The document provides information about Riemann sums and Riemann integrals. It states that if f(x) is a non-negative function on the interval [a,b], then the graph of y=f(x) can be approximated by dividing the interval into n subintervals and taking the left or right Riemann sum of the resulting rectangles. The Riemann integral from a to b of f(x) is defined as the limit of these Riemann sums as n approaches infinity. Newton and Leibniz developed the fundamental theorem of calculus that relates integrals to derivatives.
A Probabilistic Algorithm for Computation of Polynomial Greatest Common with ...mathsjournal
In the earlier work, Knuth present an algorithm to decrease the coefficient growth in the Euclidean algorithm of polynomials called subresultant algorithm. However, the output polynomials may have a small factor which can be removed. Then later, Brown of Bell Telephone Laboratories showed the subresultant in another way by adding a variant called 𝜏 and gave a way to compute the variant. Nevertheless, the way failed to determine every 𝜏 correctly.
In this paper, we will give a probabilistic algorithm to determine the variant 𝜏 correctly in most cases by adding a few steps instead of computing 𝑡(𝑥) when given 𝑓(𝑥) and𝑔(𝑥) ∈ ℤ[𝑥], where 𝑡(𝑥) satisfies that 𝑠(𝑥)𝑓(𝑥) + 𝑡(𝑥)𝑔(𝑥) = 𝑟(𝑥), here 𝑡(𝑥), 𝑠(𝑥) ∈ ℤ[𝑥]
Matrix Transformations on Some Difference Sequence SpacesIOSR Journals
The sequence spaces 𝑙∞(𝑢,𝑣,Δ), 𝑐0(𝑢,𝑣,Δ) and 𝑐(𝑢,𝑣,Δ) were recently introduced. The matrix classes (𝑐 𝑢,𝑣,Δ :𝑐) and (𝑐 𝑢,𝑣,Δ :𝑙∞) were characterized. The object of this paper is to further determine the necessary and sufficient conditions on an infinite matrix to characterize the matrix classes (𝑐 𝑢,𝑣,Δ ∶𝑏𝑠) and (𝑐 𝑢,𝑣,Δ ∶ 𝑙𝑝). It is observed that the later characterizations are additions to the existing ones
Dual Spaces of Generalized Cesaro Sequence Space and Related Matrix Mappinginventionjournals
In this paper we define the generalized Cesaro sequence spaces 푐푒푠(푝, 푞, 푠). We prove the space 푐푒푠(푝, 푞, 푠) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual. In section-3 we establish necessary and sufficient conditions for a matrix A to map 푐푒푠 푝, 푞, 푠 to 푙∞ and 푐푒푠(푝, 푞, 푠) to c, where 푙∞ is the space of all bounded sequences and c is the space of all convergent sequences. We also get some known and unknown results as remarks.
A Non Local Boundary Value Problem with Integral Boundary ConditionIJMERJOURNAL
ABSTRACT: In this article a three point boundary value problem associated with a second order differential equation with integral type boundary conditions is proposed. Then its solution is developed with the help of the Green’s function associated with the homogeneous equation. Using this idea and Iteration method is proposed to solve the corresponding linear problem.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
![Тодорхойлолт: 𝑦 = 𝑓(𝑥) нь [𝑎, 𝑏] завсарт тасралтгүй,
𝑓(𝑥) ≥ 0 функц байг.
Дээрээсээ 𝑦 = 𝑓(𝑥) функцийн график,
доороосоо 𝑂𝑥 тэнхлэг,
хоёр хажуу талаараа 𝑥 = 𝑎, 𝑥 = 𝑏 шулуунуудаар хүрээлэгдсэн
дүрсийг муруй шугаман трапец гэнэ.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)