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The permutation theorem is very useful when dealing with inequalities between sums of products of the two real number sequences. In numerous cases inequalities otherwise difficult to prove can be proven almost automatically.

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DOWNLOADS UPSC Syllabus - Dips Academy: Regenerating Mathematics

DIPS Academy is one of the best institute of Mathematics preperation for Advanced Mathematics for the exams like GATE Exam, JRF Exam, NET Exam, IAS Exam, IFS Exam, PCS Exam, ISI Exam, JNU Exam, DRDO Exam, NBHM Exam, JEST Exam, TIFR Exam, IISC Bangalore, AAI Exam, JAM Exam

U unit3 vm

1. The document introduces complex numbers and some basic results regarding complex numbers such as the complex conjugate and modulus of a complex number.
2. It then discusses functions of a complex variable, defining a complex function and its Cartesian and polar forms. It also covers continuity, derivatives, and analytic functions of a complex variable.
3. The Cauchy-Riemann equations are derived and provide a necessary condition for a function to be analytic (differentiable everywhere in a neighborhood). Two examples are provided to illustrate the Cauchy-Riemann equations and analytic functions.

An inequality painted on the vase body.

The 3D picture shows an attempt at combining applied art with pure mathematics. The vase shown in the picture is an example of ceramic vessel that could exist in real world.

確率微分方程式の導出(仮)

確率微分方程式の導出をやってみました！

UPTU Syllabus

This document provides the course details for TAS 301 Mathematics-III. The course covers the following topics over 5 units: integral transforms and their applications; functions of a complex variable including analytic functions and Cauchy's integral theorem; statistics and probability including distributions; curve fitting and solving equations; and conformal mapping. It also provides the course details for TME-301 Material Science, which covers topics such as crystal structures, mechanical properties, microstructures, phase diagrams, ferrous and non-ferrous materials, and ceramics over 5 units. Finally, it outlines the course TME 302 Applied Thermodynamics, which includes thermodynamic properties, properties of steam and boilers, steam engines, turbines, gas turbines, and

Ptolemy's theorem visualisation. 3D graphics.

Ptolemy's theorem states the following: a convex quadrilateral can be inscribed in a circle if and only if the product of the lengths of one pair of opposite sides added to the product of the lengths of the other pair is equal to the product of the lengths of the diagonals. Thus, in a cyclic quadrilateral ABCD we have
AB*DC + AD*BC = AC*BD

engineeringmathematics-iv_unit-i

This document provides an overview of functions of complex variables. It discusses key topics including analytic functions, Cauchy-Riemann equations, harmonic functions, and methods for determining an analytic function when its real or imaginary part is known. Specific methods covered are direct, Milne-Thomson's, exact differential equations, and a shortcut method. Examples are provided to illustrate determining the analytic function given properties of its real or imaginary part. The document also briefly outlines applications of complex variables and standard conformal transformations.

Complex Integral

Evaluation of integrals of the given functions along the unit circle on the complex plane. Application of the parametrization method. Evaluation of the integral of an odd function.

Unit iii analytic functions

1. The document contains 20 important questions about analytic functions in Part A and 11 additional questions in Part B.
2. The questions cover topics such as defining analytic functions, the Cauchy-Riemann equations, harmonic functions, bilinear transformations, and conformal mappings.
3. Example questions include proving properties of derivatives of analytic functions, finding the analytic function given a real or imaginary part, and determining the image of circles or lines under specific transformations.

Unit iv complex integration

This document provides 22 questions related to complex integration and contour integration. It covers key concepts like Cauchy's integral theorem, Cauchy's integral theorem for derivatives, evaluating contour integrals, Taylor series expansions, Laurent series expansions, isolated singular points, essential singular points, removable singular points, finding poles and residues, and applying Cauchy's residue theorem. The questions are divided into two parts - the first part focuses on definitions and properties, while the second part involves applying these concepts to evaluate specific contour integrals.

Cauchy integral theorem

Este documento presenta un ejemplo numérico para calcular una integral cerrada alrededor de una singularidad usando el teorema integral de Cauchy. Primero, se calcula la integral alrededor de un cuadrado que contiene un polo en z=2. Luego, se calcula la integral alrededor de una elipse vertical que contiene un polo de orden 2 en z=2. En ambos casos, el valor de la integral es igual al residuo en el polo, lo que verifica el teorema integral de Cauchy.

Fourier analysis on symmetric group

対称群上のフーリエ解析のメモです.
やっぱり群の表現論で一番大事なのは”表現行列の大直交性定理”ですね！ これで，有限群上の直交関数系が分かります！

電子光波Memo

電子光波のメモ 複素誘電率 分散関係

微分演算子と多項式の剰余環の関係 2016 october 12

微分演算子にexp(αt)を作用させる事についての考察.

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-III

This document discusses methods for finding the roots or zeros of equations, including the bisection method, Newton-Raphson method, and regula-falsi method. It provides definitions and steps for each method. The bisection method works by repeatedly bisecting the interval that contains the root. Newton-Raphson uses successive approximations to iteratively find better estimates for the root. Regula-falsi is based on finding the x-intercept of the chord between two points on the function graph. Examples are provided to demonstrate applying each method to find the roots of equations.

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-I

1. The document discusses functions of complex variables, including analytic functions, Cauchy-Riemann equations, harmonic functions, and methods for determining an analytic function when its real or imaginary part is known.
2. Some key topics covered are the definition of an analytic function, Cauchy-Riemann equations in Cartesian and polar forms, properties of analytic functions including orthogonal systems, and determining the analytic function using methods like direct, Milne-Thomson's, and exact differential equations.
3. Examples are provided to illustrate determining the analytic function given its real or imaginary part, such as finding the function when the real part is a polynomial or the imaginary part is a trigonometric function.

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-V

This document describes numerical integration and differentiation techniques taught in a B.Tech Engineering Mathematics course. It covers the Trapezoidal, Simpson's 1/3 and 3/8 rules for numerical integration of functions. For numerical differentiation, it discusses Euler's method, Picard's method, and Taylor series for solving ordinary differential equations. Examples are provided to illustrate the application of these numerical methods to evaluate integrals and solve initial value problems.

B.tech semester i-unit-ii_partial differentiation

This document provides information about an engineering mathematics course. Specifically, it is for a B.Tech program, the subject is Engineering Mathematics, and it is for Unit II at Rai University in Ahmedabad, India.

Cauchy's integral formula

This document discusses Cauchy's integral formula and its derivation from Taylor series. It shows that the derivative of an analytic function f(z) can be written as the limit of the Taylor series coefficients divided by (z-z0). Taking the integral of both sides yields Cauchy's integral formula, which expresses f(z) as an integral involving its value at z0 over a contour enclosing z0.

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-IV

This document discusses finite difference and interpolation methods. It covers topics like finite differences, difference tables, Newton's forward and backward interpolation formulas, Stirling's interpolation formula, Newton's divided difference formula for unequal intervals, and Lagrange's divided difference formula for unequal intervals. Examples are provided to demonstrate calculating finite differences, constructing difference tables, and using interpolation formulas to estimate values between given data points.

DOWNLOADS UPSC Syllabus - Dips Academy: Regenerating Mathematics

DOWNLOADS UPSC Syllabus - Dips Academy: Regenerating Mathematics

U unit3 vm

U unit3 vm

An inequality painted on the vase body.

An inequality painted on the vase body.

確率微分方程式の導出(仮)

確率微分方程式の導出(仮)

UPTU Syllabus

UPTU Syllabus

Ptolemy's theorem visualisation. 3D graphics.

Ptolemy's theorem visualisation. 3D graphics.

engineeringmathematics-iv_unit-i

engineeringmathematics-iv_unit-i

Complex Integral

Complex Integral

Unit iii analytic functions

Unit iii analytic functions

Unit iv complex integration

Unit iv complex integration

Cauchy integral theorem

Cauchy integral theorem

Fourier analysis on symmetric group

Fourier analysis on symmetric group

電子光波Memo

電子光波Memo

微分演算子と多項式の剰余環の関係 2016 october 12

微分演算子と多項式の剰余環の関係 2016 october 12

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-III

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-III

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-I

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-I

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-V

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-V

B.tech semester i-unit-ii_partial differentiation

B.tech semester i-unit-ii_partial differentiation

Cauchy's integral formula

Cauchy's integral formula

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-IV

Engineering Mathematics-IV_B.Tech_Semester-IV_Unit-IV

presentationonmatrix-160801150449 (1).pptx

The document presents information on matrices and their applications. It defines what a matrix is as a rectangular arrangement of numbers and expressions in rows and columns. It discusses various operations that can be performed on matrices, including addition, subtraction, multiplication, and finding the transpose. Examples are provided to illustrate these operations. The document also lists some fields where matrices are applied, such as geology, statistics, economics, and animation. It provides examples of how matrices are used in tasks like seismic surveys, data analysis, calculating GDP, and 3D animation.

ahmad ppt discreet.pptx

The document presents information on matrices and their applications. It defines what a matrix is and provides examples of basic matrix operations like addition, subtraction, and multiplication. It also discusses identity matrices and transposes. The document then gives examples of how matrices are used in different fields like geology, statistics, economics, and animation. It involves tasks like taking seismic surveys, plotting graphs, scientific analysis, presenting survey data, calculating GDP, 3D modeling, scaling, and transformations. In the end, the presenters ask if there are any questions.

ABC-Gibbs

The document describes a new method called component-wise approximate Bayesian computation (ABC) that combines ABC with Gibbs sampling. It aims to improve ABC's ability to efficiently explore parameter spaces when the number of parameters is large. The method works by alternating sampling from each parameter's ABC posterior conditional distribution given current values of other parameters and the observed data. The method is proven to converge to a stationary distribution under certain assumptions, especially for hierarchical models where conditional distributions are often simplified. Numerical experiments on toy examples demonstrate the method can provide a better approximation of the true posterior than vanilla ABC.

Deep learning .pdf

This document provides an overview of key concepts in probability and statistics, including:
- Definitions of probability, sample spaces, events, and the axioms of probability
- Concepts of conditional probability, Bayes' rule, independence, and discrete random variables
- How to calculate probabilities of events, expected values, variance, and conditioning probabilities on other events or random variables

Probability Formula sheet

Probability formula sheet
Set theory, sample space, events, concepts of randomness and uncertainty, basic principles of probability, axioms and properties of probability, conditional probability, independent events, Baye’s formula, Bernoulli trails, sequential experiments, discrete and continuous random variable, distribution and density functions, one and two dimensional random variables, marginal and joint distributions and density functions. Expectations, probability distribution families (binomial, poisson, hyper geometric, geometric distribution, normal, uniform and exponential), mean, variance, standard deviations, moments and moment generating functions, law of large numbers, limits theorems
for more visit http://tricntip.blogspot.com/

3.7 Indexed families of sets

Selected items from the Introduction to set theory and to methodology and philosophy of mathematics and computer programming.

Imc2016 day1-solutions

This document contains solutions to 5 problems involving mathematical proofs. The first problem proves that for a continuous function f with infinitely many zeros on an interval [a,b], either f(a) or f(b) must be 0. The second problem proves that for a preferred sequence of matrices, the number of matrices k must be less than or equal to the matrix size n. The third problem uses an identity involving integrals to prove an inequality relating sums. The fourth problem uses induction to prove a statement about families of sets. The fifth problem uses properties of permutations to prove statements about the number of permutations with a certain property being greater or less than expected for infinitely many prime numbers.

Sol40

1) The document describes a method for calculating the probability that candidate A's vote total is always greater than or equal to candidate B's vote total as votes are counted. It models the vote counting as paths on a lattice from the origin to the point (a,b) representing the final vote totals.
2) It proves that the number of "bad" paths that pass through the region where B's total is greater than A's is equal to a+b/b-1.
3) It then uses this to calculate the probability that A's total is always greater as 1 - the number of bad paths divided by the total number of paths, which equals 1 - b/(a+1).

Sol40

1) The document describes a method for calculating the probability that candidate A's vote total is always greater than or equal to candidate B's vote total as votes are counted. It models the vote counting as paths on a lattice from the origin to the point (a,b) representing the final vote totals.
2) It proves that the number of "bad" paths that pass through the region where B's total is greater than A's is equal to a+b/b-1.
3) It then uses this to calculate the probability that A's total is always greater than or equal to B's as 1 - (a+b/b-1)/(a+b/a), or 1 -

Congruence Lattices of A Finite Uniform Lattices

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.

Sets.pdf

This document defines sets and basic set operations. It begins by defining what a set is and providing examples of sets. It then discusses subsets, set equality, Venn diagrams, union, intersection, difference, and complement operations on sets. It provides examples and problems to illustrate these concepts. It also covers empty sets, disjoint sets, partitions of sets, power sets, ordered tuples, Cartesian products, set identities, and proofs using an element argument approach.

Algebra(03)_160311_02

(1) The question asks to find the last two digits of 2^1000. (2) Computing exponents modulo 100, it is shown that 2^20 = 24 (mod 100) and 2^20 = 76 (mod 100). (3) By induction, 2^n = 76 (mod 100) for any exponent n. Therefore, the last two digits of 2^1000 are 76.

matlab functions

The document describes functions and exercises for basic simulation and matrix manipulation in MATLAB. It covers creating vectors and matrices, arithmetic operations, matrix manipulations like concatenation and indexing, sorting, shifting, reshaping and flipping matrices. It also discusses generating random sequences, plotting functions, solving differential equations, and creating and accessing structures and arrays of structures. The key topics are functions for vector/matrix creation and manipulation, common mathematical operations, plotting and solving differential equations in MATLAB.

Chpt 2-sets v.3

This document provides definitions and notation for set theory concepts. It defines what a set is, ways to describe sets (explicitly by listing elements or implicitly using set builder notation), and basic set relationships like subset, proper subset, union, intersection, complement, power set, and Cartesian product. It also discusses Russell's paradox and defines important sets like the natural numbers. Key identities for set operations like idempotent, commutative, associative, distributive, De Morgan's laws, and complement laws are presented. Proofs of identities using logical equivalences and membership tables are demonstrated.

International Journal of Humanities and Social Science Invention (IJHSSI)

International Journal of Humanities and Social Science Invention (IJHSSI) is an international journal intended for professionals and researchers in all fields of Humanities and Social Science. IJHSSI publishes research articles and reviews within the whole field Humanities and Social Science, 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.

Quaternion algebra

This document provides an introduction and overview of a paper that will prove Lagrange's Four Square Theorem using quaternion algebras. It will introduce quaternion arithmetic and show that the set of quaternions being considered forms a non-commutative ring. This will allow the author to eventually prove that every positive integer can be expressed as the sum of four integer squares.

12 - Overview

I used this set of slides for an Overview lecture I gave at the University of Zurich for the 1st year students following the course of Formale Grundlagen der Informatik.

Analytic Solutions of an Iterative Functional Differential Equation with Dela...

ABSTRACT : This This paper is concerned with an iterative functional differential equation with the form
z C
x z
b
x az
x z
,
)
( )
(
1
( ) .By constructing a convergent power series solution of an auxiliary equation
b [ag(z) g( z)] [g( z) ag( z)][ g( z) ag(z)] g(z), zC 2 2 2
the analytic solutions for the original equation are obtained. We not only discuss the constant given in Schröder
transformation at resonance( i.e., at a root of the unity), but also discuss those near resonance (i.e., near a
root of the unity) under Brjuno condition.

Mcs 013 solve assignment

This document provides solved assignments for MCS-013 from Ignou in 2011. It includes truth tables and answers to questions about conditional connectives, proofs, rational and irrational numbers, Boolean algebra, logic circuits, sets, Venn diagrams, and counterexamples. Specifically, it gives examples of direct proofs, finds whether 17 is rational or irrational, explains how Boolean algebra is used in logic circuit design, draws Venn diagrams, and illustrates the use of a counterexample.

Discrete mathematics notes

This document provides an outline for a lecture on discrete mathematics. It covers topics such as propositional logic, truth tables, predicate logic, quantifiers, sets, and set operations. The goal of studying discrete mathematics is to understand how mathematics can model problems involving discrete objects, and to prove logical statements. Some key concepts discussed are logical connectives, truth values, predicates, universal and existential quantifiers, set membership, unions, intersections, complements and Cartesian products.

presentationonmatrix-160801150449 (1).pptx

presentationonmatrix-160801150449 (1).pptx

ahmad ppt discreet.pptx

ahmad ppt discreet.pptx

ABC-Gibbs

ABC-Gibbs

Deep learning .pdf

Deep learning .pdf

Probability Formula sheet

Probability Formula sheet

3.7 Indexed families of sets

3.7 Indexed families of sets

Imc2016 day1-solutions

Imc2016 day1-solutions

Sol40

Sol40

Sol40

Sol40

Congruence Lattices of A Finite Uniform Lattices

Congruence Lattices of A Finite Uniform Lattices

Sets.pdf

Sets.pdf

Algebra(03)_160311_02

Algebra(03)_160311_02

matlab functions

matlab functions

Chpt 2-sets v.3

Chpt 2-sets v.3

International Journal of Humanities and Social Science Invention (IJHSSI)

International Journal of Humanities and Social Science Invention (IJHSSI)

Quaternion algebra

Quaternion algebra

12 - Overview

12 - Overview

Analytic Solutions of an Iterative Functional Differential Equation with Dela...

Analytic Solutions of an Iterative Functional Differential Equation with Dela...

Mcs 013 solve assignment

Mcs 013 solve assignment

Discrete mathematics notes

Discrete mathematics notes

Still life with vases - a 3D visualisation.

The picture presenting a still life with two vases made of black polished ceramics, standing on blocks of granite and limestone, placed in an empty room illuminated by sunlight going through a big window.

How to draw arcs of huge circles - usage of the "drawing tool".

The slide explaining visually the procedure of drawing huge circles. A theoretical background of the method has been described in another slide.

How to draw arcs of huge circles - description.

In case you are interested in drawing circles with a huge diameter (by "huge" I mean here really big ones, measured in kilometers or so) there is a tricky idea needed because the rope-and-the-stick method won't work for circles with a diameter bigger than several dozen meters. Here you can use a method based on the well known fact from geometry stating that all angles inscribed in a circle and subtended by the same chord (lying on the same side of the chord) are equal.

Calculation of the volume of a bottle partially filled with a fluid.

How to calculate the volume of a flat-bottomed, corked bottle, partially filled with a fluid having only the ruler as a measuring tool?
The 3D graphics made by me and presented below gives an answer to this question.

The sum of the triangle sides lengths reciprocals vs a cyclic sum of a specif...

Proof of the inequality between the sum of the reciprocals of a triangle sides lengths and a cyclic sum of a specific form. Use of a transformed inequality between the arithmetic mean and the harmonic mean.

Indescribable numbers

1) There are a finite number of possible symbol sets that could be used to describe numbers, as the set of all symbols used by humans is finite.
2) While new symbols can be invented, the set of all possible symbol combinations remains finite.
3) Any description system based on a finite set of symbols can only describe countably many numbers, whereas the set of all real numbers is uncountably large. Therefore, there will always be real numbers that cannot be described.

Late Spring 2015 Photos

Photos taken in May and June 2015.

Cube root

A mathematical explanation of a simple trick that shows how to quickly calculate the cube root of a maximally 6-digit number that was given by a spectator. The spectator chooses a natural two-digit number, keeps it in secret and only information he/she gives publicly is its cube. Conjurer's task is to quickly guess the original number.

Still life with vases - a 3D visualisation.

Still life with vases - a 3D visualisation.

How to draw arcs of huge circles - usage of the "drawing tool".

How to draw arcs of huge circles - usage of the "drawing tool".

How to draw arcs of huge circles - description.

How to draw arcs of huge circles - description.

Calculation of the volume of a bottle partially filled with a fluid.

Calculation of the volume of a bottle partially filled with a fluid.

The sum of the triangle sides lengths reciprocals vs a cyclic sum of a specif...

The sum of the triangle sides lengths reciprocals vs a cyclic sum of a specif...

Indescribable numbers

Indescribable numbers

Late Spring 2015 Photos

Late Spring 2015 Photos

Cube root

Cube root

Introduction to Banking System in India.ppt

Bank – Banking – Banking System in India – Origin of Bank-Classification of Banks –Types of Customers RBI Functions- Commercial Banks – Functions

10th Social Studies Enrichment Material (Abhyasa Deepika) EM.pdf

10th Social Studies

C# Interview Questions PDF By ScholarHat.pdf

C# Interview Questions PDF

PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf

The University of Ghana has launched a new vision and strategic plan, which will focus on transforming lives and societies through unparalleled scholarship, innovation, and result-oriented discoveries.

How to Empty a One2Many Field in Odoo 17

This slide discusses how to delete or clear records in an Odoo 17 one2many field. We'll achieve this by adding a button named "Delete Records." Clicking this button will delete all associated one2many records.

Cómo crear video-tutoriales con ScreenPal (2 de julio de 2024)

Conferencia a cargo de D. Ignacio Álvarez Lanzarote dentro del Curso Extraordinario de la Universidad de Zaragoza "Recursos de apoyo en el desarrollo de la competencia digital", que se celebró los días 1, 2 y 3 de julio de 2024.

Node JS Interview Question PDF By ScholarHat

Node JS Interview Question PDF

How to Manage Early Receipt Printing in Odoo 17 POS

This slide will represent how to manage the early receipt printing option in Odoo 17 POS. Early receipts offer transparency and clarity for each customer regarding their individual order. Also printing receipts as orders are placed, we can potentially expedite the checkout process when the bill is settled.

Our Guide to the July 2024 USPS® Rate Change

Postal Advocate manages the mailing and shipping spends for some of the largest organizations in North America. At this session, we discussed the USPS® July 2024 rate change. Postal Advocate shared all the important information you need to know for this coming rate change that goes into effect on Sunday, July 14, 2024.
We Covered:
-What rates are changing
-How this impacts you
-What you need to do
-Savings tips

slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...

The ppt represent the ideology of Robin Sharma about listening

MathematicsGrade7-Presentation-July-12024.pptx

For matatag Curriculum grade 7

Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"

CERTIFICATE OF APPRECIATION
"NEUROANATOMY"
DURING THE JOINT ONLINE LECTURE SERIES HELD BY
KUTAISI UNIVERSITY (GEORGIA) AND ISTANBUL GELISIM UNIVERSITY (TURKEY)
FROM JUNE 10TH TO JUNE 14TH, 2024

C Interview Questions PDF By Scholarhat.pdf

C Interview Questions PDF By Scholarhat

SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx

Matatag Curriculum

Mail Server Configuration Using App passwords in Odoo 17

In Odoo 17, we can securely configure an email server to send and receive emails within the application. This is useful for features like sending quotations, invoices, and notifications via email. If our email service provider (e.g., Gmail, Outlook) supports app passwords, we can use them to authenticate our Odoo instance with the email server.

How to Manage Line Discount in Odoo 17 POS

This slide will cover the management of line discounts in Odoo 17 POS. Using the Line discount approach, we can apply discount for individual product lines.

2 Post harvest Physiology of Horticulture produce.pptx

Post harvest Physiology of Horticulture produce

JavaScript Interview Questions PDF By ScholarHat

JavaScript Interview Questions PDF

Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...

In this talk we will review recent research work carried out at the University of Saint Joseph and its partners in Macao. The focus of this research is in application of Artificial Intelligence and neuro sensing technology in the development of new ways to engage with brands and consumers from a business and design perspective. In addition we will review how these technologies impact resilience and how the University benchmarks these results against global standards in Sustainable Development.

Genetics Teaching Plan: Dr.Kshirsagar R.V.

A good teaching plan is a comprehensive write-up of the step-by-step and teaching methods helps students for understand the topic

Introduction to Banking System in India.ppt

Introduction to Banking System in India.ppt

10th Social Studies Enrichment Material (Abhyasa Deepika) EM.pdf

10th Social Studies Enrichment Material (Abhyasa Deepika) EM.pdf

C# Interview Questions PDF By ScholarHat.pdf

C# Interview Questions PDF By ScholarHat.pdf

PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf

PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf

How to Empty a One2Many Field in Odoo 17

How to Empty a One2Many Field in Odoo 17

Cómo crear video-tutoriales con ScreenPal (2 de julio de 2024)

Cómo crear video-tutoriales con ScreenPal (2 de julio de 2024)

Node JS Interview Question PDF By ScholarHat

Node JS Interview Question PDF By ScholarHat

How to Manage Early Receipt Printing in Odoo 17 POS

How to Manage Early Receipt Printing in Odoo 17 POS

Our Guide to the July 2024 USPS® Rate Change

Our Guide to the July 2024 USPS® Rate Change

slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...

slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...

MathematicsGrade7-Presentation-July-12024.pptx

MathematicsGrade7-Presentation-July-12024.pptx

Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"

Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"

C Interview Questions PDF By Scholarhat.pdf

C Interview Questions PDF By Scholarhat.pdf

SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx

SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx

Mail Server Configuration Using App passwords in Odoo 17

Mail Server Configuration Using App passwords in Odoo 17

How to Manage Line Discount in Odoo 17 POS

How to Manage Line Discount in Odoo 17 POS

2 Post harvest Physiology of Horticulture produce.pptx

2 Post harvest Physiology of Horticulture produce.pptx

JavaScript Interview Questions PDF By ScholarHat

JavaScript Interview Questions PDF By ScholarHat

Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...

Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...

Genetics Teaching Plan: Dr.Kshirsagar R.V.

Genetics Teaching Plan: Dr.Kshirsagar R.V.

- 1. Deﬁnition (Similarly and oppositely ordered sequences) Two sequences of real numbers (a1, . . . , an) and (b1, . . . , bn) are similarly ordered if and only if for each pair (i, j), where 1 ≤ i, j ≤ n, we have (ai − aj)(bi − bj) 0 (1) in other words (ai aj ∧ bi bj) ∨ (ai aj ∧ bi bj) Analogically, the aforementioned sequences are oppositely ordered if and only if the inequality (1) is reversed. For the purpose of the theorem formulated below, let’s introduce the following notation n k=1 akbk = a1b1 + a2b2 + · · · + anbn = a1 a2 · · · an b1 b2 · · · bn Theorem (Inequalities between sums of the products of the sequences elements) : If the sequences of real numbers (a1, . . . , an) and (b1, . . . , bn) are similarly ordered then for any permutation (b1, . . . , bn) of the given sequence (b1, . . . , bn) we have n k=1 akbk = a1 a2 · · · an b1 b2 · · · bn a1 a2 · · · an b1 b2 · · · bn = n k=1 akbk (2) If the sequences of real numbers (a1, . . . , an) and (b1, . . . , bn) are oppositely ordered then for any permutation (b1, . . . , bn) of the given sequence (b1, . . . , bn) we get the reversed version of the inequality (2). c 2015/10/13 22:41:36, Mikołaj Hajduk 1 / 1