Modeling may be construed as a science dealing with the interaction between mathematics and other subjects - an academic discipline concerning some aspects of the everyday world.
Please specify at-least one interaction between mathematics and any other subject through Modeling. It is useful for new generation of all fields.
One such example would be Envoirnmental Science, some other such disciplines include Biology, Chemistry , Medical and Engineering Sciences.
For example, we can say that the income of the consumer is divided into two parts, one part saved and one for consumption, and thus we have identical ones as follows:
Y(income)= S (save)+ C(consumption).
This equation called identical. we used mathematical tools in economic theory.
Yes by using number of method such as Matlab Sinmulink ,comsol etc.
Yeas ,by using number of methods such as matlab simulink and comsol etc.
modeling is akin to yodeling....
a "useful" adjunct to cerebral studies, but not to be construed as a science unto itself.
Mathematics and gene flow for example. Population genetics analysis is closely related to mathematics.
Gravel S (2012) Population Genetics Models of Local Ancestry. GENETICS :191(2) 607-619; https://doi.org/10.1534/genetics.112.139808
The mathematical apparatus is increasingly used in the humanities. First, it is needed in quantitative research. Secondly, the use of mathematics makes it possible to calculate the patterns of development of social phenomena.
Most of the process related phenomena are best understood through modeling the process to replicate real world behavior.
Dear K.V.L.N. Acharyulu ,
You can find your answer in the following article:
https://kobra.uni-kassel.de/bitstream/handle/123456789/2009051827549/BlumSubjects1988.pdf?sequence=1&isAllowed=y
Best regards.
Hamid
For example, we can say that the income of the consumer is divided into two parts, one part saved and one for consumption, and thus we have identical ones as follows:
Y(income)= S (save)+ C(consumption).
This equation called identical. we used mathematical tools in economic theory.
Many has already been suggested in relation to science.
Mathematics is used as technique in playing cards -gambling
Article How to Build a Course in Mathematical–Biological Modeling: C...
Systems science combines mathematics and context-sensitive processes to describe the behavior of complex systems. For example, a ballistic missile RV kill vehicle is described by the kinematic equations of both the target RV and the kill vehicle plus the interacting, concurrent processes of the kill vehicle: IR sensor, target ID and location process, and guidance process. Complex systems can be visualized as interacting concurrent processes that communicate with each other to achieve a mission: detect, ID, and guide to kill a target. OpEMCSS is a simulation system that works with ExtendSIM that was used to simulate the ballistic missile RV kill vehicle system. The simulation used special blocks to implement all the mathematics and process blocks to model system behavior. The AI and evolutionary algorithm blocks were used to experiment with novel new concepts to solve the problem. The resulting design was very effective in killing RVs, later confirmed based on telemetry data of actual target return signals. OpEMCSS is available free with my Wiley textbook “Simulation-Based Engineering of Complex Systems.”
An example interaction between the mathematics component and the process model in the above example system design is that target kinematic motion modulates the IR signal in such a way as to provide unique features that iD the target RV from all other debris in the cloud. Rules applied to all object features allows the target RV to be Identified and tracked in relation to other objects. The behavior of the sensor then provides the guidance information needed to hit the target. In particular, the mathematics models the kinematics of all objects and how the object IR return is affected by object motion (object center of gravity and shape determines how rotation affects the IR return). Thus mathematics maps physical behavior into information (used by the process model) that can discriminate among all the objects and ID the RV. Once the sensor has this ID, it can track the target and provide for kill vehicle guidance.
Mathematical models formulated through classical differential equations and numerical methods have been applied in a large number of fields of science or technology: mechanics, electricity, fluid mechanics, electronics, chemistry, biology ... In recent times also we can find in the literature, mathematical models in the field of medicine in topics such as cancer, hepatitis, tuberculosis, ..., formulated through classical and even fractional differential equations.
You can have a look on system dynamics method and its differential equations OR optimization and mathematical models (objective and constraints). Mathematics has a wide application in models developed for Economics (e.g. dynamics of housing price), Engineering (estimating the energy saving potentials of a new technology), Sociology (simulating societies behavior in terms of energy consumption), Health (simulating the diffusion of a disease) and etc.
Scientist have founded a relationship between Heat given off by an electrical conductor and the electric current flowing through it as :
Heat ((Joule) = R(résistance)xI2(current intensité)
One interaction is actually to few. The computer you are working on today cannot be manufactured without a mathematical model. No silicon chip with features smaller than approximately 180 nm (leading edge sales around the year 2000) have been manufactured without model based Optical Proximity Correction. OPC is used to enhance Photolithography, which is used to place the image of the circuit on the silicon wafer (it eventually gets diced into a chip.)
No chip with features smaller than ~65 nm can be manufactured without model based OPC. Around 65 nm, the feature will simply not print on the wafer. OPC must be used to change the mask pattern so that it will print the circuit pattern drawn by the design team and at the proper size.
In order to accomplish this task, the first step is to build is to build a mathematical model of the photolithography process. This includes the imaging and chemistry. The model is then used with the design pattern to create a pattern on the photolithography mask that will print on the wafer in the shape drawn by the design team. Without OPC, most of the small features (below Wavelength divided by Numerical Aperture) would not print, and all the features would not print at their correct sizes.
There are many articles on model based OPC, a quick google scholar search will find around 25 years of research on the subject. This link https://www.compugraphics-photomasks.com/us/our-capabilities/opcphase-shift/ has a nice picture of the impact of OPC on an ~130 nm design rule feautre vs the same feature without OPC for quick reference.
Though Mathematics and Medicine at first glance appear to be disparate fields, their synergy is the basis of the field of infectious disease epidemiology and public health. Mathematical models have been used to guide policy decisions for the control of infectious diseases - most recently in the Ebola outbreak. Modelling may be also be used to complement traditional control strategies so as to explore the relative merits of different mitigation strategies both in preparation for an outbreak and during an outbreak. (
Dear Dr.Hikmat Abdulkarim Almadhkhori ,
Your answer is in a simple way in an effective manner.Thank You.With Regards.
Dear Dr. Anastas Ivanov Ivanov ,
Nice clarification.Thank you.With Regards.
Metallic means and, especially, the golden mean have been widely used in the search to maintain certain proportions and convey a sense of beauty and harmony. Already in ancient Egypt and, specifically, in the Pyramid of Cheops, the golden mean appears among its proportions. We can also detect the omnipresence of the golden mean in Greek and Roman art, persistent in the monuments of the Gothic Middle Ages and, later, in the Renaissance. For example, the facades of the Parthenon and Notre Dame are contained in a golden rectangle.
Dear Dr. Francisco Martínez González ,
Sir,You have given valuable information with suitable examples.Thank you very much for your reply.With regards.
Mathematics is certainly not a mother, but a powerful tool of all branch of sciences. A typical approach is to describe some real system using a model, which, in its turn, is mathematical, i.e. expressed as a system of mathematical equations. This is a general approach. Very often one can hear the reproaches of the representatives of the "exact sciences" to the humanities for the unscientific (i.e. non-mathematical) of their approaches.
The problem in exact sciences is that researchers simplify the model to such an extent that it becomes solvable. Only then does it make any sense. Those, in most cases, scientists do not investigate real objects, but mathematical models ...
Mathematics is a language, mostly employed to describe and communicate physical behavior. For example, the resistance (R), voltage (V) and current (I), are related through the simple mathematics named Ohm's law; V = IR. This is the mathematical model for resistor, a simple element, commonly used in most electronic circuits.
Similarly, a spring is mathematically modeled, through the simple law F= kx, where F is force, k is the stiffness constant, and x is the displacement.
These are simple laws of mathematics to describe physics of materials. These simple laws have been very central to engineering for too many decades. However, the researchers and engineers, are trying persistently to upgrade these laws, to be valid for a larger range of operation, for example F=k1x+k2x^3, for spring of large length. These mathematical models (equations) are like system of laws governing the physics and engineering, to get them under use. As a society is governed by some types of rules (but not always these laws are respected), these models are assumed to govern the physics and engineering, but anyone knows that they do not always hold, and some type of imperfection always meddles. These laws are ideal but not very accurate. You need a mathematical law (model) or equation, to understand the behavior of a physical system. The more accurate the mathematical model (high-fidelity model), the more confident you are about your design plan.
Mathematics and weather forecasting. Differential equations containing time variables(pressure, temperature, humidity...) are a model of time.
The best representation of math applications is a simulation software for models in artificial intelligence systems, robotics Realtime.
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