In the first part of the paper I willpresentabriefreview on the Hardy-Weinberg equilibrium and it's formulation in projective algebraicgeometry. In the second and last part I willdiscussexamples and generalizations on the topic
Applied Mathematics and Sciences: An International Journal (MathSJ)mathsjournal
The main goal of this research is to give the complete conception about numerical integration including
Newton-Cotes formulas and aimed at comparing the rate of performance or the rate of accuracy of
Trapezoidal, Simpson’s 1/3, and Simpson’s 3/8. To verify the accuracy, we compare each rules
demonstrating the smallest error values among them. The software package MATLAB R2013a is applied to
determine the best method, as well as the results, are compared. It includes graphical comparisons
mentioning these methods graphically. After all, it is then emphasized that the among methods considered,
Simpson’s 1/3 is more effective and accurate when the condition of the subdivision is only even for solving
a definite integral.
AN ALGORITHM FOR SOLVING LINEAR OPTIMIZATION PROBLEMS SUBJECTED TO THE INTERS...ijfcstjournal
Frank t-norms are parametric family of continuous Archimedean t-norms whose members are also strict functions. Very often, this family of t-norms is also called the family of fundamental t-norms because of the
role it plays in several applications. In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated.
Applied Mathematics and Sciences: An International Journal (MathSJ)mathsjournal
The main goal of this research is to give the complete conception about numerical integration including
Newton-Cotes formulas and aimed at comparing the rate of performance or the rate of accuracy of
Trapezoidal, Simpson’s 1/3, and Simpson’s 3/8. To verify the accuracy, we compare each rules
demonstrating the smallest error values among them. The software package MATLAB R2013a is applied to
determine the best method, as well as the results, are compared. It includes graphical comparisons
mentioning these methods graphically. After all, it is then emphasized that the among methods considered,
Simpson’s 1/3 is more effective and accurate when the condition of the subdivision is only even for solving
a definite integral.
AN ALGORITHM FOR SOLVING LINEAR OPTIMIZATION PROBLEMS SUBJECTED TO THE INTERS...ijfcstjournal
Frank t-norms are parametric family of continuous Archimedean t-norms whose members are also strict functions. Very often, this family of t-norms is also called the family of fundamental t-norms because of the
role it plays in several applications. In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated.
This is a journal concise version (without diagrams and figures) of the preprint arXiv:1308.4060.
Abstract: Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic systems having unequal arities, is introduced via an explicit formula, together with related definitions for multiplace representations and multiactions. Concrete examples of matrix representations for some ternary groups are then reviewed. Ternary algebras and Hopf algebras are defined, and their properties are studied. At the end some ternary generalizations of quantum groups and the Yang-Baxter equation are presented.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
A talk presented at the University of New South Wales on the occasion of Ian Sloan's 80th birthday, remembering our work together and thinking about how math is used in science.
A Fixed Point Theorem Using Common Property (E. A.) In PM Spacesinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
A Generalized Sampling Theorem Over Galois Field Domains for Experimental Des...csandit
In this paper, the sampling theorem for bandlimited functions over
domains is
generalized to one over ∏
domains. The generalized theorem is applicable to the
experimental design model in which each factor has a different number of levels and enables us
to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship
between the proposed sampling theorem and orthogonal arrays is also provided.
KEY
The Purpose of Homework Problems is Insight, Not Numbers: Crafting Exercises for an Intermediate Biological Physics Class. Bradley Roth, Oakland University. Prepared for the session "Bringing Together Biology, Medicine, and Physics in Education" at the APS March Meeting, 2020.
This document presents a novel Copula based approach to generate critical sea states given a target reliability index based on the return period of the extreme event. Copula based approach is much more flexible and powerful when compared to conventional approaches using linear correlation coefficient.
Fixed Point Results In Fuzzy Menger Space With Common Property (E.A.)IJERA Editor
This paper presents some common fixed point theorems for weakly compatible mappings via an implicit relation in Fuzzy Menger spaces satisfying the common property (E.A)
On New Root Finding Algorithms for Solving Nonlinear Transcendental EquationsAI Publications
In this paper, we present new iterative algorithms to find a root of the given nonlinear transcendental equations. In the proposed algorithms, we use nonlinear Taylor’s polynomial interpolation and a modified error correction term with a fixed-point concept. We also investigated for possible extension of the higher order iterative algorithms in single variable to higher dimension. Several numerical examples are presented to illustrate the proposed algorithms.
Knowledge of cause-effect relationships is central to the field of climate science, supporting mechanistic understanding, observational sampling strategies, experimental design, model development and model prediction. While the major causal connections in our planet's climate system are already known, there is still potential for new discoveries in some areas. The purpose of this talk is to make this community familiar with a variety of available tools to discover potential cause-effect relationships from observed or simulation data. Some of these tools are already in use in climate science, others are just emerging in recent years. None of them are miracle solutions, but many can provide important pieces of information to climate scientists. An important way to use such methods is to generate cause-effect hypotheses that climate experts can then study further. In this talk we will (1) introduce key concepts important for causal analysis; (2) discuss some methods based on the concepts of Granger causality and Pearl causality; (3) point out some strengths and limitations of these approaches; and (4) illustrate such methods using a few real-world examples from climate science.
Factor Extraction method in factor analysis with example in R studio.pptxGauravRajole
In this ppt information about factor analysis is given which is part of multivariate analysis. detail description is given about the factor extraction method, a test of the sufficiency of factor numbers, Interpretation of factors, factor score, rotation of factors, orthogonal rotation methods, varimax rotation, Oblique Rotation, and an example of factor analysis in R-studio.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
The main purpose of this research is to find out the best method through iterative methods for solving the
nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the
nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st
degree based iterative methods. After that, the graphical development is established here with the help of
the four iterative methods and these results are tested with various functions. An example of the algebraic
equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two
examples of the algebraic and transcendental equation are applied to verify the best method, as well as the
level of errors, are shown graphically.
Learning dyadic data and predicting unaccomplished co-occurrent values by mix...Loc Nguyen
Dyadic data which is also called co-occurrence data (COD) contains co-occurrences of objects. Searching for statistical models to represent dyadic data is necessary. Fortunately, finite mixture model is a solid statistical model to learn and make inference on dyadic data because mixture model is built smoothly and reliably by expectation maximization (EM) algorithm which is suitable to inherent spareness of dyadic data. This research summarizes mixture models for dyadic data. When each co-occurrence in dyadic data is associated with a value, there are many unaccomplished values because a lot of co-occurrences are inexistent. In this research, these unaccomplished values are estimated as mean (expectation) of random variable given partial probabilistic distributions inside dyadic mixture model.
This is a journal concise version (without diagrams and figures) of the preprint arXiv:1308.4060.
Abstract: Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic systems having unequal arities, is introduced via an explicit formula, together with related definitions for multiplace representations and multiactions. Concrete examples of matrix representations for some ternary groups are then reviewed. Ternary algebras and Hopf algebras are defined, and their properties are studied. At the end some ternary generalizations of quantum groups and the Yang-Baxter equation are presented.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
A talk presented at the University of New South Wales on the occasion of Ian Sloan's 80th birthday, remembering our work together and thinking about how math is used in science.
A Fixed Point Theorem Using Common Property (E. A.) In PM Spacesinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
A Generalized Sampling Theorem Over Galois Field Domains for Experimental Des...csandit
In this paper, the sampling theorem for bandlimited functions over
domains is
generalized to one over ∏
domains. The generalized theorem is applicable to the
experimental design model in which each factor has a different number of levels and enables us
to estimate the parameters in the model by using Fourier transforms. Moreover, the relationship
between the proposed sampling theorem and orthogonal arrays is also provided.
KEY
The Purpose of Homework Problems is Insight, Not Numbers: Crafting Exercises for an Intermediate Biological Physics Class. Bradley Roth, Oakland University. Prepared for the session "Bringing Together Biology, Medicine, and Physics in Education" at the APS March Meeting, 2020.
This document presents a novel Copula based approach to generate critical sea states given a target reliability index based on the return period of the extreme event. Copula based approach is much more flexible and powerful when compared to conventional approaches using linear correlation coefficient.
Fixed Point Results In Fuzzy Menger Space With Common Property (E.A.)IJERA Editor
This paper presents some common fixed point theorems for weakly compatible mappings via an implicit relation in Fuzzy Menger spaces satisfying the common property (E.A)
On New Root Finding Algorithms for Solving Nonlinear Transcendental EquationsAI Publications
In this paper, we present new iterative algorithms to find a root of the given nonlinear transcendental equations. In the proposed algorithms, we use nonlinear Taylor’s polynomial interpolation and a modified error correction term with a fixed-point concept. We also investigated for possible extension of the higher order iterative algorithms in single variable to higher dimension. Several numerical examples are presented to illustrate the proposed algorithms.
Knowledge of cause-effect relationships is central to the field of climate science, supporting mechanistic understanding, observational sampling strategies, experimental design, model development and model prediction. While the major causal connections in our planet's climate system are already known, there is still potential for new discoveries in some areas. The purpose of this talk is to make this community familiar with a variety of available tools to discover potential cause-effect relationships from observed or simulation data. Some of these tools are already in use in climate science, others are just emerging in recent years. None of them are miracle solutions, but many can provide important pieces of information to climate scientists. An important way to use such methods is to generate cause-effect hypotheses that climate experts can then study further. In this talk we will (1) introduce key concepts important for causal analysis; (2) discuss some methods based on the concepts of Granger causality and Pearl causality; (3) point out some strengths and limitations of these approaches; and (4) illustrate such methods using a few real-world examples from climate science.
Factor Extraction method in factor analysis with example in R studio.pptxGauravRajole
In this ppt information about factor analysis is given which is part of multivariate analysis. detail description is given about the factor extraction method, a test of the sufficiency of factor numbers, Interpretation of factors, factor score, rotation of factors, orthogonal rotation methods, varimax rotation, Oblique Rotation, and an example of factor analysis in R-studio.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
The main purpose of this research is to find out the best method through iterative methods for solving the
nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the
nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st
degree based iterative methods. After that, the graphical development is established here with the help of
the four iterative methods and these results are tested with various functions. An example of the algebraic
equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two
examples of the algebraic and transcendental equation are applied to verify the best method, as well as the
level of errors, are shown graphically.
Learning dyadic data and predicting unaccomplished co-occurrent values by mix...Loc Nguyen
Dyadic data which is also called co-occurrence data (COD) contains co-occurrences of objects. Searching for statistical models to represent dyadic data is necessary. Fortunately, finite mixture model is a solid statistical model to learn and make inference on dyadic data because mixture model is built smoothly and reliably by expectation maximization (EM) algorithm which is suitable to inherent spareness of dyadic data. This research summarizes mixture models for dyadic data. When each co-occurrence in dyadic data is associated with a value, there are many unaccomplished values because a lot of co-occurrences are inexistent. In this research, these unaccomplished values are estimated as mean (expectation) of random variable given partial probabilistic distributions inside dyadic mixture model.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
The main purpose of this research is to find out the best method through iterative methods for solving the
nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the
nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st
degree based iterative methods. After that, the graphical development is established here with the help of
the four iterative methods and these results are tested with various functions. An example of the algebraic
equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two
examples of the algebraic and transcendental equation are applied to verify the best method, as well as the
level of errors, are shown graphically.
A NEW STUDY TO FIND OUT THE BEST COMPUTATIONAL METHOD FOR SOLVING THE NONLINE...mathsjournal
The main purpose of this research is to find out the best method through iterative methods for solving the nonlinear equation. In this study, the four iterative methods are examined and emphasized to solve the nonlinear equations. From this method explained, the rate of convergence is demonstrated among the 1st degree based iterative methods. After that, the graphical development is established here with the help of the four iterative methods and these results are tested with various functions. An example of the algebraic equation is taken to exhibit the comparison of the approximate error among the methods. Moreover, two examples of the algebraic and transcendental equation are applied to verify the best method, as well as the level of errors, are shown graphically.
Finding the Extreme Values with some Application of Derivativesijtsrd
There are many different way of mathematics rules. Among them, we express finding the extreme values for the optimization problems that changes in the particle life with the derivatives. The derivative is the exact rate at which one quantity changes with respect to another. And them, we can compute the profit and loss of a process that a company or a system. Variety of optimization problems are solved by using derivatives. There were use derivatives to find the extreme values of functions, to determine and analyze the shape of graphs and to find numerically where a function equals zero. Kyi Sint | Kay Thi Win "Finding the Extreme Values with some Application of Derivatives" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29347.pdf Paper URL: https://www.ijtsrd.com/mathemetics/other/29347/finding-the-extreme-values-with-some-application-of-derivatives/kyi-sint
FDM is an older method than FEM that requires less computational power but is also less accurate in some cases where higher-order accuracy is required. FEM permit to get a higher order of accuracy, but requires more computational power and is also more exigent on the quality of the mesh.29-Jun-2017
https://feaforall.com › difference-bet...
What's the difference between FEM and FDM? - FEA for All
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About featured snippets
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their fundamental dimensions (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms vs. grams) and tracking these dimensions as calculations or comparisons are performed.
Application of Semiparametric Non-Linear Model on Panel Data with Very Small ...IOSRJM
-This research work investigated the behaviour of a new semiparametric non-linear (SPNL) model on
a set of panel data with very small time point (T = 1). The SPNL model incorporates the relationship between
individual independent variable and unobserved heterogeneity variable. Five different estimation techniques
namely; Least Square (LS), Generalized Method of Moments (GMM), Continuously Updating (CU), Empirical
Likelihood (EL) and Exponential Tilting (ET) Estimators were employed for the estimation; for the purpose of
modelling the metrical response variable non-linearly on a set of independent variables. The performances of
these estimators on the SPNL model were examined for different parameters in the model using the Least
Square Error (LSE), Mean Absolute Error (MAE) and Median Absolute Error (MedAE) criteria at the lowest
time point (T = 1). The results showed that the ET estimator which provided the least errors of estimation is
relatively more efficient for the proposed model than any of the other estimators considered. It is therefore
recommended that the ET estimator should be employed to estimate the SPNL model for panel data with very
small time point.
Exploring 3D-Virtual Learning Environments with Adaptive RepetitionsIOSRJM
In spatial tasks, the use of cognitive aids reduce mental load and therefore being appealing to trainers and trainees. However, these aids can act as shortcuts and prevents the trainees from active exploration which is necessary to perform the task independently in non-supervised environment. In this paper we used adaptive repetition as control strategy to explore the 3D- Virtual Learning environments. The proposed approach enables the trainee to get the benefits of cognitive support while at the same time he is actively involved in the learning process. Experimental results show the effectiveness of the proposed approach.
Mathematical Model on Branch Canker Disease in Sylhet, BangladeshIOSRJM
Members of the Camellia genus of plants may be affected by many of the diseases, pathogens and pests that mainly affect the tea plant (Camellia sinensis). One of the most common diseases which are found in tea garden is known as Branch Canker (BC) [1]. Recent outbreaks of these diseases is not only hampering the production of tea, but also stupendously hampering our national economy. In this paper, a simple SEIR model has been used to analyze the dynamics of Branch Canker in the tea garden. The stability of the system is analyzed for the existence of the disease free equilibrium. We established that there exists a disease free equilibrium point that is locally asymptotically stable when the reproduction number Ro< 1 and unstable when Ro> 1. Theoretically, we analyze the BC model. Finally, we numerically tested the theoretical results in MATLAB.
Least Square Plane and Leastsquare Quadric Surface Approximation by Using Mod...IOSRJM
Now a days Surface fitting is applied all engineering and medical fields. Kamron Saniee ,2007 find a simple expression for multivariate LaGrange’s Interpolation. We derive a least square plane and least square quadric surface Approximation from a given N+1 tabular points when the function is unique. We used least square method technique. We can apply this method in surface fitting also.
A Numerical Study of the Spread of Malaria Disease with Self and Cross-Diffus...IOSRJM
: A study of the SIS model of malaria disease with a view to observing the effects of self and crossdiffusion on spatial dynamics is undertaken. Three different cases based on self-diffusion and cross-diffusion are chosen for the investigation. Two cases of cross-diffusion without self-diffusion are also considered in order to see the effects of diffusion on the transmission of malaria. Basic reproductive numbers and bifurcation values are calculated for each case. A series of numerical simulations based on self and cross-diffusion is performed. It is observed that with positive cross-diffusion and self-diffusion in the system, there is a significant increase in the proportion of both infected human and mosquito populations. The proportion of infected humans increases markedly with cross diffusion in the system. This also gives rise to some oscillations across the domain.
Fibonacci and Lucas Identities with the Coefficients in Arithmetic ProgressionIOSRJM
We define an analogous pair of recurrence relations that yield some Fibonacci, Lucas and generalized Fibonacci identities with the coefficients in arithmetic progression. One relation yields same sign identities and the other alternating signs identities. We also show some new results for negative indexed Fibonacci and Lucas Sequences.
A Note on Hessen berg of Trapezoidal Fuzzy Number MatricesIOSRJM
The fuzzy set theory has been applied in many fields such as management, engineering, theory of matrices and so on. in this paper, some elementary operations on proposed trapezoidal fuzzy numbers (TrFNS) are defined. We also have been defined some operations on trapezoidal fuzzy matrices(TrFMs). The notion of Hessenberg fuzzy matrices are introduced and discussed. Some of their relevant properties have also been verified.
Enumeration Class of Polyominoes Defined by Two ColumnIOSRJM
Abacus diagram is a graphical representation for any partition µ of a positive integer t. This study presents the bead positions as a unite square in the graph and de ne a special type of e-abacus called nested chain abacus 픑 which is represented by the connected partition. Furthermore, we redefined the polyominoes as a special type of e-abacus diagram. Also, this study reveals new method of enumerating polyominoes special design when e=2
A New Method for Solving Transportation Problems Considering Average PenaltyIOSRJM
Vogel’s Approximation Method (VAM) is one of the conventional methods that gives better Initial Basic Feasible Solution (IBFS) of a Transportation Problem (TP). This method considers the row penalty and column penalty of a Transportation Table (TT) which are the differences between the lowest and next lowest cost of each row and each column of the TT respectively. In a little bit different way, the current method consider the Average Row Penalty (ARP) and Average Column Penalty (ACP) which are the averages of the differences of cell values of each row and each column respectively from the lowest cell value of the corresponding row and column of the TT. Allocations of costs are started in the cell along the row or column which has the highest ARP or ACP. These cells are called basic cells. The details of the developed algorithm with some numerical illustrations are discussed in this article to show that it gives better solution than VAM and some other familiar methods in some cases.
Effect of Magnetic Field on Peristaltic Flow of Williamson Fluid in a Symmetr...IOSRJM
This paper deals with the influence of magnetic field on peristaltic flow of an incompressible Williamson fluid in a symmetric channel with heat and mass transfer. Convective conditions of heat and mass transfer are employed. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
Devaney Chaos Induced by Turbulent and Erratic FunctionsIOSRJM
Let I be a compact interval and f be a continuous function defined from I to I. We study the relationship between tubulent function, erratic function and Devaney Chaos.
Bayesian Hierarchical Model of Width of Keratinized GingivaIOSRJM
The purpose of this paper is to offer a method for studying the treatment result of gingival recession. A parameter showing the success of the surgical treatment of gingival recessions is the keratinized gingival width. It was measured four times: at baseline, after 1 month, after 3 months and after 6 months. Every patient has data that can be described by an individual trend. Bayesian hierarchical model of the keratinized gingiva width’s increase rate is built.
A Novel Approach for the Solution of a Love’s Integral Equations Using Bernst...IOSRJM
In this paper a novel technique implementing Bernstein polynomials is introduced for the numerical solution of a Love’s integral equations. The Love’s integral equation is a class of second kind Fredholm integral equations, and it can be used to describe the capacitance of the parallel plate capacitor (PPC) in the electrostatic field.This numerical technique developed by Huabsomboon et al. bases on using Taylor-series expansion [1], [2], [3] and [4]. We compare the numerical solution using Bernstein technique with the numerical solution obtained by using Chebyshev expansion. It is shown that the numerical results are excellent.
IN THIS NOTE WE INVOKE THE HESSIAN POLYHEDRON WITH 3 REAL AND IMAGINARY AXES THAT YIELD THE 27 APICES OF THE GRAPH OF E6 SHOWN IN FIG.1.IN PARTICULAR WE WILL IDENTIFY THE QUARKS AS BELONGING TO THE COMPLEX SPACE INTHE OUTER RING,WHICH ACCOUNTS FOR THEIR TINY MASSES THAT CAN ONLY BE ESTIMATED
: The tensor product G H of two graphs G and H is well-known graph product and studied in detail in the literature. This concept has been generalized by introducing 2-tensor product G H 2 and it has been discussed for special graphs like P n and Cn [5]. In this paper, we discuss G H 2 , where G and H are connected graphs. Mainly, we discuss connectedness of G H 2 and obtained distance between two vertices in it.
Classification of MR medical images Based Rough-Fuzzy KMeansIOSRJM
Image classification is very significant for many vision of computer and it has acquired significant solicitude from industry and research over last years. We, explore an algorithm via the approximation of Fuzzy -Rough- K-means (FRKM), to bring to light data reliance, data decreasing, estimated of the classification (partition) of the set, and induction of rule from databases of the image. Rough theory provide a successful approach of carrying on precariousness and furthermore applied for image classification feature similarity dimensionality reduction and style categorization. The suggested algorithm is derived from a k means classifier using rough theory for segmentation (or processing) of the image which is moreover split into two portions. Exploratory conclusion output that, suggested method execute well and get better the classification outputs in the fuzzy areas of the image. The results explain that the FRKM execute well than purely using rough set, it can get 94.4% accuracy figure of image classification that, is over 88.25% by using only rough set.
A Trivariate Weibull Model for Oestradiol Plus Progestrone Treatment Increase...IOSRJM
In the previous studies a hypothesis was developed from the results by using trivariate Weibull model that the increase in leptin concentrations during the second half of the menstrual cycle may be related to changes in the steroidal milieu during the pre ovulatory period and the luteal phase. The present study was undertaken to test this hypothesis further by examining the effect of treatment with oestradiol and progesterone on leptine concentrations in normal pre menopausal women. The trivariate Weibull model is used for finding survival functions and log-likelihood functions for corresponding values of oestradiol, LH and Leptin for both untreated and treated with oestradiol and oestradiol plus progesterone respectively.
A Generalised Class of Unbiased Seperate Regression Type Estimator under Stra...IOSRJM
In this paper a generalized class of regression type estimators using the auxiliary information on population mean and population variance is proposed under stratified random sampling. In order to improve the performance of the proposed class of estimator, the Jack-knifed versions are also proposed. A comparative study of the proposed estimator is made with that of separate ratio estimator, separate product estimator, separate linear regression estimator and the usual stratified sample mean. It is shown that the estimators through proposed allocation always give more efficient estimators in the sense of having smaller mean square error than those obtained through Neyman Allocation
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
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Considerations on the genetic equilibrium law
1. IOSR Journal of Mathematics (IOSR-JM)
e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 1 Ver. I (Jan. - Feb. 2017), PP 01-03
www.iosrjournals.org
DOI: 10.9790/5728-1301010103 www.iosrjournals.org 1 | Page
Considerations on the genetic equilibrium law
Simone Camosso
(Università degli studi di Milano Bicocca, Italy)
Abstract: In the first part of the paper I willpresentabriefreview on the Hardy-Weinberg equilibrium
and it's formulation in projective algebraicgeometry. In the second and last part I
willdiscussexamples and generalizations on the topic.
Keywords:Hardy-Weinberg, likelihood function, maximum likelihood estimation.
I. Introduction
The study of population genetics, evolution and its evolutionary trees are classical subjects in biology.
A mathematical approach consists in the maximum likelihood estimation, a technique largely used in statistic.
This approach leads to the problem of maximizing particular functions of certain parameters. A theoretical study
and an upper bound for the maximum likelihood degree is discussed in [3]. Different techniques in order to
solve likelihood equations are described in [6]. Applications of these methods have been used when the
statistical model is an algebraic variety, this is the case of Fermat hypersurfaces treated in [1]. In the other side
we have applications of these ideas to biological models. In this direction we refer to a work of [4] where
phylogenetic models in two different topologies have been studied by the authors. The purpose of this paper is a
“soft” introduction to these ideas with a discussion on the Hardy-Weinberg case.
II. The Hardy-Weinberg law
The Hardy-Weinberg law states that allele and genotype frequencies in a population remain constant
during the generation change. This happens under the following assumptions: the size of the population must be
very large, we have absence of migration and mutations, the mating is random and the natural selection doesn't
affect the alleles under consideration. Mathematically if p represents the number or pure dominants characters
AA, q the number of heterozygotes Aa and r the number of pure recessives aa, the following proportion holds
p:2q:r (see [5]). Another way, if p and q represent the allele frequencies of the character A anda with p+q=1,
taking the square we find that:
𝑝2
+ 2𝑝𝑞 + 𝑞2
= 1, (2.1)
where 𝑝2
, 2𝑝𝑞 and 𝑞2
represent the genotype frequencies associated to AA,Aa and aa. The equation
(2.1) describes the constancy of the genotypic composition of the population and is called the Hardy-Weinberg
principle or the Hardy-Weinberg equilibrium (HWE). We consider [11] and [12] as scholarly references on this
subject. Different generalizations of (2.1) are possible. The first concerns the number of alleles at a locus. For
example in the case of three alleles A1, A2 and A3, with frequencies respectively given by p,q and r, the genotype
frequencies are given by the following expansion (p+q+r)2
=p2
+q2
+r2
+2pq+2qr+2pr. In general, for any
number n of alleles with frequencies pi, we have that:
𝑝1+. . . +𝑝 𝑛
2
= 𝑝𝑖
2𝑛
𝑖=1 + 𝑝𝑖
𝑛
𝑖≠𝑗 𝑝𝑗 . (2.2)
In another direction the generalization is given considering the binomial (𝑝 + 𝑞) 𝑚
, with m=3,4,5,….
This is the case of polyploid. For example considering tetraploids (m=4) the procedure involves the expansion
of (𝑝 + 𝑞)4
. We observe how in this particular example the frequency of heterozygotes (given by the mixed
terms in the expansion) is 2pq(2-pq) that is considerably greater then 2pq, the frequency for a diploid organism.
More information on this topic can be found in [11].
III. Projective and algebraic geometry
In this section we shall examine how translate previous considerations in the modern language of
projective and algebraic geometry. The setting is the same of [8] in its first lecture. We shall show how the
Hardy-Weinberg law can be formulated in a fixed system of homogeneous coordinates l,m,nin 𝑃2
. First we shall
consider the open triangle ∆2 𝑙, 𝑚, 𝑛 ={𝑅+
3
: l+m+n=1}, where 𝑅+are the positive reals. Second we shall
observe that setting l=p2
,m=2pq,n=q2
to be genotype frequencies, we have the relation:
2. Considerations on the genetic equilibrium law
DOI: 10.9790/5728-1301010103 www.iosrjournals.org 2 | Page
𝑚2
= 4𝑛𝑙, (3.1)
that is the equation of a parabola in the triangle of vertex (1,0,0),(0,1,0),(0,0,1). We call the zero locus
of (3.1) denoted also by V(m2
-4ln), the Hardy-Weinberg curve (details are in [10]). In the theory of [8] (and [9])
is of particular interest a function called “likelihood function” that depends by some positive integer parameters.
This function is positive on ∆2and zero on the boundary of∆2. We shall denote this function by l and with
u0,u1,… the corresponding parameters. In the case of the Hardy-Weinberg curve this function has the following
form:
𝑙 𝑢0,𝑢1,𝑢2
= 𝑙 𝑢0 𝑚 𝑢1 𝑛 𝑢2 = 2 𝑢1 𝑝2𝑢0+𝑢1 𝑞 𝑢1+2𝑢2.
We observe that 𝑙 𝑢0,𝑢1,𝑢2
is a function depending only by the variable p (because q=1-p) and the MLE
problem consists in the estimation of p maximizing the function 𝑙 𝑢0,𝑢1,𝑢2
.Lagrange Multipliers can be used in
order to solve the problem and in this case the solution is given by the point:
𝑝 =
2𝑢0 + 𝑢1
2𝑢0 + 2𝑢1 + 2𝑢2
.
IV. Examples, generalizations and conclusion
As exercise we shall apply the same procedure in order to solve the MLE problem for the case of three
alleles and in the second time for the case of tetraploids. For the first we shall start writing the “likelihood
function” associated to the HWE given by (p+q+r)2
, where p,q and r are the usual frequencies. In this case we
have that:
𝑙 𝑢0,𝑢1,𝑢2,𝑢3,𝑢4,𝑢5
= 2 𝑢3+𝑢4+𝑢5 𝑝2𝑢0+𝑢3+𝑢5 𝑞2𝑢1+𝑢3+𝑢4 (1 − 𝑝 − 𝑞)2𝑢2+𝑢4+𝑢5 .
We shall proceed maximizing the function of two variables p,q. This is an ordinary problem of calculus that
gives as answer the point:
𝑝 =
2𝑢0+𝑢3+𝑢5
2𝑢1+2𝑢2+2𝑢4+𝑢3+𝑢5
,
𝑢4−𝑢5+2𝑢1−2𝑢0
2𝑢1+2𝑢2+2𝑢4+𝑢3+𝑢5
,
2𝑢2+𝑢5+𝑢4
2𝑢1+2𝑢2+2𝑢4+𝑢3+𝑢5
.
For the tetraploid case, before to proceed, we shall observe that callingl0=p4
,l1=q4
,l2=4pq3
,l3=4p3
q,l4=6p2
q2
the
genotype frequencies, the Hardy-Weinberg equilibrium can be represented by the following relation:
𝑙4
4
=
1
81
𝑙0 𝑙1 𝑙2 𝑙3.
The associated “likelihood function” is
𝑙 𝑢0,𝑢1,𝑢2,𝑢3,𝑢4
= 𝑙0
𝑢0
𝑙1
𝑢1
𝑙2
𝑢2
𝑙3
𝑢3
𝑙4
𝑢4
.
We shall make the expedient of consider the logarithm of the previous function instead the original finding as
maximizing point:
𝑢0
𝑢
,
𝑢1
𝑢
,
𝑢2
𝑢
,
𝑢3
𝑢
,
𝑢4
|𝑢|
,
where 𝑢 = 𝑢0 + 𝑢1 + 𝑢2 + 𝑢3 + 𝑢4 .We recommended the use of a scientific software, as Maple or
MATLAB, especially when the number of parameters is considerably high. Now I want to spend these last
words comparing analogies between the HWE and the algebraic geometry. It is clear that a possible extension of
the Hardy-Weinberg law can take the following form:
𝑝1+. . . +𝑝 𝑛
𝑚
= 𝑐, (4.1)
wherec is some constant and pi from i=0,…,n are the allele frequencies such that the sum is fixed. Now
expanding (4.1) we find the polynomial form:
𝑚!
𝑖0! … 𝑖 𝑛 !
𝑖0+⋯+𝑖 𝑛 =𝑚
𝑝0
𝑖0
… 𝑝 𝑛
𝑖 𝑛
= 𝑐.
3. Considerations on the genetic equilibrium law
DOI: 10.9790/5728-1301010103 www.iosrjournals.org 3 | Page
From the algebraic geometry point of view this is the image of the Veronese mapνm:Pn
→ 𝑃
𝑛+𝑚
𝑚
−1
given by (p0,…,pn)⟼(p0
m
,p0
m-1
p1,…,pn
m
) (see [2]). The classical Hardy-Weinberg law corresponds to the case of
ν1:P1
→ 𝑃2
that (p,q ) ⟼(p2
,pq,q2
) and c=1. Using the identification between homogeneous polynomials that
are power of linear forms and the image of the Veronese map, we can think these generalized laws as Veronese
projective varieties. From the side of algebraic geometry there are a rich collection of results concerning the
Veronese and Segre varieties, for example it is possible to compute the Hilbert polynomial and other invariants.
It is not all peace and light because the constraint ∆ 𝑛 = {(p0,…,pn) ∈ 𝑅+
𝑛+1
:p0… +pn=1} doesn't permit the
complete translation of the problem using the previousidentification.
Anyway the methods of numerical algebraic geometry seem to give good prospects in this direction
and in [7] the ML degree has been calculated for matrices with rank constraints. In particular the case of rank
one gives the ML degree equal to one, so 𝑝 is a rational function of a set of parameters u0,u1,….
References
Journal Papers:
[1]. D.Agostini, D.Alberelli, F.Grande, P.Lella, The maximum likelihood degree of Fermat hypersurfaces, arXiv:1404.5745.
[2]. E.Arrondo, Introduction to projective varieties, unpublished notes from the website: http://www.mat.ucm.es/~arrondo/projvar.pdf
(2007), 9-10.
[3]. F.Catanese, S.Hoşten, A.Khetan, B.Sturmfels, The maximum likelihood degree, Amer. J. Math. 128 (2006), no. 3, 671-697. MR
2230921.
[4]. B.Chor, A.Khetan, S.Snir, Maximum likelihood on four taxa phylogenetic trees: analytic solutions, The 7th Annual Conference on
Research in Computational Molecular Biology-RECOMB 2003, Berlin, April 2003, pp. 76-83.
[5]. G.H.Hardy, Mendelian Proportions in a Mixed Population, Science, New Series, Vol.28, 706 (1908), 49-50.
[6]. S.Hoşten, A.Khetan, B.Sturmfels, Solving the Likelihood Equations, Foundations of Computational Mathematics, Vol. 5, Issue 4,
pp 389-407, 2005.
[7]. J.Hauenstein, J.Rodriguez, B.Sturmfels, Maximum Likelihood for Matrices with Rank Constraints, Journal of Algebraic Statistics,
Vol.5, Issue 1 (2014), pp 18-38.
[8]. J.Huh, B.Sturmfels, Likelihood Geometry, Combinatorial Algebraic Geometry: LevicoTerme, Italy 2013, Springer International
Publishing, Vol.2108 of the series Lecture Notes in Mathematics (2014), 63-117.
[9]. I.J.Myung, Tutorial on maximum likelihood estimation, Journal of Mathematical Psychology 47 (2003) 90-100.
Books:
[10]. A.W.F.Edwards, Foundations of Mathematical Genetics, Cambridge University Press, Cambridge (2000).
[11]. R.Frankham, J.D.Ballou, D.A.Briscoe, Introduction to conservation genetics, Cambridge (2002), 86-90.
[12]. D.L.Hartl, A.G.Clark, Principles of population genetics, Sinauer Associates, Inc. Publishers, Sunderland, Massachusetts (Fourth
Edition).