Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Mathematical Related Abstracts

3 Presenting the Mathematical Model to Determine Retention in the Watersheds

Authors: S. Shamohammadi, L. Razavi


This paper based on the principle concepts of SCS-CN model, a new mathematical model for computation of retention potential (S) presented. In the mathematical model, not only precipitation-runoff concepts in SCS-CN model are precisely represented in a mathematical form, but also new concepts, called “maximum retention” and “total retention” is introduced, and concepts of potential retention capacity, maximum retention, and total retention have been separated from each other. In the proposed model, actual retention (F), maximum actual retention (Fmax), total retention (S), maximum retention (Smax), and potential retention (Sp), for the first time clearly defined, so that Sp is not variable, but a function of morphological characteristics of the watershed. Indeed, based on the mathematical relation of the conceptual curve of SCS-CN model, the proposed model provides a new method for the computation of actual retention in watershed and it simply determined runoff based on. In the corresponding relations, in addition to Precipitation (P), Initial retention (Ia), cumulative values of actual retention capacity (F), total retention (S), runoff (Q), antecedent moisture (M), potential retention (Sp), total retention (S), we introduced Fmax and Fmin referring to maximum and minimum actual retention, respectively. As well as, ksh is a coefficient which depends on morphological characteristics of the watershed. Advantages of the modified version versus the original model include a better precision, higher performance, easier calibration and speed computing.

Keywords: Mathematical, watershed, model, Retention, SCS

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2 A Review on Water Models of Surface Water Environment

Authors: Shahbaz G. Hassan


Water quality models are very important to predict the changes in surface water quality for environmental management. The aim of this paper is to give an overview of the water qualities, and to provide directions for selecting models in specific situation. Water quality models include one kind of model based on a mechanistic approach, while other models simulate water quality without considering a mechanism. Mechanistic models can be widely applied and have capabilities for long-time simulation, with highly complexity. Therefore, more spaces are provided to explain the principle and application experience of mechanistic models. Mechanism models have certain assumptions on rivers, lakes and estuaries, which limits the application range of the model, this paper introduces the principles and applications of water quality model based on the above three scenarios. On the other hand, mechanistic models are more easily to compute, and with no limit to the geographical conditions, but they cannot be used with confidence to simulate long term changes. This paper divides the empirical models into two broad categories according to the difference of mathematical algorithm, models based on artificial intelligence and models based on statistical methods.

Keywords: Statistical, Mathematical, Water Quality, empirical models

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1 The Cardiac Diagnostic Prediction Applied to a Designed Holter

Authors: Leonardo Juan Ramirez Lopez, Javier Oswaldo Rodriguez Velasquez


We have designed a Holter that measures the heart´s activity for over 24 hours, implemented a prediction methodology, and generate alarms as well as indicators to patients and treating physicians. Various diagnostic advances have been developed in clinical cardiology thanks to Holter implementation; however, their interpretation has largely been conditioned to clinical analysis and measurements adjusted to diverse population characteristics, thus turning it into a subjective examination. This, however, requires vast population studies to be validated that, in turn, have not achieved the ultimate goal: mortality prediction. Given this context, our Insight Research Group developed a mathematical methodology that assesses cardiac dynamics through entropy and probability, creating a numerical and geometrical attractor which allows quantifying the normalcy of chronic and acute disease as well as the evolution between such states, and our Tigum Research Group developed a holter device with 12 channels and advanced computer software. This has been shown in different contexts with 100% sensitivity and specificity results.

Keywords: Cardiac, Mathematical, Entropy, prediction, attractor, Holter

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