This formula was derived by H.C. Rajpoot to calculate rank of any linear permutation when repetition of articles is allowed. HCR’s Rank formula-2 can be applied to calculate the rank of any linear permutation when the repetition of the articles (like digits, letters & all other objects having different shape, size, colour & other aesthetic quality) is allowed.
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This document provides an overview of probabilistic reasoning and uncertainty in knowledge representation. It discusses:
1) Using probability theory to represent uncertainty quantitatively rather than logical rules with certainty factors.
2) Key concepts in probability theory including random variables, probability distributions, joint probabilities, marginal probabilities, and conditional probabilities.
3) Representing a problem domain as a probabilistic model with a sample space of possible variable states.
4) Independence of variables allowing simpler computation of probabilities.
5) The document is an introduction to probabilistic reasoning concepts to be covered in more detail later, including Bayesian networks.
Mc0079 computer based optimization methods--phpapp02Rabby Bhatt
This document discusses mathematical models and provides examples of different types of mathematical models. It begins by defining a mathematical model as a description of a system using mathematical concepts and language. It then classifies mathematical models in several ways, such as linear vs nonlinear, deterministic vs probabilistic, static vs dynamic, discrete vs continuous, and deductive vs inductive vs floating. The document provides examples and explanations of each type of model. It also discusses using finite queuing tables to analyze queuing systems with a finite population size. In summary, the document outlines different ways to classify mathematical models and provides examples of applying various types of models.
This document discusses various text functions in Microsoft Excel that can be used to manipulate and analyze text data. It provides an overview and examples of functions such as CONCATENATE, EXACT, FIND, FIXED, LEN, LOWER, MID, and others. These functions allow the user to combine, compare, extract, format, and modify portions of text from cells. Understanding and applying these functions provides flexibility in cleaning, analyzing, and presenting textual data in Excel workbooks.
Master of Computer Application (MCA) – Semester 4 MC0079Aravind NC
The document describes mathematical models and provides examples of different types of models. It discusses linear vs nonlinear models, deterministic vs probabilistic models, static vs dynamic models, discrete vs continuous models, and deductive vs inductive vs floating models. It also explains the Erlang family of distributions used in queuing systems and provides the probability density function and cumulative distribution function. Finally, it outlines the graphical method algorithm for solving a linear programming problem with two variables in 8 steps.
This document discusses theory of computation and finite automata. It begins by defining theory of computation as dealing with the logic of computation using abstract machines called automata. It then defines basic terminology like symbols, alphabets, strings, and languages. Next, it introduces finite automata as the simplest machines that recognize patterns using a finite set of states. Deterministic finite automata and nondeterministic finite automata are described as the two types of finite automata, differing in their transition functions. Transition diagrams and tables are also presented as ways to represent finite automata.
Mca 4040 analysis and design of algorithmsmumbahelp
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Mca 4040 analysis and design of algorithmsmumbahelp
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(Prefer mailing. Call in emergency )
This document provides an overview of probabilistic reasoning and uncertainty in knowledge representation. It discusses:
1) Using probability theory to represent uncertainty quantitatively rather than logical rules with certainty factors.
2) Key concepts in probability theory including random variables, probability distributions, joint probabilities, marginal probabilities, and conditional probabilities.
3) Representing a problem domain as a probabilistic model with a sample space of possible variable states.
4) Independence of variables allowing simpler computation of probabilities.
5) The document is an introduction to probabilistic reasoning concepts to be covered in more detail later, including Bayesian networks.
Mc0079 computer based optimization methods--phpapp02Rabby Bhatt
This document discusses mathematical models and provides examples of different types of mathematical models. It begins by defining a mathematical model as a description of a system using mathematical concepts and language. It then classifies mathematical models in several ways, such as linear vs nonlinear, deterministic vs probabilistic, static vs dynamic, discrete vs continuous, and deductive vs inductive vs floating. The document provides examples and explanations of each type of model. It also discusses using finite queuing tables to analyze queuing systems with a finite population size. In summary, the document outlines different ways to classify mathematical models and provides examples of applying various types of models.
This document discusses various text functions in Microsoft Excel that can be used to manipulate and analyze text data. It provides an overview and examples of functions such as CONCATENATE, EXACT, FIND, FIXED, LEN, LOWER, MID, and others. These functions allow the user to combine, compare, extract, format, and modify portions of text from cells. Understanding and applying these functions provides flexibility in cleaning, analyzing, and presenting textual data in Excel workbooks.
Master of Computer Application (MCA) – Semester 4 MC0079Aravind NC
The document describes mathematical models and provides examples of different types of models. It discusses linear vs nonlinear models, deterministic vs probabilistic models, static vs dynamic models, discrete vs continuous models, and deductive vs inductive vs floating models. It also explains the Erlang family of distributions used in queuing systems and provides the probability density function and cumulative distribution function. Finally, it outlines the graphical method algorithm for solving a linear programming problem with two variables in 8 steps.
This document discusses theory of computation and finite automata. It begins by defining theory of computation as dealing with the logic of computation using abstract machines called automata. It then defines basic terminology like symbols, alphabets, strings, and languages. Next, it introduces finite automata as the simplest machines that recognize patterns using a finite set of states. Deterministic finite automata and nondeterministic finite automata are described as the two types of finite automata, differing in their transition functions. Transition diagrams and tables are also presented as ways to represent finite automata.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
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Call us at : 08263069601
This document provides an overview of mathematical logic and set theory concepts. It discusses topics such as mathematical logic and its subfields, basic set theory concepts like membership and subsets, set operations like union and intersection, and logical concepts like negation, conjunction, and syllogisms. It also explains logical form and provides examples of open and closed sentences as well as categorical and compound sentences.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This document provides an introduction to the theory of computation, including definitions of key concepts like automata theory, symbols, alphabets, strings, languages, and sets. It discusses how automata theory deals with formal models of computation and is used in areas like text processing and programming languages. Mathematical terminology is introduced, such as symbols, alphabets, strings, languages, sets, and the power and Cartesian product of alphabets. Examples are given to illustrate concepts like strings, languages, and valid versus invalid computations based on whether a string is contained within a language.
AN IMPLEMENTATION, EMPIRICAL EVALUATION AND PROPOSED IMPROVEMENT FOR BIDIRECT...ijaia
The document summarizes an implementation and evaluation of the bidirectional splitting method for computing stable semantics in abstract argumentation frameworks. Bidirectional splitting divides a framework into two parts without requiring that all attacks between parts be directed in the same way. The study implements bidirectional splitting using minimum cut and balanced cut algorithms. Experimental results show that using a balanced cut, which divides the framework into equal halves, provides a significant improvement in computing stable semantics compared to using a minimum cut.
This document discusses the relational model and relational database concepts. It covers domains and relations, relational keys like primary keys, foreign keys, and candidate keys. It also discusses relational algebra operations like selection, projection, join, and set operations. Relational calculus is introduced. The SQL language components of DDL, DML, and DCL are mentioned for data definition, manipulation, and control. Key concepts like views, nested tables, and correlated subqueries are also summarized briefly.
This document discusses different concepts related to the relational model including domains and relations, relational data integrity, keys such as primary keys, candidate keys, foreign keys and their rules. It also discusses relational operators, relational algebra, relational calculus and SQL. Finally, it describes different types of relational algebra operations including unary operations like select, project and rename and binary operations like join, union, intersection, difference and cartesian product.
This document discusses soft computing and fuzzy sets. It begins by defining soft computing as being tolerant of imprecision and focusing on approximation rather than precise outputs. Fuzzy sets are introduced as a tool of soft computing that allow for graded membership in sets rather than binary membership. Key concepts regarding fuzzy sets are explained, including fuzzy logic operations, fuzzy numbers, and fuzzy variables. Linear programming problems are discussed and how they can be modeled as fuzzy linear programming problems to account for imprecision in the coefficients and constraints.
Matching and proof search are key concepts in Prolog. Matching occurs when two terms are equal or can be made equal through variable instantiation. Proof search involves finding facts or rules in the knowledge base that match the query goals through a top-down, depth-first search. This allows Prolog to extract the desired information by chaining together rules and facts that satisfy the query.
Some alternative ways to find m ambiguous binary words corresponding to a par...ijcsa
Parikh matrix of a word gives numerical information of the word in terms of its subwords. In this Paper an
algorithm for finding Parikh matrix of a binary word is introduced. With the help of this algorithm Parikh
matrix of a binary word, however large it may be can be found out. M-ambiguous words are the problem of
Parikh matrix. In this paper an algorithm is shown to find the M- ambiguous words of a binary ordered
word instantly. We have introduced a system to represent binary words in a two dimensional field. We see
that there are some relations among the representations of M-ambiguous words in the two dimensional
field. We have also introduced a set of equations which will help us to calculate the M- ambiguous words.
The document discusses the Boyer-Moore string searching algorithm. It works by preprocessing the pattern string and comparing characters from right to left. If a mismatch occurs, it uses two heuristics - bad character and good suffix - to determine the shift amount. The bad character heuristic shifts past mismatching characters, while the good suffix heuristic looks for matching suffixes to allow larger shifts. The algorithm generally gets faster as the pattern length increases, running in sub-linear time on average. It has applications in tasks like virus scanning and database searching that require high-speed string searching.
Image-Based Literal Node Matching for Linked Data IntegrationIJwest
This paper proposes a method of identifying and aggregating literal nodes that have the same meaning in Linked Open Data (LOD) in order to facilitate cross-domain search. LOD has a graph structure in which most nodes are represented by Uniform Resource Identifiers (URIs), and thus LOD sets are connected and searched through different domains.However, 5% of the values are literal values (strings without URI) even in a de facto hub of LOD, DBpedia. In SPARQL Protocol and RDF Query Language (SPARQL) queries, we need to rely on regular expression to match and trace the literal nodes. Therefore, we propose a novel method, in which part of the LOD graph structure is regarded as a block image, and then the matching is calculated by image features of LOD. In experiments, we created about 30,000 literal pairs from a Japanese music category of DBpedia Japanese and Freebase, and confirmed that the proposed method determines literal identity with F-measure of 76.1-85.0%.
This is a finite series which is the sum of first „n‟ natural numbers multiplied by their own respective
factorials. The series has been derived from HCR‟s Rank formula which was proposed by the author. It is
extremely useful in case studies & computations. Although HCR‟s Series is different from the Arithmetic,
Geometric, Harmonic & Taylor‟s Series of simple functions, it is the expansion of factorial of any natural
number in form of discrete summation thus it is also named as HCR‟s divergence series.
Design of second order linear time invariant systems for deadbeat responseIAEME Publication
This document summarizes a research paper that proposes a new method for analyzing the stability and deadbeat response of linear time-invariant systems using a modified Routh's table approach. The method first converts the system's characteristic equation with real coefficients into a complex coefficient equation using Romonov's transformation. It then forms a Routh-like table using the complex coefficients. Stability is determined by analyzing the sign pairs in the first column based on a proposed "Sign Pair Criterion." The method is demonstrated on an example system, verifying the number of complex roots and ability to design for a deadbeat response. The proposed approach provides an algebraic way to analyze stability and deadbeat response without determining the system's roots.
This document discusses Python programming concepts including data types, operators, expressions, and control flow. It covers core data types like integers, floats, strings, Booleans, lists, and tuples. It also describes arithmetic, comparison, assignment, logical, membership, and identity operators. Control flow concepts explained are if, if-elif-else, for, while loops, and statements like break, continue, and pass. The document is presented by B SNV Ramana Murthy of the computer science department at Aditya College of Engineering & Technology.
This document provides an overview of various functions and features in Excel. It discusses navigating the menu bar and tool bar, inserting charts and tables, applying filters and sorting, validating data, creating pivot tables and scenarios, and using functions like IF, VLOOKUP, and INDEX among others. The document is presented by Ravi Rai and consists of explanations and syntax for implementing different Excel functions and analyzing data.
HCR's Rank Formula can be applied to calculate the rank of any linear permutation of articles having different shapes, sizes, colors etc. when the repetition of articles is not allowed
The Improved Hybrid Algorithm for the Atheer and Berry-ravindran Algorithms IJECEIAES
Exact String matching considers is one of the important ways in solving the basic problems in computer science. This research proposed a hybrid exact string matching algorithm called E-Atheer. This algorithm depended on good features; searching and shifting techniques in the Atheer and BerryRavindran algorithms, respectively. The proposed algorithm showed better performance in number of attempts and character comparisons compared to the original and recent and standard algorithms. E-Atheer algorithm used several types of databases, which are DNA, Protein, XML, Pitch, English, and Source. The best performancein the number of attempts is when the algorithm is executed using the pitch dataset. The worst performance is when it is used with DNA dataset. The best and worst databases in the number of character comparisons with the E-Atheer algorithm are the Source and DNA databases, respectively.
Certain Algebraic Procedures for the Aperiodic Stability Analysis and Countin...Waqas Tariq
To evaluate the performance of a linear time-invariant system, various measures are available. In this paper employing Routh’s table, two geometrical criteria for the aperiodic stability analysis of linear time-invariant systems having real coefficients are formulated. The proposed algebraic stability criteria check whether the given linear system is aperiodically stable or not.The additional significance of the two criteria is , it can be used to count the number of complex roots of a system having real coefficients which is not possible by the use of original Routh’s Table. These procedures can also be used for the design of linear systems. In the proposed methods , the characteristic equation having real coefficients are first converted to complex coefficient equations using Romonov’s transformation. These complex coefficients are used in two different ways to form the Modified Routh’s tables for the two schemes named as Sign Pair Criterion I (SPC I) and Sign Pair Criterion II (SPC II). It is found that the proposed algorithms offer computational simplicity compared to other algebraic methods and is illustrated with suitable examples. The developed MATLAB program make the analysis most simple.
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
This document provides an overview of mathematical logic and set theory concepts. It discusses topics such as mathematical logic and its subfields, basic set theory concepts like membership and subsets, set operations like union and intersection, and logical concepts like negation, conjunction, and syllogisms. It also explains logical form and provides examples of open and closed sentences as well as categorical and compound sentences.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This document provides an introduction to the theory of computation, including definitions of key concepts like automata theory, symbols, alphabets, strings, languages, and sets. It discusses how automata theory deals with formal models of computation and is used in areas like text processing and programming languages. Mathematical terminology is introduced, such as symbols, alphabets, strings, languages, sets, and the power and Cartesian product of alphabets. Examples are given to illustrate concepts like strings, languages, and valid versus invalid computations based on whether a string is contained within a language.
AN IMPLEMENTATION, EMPIRICAL EVALUATION AND PROPOSED IMPROVEMENT FOR BIDIRECT...ijaia
The document summarizes an implementation and evaluation of the bidirectional splitting method for computing stable semantics in abstract argumentation frameworks. Bidirectional splitting divides a framework into two parts without requiring that all attacks between parts be directed in the same way. The study implements bidirectional splitting using minimum cut and balanced cut algorithms. Experimental results show that using a balanced cut, which divides the framework into equal halves, provides a significant improvement in computing stable semantics compared to using a minimum cut.
This document discusses the relational model and relational database concepts. It covers domains and relations, relational keys like primary keys, foreign keys, and candidate keys. It also discusses relational algebra operations like selection, projection, join, and set operations. Relational calculus is introduced. The SQL language components of DDL, DML, and DCL are mentioned for data definition, manipulation, and control. Key concepts like views, nested tables, and correlated subqueries are also summarized briefly.
This document discusses different concepts related to the relational model including domains and relations, relational data integrity, keys such as primary keys, candidate keys, foreign keys and their rules. It also discusses relational operators, relational algebra, relational calculus and SQL. Finally, it describes different types of relational algebra operations including unary operations like select, project and rename and binary operations like join, union, intersection, difference and cartesian product.
This document discusses soft computing and fuzzy sets. It begins by defining soft computing as being tolerant of imprecision and focusing on approximation rather than precise outputs. Fuzzy sets are introduced as a tool of soft computing that allow for graded membership in sets rather than binary membership. Key concepts regarding fuzzy sets are explained, including fuzzy logic operations, fuzzy numbers, and fuzzy variables. Linear programming problems are discussed and how they can be modeled as fuzzy linear programming problems to account for imprecision in the coefficients and constraints.
Matching and proof search are key concepts in Prolog. Matching occurs when two terms are equal or can be made equal through variable instantiation. Proof search involves finding facts or rules in the knowledge base that match the query goals through a top-down, depth-first search. This allows Prolog to extract the desired information by chaining together rules and facts that satisfy the query.
Some alternative ways to find m ambiguous binary words corresponding to a par...ijcsa
Parikh matrix of a word gives numerical information of the word in terms of its subwords. In this Paper an
algorithm for finding Parikh matrix of a binary word is introduced. With the help of this algorithm Parikh
matrix of a binary word, however large it may be can be found out. M-ambiguous words are the problem of
Parikh matrix. In this paper an algorithm is shown to find the M- ambiguous words of a binary ordered
word instantly. We have introduced a system to represent binary words in a two dimensional field. We see
that there are some relations among the representations of M-ambiguous words in the two dimensional
field. We have also introduced a set of equations which will help us to calculate the M- ambiguous words.
The document discusses the Boyer-Moore string searching algorithm. It works by preprocessing the pattern string and comparing characters from right to left. If a mismatch occurs, it uses two heuristics - bad character and good suffix - to determine the shift amount. The bad character heuristic shifts past mismatching characters, while the good suffix heuristic looks for matching suffixes to allow larger shifts. The algorithm generally gets faster as the pattern length increases, running in sub-linear time on average. It has applications in tasks like virus scanning and database searching that require high-speed string searching.
Image-Based Literal Node Matching for Linked Data IntegrationIJwest
This paper proposes a method of identifying and aggregating literal nodes that have the same meaning in Linked Open Data (LOD) in order to facilitate cross-domain search. LOD has a graph structure in which most nodes are represented by Uniform Resource Identifiers (URIs), and thus LOD sets are connected and searched through different domains.However, 5% of the values are literal values (strings without URI) even in a de facto hub of LOD, DBpedia. In SPARQL Protocol and RDF Query Language (SPARQL) queries, we need to rely on regular expression to match and trace the literal nodes. Therefore, we propose a novel method, in which part of the LOD graph structure is regarded as a block image, and then the matching is calculated by image features of LOD. In experiments, we created about 30,000 literal pairs from a Japanese music category of DBpedia Japanese and Freebase, and confirmed that the proposed method determines literal identity with F-measure of 76.1-85.0%.
This is a finite series which is the sum of first „n‟ natural numbers multiplied by their own respective
factorials. The series has been derived from HCR‟s Rank formula which was proposed by the author. It is
extremely useful in case studies & computations. Although HCR‟s Series is different from the Arithmetic,
Geometric, Harmonic & Taylor‟s Series of simple functions, it is the expansion of factorial of any natural
number in form of discrete summation thus it is also named as HCR‟s divergence series.
Design of second order linear time invariant systems for deadbeat responseIAEME Publication
This document summarizes a research paper that proposes a new method for analyzing the stability and deadbeat response of linear time-invariant systems using a modified Routh's table approach. The method first converts the system's characteristic equation with real coefficients into a complex coefficient equation using Romonov's transformation. It then forms a Routh-like table using the complex coefficients. Stability is determined by analyzing the sign pairs in the first column based on a proposed "Sign Pair Criterion." The method is demonstrated on an example system, verifying the number of complex roots and ability to design for a deadbeat response. The proposed approach provides an algebraic way to analyze stability and deadbeat response without determining the system's roots.
This document discusses Python programming concepts including data types, operators, expressions, and control flow. It covers core data types like integers, floats, strings, Booleans, lists, and tuples. It also describes arithmetic, comparison, assignment, logical, membership, and identity operators. Control flow concepts explained are if, if-elif-else, for, while loops, and statements like break, continue, and pass. The document is presented by B SNV Ramana Murthy of the computer science department at Aditya College of Engineering & Technology.
This document provides an overview of various functions and features in Excel. It discusses navigating the menu bar and tool bar, inserting charts and tables, applying filters and sorting, validating data, creating pivot tables and scenarios, and using functions like IF, VLOOKUP, and INDEX among others. The document is presented by Ravi Rai and consists of explanations and syntax for implementing different Excel functions and analyzing data.
HCR's Rank Formula can be applied to calculate the rank of any linear permutation of articles having different shapes, sizes, colors etc. when the repetition of articles is not allowed
The Improved Hybrid Algorithm for the Atheer and Berry-ravindran Algorithms IJECEIAES
Exact String matching considers is one of the important ways in solving the basic problems in computer science. This research proposed a hybrid exact string matching algorithm called E-Atheer. This algorithm depended on good features; searching and shifting techniques in the Atheer and BerryRavindran algorithms, respectively. The proposed algorithm showed better performance in number of attempts and character comparisons compared to the original and recent and standard algorithms. E-Atheer algorithm used several types of databases, which are DNA, Protein, XML, Pitch, English, and Source. The best performancein the number of attempts is when the algorithm is executed using the pitch dataset. The worst performance is when it is used with DNA dataset. The best and worst databases in the number of character comparisons with the E-Atheer algorithm are the Source and DNA databases, respectively.
Certain Algebraic Procedures for the Aperiodic Stability Analysis and Countin...Waqas Tariq
To evaluate the performance of a linear time-invariant system, various measures are available. In this paper employing Routh’s table, two geometrical criteria for the aperiodic stability analysis of linear time-invariant systems having real coefficients are formulated. The proposed algebraic stability criteria check whether the given linear system is aperiodically stable or not.The additional significance of the two criteria is , it can be used to count the number of complex roots of a system having real coefficients which is not possible by the use of original Routh’s Table. These procedures can also be used for the design of linear systems. In the proposed methods , the characteristic equation having real coefficients are first converted to complex coefficient equations using Romonov’s transformation. These complex coefficients are used in two different ways to form the Modified Routh’s tables for the two schemes named as Sign Pair Criterion I (SPC I) and Sign Pair Criterion II (SPC II). It is found that the proposed algorithms offer computational simplicity compared to other algebraic methods and is illustrated with suitable examples. The developed MATLAB program make the analysis most simple.
Microsoft Excel is a powerful tool used for creating and formatting spreadsheets. Spreadsheets allow information to be organized in rows and columns and analyzed using automatic mathematics calculations. Excel is commonly used to perform various types of calculations by using functions like IF, AND, OR, SUM, VLOOKUP, and more. Macros can also be recorded and assigned to buttons to automate repetitive tasks in Excel.
Merge sort is a sorting algorithm that works as follows:
1. It divides the array into halves until each sub-array contains a single element.
2. It then combines the sub-arrays in a sorted way such that smaller elements are placed at the lower indexes.
3. To combine sub-arrays, it compares the elements and places them in a new array in ascending order.
4. This process continues until the entire array is sorted.
Similar to HCR's Rank formula 2 (to calculate rank of any linear permutation when the repetition of articles is allowed) (9)
Mathematical analysis of a non-uniform tetradecahedron having 2 congruent reg...Harish Chandra Rajpoot
All the important parameters of a non-uniform tetradecahedron, having 2 congruent regular hexagonal faces, 12 congruent trapezoidal faces & 18 vertices lying on a spherical surface with a certain radius, have been derived by the author by applying "HCR's Theory of Polygon" to calculate solid angle subtended by each regular hexagonal & trapezoidal face & their normal distances from the center of non-uniform tetradecahedron, inscribed radius, circumscribed radius, mean radius, surface area & volume. These formulas are very useful in the analysis, designing & modeling of various non-uniform polyhedra.
Mathematical analysis of non-uniform polyhedra having 2 congruent regular n-g...Harish Chandra Rajpoot
All the important formulas have been generalized which are applicable to calculate the important parameters, of any non-uniform polyhedron having 2 congruent regular n-gonal faces, 2n congruent trapezoidal faces each with three equal sides, 5n edges & 3n vertices lying on a spherical surface, such as solid angle subtended by each face at the centre, normal distance of each face from the centre, inner radius, outer radius, mean radius, surface area & volume. These are useful for the analysis, designing & modeling of different non-uniform polyhedra.
Regular N-gonal Right Antiprism: Application of HCR’s Theory of PolygonHarish Chandra Rajpoot
A regular n-gonal right antiprism is a semiregular convex polyhedron which has 2n identical vertices all lying on a sphere, 4n edges, and (2n+2) faces out of which 2 are congruent regular n-sided polygons, and 2n are congruent equilateral triangles such that all the faces have equal side. The equilateral triangular faces meet the regular polygonal faces at the common edges and vertices alternatively such that three equilateral triangular faces meet at each of 2n vertices. This paper presents, in details, the mathematical derivations of the generalized and analytic formula which are used to determine the different important parameters in terms of edge length, such as normal distances of faces, normal height, radius of circumscribed sphere, surface area, volume, dihedral angles between adjacent faces, solid angle subtended by each face at the centre, and solid angle subtended by polygonal antiprism at each of its 2n vertices using HCR’s Theory of Polygon. All the generalized formulae have been derived using simple trigonometry, and 2D geometry which are difficult to derive using any other methods.
The document presents mathematical derivations of parameters for a regular pentagonal right antiprism. It derives analytic formulas for the antiprism's normal heights, normal distances from faces to the center, radius of the circumscribed sphere, surface area, volume, and other values in terms of the antiprism's edge length. All formulas are derived using trigonometry and 2D geometry applied to the transformation of a regular icosahedron into the antiprism shape.
Derivation of great-circle distance formula using of HCR's Inverse cosine for...Harish Chandra Rajpoot
The author derives the great-circle distance formula using hcr's inverse cosine formula. An analytic and the most generalized formula has been derived to accurately compute the minimum distance or great circle distance between any two arbitrary points on a sphere of finite radius which is equally applicable in the geometry of sphere. This formula is extremely useful to calculate the geographical distance between any two points on the globe for the given latitudes & longitudes. This formula is the most power tool which is applicable for all the distances on the tiny sphere as well as the large sphere like giant planet assuming them the perfect spheres.
The circumscribed and the inscribed polygons are well known and mathematically well defined in the context of 2D-Geometry. The term ‘Circum-inscribed Polygon’ has been proposed by the author and used as a new definition of the polygon which satisfies the conditions of a circumscribed polygon and an inscribed polygon together. In other words, the circum-inscribed polygon is a polygon which has both the inscribed and circumscribed circles. The newly defined circum-inscribed polygon has each of its sides touching a circle and each of its vertices lying on another circle. The most common examples of circum-inscribed polygon are triangle, regular polygon, trapezium with each of its non-parallel sides equal to the Arithmetic Mean (AM) of its parallel sides (called circum-inscribed trapezium) and right kite. This paper describes the mathematical derivations of the analytic formula to find out the different parameters in terms of AM and GM of known sides such as radii of circumscribed & inscribed circles, unknown sides, interior angles, diagonals, angle between diagonals, ratio of intersecting diagonals, perimeter, area, and distance between circum-centre and in-centre of circum-inscribed trapezium. Like an inscribed polygon, a circum-inscribed polygon always has all of its vertices lying on infinite number of spherical surfaces. All the analytic formulae have been derived using simple trigonometry and 2-dimensional geometry which can be used to analyse the complex 2D and 3D geometric figures such as cyclic quadrilateral and trapezohedron, and other polyhedrons.
Mathematical Analysis of Rhombicuboctahedron (Application of HCR's Theory)Harish Chandra Rajpoot
The author H C Rajpoot has derived the radius of circumscribed sphere passing through all 24 identical vertices of a rhombicuboctahedron with given edge length by applying ‘HCR’s Theory of Polygon’ & subsequently derived various formula to analytically compute the normal distances of equilateral triangular & square faces from the centre of rhombicuboctahedron, radius of mid-sphere, surface area, volume, solid angles subtended by each equilateral triangular face & each square face at the centre by using ‘HCR’s Theory of Polygon’, dihedral angle between each two faces meeting at any of 24 identical vertices (i.e. truncated rhombic dodecahedron), solid angle subtended by truncated rhombic dodecahedron at any of its 24 identical vertices.
Mathematical analysis of truncated rhombic dodecahedron (HCR's Polyhedron)Harish Chandra Rajpoot
1) The document describes H.C. Rajpoot's analysis of a truncated rhombic dodecahedron using his "Theory of Polygon".
2) Key results include formulas for the radius of the circumscribed sphere, normal distances to different face types, surface area, volume, and dihedral angles between faces.
3) The analysis involves deriving the truncated polyhedron from a rhombic dodecahedron and establishing relationships between their geometric properties.
Mathematical Analysis of Rhombic Dodecahedron by applying HCR's Theory of Pol...Harish Chandra Rajpoot
In this paper, the author Mr H C Rajpoot mathematically analyses & derives analytic formula for a rhombic dodecahedron having 12 congruent faces each as a rhombus, 24 edges & 14 vertices lying on a spherical surface with a certain radius. ‘HCR’s Theory of Polygon’ is used to derive formula to analytically compute the angles & diagonals of rhombic face, radii of circumscribed sphere, inscribed sphere & midsphere, surface area & volume of rhombic dodecahedron in terms of edge length, solid angles subtended at the vertices and dihedral angle between adjacent faces. This convex polyhedron can be constructed by joining 12 congruent elementary-right pyramids with rhombic base & certain normal height.
Mathematical Analysis & Modeling of Pyramidal Flat Container, Right Pyramid &...Harish Chandra Rajpoot
This document derives generalized formulas to compute important parameters like the V-cut angle, edge length, dihedral angle, surface area, and volume of pyramidal flat containers, pyramids, and polyhedrons with regular polygonal bases. It applies HCR's Theorem and Corollary to develop formulas for a pyramidal container with a regular n-gonal base in terms of the base side length, slant height, and face inclination angle. Steps for constructing paper models of such containers are also outlined.
HCR's theorem (Rotation of two co-planar planes, meeting at angle bisector, a...Harish Chandra Rajpoot
In this theorem, the author derives a mathematical expression to analytically compute the V-cut angle (δ) required for rotating through the same angle (θ) the two co-planar planes, initially meeting at a common edge bisecting the angle (α) between their intersecting straight edges, about their intersecting straight edges until their new straight edges (generated after removing V-shaped planar region) coincide. As a result, we get a point (apex) where three planes intersect one another out of which two are original planes (rotated) & third one is their co-plane (fixed).
This theorem is very important for creating pyramidal flat containers with polygonal (regular or irregular) base, closed right pyramids & polyhedrons having two regular n-gonal & 2n congruent trapezoidal faces.
The author has also presented some paper models of pyramidal flat containers with regular pentagonal, heptagonal and octagonal bases
How to compute area of spherical triangle given the aperture angles subtended...Harish Chandra Rajpoot
The author Mr H.C. Rajpoot has derived the general formula to compute the area of the spherical triangle having each side as a great circle arc on the spherical surface when 1.) aperture angle subtended by each of three sides at the center of sphere are known 2.) arc length of each of three sides is known. These formula are applicable for any spherical triangle to the compute area on the sphere.
This document summarizes 9 formulas derived by Harish Chandra Rajpoot related to geometry of 2D shapes like squares, triangles, trapezoids, and circles. The derivations use basic geometry and trigonometry. Formula 1 finds the angle subtended by a point inside a square. Formula 2 finds the area of a quadrilateral formed inside a square. Subsequent formulas find radii or lengths related to combinations of these basic shapes. Diagrams and step-by-step workings are provided for each formula derivation.
Mathematical derivations of some important formula in 2D-Geometry H.C. RajpootHarish Chandra Rajpoot
Here are some important formula in 2D-Geometry derived by the author Mr H.C. Rajpoot using simple geometry & trigonometry. The formula, derived here, are related to the triangle, square, trapezium & tangent circles. These formula are very useful for case studies in 2D-Geometry to compute the important parameters of 2D-figures.
All the standard formula from 'Advanced Geometry' by the author Mr H.C. Rajpoot have been included in this book. These formula are related to the solid geometry dealing with the 2-D & the figures in 3-D space & miscellaneous articles in Trigonometry & Geometry. These are useful the standard formula for case studies & practical applications.
The author has derived the formula to analytically compute all the important parameters of a disphenoid (isosceles tetrahedron with four congruent acute-triangular faces) such as volume, surface area, vertical height, radii of inscribed & circumscribed spheres, solid angle subtended at each vertex, coordinates of vertices, in-centre, circum-centre & centroid of a disphenoid for the optimal configuration in 3D space. The author has also proved the important conclusions related to a disphenoid by mathematical derivations using 3D coordinate geometry.
Volume & surface area of right circular cone cut by a plane parallel to its s...Harish Chandra Rajpoot
All the articles have been derived by the author by using simple geometry, trigonometry & calculus. All the formula are the most generalized expressions which can be used for computing the volume & surface area of minor & major parts usually each with hyperbolic section obtained by cutting a right circular cone with a plane parallel to its symmetrical (longitudinal) axis.
This formula holds good for all the regular spherical polygons. It is a very important formula (mathematical relation) applicable on any regular spherical polygon having each of its sides as an arc of the great circle on a spherical surface. It is of crucial importance to find out any of the four important parameters (i.e. radius of sphere, no. of sides, length of side, interior angle of polygon) if other three are given (known) for any regular spherical polygon. It also concludes that any three of the four parameters are self-sufficient to exactly represent a unique regular spherical polygon. A regular spherical polygon having three known parameters can be created or drawn only on a unique spherical surface of a radius which is easily found out by HCR's formula.
Mathematical analysis of sphere resting in the vertex of polyhedron, filletin...Harish Chandra Rajpoot
The generalized formula derived here by the author are applicable to locate any sphere, with a certain radius, resting in a vertex (corner) at which n no. of edges meet together at angle α between any two consecutive of them such as the vertex of platonic solids, any of two identical & diagonally opposite vertices of uniform polyhedrons with congruent right kite faces & the vertex of right pyramid with regular n-gonal base. These are also useful for filleting the faces meeting at the vertex of the polyhedron to best fit the sphere in that vertex. These are used to determine the distance of sphere from the vertex, distance of sphere from the edges, fillet radius of the faces etc. The formula have been generalized for packing the spheres in the vertices of right pyramids & all five platonic solids.
Mathematical analysis of identical circles touching one another on the spheri...Harish Chandra Rajpoot
The formula, derived here by the author H.C. Rajpoot, are applicable on a certain no. of the identical circles touching one another at different points, centered at the identical vertices of a spherical polyhedron analogous to an Archimedean solid for calculating the different parameters such as flat radius & arc radius of each circle, total surface area covered by all the circles, percentage of surface area covered etc. These formula are very useful for tiling, packing the identical circles in different patterns & analyzing the spherical surfaces analogous to all 13 Archimedean solids. Thus also useful in designing & modelling of tiled spherical surfaces.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
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This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
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The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.