Goodness Of Fit ◽  
Quadratic Function ◽  
The United States ◽  
Depression Screening ◽  
Distribution Model ◽  
Epidemiological Surveys ◽  
Screening Scale

Abstract Background Although the 6-item Kessler psychological scale (K6) is a useful depression screening scale in clinical settings and epidemiological surveys, little is known about the distribution model of the K6 score in the general population. Using four major national survey datasets from the United States and Japan, we explored the mathematical pattern of the K6 distributions in the general population. Methods We analyzed four datasets from the National Health Interview Survey, the National Survey on Drug Use and Health, and the Behavioral Risk Factor Surveillance System in the United States, and the Comprehensive Survey of Living Conditions in Japan. We compared the goodness of fit between three models: exponential, power law, and quadratic function models. Graphical and regression analyses were employed to investigate the mathematical patterns of the K6 distributions. Results The exponential function had the best fit among the three models. The K6 distributions exhibited an exponential pattern, except for the lower end of the distribution across the four surveys. The rate parameter of the K6 distributions was similar across all surveys. Conclusions Our results suggest that, regardless of different sample populations and methodologies, the K6 scores exhibit a common mathematical distribution in the general population. Our findings will contribute to the development of the distribution model for such a depression screening scale.

scholarly journals A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

Dynamics ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 9-17
Author(s):  
Andrea Natale Impiombato ◽  
Giorgio La Civita ◽  
Francesco Orlandi ◽  
Flavia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Blood Flow ◽  
Boundary Conditions ◽  
Quadratic Function ◽  
Pulsatile Blood Flow ◽  
Flow Through ◽  
Simplified Analysis ◽  
Function Models ◽  
Flow Reversals

As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated.

scholarly journals Prediction of factors affecting activation of soil erosion by mathematical modeling at pedon scale under laboratory conditions

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Saeed Shojaei ◽  
Zahra Kalantari ◽  
Jesús Rodrigo-Comino
Keyword(s):  
Soil Loss ◽  
Rainfall Intensity ◽  
Quadratic Function ◽  
Interactive Effects ◽  
Soil Protection ◽  
Single Factor ◽  
Rainfall Events ◽  
Rainfall Duration ◽  
The Impact ◽  
Runoff Production

AbstractSoil degradation due to erosion is a significant worldwide problem at different spatial (from pedon to watershed) and temporal scales. All stages and factors in the erosion process must be detected and evaluated to reduce this environmental issue and protect existing fertile soils and natural ecosystems. Laboratory studies using rainfall simulators allow single factors and interactive effects to be investigated under controlled conditions during extreme rainfall events. In this study, three main factors (rainfall intensity, inclination, and rainfall duration) were assessed to obtain empirical data for modeling water erosion during single rainfall events. Each factor was divided into three levels (− 1, 0, + 1), which were applied in different combinations using a rainfall simulator on beds (6 × 1 m) filled with soil from a study plot located in the arid Sistan region, Iran. The rainfall duration levels tested were 3, 5, and 7 min, the rainfall intensity levels were 30, 60, and 90 mm/h, and the inclination levels were 5, 15, and 25%. The results showed that the highest rainfall intensity tested (90 mm/h) for the longest duration (7 min) caused the highest runoff (62 mm3/s) and soil loss (1580 g/m2/h). Based on the empirical results, a quadratic function was the best mathematical model (R2 = 0.90) for predicting runoff (Q) and soil loss. Single-factor analysis revealed that rainfall intensity was more influential for runoff production than changes in time and inclination, while rainfall duration was the most influential single factor for soil loss. Modeling and three-dimensional depictions of the data revealed that sediment production was high and runoff production lower at the beginning of the experiment, but this trend was reversed over time as the soil became saturated. These results indicate that avoiding the initial stage of erosion is critical, so all soil protection measures should be taken to reduce the impact at this stage. The final stages of erosion appeared too complicated to be modeled, because different factors showed differing effects on erosion.

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