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https://www.math.upenn.edu/undergraduate/math-majors-and-minors/mathematics-major
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math
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Steps to declare the Math Major (Declaration Periods: Fall 9/15- 12/9 & Spring 2/1 - 4/17)
- Complete the calculus requirement (Math 1400 and Math 1410+2400 or Math 1610+2600) and one proof-based major course.
- Go to Path @ Penn to formally request to add or remove your major to the Math Office (otherwise it won't show on your transcripts).
- Use this link to complete the top portion of our course plan worksheet and email it to the major advisor we assign to you after we process your Path @ Penn request.
- After consulting with your advisor, he/she will review your worksheet for processing.
- Allow 15 business days for your major to appear on your transcript. If its not visible by day 15th email me at [email protected]
- Contact your math advisor once a semester. Email your advisor to answer questions or make changes to your course plan.
- Once you enter your semester of graduation, you must email your math major advisor to certify your math major worksheet for completion.
On This Page
- Admission to the Major Program Entrance Requirements for the Major.
- Background: The Major and its goals.
- What can I do with a math major?
- Advanced Placement Potential Credit for incoming freshmen.
- The Major Program Requirements A minimum of 13 credits are needed.
- Planning your Mathematics Major Our suggested plan for completing your major.
- Other Useful Experiences for a Math Major
- Mathematics Major: Biological Concentration
- The Mathematics Minor
- Further Recommendations Advice for students planning graduate study in mathematics or related fields.
- The Honors Program Requirements for a degree with honors.
- The Master's Program Submatriculation into graduate study at Penn.
- Advice General advice regarding the major.
- External links.
- Current Course Descriptions (for reference in course planning)
- Courses offered next semester
Permission to major in mathematics is normally obtained by the end of the sophomore year, but planning for it should begin as early as possible. It is important that majors entering their junior year commence satisfying the algebra and analysis requirements.
To be admitted to the major, a student must have completed successfully (i.e., with grades of C or better) the calculus requirement as well as one proof-based math class (such as Math 2020, 2030, 1610, 2600, 3140) in the freshman and sophomore years. A higher-level proof-based class may be substituted at the discretion of a math major advisor.
Students who plan to have math as their second major should have a cumulative GPA of at least 3.0, an average of at least 3.0 in their math courses, and no math grades lower than B-.
The Major is open to SEAS undergraduates (as a second major) as well as to students in the College.
Mathematical training allows one to take a problem, abstract its essential features, and investigate them further. This ability can assist greatly in such diverse fields as economics, law, medicine, engineering, and computer science -- as well as in the more traditional activities of research and teaching.
The goals of the major program are to assist students in acquiring both an understanding of mathematics and an ability to use it. We wish to inspire the discovery of new mathematics as well as the application of mathematics to other fields.
The mathematics major provides a solid foundation for graduate study in mathematics as well as background for study in economics, the biological sciences, the physical sciences and engineering, as well as many non-traditional areas. This flexibility is available through an appropriate choice of electives within the major. A variety of electives are offered. They are designed to serve the needs of mathematics majors and others who want more advanced training in mathematics and its applications. Most of these courses presume our basic two year calculus sequence.
The mathematics major is also excellent training for students interested in elementary and secondary education. For information on the elementary education undergraduate major or the secondary education submatriculation program which leads to a Master's degree, students should consult the Undergraduate Chair as well as the Director of Teacher Education in the Graduate School of Education.
Highly qualified and motivated students should note the possibility of obtaining both the B.A. and M.A. degrees in four years. This is discussed below.
Given the widening role of mathematics, students with special interests and needs may wish to consider the possibility of an individualized program of study, perhaps in conjunction with a major in another field. The Major Coordinator should be consulted about this.
How to Plan a Mathematics Major Prospective majors should first check the information listed under Advanced Placement. We strongly encourage students to master the basic material as early as possible, and AP credit is equal to credit for a course taken at Penn. Students are urged to read the Major Program Requirements carefully, and use it as a guideline to plot the plan. You should also read Other Useful Experience and Further Recommendations for a complete overview.
See Careers in Mathematics . It is maintained by the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics.
See Math in the Media for pointers to current general articles involving mathematics and its applications.
Note: The AP policy and more details on this subject (and on "transfer credit") can be found on our web page AP/Transfer Credit Information.
We strongly encourage students to master the basic material as early as possible. It is our policy to waive prerequisite course requirements for those students who can pass an examination that demonstrates that they know the material. These remarks apply especially to the first-year calculus courses. For these, a student may receive credit towards the degree (in addition to the waiving of prerequisites) by either of the following methods:
- Passing the external Advanced Placement BC Exam administered by the College Entrance Examination Board with a score of 5 gives credit for Math 1400. Lower scores on the BC Exam receive no course credit. No credit is given for the AB Exam. Students taking first semester calculus, math 1400, are expected to have had an AB calculus course in high school.
- Passing the internal Advanced Placement Examination administered in the first week of the fall and spring semester by the mathematics department. A student may take the examination regardless of whether he or she took the external exam described under (1) above.
Those receiving advanced placement and planning to enroll in more advanced courses should see the Major Coordinator, who will help them plan a program of study.
The Mathematics Major comprises 13 courses organized into eight basic requirements. Each of the 13 courses must be taken for a grade (i.e., not pass/fail), and must be completed with a grade of C (2.0) or better. (A student who receives a grade lower than C in a requirement consisting of more than one course may still count that course toward the major by achieving a grade of C or above in a more advanced course within the same requirement.) The math department also expects the completion of at least one proof-based math class in the freshman or sophomore year in order to be admitted into the major (usually Math 2020, 2030, 1600, 2600, or 3140), or permission of a math major advisor. Courses taken on a pass/fail basis will not count toward fulfilling the following requirements.
- Three Semester Calculus Requirement. This is satisfied by any of the three sequences 1400-1410-2400 or 10400-1610-2600. The 10400 requirement can be satisfied by AP credit for the Calculus BC exam with a score of 5. The courses 1610-2600 are proof based and provide the best preparation for higher mathematics, and in particular for Math 3600 and 3610. Math 1300 does not count toward the Math major.
- Advanced Calculus Requirement Math majors must take either a fourth semester of calculus, Math 2410, or partial differential equations Math 4250.
- Complex Analysis Requirement All math majors must take Complex Analysis Math 4100.
- Seminar Requirement This is satisfied by taking either Math 2020 (intro to analysis) or Math 2030 (intro to algebra). These courses carry one-unit of credit and are intended to be taken concurrently with calculus. For students taking honors calculus (Math 1610-2400) the seminar requirement is replaced by a higher math elective course.
Students who begin with Math 1400 in their freshman year usually postpone this requirement until their second year. Students who have already taken one of Math 2410, Math 4100 or Math 4250 can substitute a higher math elective course for the Seminar Requirement. Under exceptional circumstances, other students may also make such a substitution with the permission of the Undergraduate Chair. In general, though, we recommend that prospective math majors take a freshman seminar to gain an overview of the subject.
- Linear algebra requirement.
Math Majors must take Advanced Linear Algebra Math 3140. Math 3140 is a prerequisite for Math 3700 and Math 5020.
- Algebra Requirement This is satisfied by taking the sequence Math 3700-3710 or the more theoretical Math 5020-5030. However, you can't get credits for both Math 3700 and Math 5020, or both Math 3710 and Math 5030.
These courses all overlap considerably.
- Analysis Requirement This is satisfied by taking the sequence Math 3600-3610 or the more theoretical Math 5080-509- However, you can't get credits for both Math 3600 and Math 5080, or both Math 3610 and Math 5090.
Note: Majors who begin their mathematics studies with Math 1410-2400 plus a seminar should fulfill at least one of the linear algebra, algebra, and analysis requirements in their sophomore year.
- Mathematics Electives The total number of approved math course units required for a math major is 13. Students should determine how many course units they still need for a math major after completing requirements 1 through 6 above. This will depend on which options have been chosen in completing the requirements. The remaining courses may then be made up from Math 2100 and mathematics courses numbered 3200 or above. One mathematics elective course unit may be taken from the list of approved Cognate Courses given outside the math department. Students who are double majors may take two Cognate courses units.
Students may, for example, take Statistics 4300 (or Systems Engineering 3010 or Econ 103 or ENM 5030), and count such a course as being within the Mathematics Department. Thus by taking one of these courses, one does not lower the number of cognate courses one can take outside the math department, as explained on the page of Cognate Courses.
Example 1: A student is double majoring in math and engineering, did not take a freshman seminar, and completed the Advanced Calculus requirement by taking math 2410. This student thus takes 4 courses related to the Calculus requirements, 4 courses to complete the algebra and analysis requirements, and Math 3140 and Math 4100 for a total of 10 courses. They must take 3 electives to bring their course total up to 13. Because the student is double majoring in math and engineering, two of these electives can be Cognate Courses in other departments. Notice that on the above list of cognate courses, some courses given in other departments are listed as being counted as within the math department as far as the math major and minor are concerned. For example, the student could take Stat 4300 (which is counted as within the math department), use Physics 0150 and Physics 0151 as their cognate courses not counted as within the math department, and then choose two more electives from within the math department to complete their math major requirements.
Example 2: A student is majoring only in math, took a freshman seminar, and completed the Advanced Calculus requirement by taking math 4250. This student thus takes the freshman seminar, 3 calculus courses, math 4100 and 4250 and four algebra and analysis courses in the course of completing the above requirements, for a total of 10 courses. They must take three further electives for a math major. Only one of these can be a Cognate Course, because the student is not a double major.
Students who do not plan graduate study in mathematics or in a highly mathematics-related subject should, as a means of acquiring more background, consider Math 4100, 4200, 4250, and 4300. For glimpses of several beautiful mathematical subjects beyond the basic core, students should consider Math 3500, 5420, 5480, 5490, 5800, 5000, 5300, 4800.
Students who are interested in the physical sciences should consider Physics 0150-0151 or 0170-0171 and the courses beyond. Those interested in the social or biological sciences should consider Math 4300 or Statistics 4300-4310. Those interested in computer science should consider CSE 110, 120-121 and the courses beyond as well as Math 4500, 5700 (previously 473 and 670). For computer programming and numerical methods, students should learn a programming language such as Pascal or C and learn to use symbolic manipulation software such as Mathematica or Maple. They also should consider Math 3200-3210. For discrete methods, in addition to Math 3400 and 3410, 450, 5700 (previously 473), and 5800 (previously 440), students should consider Math 5240-5250 (previously 470) and 5810 (previously 441).
For students who plan to do research in mathematics, or in a highly mathematical subject such as statistics, the considerations which are listed just above still apply. However, since a great deal of further theoretical training is necessary, such students are directed to the basic graduate courses in mathematics: 6000, 6010, 6020, 6030, 6080, and 6090.
All this material must eventually be mastered. It needs to be understood clearly that what is required is a comprehensive grasp of theoretical mathematics. Thus, the student's attention is directed to Method B for obtaining honors in mathematics, and to the joint B.A./M.A. program, pursuing a master's degree at the same time as their undergraduate degree.
The first order of business is to satisfy the first four requirements discussed above. When this has been done, the student usually has sufficient experience and direction to complete the program in consultation with the Major Advisor . It needs to be emphasized strongly, however, that apart from the strict requirements, there are certain other things which all mathematics majors should do. These are:
- Learn to program a computer and learn how to use mathematical symbolic manipulation packages. The latter skill is taught in our Calculus courses.
- Learn statistics. This may be done by taking Math 4300 or Stat 4300 followed by Stat 4310.
- Learn how mathematics is actually used. This can be done by learning something of an applied but highly mathematical field. Operations research, engineering and physics provide examples, but there are many others. (See below.)
- Obtain some job experience. This should be done, if possible, in the summer following the junior year. It should involve some interface between mathematics and the real world.
The importance of the above four recommendations cannot be sufficiently emphasized. Equipped with them, a mathematics major is an attractive candidate for entrance into a great many fields. Without them, job opportunities are limited. These remarks apply to the most theoretical, as well as to the most practical of careers.
To be eligible for honors in mathematics, a student must have an average of at least 3.5 in his/her major and major-related courses. If this condition is satisfied, honors may be obtained by either of the following methods.
Method A. By preparing, through independent study, a body of material approximately equal in amount to a one-semester course and giving a lecture on it as the Honors Committee shall direct.
The area of study chosen should be one that is not normally covered in the department and should involve reading sources outside normal course material. The selected topic may be picked from one field of mathematics or may involve assimilation of topics from different fields. Before beginning the project, the student should ask two members of the faculty, at least one affiliated with the Mathematics Department, to serve as the Honors Committee. The Honors Committee must approve the selected topic and serve as examiners for the lecture (which should be approximately an hour long, seminar-style talk).
Method B. By passing the written Preliminary Examination in undergraduate mathematics. This is required of all incoming Ph.D candidates. Details concerning this examination may be found in the Graduate Admissions Catalogue (also see below).
For further guidance, prospective honors students should consult with their Major Advisor during their junior year. The honors project must be completed by the end of February of the senior year.
Undergraduates who wish to take courses beyond the math major program should consider submatriculation and pursuing a master's degree. The minimum requirements are a A- average in 3600-3610 or 5080-5090 and 3700-3710 or 5020-5030, and permission of the Graduate Chair. Students who plan on a master's degree should submatriculate as early as possible because only courses taken subsequently to this may be counted toward the degree. The degree itself requires the successful completion of eight graduate courses and the written examinations for the Ph.D. The requirements can sometimes be completed by the end of the fourth undergraduate year, but often a fifth year is required.
For more information see the SAS web page Submatriculation and the Math Department Submatriculation page.
- Gifted high school students from the Philadelphia area are encouraged to take courses (usually Math 2400-2410) in the department while they are still in high school. This is done through the Young Scholars Program which is administered by the College of Liberal and Professional Studies.
- High school seniors who wish to major in mathematics and think that they might like to attend the University are invited to visit the mathematics department to meet the faculty and visit classes. They should email ugrad AT math.upenn.edu or call 898-8178 for an appointment.
- For our Math Majors and Minors there is a list of courses often approved as COGNATES for Mathematics Majors (these are courses from other departments often approved for mathematics majors or minor credit). All cognates require the approval of the Undergraduate Chair and must be part of a well-planned selection of electives within the major. The statistics courses enjoy a special status: since they count as being inside the Mathematics Department as far as the major or minor is concerned. Thus, a student who takes one or two of these may count additional outside courses toward the Mathematics Elective requirement. Additional courses may also be approved as cognates upon application to the Undergraduate Chair.
- Undergraduates who plan to teach in secondary schools should refer to the section on the Bachelor of Arts/Master of Science in Education.
- Penn has an active Undergraduate Mathematics Society which conducts seminars, colloquia and other activities for those who wish to encounter Math outside the classroom. Information about Society membership and schedules of its activities can be obtained in the Math Department office or by clicking on the link above.
- Opportunities for summer research exist at many Universities. The Undergraduate Chair is a good source of information about such programs, which are usually announced in October or November.
- National Science Foundation Research Experiences for Undergraduates
- Internships and Summer Employment (maintained by Penn Career Service)
- Penn's Graduate program in Education, including information about obtaining a Masters Degree in Education by submatriculation.
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CC-MAIN-2024-18
| 20,094 | 85 |
https://academiaservices.net/21147726850/
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math
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Let y be the first 512 components in the sunspots data from package datasets. (a) Use the mra command to plot f4, f5 and f6 using the Haar wavelet. Describe the different characteristics of each of these three smooth approximations. For example, use J=5 and either [] or $S5 to find f4. (b) Repeat the above problem using the wavelet basis indexed by wf=”la8″. This wavelet is from the family of “least asymmetric” wavelets (Vidakovic (1999)). Describe the differences between the smooth approximations using the different wavelet bases.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198652.6/warc/CC-MAIN-20200920192131-20200920222131-00431.warc.gz
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CC-MAIN-2020-40
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https://www.wisc-online.com/learn/career-clusters/manufacturing/msr2702/the-care-and-use-of-a-caliper
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math
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The Care and Use of a Caliper
By Phil Peters
The learner examines the four different ways that a caliber can be used to measure dimensions and distances.
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Creative Commons Attribution-NonCommercial 4.0 International License.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583662863.53/warc/CC-MAIN-20190119074836-20190119100836-00427.warc.gz
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Polynomial Kahoot. The remainder and factor theorems. Algebra 2 9780131339989 homework help and answers.
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Is there any symbol for an electrolytic cell? An electroplating cell, for instance?
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Manager-Treasury | Reputed Company | Chennai
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s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997858892.28/warc/CC-MAIN-20140722025738-00150-ip-10-33-131-23.ec2.internal.warc.gz
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CC-MAIN-2014-23
| 2,096 | 53 |
https://corporatefraudswatch.blogspot.com/2010/09/ibofb-could-not-understand-simple.html
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math
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It is once again proved that the masked IBOFB could not understand simple English but also could not follow a simple table in the website of Amway India.
Following is the table in the website of Amway:
Total Sales Turnover of X’s group is 5,50,000 BV = 10,000 PV
Commission level for the Group at 10,000 PV = 21%
Total Group Commission 21% of 5,50,000 BV= Rs. 1,15,500 (X)
Commission earned by A’s Group 12% of 1,10,000 BV = Rs. 13,200 (A)
Commission earned by B’s Group 12% of 1,10,000 BV = Rs. 13,200 (B)
Commission earned by C’s Group 9% of 55,000 = Rs. 4,950 (C)
Commission earned by D’s Group 15% of 2,20,000 = Rs. 33,000 (D)
Net Commission earned by you = X - A - B - C - D = Rs. 51,150
Retail Profit Margin on X’s
Personal Business 20% of 55,000 = Rs. 11,000
X’s Total monthly Earnings = Rs. 62,150
The table clearly shows that the total monthly earnings of X is Rs. 62,150.
Is the table really that complicated that IBOFB could not understand what is Group A, B, C, D?.
If there is no enrollment from where these groups emerge. Will it be out of blue?
The table clearly says that the retail profit margin of X's personal business is Rs. 11,000
This is what is called pyramid scheme and the illegal money circulation scheme. The Supreme Court of India rightly pointed out that this type of chain schemes attract the provisions of the Section 420 (cheating) of Indian Penal Code apart from Section 2 (c) of the Prize Chits & Money Circulation Schemes (Banning) Act, 1978.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103640328.37/warc/CC-MAIN-20220629150145-20220629180145-00066.warc.gz
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CC-MAIN-2022-27
| 1,491 | 18 |
https://www.atticusrarebooks.com/pages/books/1573/alan-turing/practical-forms-of-type-theory-in-journal-of-symbolic-logic-volume-13-number-2-june-1948-pp-80-95-with
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math
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Menasha: Association for Symbolic Logic. 1st Edition. TWO FIRST EDITION ISSUES IN ORIGINAL WRAPS. In "Practical Forms of Type Theory," Alan Turing wished to "encourage 'mathematicians-in-the-street' to use notation and forms of argument which would safeguard their work from ambiguity and inconsistency; but to do this without forcing their work into the straitjacket of a particular logical system, or even requiring them to have detailed knowledge of such a system. To the end of his life, he thought this aim a proper one for a logician, and from time to time gave talks to mathematicians in which he would expound particular logical points. As a logician, however, he was interested in devising formal systems which could act as bridges between the formal and the informal, and this motivated him to produce the two systems set out in this paper" (Cooper, Alan Turing, 211). The issue is accompanied by a second issue in original wraps, this housing a review of Turing's paper. Item #1573
CONDITION & DETAILS: Menasha: Association for Symbolic Logic. (10 x 7 inches; 250 x 175mm). Two issues in original wraps and in pristine condition.
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CC-MAIN-2021-43
| 1,140 | 2 |
http://greens.org/s-r/recent4.html
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math
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s/r home | issues | authors | masthead
A Magazine of Green Social Thought
S I N C E 1 9 9 1
Recent issues: selected articles
Fall, 2009 S/R 50: Climate Economics: Sense & Nonsense is available.
Articles on finance, flu, Three Mile Island, the carbon tax, and the German Greens. [1 aug 09] Table of contents.
Cohousing & Ecovillage Development —Tom Braford
How the Color Green Can Sometimes Fade —Victor Grossman
Working on the Inside...But for Which Side? —Todd Chretien
Fooling With Disaster? —Sue Sturgis
"Consumerism" Is Dead - Can Obama Lead Us to a Downscaled Lifestyle? —James Howard Kunstler
What's Wrong with a 30-Hour Work Week? —Don Fitz
Spring, 2009 S/R 49: Collapse of Capitalism? is available.
[3 apr 09] Table of contents.
Climate Change Pollyannas: Global Warming for Dummies —David Orton
The Fallacy of Biofuels —Carmelo Ruiz-Marrero
Why a Green Future Is "Unconstitutional" and What to Do about It —Jane Anne Morris
The Coming Capitalist Consensus —Walden Bello
The History and "Morals" of Ethnic Cleansing —Victoria Buch
Winter, 2009 S/R 48: Surviving Climate Change
Reports from the St. Louis Roundtable [18 nov 08] Table of contents.
From Extractive to Renewable Agriculture —Wes Jackson
Renewable Energy Cannot Sustain a Consumer Society —Ted Trainer
The Political Economics of Greenwashing —Stan Cox
Meat, “Free Trade,” and Democracy —Jane Anne Morris
Thinking With Our Feet —Chris Bradshaw
Beyond Progressive Malpractice —Ronnie Cummins
Airborne Poisons: EPA Turns an Ear to the Lead Industry —Don Fitz
Fall, 2008 S/R 47: Economics of Producing Less
[7 nov 08] Table of contents.
The Economics of Less Stuff and Better Lives —Ben Wuloo Ikari
Production-Side Environmentalism —Don Fitz
Is Sustainable Capitalism an Oxymoron? —David Schweickart
Cynthia McKinney Deserves Your Support, Obama Does Not —Glen Ford
Elites vs. Greens in the Global South —Walden Bello
Summer, 2008 S/R 46: Not Just a Better Light Bulb Announcement
Announcement of conference June 27-29, 2008, at Webster University, St. Louis, Missouri, plus new articles on carbon, copper, transportation, climate justice, the Green Party, and the like. [10 may 08] Table of contents.
Homo Metallicus: Is Recycling the New Garbage? —Jane Anne Morris
Indigestible Leftovers of the Housing Bubble —Stan Cox
Rethinking the Automobile —Chris Bradshaw
Toward a New Agenda for Climate Justice —Brian Tokar
Palestine: "I Was Not Prepared for the Horrors I Saw" —Silvia Cattori interviews Hedy Epstein
Synthesis/Regeneration home page |
List of issues | masthead |
Tables of contents:
46 47 48 49 50 51 52 53 54
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| 2,718 | 46 |
https://gogetfunding.com/help-kayla-go-to-college/
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math
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Hello! My name is Kayla and I'm a senior in high school. Recently I have been accepted into Carthage College but I need to send in my deposit of $300 in order to secure my acceptance. (This is where you come in.) I'm looking to you, random kind citizens, to help me out. If you decide to help me, I would really appreciate it. Thank you so much and I hope you have a nice day!
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| 376 | 1 |
http://forums.wolfram.com/mathgroup/archive/2006/Aug/msg00815.html
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math
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- To: mathgroup at smc.vnet.net
- Subject: [mg69092] Re: [mg69056] restart?
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Wed, 30 Aug 2006 06:32:24 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <[email protected]>
- Reply-to: murray at math.umass.edu
- Sender: owner-wri-mathgroup at wolfram.com
A "clean worksheet"??? If you really mean that, then just open a new
notebook window! (From the menu, File > New.)
Or do you mean you want the Mathematica kernel to forget everything it
learned as made definitions in a notebook (or more than one notebook) at
a given Mathematica session? That's something entirely different.
For the latter, the simplest way is probably to use the menu command
Kernel > Quit Kernel > Local.
The way you asked your question, I suspect you're trapped in the
paradigm of some other symbolic algebra program.
> I am sure other folks have asked this question but I have not seen the
> answer so...
> How does one restart in Mathematica? Of course, one can just quit the
> application and then start over but surely there is a command that
> reverts to a clean worksheet.
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
Prev by Date:
RE: Something wrong with my FrontEnd?
Next by Date:
Re: generalized foldlist problem
Previous by thread:
Next by thread:
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https://independentseminarblog.com/2017/09/25/the-most-important-game-in-the-world-summer/
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math
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Today, I’m going to examine, through the lens of Game Theory, the most important game in the world, soccer (according to Yale professor Ben Polak)!
One of the most game changing moments in soccer is the penalty kick in which a player is allowed to take a shot at the goal from the penalty line while it is only defended by the goalkeeper. Especially in low scoring games, the penalty kick is often the decisive goal (check out the seven most defining penalty kicks in history). Such crucial moments can be regarded as a strategic game between two players: the kicker and the goalkeeper.
The game can be simplified as such: the kicker has three choices of directions: left, middle, and right. To start our analysis, let’s further simplify the problem and assume that the goalkeeper only has the choice of diving left or right. If the kicker and the goalkeeper choose the same direction, the kicker has 40% chance of scoring. If they choose different directions, the kicker has 90% chance of scoring. Yet, if the kicker chooses middle, s/he always has 60% chance of scoring. The goalkeeper’s payoff is considered to be the negative of chance of scoring. Thus, we have this simple payoff matrix:
|Kicker (left)/Keeper (Top)||left||right|
We can see that there is no strictly or weakly dominated strategy to delete for either party. What should we do?
In this case, we need to introduce a new concept in Game Theory: Best Response. A best response is a strategy for a player that produce the best outcome for that player given a particular combination of strategies of other players. For example, if the keeper chooses left, the best response for the kicker is right.
Yet, this concept is based on the idea that we know the choice of the other player. In the penalty kick, the keeper’s choice is not given. What should we do then?
We have to base our decisions on our expectations of the keeper’s action. We will be calculating our expected payoff instead. The formula for expected payoff is rational and simple. It is the sum of expected possibilities of individual strategies times their respective payoffs. For example, if we think that the goalkeeper has a 30% chance of diving left then our expected payoff for kicking left is:
To make this clearer, let’s draw a graph of our expected payoff with respect to our belief of keeper’s chance of diving right. Thus, we have:
From this graph, we can see that the green curve representing the expected payoff of kicking to the middle is never the highest. Thus, kicking to the middle is never the best response, no matter of your belief of the keeper’s action. Generally, game theory would advise people NOT to choose a strategy that’s NEVER the best response if you want to maximize your expected payoff. In other words, according to game theory, one should NEVER choose middle in a penalty kick.
Yet, following the skeptic tone set up in the last post, is this model a perfect representation of the reality? The answer is NO.
In this particular analysis, we have to ignore a lot of important factors in penalty kick. For example, for our convenience, we assumed that the goalie will not stay in the middle which is definitely a choice in real soccer. Also, we failed to take into account the speed of the ball. If a player can kick the ball very hard towards the middle and increase his probability of scoring to 80%, how will that affect our analysis? Try to draw the expected payoff graph for this player and let me know in the comments.
Work Cited: Yalecourses. (2008, November 20). Game theory [Video file]. Retrieved from https://www.youtube.com/watch?v=YYUPc-cfPyc
Image: [Penalty kick]. (n.d.). Retrieved from http://www.laughinggif.com/gifs/fxu3molktn %5BExpected payoff of penalty kick]. (2011, June 6). Retrieved from http://philosophicaldisquisitions.blogspot.com/2011/06/game-theory-part-6-penalty-kick-game.html
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CC-MAIN-2019-30
| 3,888 | 14 |
http://dnstube.tk/koqo/diode-series-resistance-measurement-11.php
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math
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Diode series resistance measurement
The Schottky Diode Mixer. Choosing a low value of series resistance provides the best diode. At. Figure 5 shows the measurement of conversion loss for two diodes.
Measuring the Output Impedance of Voltage References andI have plotted the I-V characteristics of a Schottky diode under strong forward bias (0-0.7V, conduction begins at about 0.3V). I have to find the series resistance.
How to Test a Silicon Diode with a Multimeter. Some multimeters with a diode check function are not designed to measure diode resistance.Using this extra data with standard one sun measurements also measures the average diode ideality factor,. lower than ideal primarily due series resistance (Rs),.
80 Series V - Transcat - Test, Measurement, and Calibrationwith N-Factor and Series Resistance Correction. remote temperature measurement range (up to +127.9375°C), diode fault detection, and temperature alert function.
Implement diode model - Simulink - MathWorksYORBA LINDA, CA - B&K Precision, a leading designer and manufacturer of reliable, cost-effective test and measurement instruments, today announced its first series of.
The Light-Emitting Diode block represents a light-emitting diode as an exponential diode in series with a current sensor.Basic Light Emitting Diode guide. From DP. If you’re too lazy to calculate the proper resistance value for every LED. LED Series Resistance Calculator.1 PN Junction Diode Parameter. effect of the series resistance, R S,. each curve with its corresponding diode. You might have to re-measure them to figure.
Effect of diode size and series resistance on barrier(series resistance). Figure 6 shows two basic types of PIN diode series switches, a Single-Pole, Single Throw (SPST) and a Single-Pole, Double-.
DIODE CIRCUITS LABORATORY - Circuits 1 ClassA new method for extracting the series resistance and thermal resistance of a Schottky diode is presented. The method avoids the inaccuracies caused by the.
An Alternative One-diode Model for Illuminated Solar Cells. Series resistance,. methods based on C-V and I-V measurements to extract Schottky diode. series resistance from I-V characteristics of Schottky diodes or.What would the multimeter shows if I connect a multimeter across A & B in resistance mode ? DFR- Diode. Diode forward/reverse resistance measurement. series.Diode detectors for RF measurement Part 1: Rectifier circuits, theory and calculation procedures. Detector with diode series resistance.METHOD OF MEASURING SHUNT RESISTANCE IN PHOTODIODES. A method of measuring the shunt resistance of diodes,. the series and shunt resistance. L O A D IL.Ohmic resistance RS. The series diode connection. Current I1 at second measurement temperature. Specify the diode current I1 value when the voltage is V1 at the.
DIODE SERIES RESISTANCE - All About CircuitsThe resistance measurement is high when the diode is forward-biased because current from the multimeter flows through the. Fluke 3000 FC Series Wireless Multimeter.
Using a Model 6517A Electrometer. The series resistor (R S) in the measurement loop is necessitated by noise. The added resistance of diode D S.
I-V and C-V methods to extract Al/polysilicon Schottky
T meas is the Measurement. current of the second diode I s2 and the solar cell. between the series resistance R s and the solar cell.Silicon Zener Diodes. equal to the diode series resistance R S in. common practice to measure the breakdown voltage of Zener diodes by application of a.
Application Note Capacitor Leakage Measurements Series
Is resistance of a silicon diode constant. You cannot measure resistance of the diode using a. and also if they have a two part series or season.By measuring the voltage drop across the diode or resistor as. Resistors are often used in series with another circuit component to reduce the. Resistance. 7.A novel one-diode model is proposed for illuminated solar cells, which contains an additional variable resistance describing minority carrier diffusion from the bulk.Effect of diode size and series resistance on barrier height and ideality factor in nearly ideal Au/n type-GaAs micro Schottky contact diodes. I V measurement I.
Extraction of Schottky diode parameters with a bias dependent barrier height V. Mikhelashvili,. pendent and which contains a linear series resistance.Piecewise Linear. Piecewise Linear., you specify two voltage and current measurement points on the diode I-V curve and. The series diode connection resistance.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583513844.48/warc/CC-MAIN-20181021094247-20181021115747-00210.warc.gz
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CC-MAIN-2018-43
| 4,496 | 17 |
http://www.solutioninn.com/continue-to-use-the-data-in-the-preceding-problem-suppose
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math
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Continue to use the data in the preceding problem. Suppose that you want to construct a two- year-maturity forward loan commencing in three years.
a. Suppose that you buy today one three- year- maturity zero- coupon bond. How many five- year-maturity zeros would you have to sell to make your initial cash flow equal to zero?
b. What are the cash flows on this strategy in each year?
c. What is the effective two- year interest rate on the effective three- year- ahead forward loan?
d. Confirm that the effective two- year interest rate equals (1 + f4) × (1 + f5) - 1. You therefore can interpret the two- year loan rate as a two- year forward rate for the last two years. Alternatively, show that the effective two- year forward rate equals
(1+y5)5 / (1+y3)3 – 1
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s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823220.45/warc/CC-MAIN-20171019031425-20171019051425-00460.warc.gz
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CC-MAIN-2017-43
| 766 | 6 |
https://www.hindawi.com/journals/jam/2013/802791/
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math
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Algorithms for Some Euler-Type Identities for Multiple Zeta Values
Multiple zeta values are the numbers defined by the convergent series , where , , , are positive integers with . For , let be the sum of all multiple zeta values with even arguments whose weight is and whose depth is . The well-known result was extended to and by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers and then gave a direct formula for for arbitrary . In this paper we apply a technique introduced by Granville to present an algorithm to calculate and prove that the direct formula can also be deduced from Eisenstein's double product.
The multiple zeta sums, are also called Euler-Zagier sums, where are positive integers with . Clearly, the Riemann zeta function , is the case in (1). The multiple zeta functions have attracted considerable interest in recent years.
For Riemann’s zeta function , Euler proved the following identity: Recently, some identities similar to (3) have also been established. Given two positive integers and (suppose ), define a number by Then, for , the value of is known [1–5].
Following , for , let be the sum of all multiple zeta values with even arguments whose weight is and whose depth is ; that is,
In , Gangl et al. proved the following identities:
Recently, using harmonic shuffle relations, Shen and Cai proved the following results in :
In , applying the theory of symmetric functions, Hoffman established the generating function for the numbers . He proved that Based on this generating function, some formulas for for arbitrary are given. For example, Hoffman obtained that where is the th Bernoulli number.
In this paper we use a technique introduced by Granville to present an elementary recursion algorithm to calculate , we also give some direct formula for for arbitrary . Our algorithm may be of some interest if we note that it is obtained through an elementary analytic method and that the statement of the algorithm is fairly simple.
2. Statements of the Theorems
Theorem 1. Let denote a positive integer. Let , be a series of numbers defined by Then, for any two positive integers and with , one has
Theorem 2. Given a positive integer , we have
When is not large, we may use the following recursion algorithm to calculate then use Theorem 1 to get the formula for .
Theorem 3. The coefficients , can be calculated recursively by the following formulas: where , are the numbers defined by
In , Hoffman established an interesting result [6, Lemma 1.3] to obtain his formula (10) for . This lemma might be deduced from the theory of Bessel functions. Using the expressions for the Bessel functions of the first kind with a half integer index, we may deduce from the generating function (13) a direct formula for .
Theorem 4. For , one has
To deduce (17) from (16), we only need to write the expression of , respectively, according to whether is odd or even, and use (if is odd) or (if is even) to replace . In the two cases, we will get the expression (17) for . By Theorem 1, we have which reproduces Hoffman’s formula (10).
3. Proofs of the Theorems
Proof of Theorem 1. The left side of (12) is
The second sum in (19) is the coefficient of in the formal power series
It follows that the coefficient of earlier is
Hence, the sum (19) is
Now, consider the function We partition into two parts. Let Then, we have , , for all, and
Consider the sum (22). For , we treat each sum in (22) with respect to as follows: In the last step, begins with 1 since for .
It follows that the sum (22) becomes that Clearly, the sum in (27) is the coefficient of in the Cauchy product of that is, it is the coefficient of in the power series Therefore, the sum (27) is The proof is completed.
Remark 5. If we take to be a complex variable, then the series is absolutely and uniformly convergent for in any compact set in the complex plane; thus, the function is analytic in the complex plane. Hence, it may be expanded as a Taylor series.
Proof of Theorem 2. First we recall Euler’s classical formula Similar to Euler’s formula, Eisenstein studied a product of two variables and proved that for the following formula holds (see [10, page 17]): Let be temporarily fixed. By (34), for we have Now, let . We get We write . Or equivalently, let . Then, we get
Proof of Theorem 3. Taking logarithms of both sides of (32), we get that By Remark 5, the series may be differentiated term-by-term; hence, we have where we denote The order of the summation can be changed since the series is dominated by for some positive constant . From (39), we get that or Write out the Cauchy product in the right side of (42), then compare the coefficient of on both sides. We get that
Proof of Theorem 4. We now study the the generating function
We may use L’Hospital’s rule to verify that
Now we expand out . We have
By (11) and (13), we have
Consider the function Clearly, the sum in (47) can be rewritten as where means the th derivative of a function with respect to .
We denote . Then, we have and, hence, which implies that Finally, from (47) (49) we get that
We may apply Hoffman’s result [6, Lemma 1.3] to get the direct formula for Here, we use some simple properties of the Bessel functions of the first kind to give its direct expression.
Lemma 6. Let be an integer and let . Then one haswhere denotes the Bessel function of the first kind of index .
The Bessel functions with a half-integer index can be represented by elementary functions. The following lemma is well known.
Lemma 7. Let be an integer, and let . Then, one has
From Lemmas 6 and 7, and (53), we get that This completes the proof of Theorem 4.
The direct formula for can be found from Theorem 4. However, we would like to use Theorem 3 to present some concrete examples to show how to calculate for small . The difficult part of the recursion formula (14) is for to calculate the sum where we denote and .
It follows from that Generally, we can use induction on to prove that if for we have gotten some positive integers such that then the expression for is
Note that if is an even integer, then we have Similarly, if is an odd integer, then we have
From formula (14), we get that
This work is supported by the National Natural Science Foundation of China (1127208).
H. Gangl, M. Kaneko, and D. Zagier, “Double zeta values and modular forms,” in Automorphic Forms and Zeta Functions. In Memory of Tsuneo Arakawa. Proceedings of the Conference, Rikkyo University, Tokyo, Japan, September 2004, pp. 71–106, World Scientific, Hackensack, NJ, USA, 2006.View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet
R. Remmert, Classical Topics in Complex Function Theory, vol. 172 of Graduate Texts in Mathematics, Springer-Verlag, New York, NY, USA, 1998.View at: MathSciNet
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CC-MAIN-2023-06
| 6,852 | 46 |
https://www.hzdr.de/db/Cms?pOid=13478&pNid=0&pLang=en
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math
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The Magnetic Field of the Hybrid Undulator U27
In order to ensure sufficient overlap of the electrons with the optical beam, the center of the electron trajectory should be at the same position independently of electron energy and of the strength of the magnetic field. The principle of the magnetic structure of such a nearly "passive" undulator is shown in fig. 1. The structure consists of NdFeB permanent magnets and poles of decarborized iron. The field of these arrangement has been investigated by the code RADIA . Corresponding results have been reported . To ensure the correct slope and position of the electron beam at the undulator exit one has to add an additional magnet (m2) and an iron pole (p2) on either side producing appropriate fringe fields.
The undulator was adjusted for a gap g = 12 mm by varying the y-coordinate of p2 and the distance between m2 and p2 (see fig. 1). The resulting displacement and the slope of the trajectory at the exit can be corrected by coils mounted at the entrance sides of both sections and allowing to inject the electrons at a small angle to the z-axis.
Fig. 1: Principle of the magnetic structure of U27. The blue rectangles represent NdFeB permanent magnets, the red ones show poles of decarborized iron. The symbols p2 and m2 denote poles and magnets of reduced thicknesses mounted at the same girder like the rest of the structure.
The undulator field was measured and tuned at HASYLAB (DESY) by means of the Hall probe as shown in fig. 2. After transporting the undulator to Rossendorf control mesurement of the undulator fields have been performed using the pulsed-wire method.
At DESY the probe was mounted on a goniometer with six degrees of freedom for right adjustment within the magnetic structures. The poles were tuned with the aim to get a minimum electron displacement at the exit sides of the modules as well as a peak field roughness lower than 0.4%. As a result of the measurements the fig. 3 shows the field component By(0,0,z) in the middle plane of both undulator units for a gap of g = 12 mm and a distance d = 250 mm between the sections (part a) and the first integral over the measured field (part b). The trajectory of a reference electron with an energy of E = 20 MeV in the wiggle plane is shown in part (c). Only weak magnetic fields of about 2 mT are necessary to keep the electrons within the optical mode. Fig.4 shows the magnetic field distribution By(x,0,z5) perpendicular to the electron beam at different gaps , where z5 is the z coordinate of the 5th pole.
Fig. 2: The Hall probe mounted on a goniometer for field measurements on the axis of one of the undulator sections.
In order to estimate the influence of the remaining field inhomogeneities on the lasing process, we determined for various gap widths the maxima (minima) Bi of the field, their average values Bav and the differences Bi - Bav. For g = 14 mm the results are shown in fig. 5. The standard deviations σB of the Bav contribute to the inhomogeneous line broadening of the emitted light corresponding to the following formula:
Fig. 5: Maxima and minima of the magnetic field By (z) in the middle plane of the whole undulator. For both sections the average values Bav and their standard deviations σ are denounced. The values σB/Bav characterizing the field roughness are given in parenthesis.
The fast Fourier transform obtained from the measured field distribution By(z) is shown in the fig. 6, which indicates for gap widths of g = 8, 12, 16 and 20 mm the absolute values |f(n)| of the contributions of the first, third and fifth harmonics to the magnetic field. The employed FFT - procedure delivers the wave numbers kz as a multiple of the quantity k0:
where L is the length (mm) of the interval used for the analysis. For each gap a window of 1690 points and a length of 885.0 mm was analysed containing 31 full magnetic periods. The quantity k0 has therefore the value k0 = 0.007099 mm-1. Since the momenta A3 in f(n) exhibit always a positive sign, the measured field By(z) is a bit more flat and more broad than a pure sine function. The reason for the appearence of higher harmonics is the width wz = 5 mm of the iron poles in z-direction, influencing the form of the field mostly for lower gap values.
Fig. 6: The Fourier Transform (FFT) of the measured field distribution By(z) for various gap values
If the FEL works with maximum power the energy factor γ of the electrons decreases by dγ = γ/2 Nu (for the first harmonic) along the electron path due to the interaction of the electron beam with the electromagnetic field, where Nu = 68 is the total number of magnetic periods in the two undulator units. The electron energy changes continuously from the undulator entrance to the exit leading to a resonance wavelength λ(z) which depends on the coordinate z along the undulator
Within a certain interval dλ this effect can be compensated by differentially increasing the gap, and hence decreasing the magnetic field along the undulator. To compensate the energy loss dγ by a reduction dB of the magnetic field one has to ensure
from which follows
For hybrid undulators, the Halbach equation allows to estimate the tapering of the gap g needed for the variation dB of the field corresponding to equation (4). Figure 7 shows the effect of field tapering in both sections of the undulator U27, which would be used in a situation typical for high intensity lasing.
For variable gaps the radiation wavelength is changed and consequently the phasing between the two undulator systems has to be changed as well. This has to be done by properly choosing the electron flight path d between the two sections.
The optical phase in an undulator has been analyzed in detail by Walker . It can be expressed by
Here z is the coordinate along the beam axis, λ is the radiation wavelength, γ is the electron kinetic energy in units of its rest mass and Θ is the electrons deflection angle. The terms in the bracket have the following descriptive meaning: the first gives the contribution to the phase, if the electron travels just a distance z in free space, the second term represents the additional contribution due to the magnetic field. The function Θ(z) can be derived from By(z) by
Using the eqs. (5) and (6) the phasing of the two undulator sub-systems can be determined experimentally by measuring By(z) along the axis of the entire undulator.
The phase on the poles in the second section varies with the distance d, which depends on the K-value and has to be chosen appropriately. Moreover, phase matching is obtained periodically after an increase of d by Δd = λu(1+Krms 2). The deviation of the optical phase angle from its nominal value obtained for a perfect undulator is denoted by ΔΨ(z). For a gap g = 17 mm measurements for ΔΨ(z) are shown in fig. 8. The K-value for this case was 0.6688. The nominal phase deviation on the poles is nearly zero, only at the end poles before and after the interspace the phases deviate from zero. The proper choice of the distances d as functions of the K-value as determined experimentally is shown in fig. 9. Six different curves have been measured. They are shifted horizontally by Δd = λu(1+Krms 2(g)). These curves have to be used to choose phasing distances dph in dependence on the gap g.
Fig. 8: Phase differences ΔΨ(z) for a gap g = 17 mm. The K-value is 0.6688. Three phasing distances dph are shown.
Fig. 9: Phasing distances dph (points) between the two sections of U27. The right axis shows the gap widths g, for which the values dph have been found, the left axis shows the corresponding K-values in a linear scale.
P. Elleaume, O. Chubar and J. Chavanne, J. Synchr. Rad. 5 (1998) 481
P. Gippner, W. Seidel and A. Schamlott, Annual Report 1998, FZD-271, p.16
R. P. Walker, Nucl. Instr. Meth. A335 (1993) 328
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|Part of a series of articles about|
is geometric, because each successive term can be obtained by multiplying the previous term by 1/2.
Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property. Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of convergence of series. Geometric series are used throughout mathematics, and they have important applications in physics, engineering, biology, economics, computer science, queueing theory, and finance.
The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant. This relationship allows for the representation of a geometric series using only two terms, r and a. The term r is the common ratio, and a is the first term of the series. As an example the geometric series given in the introduction,
may simply be written as
- , with and .
The following table shows several geometric series with different common ratios:
|Common ratio, r||Start term, a||Example series|
|10||4||4 + 40 + 400 + 4000 + 40,000 + ···|
|1/3||9||9 + 3 + 1 + 1/3 + 1/9 + ···|
|1/10||7||7 + 0.7 + 0.07 + 0.007 + 0.0007 + ···|
|1||3||3 + 3 + 3 + 3 + 3 + ···|
|−1/2||1||1 − 1/2 + 1/4 − 1/8 + 1/16 − 1/32 + ···|
|–1||3||3 − 3 + 3 − 3 + 3 − ···|
The behavior of the terms depends on the common ratio r:
- If r is between −1 and +1, the terms of the series become smaller and smaller, approaching zero in the limit and the series converges to a sum. In the case above, where r is one half, the series has the sum one.
- If r is greater than one or less than minus one the terms of the series become larger and larger in magnitude. The sum of the terms also gets larger and larger, and the series has no sum. (The series diverges.)
- If r is equal to one, all of the terms of the series are the same. The series diverges.
- If r is minus one the terms take two values alternately (e.g. 2, −2, 2, −2, 2,... ). The sum of the terms oscillates between two values (e.g. 2, 0, 2, 0, 2,... ). This is a different type of divergence and again the series has no sum. See for example Grandi's series: 1 − 1 + 1 − 1 + ···.
The sum of a geometric series is finite as long as the absolute value of the ratio is less than 1; as the numbers near zero, they become insignificantly small, allowing a sum to be calculated despite the series containing infinitely many terms. The sum can be computed using the self-similarity of the series.
Consider the sum of the following geometric series:
This series has common ratio 2/3. If we multiply through by this common ratio, then the initial 1 becomes a 2/3, the 2/3 becomes a 4/9, and so on:
This new series is the same as the original, except that the first term is missing. Subtracting the new series (2/3)s from the original series s cancels every term in the original but the first,
A similar technique can be used to evaluate any self-similar expression.
For , the sum of the first n terms of a geometric series is
where a is the first term of the series, and r is the common ratio. We can derive this formula as follows:
As n goes to infinity, the absolute value of r must be less than one for the series to converge. The sum then becomes
When a = 1, this can be simplified to
the left-hand side being a geometric series with common ratio r.
The formula also holds for complex r, with the corresponding restriction, the modulus of r is strictly less than one.
Proof of convergence
Since (1 + r + r2 + ... + rn)(1−r) = 1−rn+1 and rn+1 → 0 for | r | < 1.
Convergence of geometric series can also be demonstrated by rewriting the series as an equivalent telescoping series. Consider the function,
So S converges to
For , the sum of the first n terms of a geometric series is:
This formula can be derived as follows:
A repeating decimal can be thought of as a geometric series whose common ratio is a power of 1/10. For example:
The formula for the sum of a geometric series can be used to convert the decimal to a fraction,
The formula works not only for a single repeating figure, but also for a repeating group of figures. For example:
Note that every series of repeating consecutive decimals can be conveniently simplified with the following:
That is, a repeating decimal with repeat length n is equal to the quotient of the repeating part (as an integer) and 10n - 1.
Archimedes' quadrature of the parabola
Archimedes' Theorem states that the total area under the parabola is 4/3 of the area of the blue triangle.
Archimedes determined that each green triangle has 1/8 the area of the blue triangle, each yellow triangle has 1/8 the area of a green triangle, and so forth.
Assuming that the blue triangle has area 1, the total area is an infinite sum:
The first term represents the area of the blue triangle, the second term the areas of the two green triangles, the third term the areas of the four yellow triangles, and so on. Simplifying the fractions gives
This is a geometric series with common ratio 1/4 and the fractional part is equal to
The sum is
For example, the area inside the Koch snowflake can be described as the union of infinitely many equilateral triangles (see figure). Each side of the green triangle is exactly 1/3 the size of a side of the large blue triangle, and therefore has exactly 1/9 the area. Similarly, each yellow triangle has 1/9 the area of a green triangle, and so forth. Taking the blue triangle as a unit of area, the total area of the snowflake is
The first term of this series represents the area of the blue triangle, the second term the total area of the three green triangles, the third term the total area of the twelve yellow triangles, and so forth. Excluding the initial 1, this series is geometric with constant ratio r = 4/9. The first term of the geometric series is a = 3(1/9) = 1/3, so the sum is
Thus the Koch snowflake has 8/5 of the area of the base triangle.
The convergence of a geometric series reveals that a sum involving an infinite number of summands can indeed be finite, and so allows one to resolve many of Zeno's paradoxes. For example, Zeno's dichotomy paradox maintains that movement is impossible, as one can divide any finite path into an infinite number of steps wherein each step is taken to be half the remaining distance. Zeno's mistake is in the assumption that the sum of an infinite number of finite steps cannot be finite. This is of course not true, as evidenced by the convergence of the geometric series with .
Book IX, Proposition 35 of Euclid's Elements expresses the partial sum of a geometric series in terms of members of the series. It is equivalent to the modern formula.
For example, suppose that a payment of $100 will be made to the owner of the annuity once per year (at the end of the year) in perpetuity. Receiving $100 a year from now is worth less than an immediate $100, because one cannot invest the money until one receives it. In particular, the present value of $100 one year in the future is $100 / (1 + ), where is the yearly interest rate.
Similarly, a payment of $100 two years in the future has a present value of $100 / (1 + )2 (squared because two years' worth of interest is lost by not receiving the money right now). Therefore, the present value of receiving $100 per year in perpetuity is
which is the infinite series:
This is a geometric series with common ratio 1 / (1 + ). The sum is the first term divided by (one minus the common ratio):
For example, if the yearly interest rate is 10% ( = 0.10), then the entire annuity has a present value of $100 / 0.10 = $1000.
This sort of calculation is used to compute the APR of a loan (such as a mortgage loan). It can also be used to estimate the present value of expected stock dividends, or the terminal value of a security.
Geometric power series
The formula for a geometric series
Similarly obtained are:
- Divergent geometric series
- Generalized hypergeometric function
- Geometric progression
- Neumann series
- Ratio test
- Root test
- Series (mathematics)
- Tower of Hanoi
Specific geometric series
- Grandi's series: 1 − 1 + 1 − 1 + ⋯
- 1 + 2 + 4 + 8 + ⋯
- 1 − 2 + 4 − 8 + ⋯
- 1/2 + 1/4 + 1/8 + 1/16 + ⋯
- 1/2 − 1/4 + 1/8 − 1/16 + ⋯
- 1/4 + 1/16 + 1/64 + 1/256 + ⋯
- Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 10, 1972.
- Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 278–279, 1985.
- Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 8, 1987.
- Courant, R. and Robbins, H. "The Geometric Progression." §1.2.3 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 13–14, 1996.
- Pappas, T. "Perimeter, Area & the Infinite Series." The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 134–135, 1989.
- James Stewart (2002). Calculus, 5th ed., Brooks Cole. ISBN 978-0-534-39339-7
- Larson, Hostetler, and Edwards (2005). Calculus with Analytic Geometry, 8th ed., Houghton Mifflin Company. ISBN 978-0-618-50298-1
- Roger B. Nelsen (1997). Proofs without Words: Exercises in Visual Thinking, The Mathematical Association of America. ISBN 978-0-88385-700-7
- Andrews, George E. (1998). "The geometric series in calculus". The American Mathematical Monthly. Mathematical Association of America. 105 (1): 36–40. doi:10.2307/2589524. JSTOR 2589524.
History and philosophy
- C. H. Edwards, Jr. (1994). The Historical Development of the Calculus, 3rd ed., Springer. ISBN 978-0-387-94313-8.
- Swain, Gordon and Thomas Dence (April 1998). "Archimedes' Quadrature of the Parabola Revisited". Mathematics Magazine. 71 (2): 123–30. doi:10.2307/2691014. JSTOR 2691014.
- Eli Maor (1991). To Infinity and Beyond: A Cultural History of the Infinite, Princeton University Press. ISBN 978-0-691-02511-7
- Morr Lazerowitz (2000). The Structure of Metaphysics (International Library of Philosophy), Routledge. ISBN 978-0-415-22526-7
- Carl P. Simon and Lawrence Blume (1994). Mathematics for Economists, W. W. Norton & Company. ISBN 978-0-393-95733-4
- Mike Rosser (2003). Basic Mathematics for Economists, 2nd ed., Routledge. ISBN 978-0-415-26784-7
- Edward Batschelet (1992). Introduction to Mathematics for Life Scientists, 3rd ed., Springer. ISBN 978-0-387-09648-3
- Richard F. Burton (1998). Biology by Numbers: An Encouragement to Quantitative Thinking, Cambridge University Press. ISBN 978-0-521-57698-7
- John Rast Hubbard (2000). Schaum's Outline of Theory and Problems of Data Structures With Java, McGraw-Hill. ISBN 978-0-07-137870-3
- Hazewinkel, Michiel, ed. (2001), "Geometric progression", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4
- Weisstein, Eric W. "Geometric Series". MathWorld.
- Geometric Series at PlanetMath.org.
- Peppard, Kim. "College Algebra Tutorial on Geometric Sequences and Series". West Texas A&M University.
- Casselman, Bill. "A Geometric Interpretation of the Geometric Series" (Applet).
- "Geometric Series" by Michael Schreiber, Wolfram Demonstrations Project, 2007.
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Drops, Tongues & Bullets
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https://studysoup.com/note/39742/msu-cem-835-fall-2015
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Adv Analytical Chemistry II
Adv Analytical Chemistry II CEM 835
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Spectrochemical Measurements Expressions of Intensity 39 Quantities based on radiometric system not photometric system 0 Basic unit is joule and other SI units sometimes nonSi units for convenience 39 Often de nitions include area volume or solid angle Spectral quantities Bx 7L Partlal quantltles Bk 1 2 k2 Bkdk 1 Total quantities B I Bkdk TABLE 2 1 Radiometric system Quantity Symbols Description Defining equationa Units General Radiant energy Q Energy in the form of radiation J ergs Radiant energy density U Radiant energy per unit U 192 J cm 3 volume 3V Radiant ux or radiant power P Rate of transfer of radiant I 92 W energy at Source Radiant intensity I Radiant power per unit solid 933 W sr 1 angle from a point source an Radiant emittance or radiant M Radiant power per unit area 532 W cm 2 ex1tance 3A Radiant emissivity J Radiant power per unit solid 621 W sr 1 cm 3 angle per unit volume 39 3V Radiance BL Radiant power per unit solid 621 W sr l cmquot2 angle per unit projected area an GAP 621 69 6A cos 0 Receiver Irradiance E Radiant power per unit area E 32 W cm 2 8A I 2 Radlant exposure H Integrated 1rrad1ance H L E dt J cm CEM 835 page 11 Important quantities Radiant flux 1 rate of energy transfer J s391 W Radiant intensity I radiant ux from a point source per unit solid angle QD4n applies to source J s391 sr391 Radiance B radiant intensity I per projected area CD475A applies to source gt depends on angle between detector and radiation propagation direction see Fig 23 Js391sr391cm392 Irradiance E radiant ux CD ontofrom a surface per unit area QDA applies to source or detector Js 1cm392 radiant Exposure H timeintegrated irradiance tAdt J cm392 Fluence often used but meaning is imprecise CEM 835 page 12 Geometric factors Often radiometric quantities include a solid angle or projected area Solid angle l steradian sr is the part of the surface area of a sphere of radius r having an area of r2 2 Asphere 4 7T39 r 4 75 r2 sterad1ans 1n sphere 2 4 71 1257 r 0 x Arc r y r Plane angle One radian 60 Area One steradian Solid angle iIgu b For example intensity is the radiant ux per unit solid angle I 1 4n CEM 835 page 13 How are these quantities related to spectrochemical techniques Emission Spectroscopy Emitted radiation 4 5 E21 hl 21 hcAZI E2 hvz hcKZ E1 hvl hcK1 b 4 5 Thermal electrical A or chemical l I L A energy K2 K1 21 a C 0 Emission refers to thermally excited atoms or molecules ame ICP electrical discharge plasma Interested in number of atoms per unit volume element observed Demission Aji 39hVij 39nj 39V observation volume atoms in excited state j energy per transition Einstein coef cient transition probability j gti CEM 835 page 14 Ilj can be de ned if in thermal equilibrium by Boltzmann expression Demission Aij 39hVij 39nj 39V EjkT gj e oo E kT 39V Z e 1 10 1 fraction of total in state j Z Aij 39hVij 39ntotal The weighting factor gj statistical weight is the number of degenerate states at each energy E g 2 2J 1 J is the total angular momentum LS LSl LS Example g2s2 g2p122 g2p324 Hence radiant ux Qemission can absolutely determine the concentration of atoms in detection volume CEM 835 page 15 Absorption Spectroscopy Incident Transmitted radiation radiation QO P a b E2 hV2 E1 hvl hcAl c Absorbance A given by Beers39 Law related to the measured quantities DO and CD radiant ux by CD A l T l b og ogq 8 c 0 concentration molL39l cell pathlength cm molar absorptiVity L mol391 cm391 lt1 13010 839b39C Luminescence measurements Scattering measurements CEM 835 page 16 Optical Instruments Many spectrochemical instruments share common components 0 a radiation source 0 optics to de ne light paths 0 a sample container 0 a dispersion element 0 detector transducer Speci c names are applied to the various instruments Aperture Photographic film a Spectrochemical or pg fegioimy encoder Exit slit b W Photodetector Dispersion Entrance element Focal slit plane I Q and image transfer system Photodetectors A spectroscope disperses a range of X39s for Visual Viewing A spectrograph disperses a range of X39s onto focal plane for simultaneous measurements by a photographic lm or array detector A monochromator uses entrance slit eXit slit and a dispersion element to separate X39s in space If multiple eXit slits are used the term polychromator is used CEM 835 page 17 A photometer measures intensity but has no provision for 9 scanning X39s can be selected by use of lters A spectrometer includes means of manually or automatically scanning wavelength A spectrophotometer has provision for scanning measurements using two beams of light useful for ratioing incident and transmitted light An interferometer is a nondispersive device that relies on interference to obta1n spectral 1nformatlon A detector is any device whose output is proportional to the intensity of light falling on it A transducer more speci c uses electrical signals CEM 835 page 18 Components of Measurement Instruments Radiation Sources Many radiation sources are based on black body radiation 39 perfect absorber of radiation at all X39s 0 if in thermal equilibrium must also be perfect radiation emitter 2000K E 1750K dWd J m 4 1000 1250K 0 1000 2000 3000 4000 5000 7 visible region 39 391 nm Two obvious points 39 total amount of energy radiated increases rapidly with T U a T4 Stefan39s Law Radiant energy density J cm3 39 position of the maximum spectral radiance kmax blue shifts with increasing T C A 2 max 4965 T where c2 143 8X107 nm K CEM 835 page l9 Energy density U J cm3 is dif cult to measure usually work in radiance B Js1sr1cm2 U c B c B L B V V 47 7 Planck deduced black body equation after consideration of thermodynamics of system with discrete energy levels multiples of hv the beginning of quantum mechanics 2h3 1 B V v C2 ehvkT 1 or in terms of wavelength BKZM 7L5 ehcxkr1 3195 Planck39s radiation law where c12hc2 119x1016 Wnm4cm392sr391 and c2hck same as above 1438x107 nmK CEM 835 page 110 Einstein coef cients Three Einstein coef cients Bij describes probability of absorption from level i gt j Bji describes probability of stimulated emission from level j gti Note These two are simply timereversed processes Aji describes probability of spontaneous emission from level j gti l B A j 8 i i v Absorption Spontaneous Stimulated emission emission The rate of absorption per unit volume s391 cm393 depends on i number of atoms in initial state i ni ii probability of absorption from state i to another state j Bij iii the spectral energy density of incident radiation UV dni B U n dt 1 V 1 absorption removes population from state i so ni decreases CEM 835 page 111 Similarly rate of stimulated emission is The rate of absorption and stimulated emission are the same if there is an equal population in both states Bji 8139 Bij 39gi g is the degeneracy statistical weight Rate of spontaneous emission doesn39t include a UV term E dt If black body is in thermal equilibrium with surroundings rate of absorption and emission must be equal 39Uv ni 39nj Uv nj absorptlon spontaneous stnnulated emission emission U Aji39nj V Bji 39Ili Bji Aji 39nj Alin lt substitutingB g B g ji39 j ij39 i Bjinigigj39nj Aji 39nj CEM 835 page 112 At equilibrium Boltzmann equation can be used to nd nj from ni Aji 39nj Bjini gi gj39nj substituting nj ni eXp hvij kT V Aji 39nj V Bjini gi gj ni eXphVij 1ltT This looks similar in form to Planck39s radiation law B 2hv3 1 v C2 ehvkT1 and gives us the rate of spontaneous emission and absorption UVc 8 h 3 Aji WBij remember1ng BV gjc 4TB Bji39gj Bij39gi CEM 835 page 113 Reflection and Refraction Maxwell39s equations lead to de nition for the velocity of electromagnetic radiation in a vacuum 1 C xSo 39Ho where 80 is the permittivity of freespace 8854x103912 C2N391 m392 uO is the permeability of freespace 4710397 kgmC392 In a medium velocity is reduced VIM The ratio of the velocity in a medium to freespace is refractive indeX gt 100 in a medium 11 varies with wavelength usually increases with frequency called normal dispersion decreases with frequency in region of absorption called anomalous dispersion CEM 835 page 31 7t nm 11 351 1539 458 1525 486 1522 532 1519 644 1515 830 1510 Important Frequency of radiation is xed by source Hence wavelength of radiation in a medium must increase c kz s1ncevot T1 xmedium gt xvacuum When a wave passes from medium with refractive index 111 to medium of refractive index 112 we can write hZ c X nz u 9L1 1121 c 112 CEM 835 page 32 Based on wave representation of electromagnetic radiation and geometry we can quickly deduce the angle of re ection Re ected wavefront Incident wavefront 771 a b 9i 2 93 Law of specular re ectance CEM 835 page 33 The refracted beam does not travel at same velocity as the incident beam v2 v1 411112 first part of the wavefront to strike the interface is retarded preferentially light beam bends towards the interface normal when n2gtm n1 sin61 n2 sin62 Snell39s law of refraction no refraction when 61 00 no transmittance when 61 gt Be critical angle total internal re ection sin 61 sin 62 Snell39s law 111 when sin 62 9O0 61 60 sin 1 111 For airglass 60 z 42 CEM 835 page 34 90 CEM 835 page 35 Fresnel Equations Re ectance losses occur at all at interfaces 0L0 TL pt 1 Conservation Law magnitude increases as the di erence in the refractive indices increases dependent on incidence angle Equation describing the re ectance p00 is the Fresnel equation 1 l sin20i 0 1t2111291 9r 2 Lsin20i 0 1 tan291 9rgti 90 Where 0 i is incidence angle and 01 is refraction angle For the airglass at 589 nm re ectance is about 004 or 4 per interface 10 08 06 Re ectance 04 02 004 CEM 835 page 36 p0 constant for small angles p0 increases rapidly at large angles grazing incidence m Serves several purposes in a spectrometer change the direction of a beam change the polarization of a beam split a beam into two disperse the beam A variety of shapes and materials are available to perform these functions Dispersing prism According to Snell39s Law sinGl sin 62 Snell39s law 111 there will be no dispersion if not is constant dispersion in prism occurs because of the change in refractive index of the prism material as a function of wavelength 0 if prism material exhibits normal dispersion higher frequency shorter wavelength light experiences a higher refractive index than lower frequency longer wavelength light CEM 835 page 37 Light of different wavelengths become divergent and become separated in space angle between incident and refracted beam is called the deviation The variation in deviation with wavelength is called the angular dispersion d6 d6 dn D A dx dn g prism dispersion first term depends on size and shape of the prism and the incidence angle second term prism dispersion depends on the material of the prism and the wavelength 3 glass357 nm 2 194x10 4 nm1 dn 5 1 a glass825 nm 178XlO nm Prisms not often used as dispersion elements because of non constant D A with wavelength produces nonconstant bandwith means range of X39s projected onto eXit slit varies with 9 CEM 835 page 38 Electromagnetic radiation An electromagnetic wave is a transverse wave electric and magnetic elds perpendicular to the propagation direction Plane linearly polarized beam has constant plane containing the electric and magnetic vectors often called unpolarized The timedependent electric eld is E Eosinoa t where E0 is the maximum electric eld strength 0 is the angular frequency 2751 t is time I is the angular phase The angular phase is d0275Xt where X is distance and bo is the phase at x0 275 is number of waves per unit length If two waves maintain the same relative phase difference over i extended period of time ii length they are said to be coherent CEM 835 page 39 Superposition The superposition of two waves states two plane polarized waves can be algebraically summed to produce a resultant wave If waves have same frequency E 2 E1 E2 2 E021 sin03t 11 E022 sin03t 12 Amplitude intensity of wave is E2 E2 2 E1 E22 2 E12 E22 E139E2 E0212 13022 2E0 1 EO Z COS 2 interference term If 1 2 O 27 47 cos0 27 47 l wave amplitude will be reinforced constructive interference If1lt2 7 37 57 cos7 37 57 l wave amplitude will be reduced to zero destructive interference CEM 835 page 310 Interference can result from difference in pathlength If the waves initially start out with same phase the difference in phase 6 due to different paths is 5 1 2 27X1 2nX2 x x 275X1 X2 7 where X1 and X2 are the lengths to the measurement point from source 275 is the number of a complete waves per unit length Thus when 6 O 27 an integral number of wavelengths 275 m 2 n 2 X1 X2 9 5 m 9t 2 construct1ve1nterference 7 when 6 7 37 an integral number of wavelengthsl2 2m 1 5 2 j 2 destruct1ve1nterference Tc CEM 835 page 311 Diffraction Eschellete gratings Parallel grooves etched blazed onto re ective surface asymmetric in profile Groove facet Diffracted ray Incident ray Grating 39 normal N a b Incident light striking long facet is re ected in specular direction With respect to the groove normal light from neighboring grooves travels different distances and so interference occurs in outgoing beam Note angles or and B are de ned With respect to the grating normal not the groove normal Constructive interference occurs When the pathlength difference is an integral number of wavelengths extra pathlength associated With the incident beam is AC AC 2 d sin or extra pathlength associated With the outgoing beam is AD AD 2 d sin B CEM 835 page 312 The total pathlength difference is AC AD AC AD dsinoc sinB m dsin CC sin 3 Grating Formula minimum value of d as M2 because the maximum value of sinoc sinB is 2 The first order m 1 diffraction angle can be calculated for any incidence angle by rearranging the grating formula m s1noc s1nB d m s1nB Y s1n0L where d is found from the groove spacing Important diffraction angle depends on d longer X39s diffracted more than shorter ones 3600 m gt 3500 nm When m0 zero order sinoc sinB or OL B In this case all X39s are diffracted at the same angle If blaze was parallel to the grating plane y 0 the zero order beam would also appear in the specular direction most of the re ected light not dispersed If blaze angle 7 0 specular and zeroorder angles do not correspond and majority of the light is dispersed CEM 835 page 313 Specular re ection Specular re ection Groove normal l3 Incident Incident ray 4 ra Oorder Grating 7 y normal Oorder a b In the special case when incident beam is along the surface normal 0cO and rstorder beam is in specular direction in this case 3 is twice the blaze angle y The wavelength at this angle is called the blaze wavelength m t blaze dsin 0c sin 3 kblaze dSin 3 dsin 2y CEM 835 page 314 Dispersion The angular dispersion D A of the grating can be obtained by differentiating the grating formula with respect to wavelength For constant incidence angle ml dsin 0t sin 3 Grating Formula 1 m DA d E d cosB dsin 0L sin 3 Z d cos 3 sin 0t sin 3 9 cos B sin 0t xed For nearly normal incidence CC is small so 3 is small and so cosB does not change much with k D A does not change much with wavelength much better dispersion element than prism CEM 835 page 315 Monochromators Comprised of 0 dispersive element 0 image transfer system mirrors lenses and adjustable slits an image of the entrance slit is transferred to the eXit slit after dispersion One of the most common arrangements is the CzernyTurner monochromator Entrance Grating SM 81 Collimating mirror M1 Focusing mirror M2 CEM 835 page 316 Wavelength selection Wavelength selection is accomplished by rotating the grating Grating Grating 13 Since angle between the entrance slit grating and exit slit is xed 24 grating formula can be expressed in terms of the grating rotation angle 9 between grating normal and optical axis Sinceoc9and39 mk dsin9 sin9 2dsin 9 coscl the trigonometric identity l2sinABsinAB is sinAcosB Grating formula now in experimental variables 9 the grating rotation angle and I halfangle between the entrance grating and exit and slit CEM 835 page 317 Dispersive characteristics Already mentioned the angular dispersion rate of change of diffraction angle with wavelength for a grating D an ular dis ersion A Cm g P However in monochromator much more interested in dispersion at focal plane eXit slit defined by the linear dispersion D1 gt2 Al K 7 gt 1 x 1 A5 x T Focusing 39 r Ax element 4 TAB gt 2 i l 7 x2 Focal I plane I I r4 f gt dX D1 a lmear d1spers1on units of D1 are mm nm391 or similar For a CzernyTurner arrangement the linear dispersion is D1 f DA where f is the focal length of the focusing exit optic CEM 835 page 318 Sometimes the inverse linear dispersion Rd is used units of 1 nm mm39 or similar d Rd Dfl d 1nverse11near d1spers1on X sin 0t sin 3 A kcos B 1 Rd 2 f D A 9 cosB fsinoc sin 3 Spectral bandpass and the slit function The spectral bandpass nm is the halfwidth of the range of wavelengths passing through the exit slit The geometric spectral bandpass sg Rd W geometric spectral bandpass where Rd is the inverse linear dispersion W is slit width CEM 835 page 319 In a monochromator an image of entrance slit is focused at the eXit slit When input is polychromatic a monochromated version of the image appears at the eXit slit When input is monochromatic image rotating the grating angle 9 Will sweep monochromatic image across the eXit slit W Slit width Fixedpolsition ex1t s it outline I Shtlu ght Moving gt 0 entrance slit image I I i I I l I I I I I I i I I I I I 7 Sg No overlap I I I I I l I l I x I l 39 I I I A 3 sg 25 overlap Z I I I l I I 7 I Direction I I gt of image I 39 travel l A sg 50 overlap I I I l I 7 39 I A III sg 75 overlap l I Z l 7r A 100 overlap I I IA I l i I I I I I I I I l I 39 100 I I I I I I Halfwidth 00 Percentage of image I of ham radiation emerging I Sg from exit slit 39 I 50 l I l l 1 l V o 50 100 200 gto 39 5g 7 0 0 Sg Percentage of image overlap slit function a b CEM 835 page 320 The total intensity t0 measured at the exit slit as image is translated is called the slit function for equal entrance and eXit slits shape is triangular for unequal entrance and eXit slits shape is trapezoidal with a base of s and halfwidth of sg Mathematically the slit function is 9 9 tot 1 x0 sg g x 3 k0 sg s g t0 O elsewhere where 9 is the incident monochromatic wavelength at entrance slit k0 is the wavelength setting of the monochromator the wavelength directed to the center of the eXit slit Resolution Resolution quanti es how well separated two features are at the eXit slit closely related to linear dispersion D1 or angular dispersion DA and physical dimensions of the monochromator through f 0 slit width W CEM 835 page 321 Radiation Sources Continuum sources produce broad featureless range of wavelengths black and gray bodies high pressure arc lamps Line sources produce relatively narrow bands at speci c wavelengths generating structured emission spectrum lasers low pressure arc lamps hollow cathode lamps Line plus continuum sources contain lines superimposed on cont1nuum background medium pressure arc lamps D2 lamp Sources may be continuous or pulsed in time CEM 835 page 21 Continuum sources 0 Continuum sources are preferred for spectroscopy because of their relatively at radiance versus wavelength curves Platinum lead q Glower Re ector H Platinum Platinum wire heater lead L a A 63 U C d Parabolic re ector Anode Window Cathode e a Nernst glower b W lament c D2 lamp d are e are plus re ector CEM 835 page 22 Black body sources Nernst glowers ZrOz YOZ Globars SiC 10001500 K in air 7 lies in IR max 0 relatively fragile 0 low spectral radiance Bi lO394 W39Cm392 nm391 sr391 7500 o Blackbody theoretical at 900 C a Globar 39E 750 P A Nernst glower W a Mantle I 3 739 g 750 3 co I 2 z 75 In 1 4 J 1 l 1 1 1 1 1 1 1 l 1 1 1 A l 1 2 6 10 14 18 22 26 3O 34 38 Wavelength pm a CEM 835 page 23 Heated laments W incandescent lamp QTH 0 20003000 K in evacuated envelope greater radiance UaT4 B7 10392 Wcm39Znm39lsr391 greater UVVis output kmax still in IR QTH heated up to 3600 K wo wg Wg12 gt W12 g WIZ WsIZ Arc sources Hg Xe D2 lamps 0 AC or DC discharge through gas or metal vapor 2070 V 10 mA20 A Ionization necessary for conduction hot cathode thermionic emission cold cathode ignition voltage Nonuniform radiance CEM 835 page 24 50 100 150 150 100 50 Hg are radiance 10 1 I I l lllllll 102 EA uW cm 2 nmquotl ll IIIIIH 10 3 I 39 Irradianee BA from D2 lamp measured by a detector at 25 em CEM 835 page 25 IIHH quotIquot I I Tllllquot I III Bx W cmnzsr391 nlmquot1 9 00 d N d d i y i h h b I I 000I 111111 200300400500600700800 Wavelength nm 39 a high pressure Xe lamp b low pressure Hg lamp Hg arc lamps Hg3P1 gt Hg 1SO hv2537 nm Hg1P1 gt Hg 1SO hv1894 nm 0 if P high gt10 atm pseudocontinuum large current gt5 A many atoms excited I 1 radiance Bx gt10 Wcm39Znm39 sr39 if P low lt1 atm line or line plus continuum small current 1 A 10W radiance Bx ltlO4 WcmZnm1 sr1 selfabsorption at high radiant ux CEM 835 page 26 HIIH W Hg arc lamp selfabsorption CEM 835 page 27 vlam Line sources Generally not much use for molecular spectroscopy useful for luminescence excitation photochemistry eXperiments Where high radiant intensity at one 7 required Arc lamps 0 low pressure lt10 Torr With many different fill vapors Hg Cd Zn Ga In Th and alkali metals 0 excellent wavelength calibration sources Hollow cathode lamps HCL Hollow cathode bk 7 f r Anode Quartz Glass Ne or Ar 0T Pyrex shield at 15 torr window 0 primary line sources in atomic spectroscopy 0 low gas pressure lt10 mtorr linewidths 001 A high currents gtfew mA reduces lifetime and broadens lines 0 single or multielement cathodes 0 moderate radiance Bx 10392 W cm392 nm391sr391 CEM 835 page 28 Electrodeless discharge lamps EDL RF coil Ceramic holder 0 contain a microwave or RFexcited plasma need ignition pulse to start plasma 0 electric eld of RF or microwave drives ions and electrons in plasma no electrodes 0 gas pressures and temperatures relatively low slight pressure broadening linewidths are not as narrow as the HCL lt1A 0 moderate radiance 13 101 W cm392 nm391 sr391 CEM 835 page 29 Lasers intense radiance Bx gt104 Wcm392nm391sr391 nearly monochromatic 00lOl A coherent temporally and spatially directed small divergence pulsed or continuous stable Allow measurements not possible with conventional sources Consider radiation traveling through absorbing medium the change in radiant ux due to absorption is dCD CD ni 6 dz lt change due to absorption length of the medium absorption probability number of molecules in state i radiant ux Similarly for stimulated emission dCD CIgt nj 6 dz lt change due to stimulated emission Total change in ux is amount absorbed minus the amount gained by stimulated emission dd CDcsnj nidz lt total change CEM 835 page 210
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719453.9/warc/CC-MAIN-20161020183839-00272-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 23,708 | 15 |
https://math.answers.com/other-math/What_is_the_formula_for_finding_the_area_and_perimeter_of_a_square
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math
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The formula for the area (A) of a square is A = L2 where L is the side length of the square. Therefore L = √A. The formula for the perimeter (P) of a square is P = 4L : as L = √A, then P = 4√A When A = 144, then P = 4 √144 = 4 x 12 = 48.
The formula for the area of a square is: s * s where s = length of a side The formula for the perimeter of a square is: 4 * s where s = length of a side
The formula for the area of a square is: A=2S, where A=area S= length of one side of the square
The formula for measuring the area of a square is s2, where s is the length of one of the sides. The perimeter would be 4s.
Area of regular polygon: 0.5*apothem*perimeter
Formula for finding the surface area of a sphere = 4*pi*radius2 in square units. Formula for finding the volume of a sphere = 4/3*pi*radius3 in cubic units. Or did you mean the formula for finding the area of a square? in which case it is Length*Height in square units.
perimeter is the measure around the figure; area is the measure within the figure formula: perimeter: length+length+width+width=perimeter (for square or rectangle) area: length times width= area ( for square or rectangle)
Length of side squared
The area of a Parallelogram is Base * Height The Perimeter is 2(side1 + side2)
Area of a square can be calculated using the formula A = a^2, where "a" is the length of a side of the square. Its perimeter is P = 4*a. 49 = a^2 => a = 7cm P = 4*7 = 28cm The perimeter of the square is 28cm.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572833.78/warc/CC-MAIN-20220817001643-20220817031643-00783.warc.gz
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CC-MAIN-2022-33
| 1,468 | 10 |
https://brainmass.com/physics/computational-physics/pendulum-calculation-g-562361
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math
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KIndly answer the questions from A to G. Thanks.
B. How did the change in amplitude affect the resulting period and frequency?
C. How did the change in the length of the pendulum affect the period and frequency?
E. Hypothesize about how a magnet placed directly under the center point would affect an iron bob. As an optional activity, design an experiment to see if a magnetic will affect the period of a pendulum.
G. What would you expect of a pendulum at a high altitude, for example on a high mountaintop?
What would your pendulum do under weightless conditions?
A. Since the period of the pendulum does not depend on the mass of the bob, neither the period nor the frequency (i.e. inverse of period) change.
B. For small changes in amplitude, the period does not change (and neither does frequency; also look at the first equation). But if the change in amplitude is more than a certain amount, the period will be longer and the frequency will ...
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583660020.5/warc/CC-MAIN-20190118090507-20190118112507-00077.warc.gz
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CC-MAIN-2019-04
| 952 | 8 |
https://www.mycoursehelp.com/QA/assessing-simultaneous-changes-in-cvp-re/67920/1
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math
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Assessing simultaneous changes in CVP relationships
Vanhorn Company sells tennis racquets; variable costs for each are $75, and each is sold for $105.
Vanhorn incurs $270,000 of fixed operating expenses annually.
a. Determine the sales volume in units and dollars required to attain a $120,000 profit. Verify your answer by preparing an income statement using the contribution margin format.
b. Vanhorn is considering establishing a quality improvement program that will require a $10 increase in the variable cost per unit. To inform its customers of the quality improvements, the company plans to spend an additional $60,000 for advertising. Assuming that the improvement program will increase sales to a level that is 5,000 units above the amount computed in Requirement a, should Vanhorn proceed with plans to improve product quality? Support your answer by preparing a budgeted income statement.
c. Determine the new break-even point and the margin of safety percentage, assuming Vanhorn adopts the quality improvement program.
d. Prepare a break-even graph using the cost and price assumptions outlined in Requirement b.
Under what circumstances are strikes and lockouts justified in place of mediation or arbitration?Jun 02 2020
Explicitly evaluate πp of Eq. (4.7.15); then differentiate πp with respect toand φ2 and set each of these equations to zero (that is, minimize πp) to obtain the four elem...Aug 01 2020
Suppose that 20 sticks are broken, each into one long and one short part. By pairing them randomly, the 40 parts are then used to make 20 new sticks.(a) What is the proba...Aug 03 2020
During the 1950s the wholesale price for chicken for a country fell from 25¢ per pound to 14¢ per pound, while per capita chicken consumption rose from 23.5 pounds per ye...Aug 08 2020
What is the answer of x over 3 - equlas to 8?Apr 23 2020
Chapter 8 Global Shift by Peter Dickens 1.Which of the five output levels corresponds to the highest level of total revenue? B - Which of the five output levels correspon...Apr 09 2020
Explain the structure and working of ferry's total radiation pyrometerMar 25 2020
Your company bonds have a par value of $1,000, a current price of $1,234, and they will mature in 20 years. What is the yield to maturity on these bonds if the bonds have...Sep 07 2020
Suppose your firm is considering investing in a project with the cash flows shown below, that the required rate of return on projects of this risk class is 7 percent, and...Aug 12 2020
1. A W8x24, A992 column has an effective length of 12.5 ft about the y-axis and 28 ft about the x-axis. Determine the available compressive strength and indicate whether ...May 25 2020
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038062492.5/warc/CC-MAIN-20210411115126-20210411145126-00441.warc.gz
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CC-MAIN-2021-17
| 2,675 | 17 |
https://de.mathworks.com/matlabcentral/answers/312889-fitting-curve-with-an-exponential-function
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math
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You can't do this well, at least as you have posed the problem. Conversely, you CAN do this, but you will do a poor job of it. For example, you COULD use the curvefitting toolbox, with a pure simple exponential model. That would lump any noise together with the oscillatory component. Unless the oscillatory component is perfectly orthogonal to the exponential decay component, then the decay will be measured incorrectly.
What you need to do to do this well is to choose a model for the oscillatory component, as well as the exponential component. Then fit the complete model together. Again, the CFT can do this, but only after you have chosen an intelligent model for the complete process.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655887360.60/warc/CC-MAIN-20200705121829-20200705151829-00037.warc.gz
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CC-MAIN-2020-29
| 692 | 2 |
https://school.nelson.com/whats-right-about-wrong-answers-learning-from-math-mistakes-grades-4-5/
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math
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You cant learn to hit a three-point shot without missing a lot of shots. You cant learn to play a piece of music correctly without striking a lot of wrong notes. And, as Nancy Anderson explains in Whats Right About Wrong Answers, you cant learn math without making mistakes. Nancy turns mistakes on their head and helps you cleverly use them to students advantage. Each of the twenty-two activities in this book focuses on important ideas in grades 45 mathematics. By examining comic strips, letters to a fictitious math expert from confused students, and sample student work containing mistakes, your learners explore typical math mistakes, reflect on why theyre wrong, and move toward deeper understanding.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987781397.63/warc/CC-MAIN-20191021171509-20191021195009-00337.warc.gz
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CC-MAIN-2019-43
| 708 | 1 |
https://www.wowessays.com/topics/encryption/
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math
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Throughout human history, there is an array of revolutionary technological innovations. One such innovation is cryptography that brought about a revolution in the society by facilitating privately encrypted messages. I got very much interested in this technology after learning that all the secured data transaction is encrypted. There are majorly two basic types of encryption used asymmetric and symmetric key encryption.
What is RSA encryption?
Symmetric key encryption has one weakness that its integrity is dependent on the exclusive sharing of its private keys. Here, different encryption scheme is needed that is asymmetric or public key encryption. Public key cryptography is a mathematical ...
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038061562.11/warc/CC-MAIN-20210411055903-20210411085903-00207.warc.gz
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CC-MAIN-2021-17
| 702 | 3 |
http://skepticalavenger.tumblr.com/post/9918009531/the-creationist-and-improbably-low-numbers
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math
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Suppose you take a deck of cards, toss it in the air, and note how everything falls.
You analyze the order, left to right, of how the cards fell. You note how many were face down, face up, and skewed at various angles. You note exactly the degree to which some cards overlap others.
Then you get out a calculator (actually, you might need a high powered computer), and calculate the weight of the cards, wind velocities, and card aerodynamics. You do a lot of very impressive research.
Then you come out and say something like, “The odds against the cards falling this exact way is 7.6 x 10^87 to one. This means I could toss cards up in the air once every second for 4 million times longer than the scientist says the universe is old, and still never get this combination.
"It is is obviously ridiculous to believe that this happened by mere chance, but it’s what the SCIENTISTS want you to believe. It is obvious to anyone with a brain that God must have done it!"
And yeah, many Intelligent Design arguments and Creationist arguments involving math involve exactly this kind of calculation.
In case it isn’t obvious, let me spell out what is wrong with this argument. When you tossed the cards in the air, they HAD to come down in some configuration. One to One probability.
What the Creationist has done is taken all the factors and tried to predict the odds of this particular configuration of cards coming down in this specific way before it happened. While this is a good way of coming up with very large improbabilities, the only way the number has any meaning is if you take the same deck of cards, shuffle ‘em up, toss them in the air again, and have all the cards fall EXACTLY the same way as they did the first time. The probability of that happening may have some relation to what the Creationist has come up with.
Similar arguments are used in abiogenesis, but really, there is so much that is unknown about the chemical reactions that may have given rise to life on this planet that trying to use any numerical calculations of odds is a meaningless exercise. Using the above argument, with abiogenesis we don’t know the wind velocity, the weight of the cards, or many of the factors that determine how the cards will fall. So the Creationist uses simple-minded estimations do calculate the odds; estimations deliberately designed to make the odds seem lower.
So, beware when the Creationist or Intelligent Design push numerical improbability at you. While this may not be an exact analogy in every case, it certainly is in many.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507444209.14/warc/CC-MAIN-20141017005724-00114-ip-10-16-133-185.ec2.internal.warc.gz
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CC-MAIN-2014-42
| 2,553 | 10 |
https://www.nagwa.com/en/videos/135157439821/
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math
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A teacher has 22 pencils that they
want to share equally between four children. What is the maximum number of
pencils each child will receive? Some pens might be left over.
This problem is all about sharing
equally, which means it’s a division problem. The teacher wants to share 22
pencils equally between four children. We have to work out how many
pencils each child will receive. We’ve modeled the number 22 using
these bricks. Can you think of a way of sharing
these pencils equally between four children? That means each group has to
contain an equal number of bricks. There we go. We’ve made four groups, and each
group contains an equal amount of bricks. Can you see how many bricks are in
each group? We’ve made four groups of five, and
there are two bricks left over.
If we have 22 pencils and shared
them equally between four children, each child will have five pencils and there will
be two left over. 22 divided by four equals five
remainder two. So the maximum number of pencils
each child will receive is five. We can’t share the two that are
left over equally between four children. So the most pencils the children
can get is five each.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487621273.31/warc/CC-MAIN-20210615114909-20210615144909-00636.warc.gz
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CC-MAIN-2021-25
| 1,163 | 20 |
https://www.physicsforums.com/threads/light-as-a-wave.404217/
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math
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Hey guys, I don't see how light can be a wave. If it is, then that means the velocity of light would not be constant. It would have to speed up when blue shifted because the wavelength is shorter. When the wavelength is short, it would have to travel faster up and down to make up for the horizontal speed. I'm thinking of light as literally moving like a ripple. A broader question would be, what is a wave? Does light move in an up and down motion like a ripple or is it actually linear? An idea my friend and I came up with is that light isn't a wave, but a pulse. The shorter the wavelength, the faster the light pulses. Are we right, or is light just a constant stream? BTW I'm talking about the physical aspect of light moving through a vacuum (the actual lights motion).
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826530.72/warc/CC-MAIN-20181214232243-20181215014243-00314.warc.gz
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CC-MAIN-2018-51
| 777 | 1 |
http://core-cms.prod.aop.cambridge.org/core/search?filters%5BauthorTerms%5D=Takuji%20Ishikawa&eventCode=SE-AU
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math
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The rheological properties of a cell suspension may play an important role in the flow field generated by populations of swimming micro-organisms (e.g. in bioconvection). In this paper, a swimming micro-organism is modelled as a squirming sphere with prescribed tangential surface velocity, in which the centre of mass of the sphere may be displaced from the geometric centre (bottom-heaviness). Effects of inertia and Brownian motion are neglected, because real micro-organisms swim at very low Reynolds numbers but are too large for Brownian effects to be important. The three-dimensional movement of 64 identical squirmers in a simple shear flow field, contained in a cube with periodic boundary conditions, is dynamically computed, for random initial positions and orientations. The computation utilizes a database of pairwise interactions that has been constructed by the boundary element method. The restriction to pairwise additivity of forces is expected to be justified if the suspension is semi-dilute. The results for non-bottom-heavy squirmers show that the squirming does not have a direct influence on the apparent viscosity. However, it does change the probability density in configuration space, and thereby causes a slight decrease in the apparent viscosity at O(c2), where c is the volume fraction of spheres. In the case of bottom-heavy squirmers, on the other hand, the stresslet generated by the squirming motion directly contributes to the bulk stress at O(c), and the suspension shows strong non-Newtonian properties. When the background simple shear flow is directed vertically, the apparent viscosity of the semi-dilute suspension of bottom-heavy squirmers becomes smaller than that of inert spheres. When the shear flow is horizontal and varies with the vertical coordinate, on the other hand, the apparent viscosity becomes larger than that of inert spheres. In addition, significant normal stress differences appear for all relative orientations of gravity and the shear flow, in the case of bottom-heavy squirmers.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572289.5/warc/CC-MAIN-20190915195146-20190915221146-00518.warc.gz
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CC-MAIN-2019-39
| 2,043 | 1 |
https://tranio.com/spain/adt/1717959/
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math
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Large urban building plot for sale with sea views in javea. this plot totals 7000 square metres but is a combination of two plots of 2000 and 5000 metres squared. there is a project in place for a villa of 400 metres on the 7000 plot, but each smaller one can be sold separately.
Development land – Javea (Xabia), Valencia, Spain
995,000 €Mortgage calculator
Land area: 7,000 m²
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827596.48/warc/CC-MAIN-20181216073608-20181216095608-00541.warc.gz
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CC-MAIN-2018-51
| 383 | 4 |
https://www.iwakuroleplay.com/threads/marvel-comic-group-rp-anyone.70819/
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math
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I know there already is one but they're not currently looking for members. I don't really know what all I'd want yet, but probably a smaller group, five-ish maybe, and we could plot out together if you want a basic plot to start. It would be cool if anyone wanted a chatplay of it, but if there's more interest in paragraph form I'd definitely do that. Right now I'm basically just seeing if anyone even would be interested, and then we can figure out the details from there. So please answer this or private message me if this sounds fun to you. Thanks!
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267865081.23/warc/CC-MAIN-20180623132619-20180623152619-00537.warc.gz
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CC-MAIN-2018-26
| 554 | 1 |
https://www.omnicalculator.com/conversion/light-year-conversion
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math
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With this light year conversion tool, we aim to help you convert light year into different length units. To understand more on this topic, please check out our speed of light calculator and light year calculator.
We have written this article to help you understand the following:
- What light year is;
- How to convert light years to miles;
- How to convert light years to kilometers; and
- How to convert light years to meters.
We will also demonstrate some examples to help you understand the light year conversion calculation.
What is light year?
A light year is the distance that light travels in one year, which is about 5.88 trillion miles or 9.46 trillion kilometers. Because the speed of light is constant, this distance provides a useful way to measure the vast distances in space.
For example, the closest star to Earth, Proxima Centauri, is about 4.24 light years away, meaning that the light we see from that star today left it over four years ago.
How to convert light years to miles?
To convert light years into miles or kilometers, we need to multiply the distance in light years by the number of miles or kilometers in one light year, which is 5.88 trillion miles (9.46 trillion km).
For example, if we want to know how many miles are in 3 light years, we would multiply 3 by 5.88 trillion miles to get 17.64 trillion miles.
How to convert light years to kilometers?
For the conversion of light years into kilometers, we need to multiply the distance in light years by the number of miles or kilometers in one light year. One light year is approximately 9.46 trillion kilometers, so we can use this conversion factor to convert between the two units.
For example, if we want to know how many kilometers are in 2 light years, we would multiply 2 by 9.46 trillion kilometers to get 18.92 trillion kilometers.
How to convert light years to astronomical units?
Another unit of measurement often used in astronomy is the astronomical unit (AU), which is the average distance between the Earth and the Sun. This distance is approximately 93 million miles (150 million kilometers) and is often used to measure distances within our own solar system.
For the conversion of light years into astronomical units, we need to divide the distance in light years by the number of light years in one astronomical unit, which is 0.000015813.
For example, if we want to know how many astronomical units are in 5 light years, we would divide 5 by 0.000015813 to get approximately 316,602 astronomical units.
With our calculator, we can also help you convert light years into Earth radii, Sun radii, and megaparsecs. You can also check out our length converter to understand more about this topic.
It's worth noting that these distances are so vast that they are difficult to comprehend. Even the distance to our closest star, Proxima Centauri, is so large that it would take over 30,000 years to travel there at the speed of our fastest spacecraft.
What is 1 light year converted to miles?
1 light year is approximately 5.88 trillion miles. 1 light year is converted to miles by multiplying 1 by 5.88 trillion.
Is a light year a unit of time or distance?
A light year is a unit of distance, specifically the distance that light travels in one year.
Can we travel faster than the speed of light?
According to our current understanding of physics, it is not possible for anything with mass to travel faster than the speed of light.
How to convert light years to meters?
You can convert light years into meters in 3 steps:
- Determine the number of light years to convert.
- Multiply the number of light years by 9,461 trillion.
- Analyse the results in meters.
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https://forum.biologyonline.com/topic/chloroplast-dna-isolation-terminology
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I have three questions:
First, could I use this protocol with arabidopsis plants?
Second, what does "7 vol LL" mean in that first step? I’ve looked all over his site and I can’t find anything on it. Thanks in advance for your help!
Third, what does "DIECA/L" mean (also in the first step)?
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https://www.arxiv-vanity.com/papers/1603.05002/
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Chiral condensate in the Schwinger model with Matrix Product Operators
Tensor network (TN) methods, in particular the Matrix Product States (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the non-zero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.
Keywords:lattice field theory, Schwinger model, chiral symmetry, non-zero temperature
Investigations of gauge field theories within the Hamiltonian approach have progressed substantially in the last years with the help of tensor network (TN) techniques verstraete08algo ; cirac09rg ; orus2014review . Taking the example of the Schwinger model, numerical calculations have been performed to investigate ground state properties Byrnes:2002nv ; Cichy:2012rw ; Banuls:2013jaa ; Banuls:2013zva ; Rico:2013qya ; Buyens:2015dkc , to demonstrate real-time dynamics Buyens:2013yza ; Buyens:2014pga and to address the phenomenon of string breaking Pichler:2015yqa ; Buyens:2015tea , which has also been explored in non-Abelian models Kuhn:2015zqa . In Refs. Banuls:2015sta ; Saito:2014bda ; Saito:2015ryj , thermal properties of the Schwinger model were studied for massless fermions. From a more conceptual point of view, TN have been developed that incorporate the gauge symmetry by construction, and constitute ground states of gauge invariant lattice models Tagliacozzo:2014bta ; Silvi:2014pta ; haegeman15gauging ; zohar2015peps . Yet a different line of work is the study of potential quantum simulations of these models, using ultracold atoms, see Refs. wiese2013review ; Zohar:2015hwa ; Dalmonte:2016alw for a review. Also in this field, TN techniques can play a determinant role to study the feasibility of the proposals kuehn2014schwinger .
The last numerical developments go beyond standard Markov Chain Monte Carlo (MC-MC) methods. At zero temperature, the Hamiltonian approach allows us to go substantially closer to the continuum limit and reach a much improved accuracy compared to MC-MC. When temperature is switched on, a broad and very large set of non-zero temperature points can be evaluated, ranging from very high to almost zero temperature. In the string breaking calculation, a nice picture of the string breaking phenomenon and the emergence of the hadron states can be demonstrated. Finally, real-time simulations are not even possible in principle with MC-MC methods.
The key to this success is the employment of tensor network states and, in the case of one spatial dimension, as for the Schwinger model, the Matrix Product States (MPS). In this approach, which is closely linked to the Density Matrix Renormalization Group (DMRG) white92dmrg , the problem, which has an exponentially large dimension in terms of the system size, is reduced to an –admittedly– sophisticated variational solution which can be encoded in substantially smaller matrices. The ansatz can represent arbitrary states in the Hilbert space if is large enough (exponential in the system size). Instead in numerical applications, usually an approximation is found to the desired state within the set of MPS with fixed . By varying , an extrapolation of results to can be performed allowing thus to reach the solution of the real system under consideration. A different approach also using tensor network techniques was applied to the Schwinger model with a topological -term in Refs. Shimizu:2014uva ; Shimizu:2014fsa , where the exact partition function on the lattice was expressed as a two dimensional tensor network and approximately contracted using the Tensor Renormalization Group (TRG).
The application of the MPS technique discussed in the present paper is concerned with non-zero temperature properties of the Schwinger model. In Refs. Banuls:2015sta ; Saito:2014bda ; Saito:2015ryj , we have for the first time investigated the thermal evolution of the chiral condensate in the Schwinger model. In the first paper, where we only studied the massless case, we could demonstrate that the MPS technique can be successfully used to compute such a thermal evolution from very high to almost zero temperature. For massless fermions, the results from our MPS calculation could be confronted with the analytical solution of Ref. Sachs:1991en and a very nice agreement was found demonstrating the correctness and the power of the MPS approach.
In the present paper, we will extend our calculations of the thermal evolution of the chiral condensate to the case of non-vanishing fermion masses. Here, no exact results exist anymore, but only approximate solutions are available Hosotani:1998za which can be tested against our results. For our work at zero fermion mass, we also introduced a truncation of the charge sector Banuls:2015sta which was necessary to obtain precise results at high temperature. Here, we will employ this truncation method, too.
It needs to be stressed that the calculations with MPS, as performed here, have a number of systematic uncertainties which are very important to control. This concerns in particular:
an estimate of results for infinite bond dimension; 111For a given system size, , exact results would actually be attained with finite bond dimension, verstraete04dmrg , which is many orders of magnitude larger than the largest one we use in the simulations.
an extrapolation to zero step size in the thermal evolution process;
a study of the truncation in the charge sector of the model;
an infinite volume extrapolation;
and a careful analysis of the continuum limit employing various extrapolation functions with different orders in the lattice spacing.
Controlling these systematic effects renders the calculations with MPS demanding, but it is absolutely necessary to obtain precise and trustworthy results. We have therefore made a significant effort to perform the above extrapolations and we will provide various examples in this paper for the studies of systematic effects carried through here.
2 The Schwinger model and chiral symmetry breaking
The one-flavour Schwinger model schwinger62 , i.e. Quantum Electrodynamics in 1+1 dimensions, is one of the simplest gauge theories and a toy model allowing for studies of new lattice techniques before employing them to real theories of interest, like Quantum Chromodynamics (QCD). Despite its apparent simplicity, it has a non-perturbatively generated mass gap and shares some features with QCD, such as confinement and chiral symmetry breaking, although the mechanism of the latter is different than in QCD – it is not spontaneous, but results from the chiral anomaly.
We start with the Hamiltonian of the Schwinger model in the staggered discretization, derived and discussed in Ref. Banks:1975gq :
where is the site index, , is the lattice spacing, is the coupling, and with denoting the fermion mass and the number of lattice sites. We use open boundary conditions (OBC). The gauge field, , can be integrated out using the Gauss law:
Thus, only at one of the boundaries is an independent parameter and we take , i.e. no background electric field.
We work with the following basis for our numerical computations: Banuls:2013jaa , where is the spin state at site and all the gauge degrees of freedom have been integrated out.
In this paper, we are interested in the chiral symmetry breaking (SB) in the Schwinger model, both at zero and non-zero temperature. The order parameter of SB is the chiral condensate , which can be written in terms of spin operators as . The ground state and thermal expectation values of the chiral condensate diverge logarithmically in the continuum limit for non-zero fermion mass deForcrand98 ; duerr05scaling ; Christian:2005yp . This divergence is present even in the non-interacting case, where the theory is exactly solvable and the Hamiltonian (2) reduces to the XY spin model in a staggered magnetic field. The ground state energy of this model (with OBC) reads: . The ground state expectation value of can then be computed from the derivative :
The free condensate value computed from this formula can be used to subtract the divergence in the interacting case at a finite lattice size , a finite lattice spacing and a given fermion mass . However, one can exactly evaluate the infinite volume limit of the free condensate first, yielding:
where is the complete elliptic integral of the first kind abramowitz . Note that by expanding this expression in the limit , the divergent logarithmic term is indeed seen already in the free case. In this way, we can extrapolate our lattice interacting condensate first to infinite volume limit, , at a finite and a given and then subtract the infinite volume free condensate () given by Eq. (4):
obtaining finally the subtracted condensate , which can then be extrapolated to the continuum limit . Note that a non-zero temperature does not bring any further divergence, hence the above renormalization scheme, subtracting the zero temperature free condensate in the infinite volume limit, can be applied for any . Actually, one can equivalently subtract the free condensate at any finite . This defines an alternative renormalization scheme that we can also implement. Both options would lead to the correct value at , i.e. compatible with the one directly obtained from the ground state calculations, but in order to compare to other results in the literature, we adopt in the following the renormalization scheme for all temperatures.
In the massless case, the temperature dependence of the chiral condensate was computed analytically by Sachs and Wipf Sachs:1991en :
where , is the Euler-Mascheroni constant and is the non-perturbatively generated mass of the lowest lying boson (the vector boson). According to the above formula, chiral symmetry is broken at any finite temperature (zero or non-zero) and it gets restored () only at infinite temperature. There is no phase transition, i.e. chiral symmetry restoration is smooth.
In the massive case, there is no analytical formula describing the temperature dependence of the condensate. However, the massive model was treated by Hosotani and Rodriguez with a generalized Hartree-Fock approach in Ref. Hosotani:1998za , yielding an approximate thermal dependence of . In the following, we will confront our results with ones from this approximation and thus conclude about its validity.
3 Tensor network approach
In this work, we make use of two different applications of tensor network ansatzes. In order to obtain the results at zero temperature, we approximate variationally the ground state of the Schwinger model Hamiltonian (2) on a finite lattice using a MPS. For the temperature dependence, we employ the matrix product operator (MPO) to describe the thermal equilibrium states at finite temperatures.
Although the details of these ansatzes and the basic algorithms involved can be found in the literature, for completeness we compile in this section the fundamental ideas of both approaches, with special emphasis on the particularities associated to the problem at hand.
where is the dimension of the local Hilbert space for each site. For two-level quantum systems, as in the case we are studying, . The state is parametrized by the matrices, , which have dimension , except for the ones at the edges, and , which, for the open boundary conditions we consider, are -dimensional vectors. The parameter is called the bond dimension, and determines the number of variational parameters in the ansatz. The MPS can efficiently approximate ground states of local gapped Hamiltonians in one spatial dimension, and the ansatz lies at the basis of the success of the Density Matrix Renormalization Group (DMRG) method white92dmrg ; schollwoeck11age . In practice, they have been successfully applied to much more general problems, including long range interactions and two dimensional systems.
Different algorithms exist to find an MPS approximation to the ground state of a certain Hamiltonian. We use a variational search verstraete04dmrg ; schollwoeck11age , in which the energy is minimized over the set of MPS with a given bond dimension, , by successively optimizing over one of the tensors, while keeping the rest fixed. The procedure is repeated, while sweeping over all the tensors, until convergence is attained in the value of the energy, to a certain relative precision, , ultimately limited by machine precision. The computational cost of this procedure scales as with the dimensions of the tensors. The effect of running the algorithm with a limited bond dimension is to suffer a truncation error. By running the algorithm with increasing values of , we can estimate the magnitude of this error and extrapolate to the limit, as discussed in detail in Sec. 4.
While any MPS (7) can represent a valid physical state, as far as it is normalized, in order to describe a physical density operator, the MPO needs in addition to be positive. This condition cannot be guaranteed locally for generic tensors . However, it is possible to ensure the positivity of a MPO using the purification ansatz verstraete04mpdo ; delascuevas2013 , in which each tensor of the MPO has the form . This corresponds to a (pure state) MPS ansatz for an extended chain, with one ancillary system per site, such that is the reduced state for the original system, obtained by tracing out the ancillas. It has been shown that thermal equilibrium states of local Hamiltonians can be well approximated by this kind of ansatz hastings06gapped ; molnar15gibbs in arbitrary dimensions.
In the case of finite temperature, a MPO approximation can be constructed for the Gibbs state via imaginary time evolution of the identity operator verstraete04mpdo , , where is the inverse temperature. To achieve this, we apply a second order Suzuki-Trotter expansion trotter59 ; suzuki90 to the exponential, and approximate every step of width by a product of five terms,
where is diagonal in the basis, and the hopping term is split in two sums , with the () term containing the two-body terms that act on each even-odd (odd-even) pair of sites. If each of the exponential terms can be exactly computed, the error of this approximation scales as . The exponentials of and have indeed an exact MPO expression with constant bond dimension . The term contains long range interactions, but its structure allows us to also write it exactly as a MPO, with bond dimension , as detailed in Ref. Banuls:2015sta . The only non-vanishing elements of the tensors specifying the MPO are , for , where for , and . The virtual bond then carries the information about the electric flux on each link, which can assume values . Instead of working with the exact exponential of , which has a bond dimension , we find it convenient, given the large system sizes we want to study, to truncate the dimension of the MPO, by defining a maximum value the virtual bond can attain, . This is equivalent to truncating the physical space to those states where the electric flux on a link cannot exceed and is thus related to approaches where one explicitly truncates the maximum allowed occupation number of the bosonic gauge degrees of freedom Buyens:2013yza .
Starting with the identity operator, , which has a trivial expression as a MPO with bond dimension one, we successively apply steps of the evolution, using the approximation above, and approximate the result by a MPO with the desired maximum bond dimension. This is achieved with the help of a Choi isomorphism choi , , to vectorize the density operators, such that the MPO is transformed in a MPS, with physical dimension per site , on which the evolution steps act linearly. The approximated effect of the evolution is then found by minimizing the Euclidean distance between the original and final MPS. The procedure can be repeated until inverse temperature is reached. Then we construct (up to normalization) such that the purification ansatz is realized and we ensure a positive thermal equilibrium state. The computational cost of this calculation is the same as that of time evolution of a MPS state, with the increased physical dimension, i.e. it scales as .
Using the MPO ansatz with limited bond dimension induces also a truncation error in the case, which is not equivalent to the one described for . First of all, different ansatzes are used for both cases, and while the MPS truncation in the pure state case can be related to the entanglement in the state, the same is not true for the MPO ansatz in the case of mixed states. 222In the case of operators one should instead talk about operator space entanglement entropy, a measure related to truncation error in the MPO that was introduced in Ref. PhysRevA.76.032316 . Moreover, the distinct numerical algorithms used in both cases also mean that errors are introduced in different ways. In the thermal algorithm, each application of one of the exponential factors in (9) potentially increases the bond dimension of the resulting MPO. Hence, after every step, the ansatz needs to be truncated to the maximum desired value of the bond dimension. In practice, this is achieved by minimizing a cost function that corresponds to the Frobenius norm of the difference to the true evolved operator. As in the ground state search, this optimization is done by an alternating least squares (ALS) scheme, in which all tensors but one are fixed, and repeated sweeping is performed over the chain. Also in this case, we use a tolerance parameter, , to decide about the convergence of the iteration, but now the value bounds the relative change in the cost function during the sweeping that follows the application of each single exponential factor. This procedure leads to errors accumulating along the thermal evolution, and while at the state can be exactly written as a MPO with , the largest truncation errors will occur for the lowest temperatures. Thus, recovering zero temperature results from such a procedure is a non-trivial check that the method is working correctly. The calculation, in contrast, does not suffer from this effect, as it directly targets the ground state variationally.
Additionally, the Suzuki-Trotter expansion (9) introduces another systematic error in the thermal evolution, by using a finite step width , which we need to extrapolate to , and another one in the form of the truncation of the physical subspace to a maximum , described above. All these factors need to be taken into account when performing the extrapolations required to extract the continuum values of the observables under study (see Sec. 4 for details).
4.1 Zero temperature
We begin with our results for the ground state chiral condensate for various fermion masses. For the massless case, an analytical result can be obtained, . We are able to reproduce this number with great accuracy and also obtain results in the massive case, where no analytical results exist.
Our numerical procedure consists in computing several sets of data points corresponding to different values of (, , ) and extrapolating in the way described below.
Infinite bond dimension () extrapolation. We use several values of to check the effects from changing the bond dimension. Our final value is taken as the condensate corresponding to the largest computed value of and its error as the difference between the value for and . The lower values of serve to ensure that the two highest bond dimensions are large enough, such that it can be argued that the difference between and is smaller than the one between and , which makes our error estimate valid.
A typical example of such extrapolation is shown in Fig. 1 for and in Fig. 2 for , at . In both cases, we observe very good convergence towards the limit, with the above defined error from this step being of for the former and for the latter. This error is represented by a red band. Note that despite going to , the convergence in bond dimension is so good that actually even with we would already obtain the result with an outstanding precision, of for (i.e. only an order of magnitude worse than with ) or even of for (i.e. the same as with ). The case illustrates that in some cases the convergence in is so good that our uncertainty comes from issues with the numerical precision. The MPS optimization procedure is considered to be converged when the relative change in the ground state energy in subsequent sweeps falls below a certain tolerance parameter, taken to be in our case. Notice, however, that this precision refers to the ground state energy, which typically converges better than other observables, so it will correspond to a somewhat worse precision in the chiral condensate, which we estimate to be in the region. In the case, the variation of values for different becomes smaller than this, which explains the irregular behaviour of the -dependence for this case (left plot of Fig. 2), compared to the apparently regular convergence for the case . We account for this bias (that happens only for our smallest values) in our next step, the infinite volume extrapolation. We emphasize that this is definitely not a drawback of the method, but even better precision could be attained for certain parameter ranges with the same values, by adopting a more demanding convergence criterion. On the other hand, since the ultimate limit of machine precision, which we label by , affects the optimization of individual tensors, so that after one sweep over the whole chain, it may affect the value of the energy in This means that for chains of hundreds of sites, as required for the largest values of we explore, is the best allowed by double precision numerics.
Infinite volume () extrapolation. The results corresponding to our estimates of the limit can then be extrapolated to infinite volume by using a linear fitting ansatz:
where is the infinite- condensate for a fixed fermion mass, volume and lattice spacing. The fitting parameters are (infinite volume condensate at a given lattice spacing and fermion mass) and the mass and lattice spacing-dependent slope of the finite volume correction, .
We show an example of such extrapolation in Fig. 3, again for (left) and (right), at .
We always choose the volumes to be large enough, such that the above linear fitting ansatz yields a good description of data.
We have found that this holds when the volumes used are scaled proportionally to and we take .
Indeed, in all cases where no issues with machine precision are observed, this leads to very good fits.
The resulting error of the fitting coefficient is the propagated error from the -extrapolation.
For very small values of (lower than approx. 30), we need to deal with the numerical precision bias.
The errors from the -extrapolation are in such case underestimated, since they do not take into account the finite numerical precision.
This leads to values of .
However, we know from the analysis for large values of that the linear fitting ansatz (10) yields an excellent description of data, with usually much smaller than 1.
Hence, we account for the bias by inflating the -extrapolation errors to such levels that by construction.
In this way, the final error after the infinite volume extrapolation step is properly rescaled and becomes comparable to the one at larger (e.g. approx. for and for ).
In the end, all our errors of infinite volume condensates, , differ by less than an order of magnitude in the whole considered range of and for all fermion masses.
Continuum limit () extrapolation. Finally, the infinite volume results can be extrapolated to the continuum limit. First, we subtract the infinite volume free condensate according to Eq. (5), obtaining the subtracted condensate . Then, we apply the following fitting ansatz:
with fitting parameters (the continuum condensate for a given fermion mass), , and . This is a fitting ansatz quadratic in the lattice spacing (the role of the lattice spacing is played by ), with logarithmic corrections. The latter appear already in the free theory, where their presence can be shown analytically (see Sec. 2). Note that the final result obtained from this procedure will, to some extent, depend on the fitting range in . To quote final values independent from such choices, we adopt a systematic procedure analogous to the one we used in our spectrum investigation in the Schwinger model, described in detail in the appendix of Ref. Banuls:2013jaa . In short, this consists in performing fits in different possible fitting ranges by varying the minimal and maximal values of entering the fits. The number of fits that we obtain in this way is of and allows us to build a distribution of the continuum values, weighted with of the fits. The final value that we quote is the median of the distribution and the systematic error from the choice of the fitting range comes from the 68.3% confidence interval (such that in the limit of infinite number of fits it corresponds to the width of a resulting Gaussian distribution). This error is then combined in quadrature with our propagated error from - and -extrapolations, which we take as the error of one selected fit, taken to be the one in the interval .
|Our result||Ref. Buyens:2014pga||Exact ()|
|or Ref. Hosotani:1998za ()|
Our continuum limit extrapolations are shown in Fig. 4 for all fermion masses that we considered. We show in these plots the fit from which we estimated our propagated error from earlier extrapolations (), i.e. one of the fits that enter the distribution built to assess our final values and their uncertainties. The final values for each fermion mass are summarized in Tab. 1. We compare to the result of a similar calculation in Ref. Buyens:2014pga and to the exact result in the massless case or the approximation of Ref. Hosotani:1998za . For the former, we observe perfect agreement, which is quite remarkable given the precision of both results being at the level. Similarly good is the agreement with the analytical result at . We will comment more on the agreement with Ref. Hosotani:1998za in the next subsection.
4.2 Thermal evolution
In our previous papers Saito:2014bda ; Saito:2015ryj ; Banuls:2015sta , we showed results for the temperature dependence of the chiral condensate in the massless case. We employed a method without any truncations in the gauge sector and found that it is numerically very demanding to achieve lattice spacings small enough to reliably extrapolate to the continuum at high temperatures. This led us to the method of introducing a finite cut-off, , in the gauge sector and we showed that this method works very well in the massless case, allowing for good precision of results for the whole range of temperatures. In the present paper, we test the method, explained in detail in Sec. 3, in the massive case. Although this method is different from the one used for , the analysis procedure at a given temperature is rather similar to the one described in the previous subsection. We begin by shortly outlying the new parts of the analysis in the thermal case. In the following, we typically express the temperature with its inverse, .
There are two new parameters with respect to computations, apart from the bond dimension, , the system size, , and the inverse coupling, — the parameter describing the cut-off in the gauge sector and the step width, . Thus, our sequence of extrapolations follows the order given below.
Infinite bond dimension () extrapolation.
This extrapolation is done as in the case and we again take the result at our largest as the central value and the difference between this value and one at as the estimate of the uncertainty from the finite bond dimension.
Examples of such extrapolations are shown in Figs. 5 and 6, for and , respectively (both at , , ).
They illustrate a general feature in the -dependence of the chiral condensate — the convergence becomes worse towards the continuum limit.
However, this convergence is in all cases good — the difference between our two largest bond dimensions (140 and 160) is of at and of at .
This difference also depends on the temperature — since lower temperatures are reached by increasing , the error from the finite bond dimension also increases at increasing , approximately linearly.
Note that in the thermal case, the convergence in is somewhat worse than at and we do not observe issues with insufficient machine precision (cf. Sec. 4.1 and the comments about double precision as not enough for certain parameter ranges).
Finally, there is little dependence on the value of , the volume and on the fermion mass.
Zero step width () extrapolation. We denote the results from the previous step as and they differ from the limit by . Hence, we extrapolate to with:
with the fitting parameters and . We always use three values of for each , which allows us to verify that a fitting ansatz linear in is proper. Since we want to access inverse temperatures with a step of , we use values of small enough such that this is possible. Examples are shown in the lower right plots of Figs. 5 and 6, for and , respectively (again at , , ), and three volumes that are later used for infinite volume extrapolation. Since the resulting errors are the propagated errors from the -extrapolation, one again observes similar parameter dependences for the error obtained at this step. We also note that the linear ansatz (12) works very well.
Infinite volume () extrapolation.
The results corresponding to our estimates of the and limits are extrapolated to infinite volume by using the same kind of linear fitting ansatz as in the case, i.e. Eq. (10), and volumes .
An example extrapolation is shown in Fig. 7, for , , five values of the lattice spacing and two temperatures: (left) and (right).
As in the case, we observe that the fitting ansatz gives very good description of our data.
Removing the cut-off ( extrapolation). The physical results have to be independent of the used gauge sector cut-off. We found empirically that for all ranges of our parameters, always yields results compatible with and . Hence, this value of is effectively and no explicit extrapolation is needed (see also Ref. Banuls:2015sta ).
Continuum limit () extrapolation. As our final step, we perform the continuum limit extrapolation of the infinite volume results . Before this is done, we subtract the infinite volume free condensate according to Eq. (5) and obtain the subtracted condensate . We consider the following three fitting ansatzes:
which differ by the order of the polynomial in . We refer to them as linear+log, quadratic+log and cubic+log, respectively. We observe that the discretization effects are very different at different temperatures, in particular these effects become very strong at high temperatures and a polynomial cubic in is needed to obtain a good description of data. We adopt a modified procedure to obtain the systematic error from the choice of the fitting range and the fitting ansatz. The procedure used to analyze the data is inappropriate here, because of the large dependence of the uncertainty from the -extrapolation on the lattice spacing. This uncertainty at a fine lattice spacing () is up to four orders of magnitude larger than the one for our coarsest lattice spacings. Hence, the analogue of the weighted histogram built at is no longer reliable, as it contains fits with very large uncertainties. This does not happen at , where the fine lattice spacings have only slightly larger uncertainties from the and -extrapolations than the coarse lattice spacings. This reflects the difference in strategies used to approximate thermal and ground states as tensor networks. In practice, it translates into a somewhat different manner the truncation errors are accumulated in the thermal evolution with respect to the algorithm. At large , i.e. after several steps of imaginary time evolution, the truncation errors are much larger than in the ground state. As a consequence, the procedure of obtaining the systematic error does not make sense in the case, since only one or two fits dominate the weighted histogram.
For this reason, the procedure to extract the fitting range/ansatz uncertainty is the following. It is performed separately for each temperature at a given fermion mass . We fix the maximum entering each fit to be the one corresponding to the finest lattice spacing. Then, we build all possible fits of Eqs. (13)-(15) changing only the minimal entering (). We take as the central value that corresponds to the smallest uncertainty propagated through , and -extrapolations, but one that satisfies the condition and has all its fitting coefficients statistically significant. We denote it by and its error by . We combine this uncertainty quadratically with the uncertainty from the choice of the fitting interval, , and from the choice of the fitting ansatz, . The former is defined as the difference between and the most outlying (corresponding to the same , i.e. the same functional form of the fitting ansatz) which has still all the fitting coefficients statistically significant. The latter is taken to be the difference between and the most outlying (where , i.e. from another fitting ansatz) which has again statistically significant fitting coefficients.
Below, we illustrate this procedure with a few examples at the fermion mass (Fig. 8). We start with a low temperature, , effectively corresponding to (after a certain -dependent , the continuum result does not change any more — in the case of , zero temperature is reached around ). Here, taking the linear+log fitting ansatz and yields a good fit, with . It can be compared to only two other fits, both of them linear+log, with and . Increasing further or changing the fit form to quadratic+log or cubic+log leads to at least one of the fitting coefficients becoming statistically insignificant. Hence, our final result for this temperature and fermion mass is and is dominated by the uncertainty from the choice of the fitting interval. The error from the choice of the fitting ansatz is zero, since no quadratic+log or cubic+log fit produces a significant result. Since is effectively , this result can be compared to our result at this fermion mass in Tab. 1. We observe full consistency, although the precision of the thermal computation is four orders of magnitude worse than of the ground state one. This is hardly surprising, as thermal evolution is definitely not the best method to investigate ground state properties.
Another example continuum extrapolation is shown for (upper right plot of Fig. 8). In this case, the central value comes from a linear+log fit with and it is compared to the same functional form of the fit with as well as to a quadratic+log fit with . Finally, we get . Towards higher temperatures, cut-off effects become increasingly important, in the sense that one needs higher order polynomials in . For (lower left of Fig. 8), the central value that we take comes from a quadratic+log fit with , compared to and a cubic+log fit with . This leads to . Our final example is (lower right of Fig. 8). Here, the central value comes from a cubic+log fit with , compared to and a quadratic+log fit with . We get . In all these cases, the error is dominated by the uncertainty from the choice of the fitting interval and ansatz. Nevertheless, with the adopted systematic error estimation procedure, one can have these uncertainties reliably under control.
We repeat the analysis steps for all our fermion masses and we summarize the continuum limit results in Fig. 9, where we show results up to ( and ) or (). The most important feature confirming the validity of our results is that we always reproduce the result within our errors — actually the difference between our central values at large enough and the MPS result is much smaller than our errors, suggesting that the error estimation procedure is rather conservative. We also note that our systematic error procedure makes the final errors strongly dependent on temperature — with sometimes irregular jumps of the error caused by some other fitting interval or fitting ansatz entering the procedure at certain values333For example, at all the quadratic+log fits have at least one fitting coefficient statistically insignificant above and at this temperature and higher (smaller ), quadratic+log fits become statistically significant and thus enlarge our error.. Apart from the agreement with the result, we observe that the approach to this result is faster for higher fermion masses — for , is already effectively zero temperature, while for our lowest mass, , we have small changes of the central value even above . Concerning the agreement with the approximation of Ref. Hosotani:1998za (referred to as “Hosotani HF” in the plot), the latter provides good qualitative description of the temperature dependence of the chiral condensate. However, the quantitative agreement is not perfect, with typical deviations of 10-20%. It is known that the approximation becomes exact in the massless limit and indeed, e.g. Hosotani’s result at is relatively closer to the MPS result than the one at . On the other hand, the approximation of Ref. Hosotani:1998za also approaches the analytical result of zero at infinite fermion mass and — hence one also expects an increasing agreement in this regime. Indeed, the relative difference at is the smallest from among all our considered masses. However, when we consider the slope of the -dependence, we clearly observe that the agreement between Hosotani HF and our computation becomes better towards small fermion masses, with both curves being almost parallel for .
5 Summary and prospects
In this paper, we have performed a study of the temperature dependence of the chiral condensate for the one-flavour Schwinger model using a Hamiltonian approach. We emphasize that while for zero temperature we employ a matrix product state (MPS) ansatz, for non-vanishing temperature we use a matrix product operator (MPO) ansatz. In addition, for the non-zero temperature calculation, we have to perform a thermal evolution by starting from a well defined infinite temperature state and evolve the system in incremental inverse temperature steps towards zero temperature using a density operator.
Thus, non-zero temperature calculations within the Hamiltonian approach are rather different from the so far carried out zero temperature ones and hence non-zero temperature computations for gauge theories are novel and need to be tested. While in Ref. Banuls:2015sta we have initiated such non-zero temperature computations for massless fermions, in this paper we went substantially beyond this work by studying the system at various fermion masses. In addition, we employed consistently a truncation of the gauge sector. This allowed us to reach very large system sizes and, keeping the physical extent of the model fixed, very small values of the lattice spacing.
Within our calculation of the chiral condensate, we carried out a substantial and challenging effort to control the systematic effects. To this end, we performed extrapolations to zero thermal evolution step size, infinite bond dimension, infinite volume and zero lattice spacing. In addition, we tested that our cut parameter for the gauge sector truncation has been sufficiently large. The final non-trivial check of the validity of our approach has been to recover the zero temperature result of the chiral condensate after the long thermal evolution performed.
As a result of our work, we could compute the chiral condensate over a broad temperature range from infinite to almost zero temperature with controlled errors. This has been done for zero, light and heavy fermion masses. For zero fermion mass, we found excellent agreement with the analytical results of Ref. Sachs:1991en . Moving to non-zero fermion masses, a comparison to Ref. Hosotani:1998za did not lead to a clear conclusion, see Fig. 9. Although qualitatively the temperature dependence of the chiral condensate shows a comparable behaviour between the analytical result of Ref. Hosotani:1998za and our data, there does not seem to be an agreement on the quantitative level. This is presumably due to the fact that the approximations made in Ref. Hosotani:1998za are too rough to reach a satisfactory quantitative agreement.
We consider the here performed work, besides of the clear interest in its own, as a necessary step towards investigating the Schwinger model when adding a chemical potential. This setup leads to the infamous sign problem and it would be very reassuring to see whether the here used MPS and MPO approaches can lead to a successful application for this very hard problem, which is very difficult, if not impossible to solve by standard Markov chain Monte Carlo methods.
Acknowledgements.We thank J. I. Cirac for discussions. This work was partially funded by the EU through SIQS grant (FP7 600645). K.C. was supported in part by the Helmholtz International Center for FAIR within the framework of the LOEWE program launched by the State of Hesse and in part by the Deutsche Forschungsgemeinschaft (DFG), project nr. CI 236/1-1 (Sachbeihilfe). Calculations for this work were performed on the LOEWE-CSC high-performance computer of Johann Wolfgang Goethe-University Frankfurt am Main and in the computing centers of DESY Zeuthen and RZG Garching.
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https://www.gongkangya.com/product/ruin-probabilities-2nd-edition-by-soren-asmussen/
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math
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Ruin probabilities (2nd edition) by Søren Asmussen
By: Asmussen Soren
Publisher: World Scientific
Print ISBN: 9789814282529, 9814282529
eText ISBN: 9789814282536, 9814282537
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg’s inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.
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https://www.oyetimes.com/lifestyle/food/18621-italian-limoncello-recipe-lemon
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• 1 litre of 90 proof alcohol
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3• Filter contents.
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Special note: Make sure your preperation bottle is glass and can hold at least two litres.
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http://regenbogenstern.at/index.php/lib/introduction-to-aircraft-performance
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math
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By Asselin M.
Read or Download Introduction to Aircraft Performance PDF
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There's expanding curiosity within the strength of UAV (Unmanned Aerial automobile) and MAV (Micro Air automobile) expertise and their huge ranging functions together with defence missions, reconnaissance and surveillance, border patrol, catastrophe area overview and atmospheric study. excessive funding degrees from the army quarter globally is using learn and improvement and extending the viability of independent systems as replacements for the remotely piloted automobiles more often than not in use.
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The subtraction of zero from any number will not alter that number. f) n − n = 0. Subtraction of any number from itself will always equal zero. g) n/0 = ? Division by zero is not defined in mathematics. The commutative, associative and distributive laws We all know that 6 × 5 = 30 and that 5 × 6 = 30, so is it true that when multiplying any two numbers together, the result is the same no matter what the order? The answer is yes. The above relationship may be stated as: The product of two real numbers is the same irrespective of the order in which they are multiplied.
4 1. What is 15% of 50? 2. 5 million. Each year 10% of the value of the test equipment is written off as depreciation. What is the value of the equipment after two full years? 3. 25 hours and travels 1620 km. What is the aircraft’s average speed? 4. A car travels 50 km at 50 km/h and 70 km at 70 km/h. What is its average speed? 5. A car travels 205 km on 20 litres of petrol. How much petrol is needed for a journey of 340 km? 6. Four men are required to produce a certain number of components in thirty hours.
206077518 × 10−11 . The error in this very small number (compared with our estimation) is something like two in one thousand million! Of course, the errors for very large numbers, when squared or raised to greater powers, can be significant! Simplify a) You might be able to provide an estimate for this calculation without converting to standard form. For the sake of completeness and to illustrate an important point, we will solve this problem using the complete process. 24 × 10−1 ). 27. In other words it is already in standard form!
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http://www.algebra-class.com/evaluating-functions.html
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math
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In our introduction to functions lesson, we related functions to a vending machine. You "input" money and your "output" is candy or chips!
We're going to go back to that visual as we begin evaluating functions. We are going to "input" a number and our "output" is the answer.
If you can substitute and evaluate a simple equation, then you can evaluate functions. Remember, a function is basically the same as an equation. The only difference is that we use that fancy function notation (such as "f(x)") instead of using the variable y.
Pay close attention in each example to where a number is substituted into the function. I promise you will have no trouble evaluating function if you follow along. Take a look....
Did you notice how we just substituted for x and we found our answer? Not too hard, is it?
Next you will see how using function notation makes it easier to display your answer if you are asked to evaluate the function more than one time.
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I hope you are finding this to be pretty easy! You actually already know how to evaluate functions if you can evaluate equations. We are just giving it a different name.
In the next lesson we will move onto linear functions. You will also find that if you understand linear equations, then linear functions will be a piece of cake!
Sign Up for Algebra Class E-courses
Copyright © 2009-2015 Karin Hutchinson ALL RIGHTS RESERVED
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https://simple.m.wikipedia.org/wiki/Arithmetic
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In mathematics, arithmetic is the basic study of numbers. The four basic arithmetic operations are addition, subtraction, multiplication, and division, although other operations such as exponentiation and roots are also studied in arithmetic.
Most people learn arithmetic in primary school, but some people do not learn arithmetic and others forget the arithmetic they learned. Many jobs require a knowledge of arithmetic, and many employers complain that it is hard to find people who know enough arithmetic. A few of the many jobs that require arithmetic include carpenters, plumbers, mechanics, accountants, architects, doctors, and nurses. Arithmetic is needed in all areas of mathematics, science, and engineering.
Some arithmetic can be carried out mentally. A calculator can also be used to perform arithmetic. Computers can do it more quickly, which is one reason Global Positioning System receivers have a small computer inside.
Examples of arithmetic change
- (addition is commutative: is the same as )
- (subtraction is not commutative: is different from )
- (multiplication is commutative: is the same as )
- (division is not commutative: is different from
Related pages change
- "List of Arithmetic and Common Math Symbols". Math Vault. 2020-03-17. Retrieved 2020-08-25.
- "Definition of Arithmetic". www.mathsisfun.com. Retrieved 2020-08-25.
- "Arithmetic". Encyclopedia Britannica. Retrieved 2020-08-25.
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https://www.slideshare.net/Avinio/what-is-social-media-sc-media
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math
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What is social media?
• How people discover, read and share news, information and content.
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Prospecting, Lead Generation
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Integration, Communication Automation, Website Optimization/Blog Integration
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Social Media platforms:
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• Social Networking Sites - Facebook, MySpace, LinkedIn, Plaxo, etc.
• Microblogging Sites - Twitter, Plurk, etc.
• Pod and Video Casts - YouTube, Veoh, Vimeo, etc.
• Photo Sharing Sites - Flikr, Photobucket, Zoomr, etc.
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• Instant Messaging
Social Media Overview:
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• Everyday 60,000 videos are added to You Tube
• 10 hours of video uploaded to YouTube every minute
• 70,000,000 – number of total videos on YouTube (March 2008)
• 200,000 – number of video publishers on YouTube (March 2008)
• 100,000,000 – number of YouTube videos viewed per day (this stat from 2006 is
the most recent I could locate)
• 112,486,327 – number of views the most viewed video on YouTube has (January,
• 2 minutes 46.17 seconds – average length of video
• 412.3 years – length in time it would take to view all content on YouTube (March
• 26.57 - average age of uploader
• 13 hours – amount of video are uploaded to YouTube every minute
• Everyday 250,000 people join Facebook.
• Facebook has just reached 250m active users
• 8m+ FB users become fans of Pages every day
• Highest indexing age groups on Facebook are those 25-34 (27%) and 35-49 (23%)
• Fastest growing user group on Facebook is 35+
• ABC1s are more likely to have a Facebook profile
• 200,000,000 – number of active users
• 100,000,000 - number of users who log on to Facebook at least once each day
• 170 - number of countries/territories that use Facebook
• 35 - number of different languages used on Facebook
• 2,600,000,000 – number of minutes global users in aggregate spend on Facebook
• 100 – number of friends the average user has
• 700,000,000 – number of photos added to Facebook monthly
• 52,000 – number of applications currently available on Facebook
• 140 - number of new applications added per day
• LinkedIn gains 1 new user per second
• Executives from all Fortune 500 companies on LinkedIn
• The average age of a LinkedIn user is 41
• The average earnings of a LinkedIn user is $109k
• 46% of LinkedIn users are Decision Makers
• LinkedIn has the highest average income ($89,000) and users joined the network for
business or work purposes.
• LinkedIn is more likely to be male - it’s ratio of male to female users is 57% to 43%.
• Everyday 120,000 blogs are created
• 133,000,000 – number of blogs indexed by Technorati since 2002
• 346,000,000 (77%) – number of people globally who read blogs (comScore March
• 900,000 – average number of blog posts in a 24 hour period
• 81 - number of languages represented in the blogosphere
• 59% – percentage of bloggers who have been blogging for at least 2 years
• Time spent on Twitter has soared 3,702% YoY
• The average age of a Twitter user is 31
• 1,111,991,000 – number of Tweets to date (see an up to the minute count here)
• 3,000,000 – number of Tweets/day(March 2008) (from TechCrunch)
• 165,414 - number of followers of the most popular Twitter user (@BarackObama) –
but he’s not active
• 86,078 – number of followers of the most active Twitter user (@kevinrose)
• 63% – percentage of Twitter users that are male (from Time)
• 236,000,000 – number of visitors attracted annually by 2008 (according to a
• 56% - percentage of Digg’s frontpage content allegedly controlled by top 100 users
• 124,340 - number of stories MrBabyMan, the number one user, has Dugg (see
updated number here)
• 612 - number of stories from Cracked.com that have made page 1 of Digg (see all
41 pages of them here)
• 36,925 – number of Diggs the most popular story in the last 365 days has received
(see story here)
• Off stuff:
• Only 14% of people trust advertisements.
• 78% trust recommendations of other consumers.
Why do you Need Social Media Marketing
• Your competition is doing it.
• Your customers are using it (though maybe indirectly)
• Your vendors and partners are using it
• More Social = more Search. More Search = More Customers. More customers = More
• Paid search prices are rising.
• SEO isn’t easy anymore
• You can’t buy links anymore
• Your website is only a billboard
• Great ROI on the Marketing Budget
• Customer Service
• Market Research
• Communication/Brand Management
• “Thought Leadership”
• Stay current.
• Reduce email overload.
• Communicate anytime, anywhere.
• Create and contribute to ideas, content, and products.
• Participate in existing and new online communities.
• Listen to others.
• Learn from others.
• Share with others.
• Engage others.
• Build relationships.
• Relate to new and traditional audiences.
• Corporate Transparency
• Build Trust with Customers
• Generate Inbound Links
• Reputation Management
• Promote your blog and website
• Be a part of the conversation that is already going on
• Extend your events, seminars, webcasts, conventions
• Provides a new way to engage and communicate with your customers
• Engagement: Increase loyalty, foster word of mouth
• Research: Identify trends/niches, consultation
• Marketing: Promote business, brand awareness
• SEO: link building, content factors
• PR: Manage reputation, get news out
• Management: Collaboration, knowledge sharing
• Sales: Gain new business, new contact routes
Social Networks in General
1. People visit social networking sites 5 days per week, checking their
accounts 4 times a day
2. 52% of social networkers had friended or become a fan of at least one
3. 64% were neutral or didn’t care about brands on social networks
4. 45% connect only to family and friends and 18% will connect only to people
they’ve met in person
• More than 250 million active users
• More than 120 million users log on to Facebook at least once each day
• More than two-thirds of Facebook users are outside of college
• The fastest growing demographic is those 35 years old and older
• Average user has 120 friends on the site
• More than 5 billion minutes are spent on Facebook each day (worldwide)
• More than 30 million users update their statuses at least once each day
• More than 8 million users become fans of Pages each day
• People demographics on Facebook are more likely to be married (40%),
white (80%) and retired (6%) than users of the other social networks.
• Facebookers have the second-highest average income ($61,000) and an
average of 121 connections.
• 75% say Facebook is their favorite site with 59% saying they’ve increased
their usage over the past 6 months.
• More than 1 billion photos uploaded to the site each month
• More than 10 million videos uploaded each month
• More than 1 billion pieces of content (web links, news stories, blog posts,
notes, photos, etc.) shared each week
• More than 2.5 million events created each month
• More than 45 million active user groups exist on the site
• More than 50 translations available on the site, with more than 40 in
• About 70% of Facebook users are outside the United States
Twitter Users Are Trending Older
• 72.5% of all users joining during the first five months of 2009.
• 85.3% of all Twitter users post less than one update/day
• 21% of users have never posted a Tweet
• 93.6% of users have less than 100 followers, while 92.4% follow less than
• 5% of Twitter users account for 75% of all activity
• New York has the most Twitters users, followed by Los Angeles, Toronto,
San Francisco and Boston; while Detroit was the fast-growing city over the
first five months of 2009
• More than 50% of all updates are published using tools, mobile and Web-
based, other than Twitter.com.
• There are more women on Twitter (53%) than men (47%)
• Of the people who identify themselves as marketers, 15% follow more than
2,000 people. This compares with 0.29% of overall Twitter users who follow
more than 2,000 people.
• Average Twitter user has 28 followers and follows 32 others
Why you need Twitter?
• Fastest Growing Social Networking site - +813% from January 2008 to January 2009
• 44.500.000 users
• Twitter is dominated by newer users - 70% of Twitter users joined in 2008
• An estimated 5-10 thousand new accounts are opened per day
• 35% of Twitter users have 10 or fewer followers
• 9% of Twitter users follow no one at all
• There is a strong correlation between the number of followers you have and the
number of people you follow Level Access to Influencers
• Very Social
• Conversation Monitoring
• Real Time Couponing
• Passive Chatting
• Comcast Cares, Dell Outlet
• Meet Cool Tweeple (not a word)
• Not surprisingly, most users (97%) agree that brands should engage their customers
on Twitter. This is 8 percentage points higher than the fall survey. Clearly Twitter
users want to engage with their brands.
• The majority also have a better impression of brands that use Twitter for customer
• Proper usage of Twitter however, is paramount as 90% of users would frown upon
poor or inappropriate brand use of Twitter.
• The power of a relationship is extremely strong on Twitter. 80% of respondents
would recommend a company based on their presence on Twitter, a huge 20
percentage point increase from the prior survey and 84% of Twitter users will
reward those brands they have key relationships by being more willing to purchase
from them. This was a 5 percentage point increase from the original survey.
• Influencers: More than 80% of respondents have 100+ followers and almost 35% of
respondents have posted more than 1000 Tweets since they signed up for the
• Twitter is a growing microblogging network where people answer the question:
What are you doing now? And write their answer in 140 characters or less.
• Originally designed for text messaging via cellphones (which have a limit of 140
characters for text messages), Twitter has become a whole lot more than the
answer to What are you doing now?
• 9.4 million people belong to Twitter right now. More than 7,500 people join Twitter
• About 500 users have 20,000 or more followers. The average tweeter probably has
500 followers or less. 35% of Twitterati have 10 or less followers; 9% have none.
• Those numbers will change as people begin to realize the true value of Twitter for
helping to create relationships, forge partnerships, and engage in meaningful
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187828356.82/warc/CC-MAIN-20171024090757-20171024110757-00738.warc.gz
|
CC-MAIN-2017-43
| 11,379 | 211 |
https://www.mysciencework.com/publication/show/boundary-conditions-from-boundary-terms-noether-charges-trace-k-lagrangian-general-relativity-78719328
|
math
|
We present the Lagrangian whose corresponding action is the trace K action for General Relativity. Although this Lagrangian is second order in the derivatives, it has no second order time derivatives and its behaviour at space infinity in the asymptotically flat case is identical to other alternative Lagrangians for General Relativity, like the gamma-gamma Lagrangian used by Einstein. We develop some elements of the variational principle for field theories with boundaries, and apply them to second order Lagrangians, where we stablish the conditions -- proposition 1 -- for the conservation of the Noether charges. From this general approach a pre-symplectic form is naturally obtained that features two terms, one from the bulk and another from the boundary. When applied to the trace K Lagrangian, we recover a pre-symplectic form first introduced using a different approach. We prove that all diffeomorphisms satisfying certain restrictions at the boundary -- that keep room for a realization of the Poincar\'e group -- will yield Noether conserved charges. In particular, the computation of the total energy gives, in the asymptotically flat case, the ADM result.
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267866965.84/warc/CC-MAIN-20180624141349-20180624161349-00362.warc.gz
|
CC-MAIN-2018-26
| 1,172 | 1 |
https://plantyourpencil.com/how-do-you-calculate-the-perimeter-of-a-triangle/
|
math
|
Before answering your question, let me give you a brief introduction of what perimeter actually means.
In geometry, the perimeter is the length of the outer line of a shape. Perimeter is defined as the uninterrupted continuous line that makes the boundary of a closed geometrical figure. The term ‘perimeter’ originates from the Greek word ‘peri’ meaning around and ‘metron’ meaning measure.
The perimeter of any two-dimensional shape is defined as the distance around that shape. If a shape is expanded into a linear form, then the length of that linear form will be the perimeter.
A triangle is one of the most common shapes in geometry. It is a closed two-dimensional figure. Triangles consist of three sides; hence, they are also a three-sided polygon. All sides are composed of straight lines. The point where two straight lines meet is known as the vertex and each vertex forms an angle. Thus, a triangle consists of three vertices as well as three angles. The sum of the interior angles of a triangle makes an angle of 180°. Among all the polygons, the triangle is a polygon with the least number of sides. So, a triangle can be defined as a three-sided two-dimensional geometrical figure whose interior angles are equal to 180°.
On the basis of the angles and side length, the triangles can be categorized into six types:
Based on the length of the sides – Scalene Triangle, Isosceles Triangle & Equilateral Triangle
Based on the angles – Acute Angle Triangle, Obtuse Angle Triangle & Right-Angle Triangle
A perimeter of a triangle is defined as the total length of the outline of the triangle. Since a triangle has three sides, therefore, the perimeter of any given triangle, irrespective of their types, is equal to the sum of all its three sides. The measurement unit of the perimeter is the same as the unit of sides of the triangle.
Perimeter = Sum of all three sides
For example, let us suppose ABC is a triangle; if AB, BC and AC are the lengths of its sides, then the perimeter of ABC will be:
Perimeter = AB+BC+AC
A Right triangle consists of a base(b), a perpendicular(p) and a hypotenuse (h) as its sides, From the Pythagoras theorem, we know that,
h2 = b2 + p2
Hence, the Perimeter of a right-angle triangle will be,
Perimeter = b + p + h
Area and perimeter are two crucial key concepts of mathematics. They build the foundation for advanced mathematics. Both area and perimeter are used to determine the physical space occupied by an object. The area is defined as the 2-dimensional space that is occupied or covered by a closed figure, whereas the perimeter is the distance of the boundary surrounding the closed figure. Both concepts have a practical use and are applied in our day-to-day life.
Area and perimeter are applicable in our everyday life. We know that the area is basically the space covered by a shape and perimeter is the distance around the shape. For example, the area can be used to calculate the size of the carpet required to cover the whole floor of a room. The perimeter, on the other hand, can be used to calculate the length of the fence that will be required to surround a garden. Two shapes may possess the same perimeter, but different areas or may possess the same area, but different perimeters. The area is measured in square units i.e., square kilometres, square feet, etc. While, measurement of the perimeter of a shape is done in linear units like kilometres, inches, feet, etc. Perimeter measures only one dimension, i.e., length of the object. Whereas, area measures two dimensions, i.e., length and width of the object.
Although the two mathematical concepts are different from each other, however, one can be used to calculate the other.
Here I will also suggest you to practice mathematics as much as possible. Try questions with different pattern. It will help you to understand the topic more clearly. You must understand that you can’t learn mathematics by just mugging up. You have to understand every step. Try to solve all the example question form the text book. It will help you to solve the problems from the exercise part.
Hope this helped you to clear your doubts.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817014.15/warc/CC-MAIN-20240415174104-20240415204104-00594.warc.gz
|
CC-MAIN-2024-18
| 4,155 | 20 |
https://www.econstor.eu/handle/10419/129980
|
math
|
This paper assesses the relationship between courses taken in high school and college major choice. Using High School and Beyond survey data, I study the empirical relationship between college performance and different types of courses taken during high school. I find that students sort into college majors according to subjects in which they acquired more skills in high school. However, I find a U-shaped relationship between the diversification of high school courses a student takes and their college performance. The underlying relation linking high school to college is assessed by estimating a structural model of high school human capital acquisition and college major choice. Policy experiments suggest that taking an additional quantitative course in high school increases the probability that a college student chooses a science, technology, engineering, or math major by four percentage points.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549436316.91/warc/CC-MAIN-20170728002503-20170728022503-00425.warc.gz
|
CC-MAIN-2017-30
| 907 | 1 |
https://virtualnerd.com/middle-math/decimals/dividing/word-problem-division-rounding
|
math
|
Turning a word problem into a math problem you can solve can be tricky. Luckily, there's some key words to look out for in a word problem that help tell you what math operation to use! This tutorial shows you some of these key words to look for in a word problem.
Have you ever looked at the price of something? It's usually given as a decimal! Decimals are a very helpful part of math and can be found in may places in the real world. Watch this tutorial to learn all about decimals!
We know that calculators are everywhere, but that doesn't mean that long division isn't important! Sometimes you won't be allowed to use a calculator, and when those times occur, you'll be thankful that you watched this video!
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439739328.66/warc/CC-MAIN-20200814130401-20200814160401-00198.warc.gz
|
CC-MAIN-2020-34
| 711 | 3 |
https://statindex.org/journals/640/45
|
math
|
Current Index to Statistics
IEEE Transactions on Reliability
Hypothesis-test for reliability in a stress-strength model, with prior information
Nandi, S. B.
Aich, A. B.
Modified `practical Bayes-estimators'
Forced-outage rates of generating units based on expert evaluation
Noor, S. Fayyaz
McDonald, J. R.
The use of imprecise component reliability distributions in reliability calculations
Roberts, Ian D.
Samuel, Andrew E.
Fuzzy reliability using a discrete stress-strength interference model
Wang, J. D.
Liu, T. S.
Weibull component reliability-prediction in the presence of masked data
Usher, John S.
Bayes estimation of component-reliability from masked system-life data
Lin, Dennis K. J.
Usher, John S.
Guess, Frank M.
Estimating component-defect probability from masked system success/failure data
Flehinger, Betty J.
Conn, Andrew R.
A cautionary tale about Weibull analysis
Mackisack, M. S.
Stillman, R. H.
Characterization of bivariate mean residual-life function
Kulkarni, H. V.
Rattihalli, R. N.
Linear-spline approximation for semi-parametric modeling of failure data with proportional hazards (STMA V38 1917)
Love, C. E.
A reliability model of a system with dependent components (STMA V38 2380)
Robust parameter-estimation using the bootstrap method for the 2-parameter Weibull distribution
Optimum 3-step step-stress tests
Khamis, Imad H.
Higgins, James J.
Nonparametric model for step-stress accelerated life testing
Tyoskin, Oleg I.
Krivolapov, Sergey Y.
Some results on discrete mean residual life
Salvia, Anthony A.
Engineering notion of mean-residual-life and hazard-rate for finite populations with known distributions
Estimating the cumulative downtime distribution of a highly reliable component
Jeske, Daniel R.
A system-based component test plan for a series system, with type-II censoring
Development test programs for 1-shot systems: 2-state reliability and binary development-test results
Vardeman, Stephen B.
Proportional hazards modeling of time-dependent covariates using linear regression: A case study (STMA V38 3217)
Computational algebra applications in reliability theory (STMA V38 3686)
The use of precautionary loss functions in risk analysis (STMA V38 3705)
Norstroem, J. G.
Norstrom, J. G.
Norstrøm, J. G.
Solving ML equations for 2-parameter Poisson-process models for ungrouped software-failure data (Corr: 1997V46 p349 STMA V39 4232))
Knafl, George J.
Using neural networks to predict software faults during testing (STMA V38 3692)
Khoshgoftaar, T. M.
Szabo, R. M.
Generalized linear models in software reliability: Parametric and semi-parametric approaches (STMA V38 3681)
El Aroui, M.-A.
Bayes estimation for the Pareto failure-model using Gibbs sampling
Tiwari, Ram C.
Zalkikar, Jyoti N.
Hierarchical Bayes estimation for the exponential-multinomial model in reliability and competing risks
Papadopoulos, Alex S.
Tiwari, Ram C.
Zalkikar, Jyoti N.
Predictive Bayes design of Scram systems: Related mathematics and philosophical implications
Clarotti, Carlo A.
A Bayes approach to step-stress accelerated life testing
van Dorp, J. Rene
van Dorp, J. René
Mazzuchi, Thomas A.
Fornell, Gordon E.
Pollock, Lee R.
A Bayes approach to step-stress accelerated life testing (STMA V38 3715)
van Dorp, J. R.
Mazzuchi, T. A.
Fornell, G. E.
Pollock, L. R.
A Bayes ranking of survival distributions using accelerated or correlated data
Zimmer, William J.
Deely, John J.
A reliability-growth model in a Bayes-decision framework
How to model reliability-growth when times of design modifications are known
Needed resources for software module test, using the hyper-geometric software reliability growth model (STMA V38 5088)
A conservative theory for long-term reliability-growth prediction (STMA V38 5078)
A survey of discrete reliability-growth models
Comparing the importance of system components by some structural characteristics
Meng, Fan C.
Accelerated life tests for products of unequal size
Bai, D. S.
Yun, H. J.
Accelerated life tests analyzed by a piecewise exponential distribution via generalized linear models
Barbosa, Emanuel P.
Colosimo, Enrico A.
Optimal release policy for hyper-geometric distribution software-reliability growth model (STMA V38 5089)
A Bayes nonparametric framework for software-reliability analysis (STMA V38 5084)
The failure of Bayes system reliability inference based on data with multi-level applicability
Philipson, Lloyd L.
Bayes and classical estimation of environmental factors for the binomial distribution
Elsayed, E. A.
Prediction intervals for Weibull observations, based on early-failure data
Hsieh, H. K.
Confidence interval for the mean of the exponential distribution, based on grouped data
A coherent model for reliability of multiprocessor networks (STMA V38 5079)
Failure-rate functions for doubly-truncated random variables
Ruiz, Jose M.
Analysis of step-stress accelerated-life-test data: A new approach
Tang, L. C.
Sun, Y. S.
Goh, T. N.
Ong, H. L.
A discretizing approach for stress/strength analysis
English, John R.
Landers, Thomas L.
An input-domain based method to estimate software reliability (STMA V38 1002)
De Agostino, E.
Di Marco, G.
|
s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987769323.92/warc/CC-MAIN-20191021093533-20191021121033-00198.warc.gz
|
CC-MAIN-2019-43
| 5,132 | 120 |
http://movies.stackexchange.com/questions/tagged/jetsons?sort=active
|
math
|
Movies & TV
Movies & TV Meta
to customize your list.
more stack exchange communities
Reputation and Badges
Start here for a quick overview of the site
Detailed answers to any questions you might have
Discuss the workings and policies of this site
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What did they use to make the Jetsons flying car sound effects?
How did the Foley artist make the futuristic Jetson flying car sounds in 1962?
Nov 22 '14 at 5:25
recently active jetsons questions feed
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|
s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443736678574.43/warc/CC-MAIN-20151001215758-00202-ip-10-137-6-227.ec2.internal.warc.gz
|
CC-MAIN-2015-40
| 2,284 | 62 |
https://excelunusual.com/the-easy-way-of-solving-systems-of-linear-equations-in-excel-using-the-inverse-spreadsheet-function/
|
math
|
This brief tutorial explains how to calculate the solution vector of a system of linear equations using the Excel spreadsheet function MINVERSE() which calculate the inverse of a matrix.
Solving linear systems of equations in Excel – the easy way
by George Lungu
– This is a tutorial showing an easy and convenient method of solving moderate size systems of
linear equations in Excel by using the built-in formulas for matrix inversion, MINVERSE() and
matrix multiplication, MMULT().
– There are many different ways of solving such systems, a lot of this methods are studied in
school or college. This presentation will not deal with the theory of these methods or even
mentioning them. Whoever wants to learn more must do a Google search into “system of linear
equations”. Wikipedia has a good entry on this topic too.
We can turn the system of linear equations
previous system of equations in
with 3 unknowns
looks like this: 3
and [B] is
Where [A] is the [X] is the matrix
coefficient matrix: of unknowns:
Solving the system of equations using the INVERSE matrix:
If we can find the inverse of the coefficient
matrix we can solve the matrix equation by
multiplying both sides of the equation with
the inverse of that matrix from the left side:
Using the associativity of matrix
multiplication we can write:
the identity matrix
Excel implementation example for a 3 x 3 system of linear equations:
– In an new worksheet input two
matrices as arrays of numbers: the
matrix of coefficients in the range
B3:D5 and the matrix of constants
in the range B10:B12.
– The formulas for calculating the
solution will be placed in range
– You can use different labels and
colors if you wish so.
How to fill the solution matrix formula:
– Select cell D10, type “=MMULT(MINVERSE(B3:D5),B10:B12)” then hit return.
– Select range D10:D12 and press F2+Ctrl+Shift+Enter in this order.
– The solution vector should appear in the range D10:D12.
– If the system has no solution or infinite solutions, you will get the #NUM! error message in
the solution range. If you left a cell blank the result will be #VALUE! error message in the cells
of the result range.
Verify the result:
-Let’s calculate vector [B] from the solution backwards to confirm the correctness of the result:
=> D15: “=B3*D$10+C3*D$11+D3*D$12” then copy D15 down to cell D17
– Range D15:D17 will contain results equal to the numbers in the vector of constants [B] which
proves that the algorithm used for calculating the solution (in range D10:D12) is correct.
Calculate the result in a horizontal vector form:
– Sometimes it is useful to have the result as a horizontal vector and we
can get that using the function TRANSPOSE()
– Select cell B19 and type “=TRANSPOSE(MMULT(MINVERSE(B3:D5),
B10:B12))” then hit return.
– Select range B19:D19 and press F2+Ctrl+Shift+Enter in this order.
– The solution vector should appear in the range B19:D19.
|
s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511220.71/warc/CC-MAIN-20231003192425-20231003222425-00799.warc.gz
|
CC-MAIN-2023-40
| 2,941 | 54 |
https://solvedlib.com/n/evaluate-the-surface-integralds-for-the-given-vector-field,6300200
|
math
|
So we're looking to calculate the flux of our surface flux can be represented by the service in a girl of Flux Times DS. And in this case and Z is equal to or is he can be rewritten to be equal in terms of X and y. You could be using the formula that the sequence the integral of negative p times a g partial with respect to X minus que There's the G partial with respect toe wine, plus our d a. Now what do you mean by weaken right Z in terms of X and y well, since we're given the X squared plus y squared plus Z squared is equal to four we can solve for Z and write that Z is equal to the square root of four minus X squared minus y squared. So now we have a function in terms of, um, see being in terms of x and y so we can use the U formula buff and were given the F is equal to X I minus zj plus y que Now we need to come up with the X and y partials of F.
And when we plugged this in this will be equal to the negative. Integral, I'll go over way. That's negative. In a second of negative X multiplied by negative X over Skerritt four minus X squared minus y squared. Um, minus negative C of negative.
Why over square it four minus X squared minus y squared. Plus why, dear? So this is negative, by the way, because our equation is sloping downwards. And then this particular formula Onley where x one, we're going upwards so we can make it negative. And that will make you go from upwards downwards. So simplifying what we have here, we'll get that this is equal Teoh X squared over square it four minus X squared minus y squared d A.
Um, we got rid of the Z, by the way by, um converting the sea which is equal to skirt four miles Expert minus y squared, um, week sought out. See, for through this right here. So now we just need to come up with the limits of integration. And we have expert in Life Square, which is a good representation, that we should be switching to polar. And it's doing so we'll give, um, in our value from zeros too, And the state of value from zero to pi over two and then converting.
We'll have that. This is equal to zero to pi over two. Syria did too. Of our cubes coast sine squared data over the square root of four minus are square drd fada. And this will be equal Teoh negative zero to pi over two of coastline squared fada de theater I won't supplied by and a girlfriend is devoted to of our cubes over square it four minus r squared d r.
So what we're doing here is, since we can write this as purely in terms of Fada and purely in terms of art were breaking apart and doing them separately, this prevents us from having to do any weird integration do the coastline. So solving this will give the first integral will be equal to 1/2 of theater plus 1/2 sign to theater from zero by over two, and this will be equal to pi over four. So now we have pi over four times the integral from 0 to 2 of our cubes over square at four to minus are square D r. Okay. And for this prom, we're gonna have to use a substitution.
Um, setting four minus R squared, equal to you and negative to our d are equal to do you. And this will change our integration from 0 to 2, 20 to 4. Sorry, Ford is your So we'll have to We write. This has a negative 1/2. When a girl from his Drew 22 of our square I swear it's four minus r squared times negative two R d r.
This will be equal to negative 1/2 in a girl from 4 to 0 a four minus you over square roots you do you We have to swap the order of integration by most when buying negatives this to become 1/2 you go from 0 to 4 of fourty to the negative 1/2 mine is t to the 1/2. Sorry. Do you and this of equal to 1/2 times eight teach the 1/2 minus 2/3 Tito the three house from 0 to 4 And we saw that outs that would be equal to 16. Interesting. This will be equal to 16/3.
So to me, the flux we take the answer both in troubles won't fight together. This will be negative. Pi over four I want to buy by 16/3, which is equal to negative four pi over three and I would be the flux of our surface..
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CC-MAIN-2022-27
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https://m.scirp.org/papers/68871
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math
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Received 30 May 2016; accepted 19 July 2016; published 22 July 2016
1. Literature review
During the last few years and due to the numerous advances in information systems, the use of means designed for the acquisition of data such as web and mobile applications, social networks, etc. has massively increased. As a result of this “information revolution”, the world of science has been saturated with data of varied origin. It is estimated that 90% of all data have been created in the last two years (2013-2015) . At the IOD (Information On Demand) Conference held in 2011, IBM presented the explosion of data in today’s society as a problem, and put forward how companies are facing the challenge of obtaining relevant and valuable information from this vast amount of data. The amount of data in the world is expected to double every two years, according to the data scientist Mark van Rijmenam, founder of Datafloq, in addition to increase 2.5 exabytes per day .
This enormous amount of information is known as Big Data. The vast majority of these data, which come from astronomy, genomics, telephony, credit card transactions, Internet traffic and web information processing, primarily, are acquired systematically with a certain frequency, being therefore time series - . The tendency to manipulate large quantities of data is due to the need, in many cases, to include the data obtained from the analysis of large databases in new databases, such as business analyses . Besides data manageability, other factors to consider are the speed of analysis/scanning speed, access, search and return of any element. It is important to understand that conventional databases are a significant and relevant part of an analytical solution .
Today, the explosion of data poses a problem given the amount of these increases overwhelmingly; in fact this situation reaches occasionally the point when it is not possible to gain an useful insight from them. Therefore, it is necessary to organise, classify, quantify and of course exploit this information to obtain maximum performance for the benefit of scientific research. In response to this difficulty the concept of Data Mining arises that refers to the non-trivial automated process which identifies valid, previously unknown, potentially useful and funda- mentally understandable patterns in the data.
The literature shows that Data Mining techniques are used to extract information from very diverse back- grounds as the power consumption of a region , modelling and optimisation of wastewater pumping systems and the establishment of the position of wind turbines to obtain the maximum possible wind currents .
A common pattern of all previous studies is the use of time series for the analysis and visualisation of information. A way to perform the processing of time series is through the creation of mathematical models that identify and predict their behaviour. One of these are the ARIMA models , that extract the most relevant data from the dataset identifying the patterns of the series at different levels of the timescale and simplify a large amount of data in a simple equation, hence their utility and application in Data Mining. ARIMA models are within the Data Mining techniques, as these are used in time series, therefore being a very useful tool to extract relevant information from Big Data.
In the field of the analysis and visualisation of data, the development of free software is a good tool for both analytical and visual integration of information. In this section of the processing of data, software for the analysis and visualisation of data allow to work with large volumes of data completed over a period of time . The development of statistical software that allows to work on the analysis of time series further facilitates the implementation of ARIMA models.
The use of free access software as Rstudio, which is an integrated development environment for R, has the advantage of enabling programming statistical packages as required, as well as of applying all kinds of time series analysis, in addition to reducing economic costs in any research project. In the present work a script has been developed in the environment of programming R language that allows the implementation, processing and visualisation of ARIMA models, in order to make it easier for scientists to know about the exploration, exploitation and manipulation of large volumes of univariate data carrying associated timescales. The script development and implementation structure is shown in Figure 1.
this script achieves the implementation of the Box-Jenkins methodology for the development of ARIMA-models; in this way, the researcher is able to decompose the time series and to obtain the most relevant information of the characteristics of the temporal series, showing the extent to which this script helps in the exploration, exploitation and manipulation of data.
2. Information about the ST.R File
This document provides information about what is and how to use the ST.R script.
2.1. What Is ST.R?
ST.R is a code in R language developed for the treatment of time series and the realisation of ARIMA models following the Box-Jenkins methodology . The script is split into two blocks. The first one is a collection of
Figure 1. Structure of development and implementation of the script in R. The different actions to be followed for the implementation of the script are shown. It is a conceptual model of implementation where Excel is used as a possible tool for data management. Source: own elaboration.
commands for the numerical and graphic description of the time series, and the development of the ARIMA models. In the second block the commands of different precision measurements are set up, which allow to compare the forecasts made by the models with the actual data with the aim of selecting the model with the most optimal fit to actual observations .
2.2. How to Use ST.R
In order to successfully run the ST.R script, the necessary libraries are lmtest and tseries. These libraries are available from the repository Comprehensive R Archive Network (CRAN) at http://CRAN.R-project.org/package=OptGS. In this work, the R “stat” package version 3.3.0 was used, using “ARIMA” argument. The fitting methods are described in the R manual .
2.3. ST.R Structure
2) Trend analysis: the existence or non-existence of the trend is studied from the graphical results. A linear trend will be removed with first differences. However, for a nonlinear trend two differences are used. The Dickey-Fuller and KPSS tests are used for the analysis (Figure 4).
3) Homocedasticity analysis: This is done from both a visual and a mathematical perspective. From a visual point of view, it is carried out through the study of the thickness of the series. If this thickness remains constant, with no major irregularities observed, the series will be homocedastic; otherwise, the series will be considered heterocedastic. From a mathemathical, it is carried out with the application of the homoscedasticity Breusch- pagan test (Figure 5).
Figure 2. An R Graphical User Interface (GUI) for step 1. Graphical representation.
Figure 3. An R Graphical User Interface (GUI) for step 1. Graphical representation.
4) Stationarity analysis: As a result of the steps above, when neither seasonal cycle, nor trend, nor a significant thickness alteration of the series are to be perceived, the series is regarded as stationary (Figure 5).
5) Model identification: the most optimal model type is determined from the order of the Autoregressive procedure and moving averages of the constituents, both uniform and seasonal. This choice is made from autocorrelation (FAC) and partial autocorrelation (partial FAC) functions (Figure 5).
6) Estimation of the coefficients of the model: the order of the model having been established, the estimation of its parameters is made. Given it is an iterative calculation process, initial values (pool of models) can be suggested (Figure 5).
Figure 4. An R Graphical User Interface (GUI) for step 2. Trend analysis.
Figure 5. An R Graphical User Interface (GUI) for steps 3 - 7, 10. Homocedasticity analysis; stationarity analysis; model identification; estimation of the coefficients of the model; detailed error analysis; forecast.
7) Detailed error analysis: It is made from the verified differences between values observed empirically and estimated by the model for their final assessment. It is necessary to check an inconsistent regime of them and analyse the existence of significant errors. The Ljung-Box test is applied (Figure 5).
8) Contrast of model validity: the model or models initially selected are quantified and valued using various statistical measures. The measures applied are: R2 (coefficient of determination), % SEP (standard error percentage), E2 (coefficient of efficiency), ARV (average relative variance), AIC (Akaike information criterion), RMSE (root mean square error) and MAE (mean absolute error) (Figure 6).
9) Model selection: based on the results of the previous steps, the model to work on is decided upon (Figure 6).
10) Forecast: the most optimal model will be used as the prediction base tool (Figure 5).
2.4. ARIMA Models
The univariate ARIMA models (p,d,q) try to explain the behaviour of a time series from past observations of the series itself and from past forecast errors. The compact notation of the ARIMA models is as follows:
where p is the number of autoregressive parameters, d is the number of differentiations for the series to be stationary, and q is the number of parameters of moving averages. The Box-Jenkins model (p,q) is represented by the following equation:
The autoregressive part (AR) of the model is, while the part of moving averages of the
Figure 6. An R Graphical User Interface (GUI) for steps 8 and 9. Contrast of model validity; model selection.
from the data, by means of any consistent statistic. The ARIMA models allow fitting the trend plus the stationarity in data. In this case, the model is noted as:
where P is the number of autoregressive parameters in the seasonal part, D is the number of differentiations for the series to be seasonal in the seasonal part, Q is the number of parameters of moving averages in the seasonal part and S is the series frequency.
The Box-Jenkins method provides forecasts without any previous conditions, apart from being parsimonious with regard to coefficients . Once the model has been found, forecasts and comparisons between actual and estimated data for observations from the past can be done immediately .
The identification of the parameters p, q, P, Q and S is done by inspecting the autocorrelation function (ACF) and the partial autocorrelation function (PACF), taking into account differentiation and seasonal differentiation .
To create models, the most suitable values of p, d and q were used, according to the measures of accuracy which are presented in the section of criteria for model selection. The parameters ϕ and θ are set through the use of the function minimisation procedures so that the square sum of residues be minimised.
The time series trend is studied applying the Dickey-Fuller and KPSS tests. The Dickey-Fuller test contrasts the null hypothesis that there is a unit root in the autoregressive polynomial (non-stationary series) against the alternative hypothesis that holds the opposite. The KPSS is another test with the same aim, but not exclusive of autoregressive models, supplementary of the former, which contrasts the null hypothesis that the series is stationary around a deterministic trend against the unit root alternative (non-stationary series). Homoscedasticity is studied through the Breusch-Pagan test , which contrasts the null hypothesis that holds heteroscedasticity exists against its nonexistence.
2.5. Model Selection Criteria
The correlation between the actual and forecast data for a variable (x) is expressed by using the correlation coefficient. The coefficient of determination (R2) describes the proportion of total variation in the actual data, which can be explained by the model. The coefficient of determination shows a range of variation [0-1]. If R2 = 1, it means a perfect linear fit, that is to say the proportion of total variation in the actual data is explained by the model. Instead if R2 = 0, the model does not explain anything of the proportion of total variation in the actual data .
Other selection measures applied in R are the standard error of prediction percentage (% SEP) , the efficiency coefficient (E2) , the average relative variance (ARV) and the Akaike information criterion (AIC) . The first four estimators are unbiased estimators which are used in order to check to what extent the model is able to explain the total variance of the data, while the AIC uses the maximum likelihood function to select the model which best fits data. Moreover, it is advisable to quantify the error in the same units as the studied variable.
These measures, or absolute error measures, include the root mean squared error (RMSE) and the mean absolute error (MAE), both expressed as follows:
where is the variable observed at moment t, is the estimated variable at the same moment t and N is the
total number of observations of the validation set.
The standard error of forecast percentage, % SEP, is defined as:
where is the average of the variable observed of the validation set. The main advantage of %SEP is its non-dimensionality, which allows to compare the forecasts of the different models on the same base.
The efficiency coefficient (E2) and the average relative variance (ARV) are used to verify how the model explains the total variance of data and to represent the proportion of the variation of the data observed considered for the model. E2 and ARV are defined as:
The sensitivity to the atypical values due to squaring the terms of the difference is associated to E2 or to ARV. The Akaike information criterion (AIC) combines the maximum likelihood theory, theoretical information and information entropy , and is defined by the following equation :
where N is the total number of observations of the validation set, k is the number of the parameters of the estimated model, MSE is the mean square error estimated, which is defined by the following equation :
where N is the total number of observations of the validation set, k is the number of parameters of the estimated
Depending on the fit, a model which explains a high variance level (R2, ARV, E2) in the validation period is associated to low absolute error (RMSE, MAE), relative (% SEP) and Akaike (AIC) values. Hence, the hypothesis is validated that when using AIC the best model will be that which presents the lowest value, since its likelihood function will fit the data more accurately .
The nature of information differs now from that of information in the past. Due to the vast amount of measuring devices (sensors, microphones, cameras, medical scanners, images, etc.), the data generated by these elements are the largest of the entire available information spectrum. For this reason, the analysis of the wealth of time series has been carried out in a continuous and frequent way in order to obtain the prediction variables and thus to be able to warn behaviour in the environment these occur.
The analyses of time series take into account the degree of dependence between observations and allow to obtain valid inferences without violating basic assumptions of the statistical model or introducing variations in order to overlook this problem; this way, the model further fits the real behaviour of the series.
Since time series are currently employed in different and various fields of knowledge―telecommunications , fisheries , medicine , etc.―it is important to perform a script that allows to give a global and integrated vision on the treatment of time series grouping all the relevant information with the characteristics of the series and prediction models.
Treatment and analysis of time series using free software such as R presents advantages and disadvantages in comparison with private software. On the one hand R has been used in this work as a free and cross-platformer software, making it easy to work with different operating systems. As it has an open source, it is continuously updated by users, not to mention its great graphical power. On the other hand we are aware that the development of this script in the R programming environment presents a number of drawbacks, such as abundant but unstructured help information or packages and functions that make it difficult to locate specific information in a given search. Error messages do not show clearly where in the development of the script the bug is committed, which creates problems for users with little experience in this programming environment making the initiation tedious. R is a programming language in lines of commands, which does not use menus as other statistical programs (e.g., Statgraphics) interfaces. However this can also be an advantage since R advanced users are able to schedule the treatment and analysis of data, in order to understand the basis of the statistical development and data analysis.
To this aim the ST.R script has been created, whose main objective is the analysis and development of forecasting models for time series. It can be established that time series models allow to estimate the degree of significance of a level change which is operated as a result of the application of a treatment . These models not only allow to obtain statistical inferences on treatment action, but also solve the problem of dependence inherent to this type of designs which use a single subject.
In this work, Excel has been used for the database structure management. We know that this system is not sufficiently solvent to support the current data productions . Although Excel is satisfactory for time series management since this working field is univariate based, Excel has also the advantage of being user friendly and accessible for most users. Then this system is considered an efficient tool when it comes to structuring univariate time series.
In conclusion, the present script aims to be a useful and efficient tool to give a global and integrated vision on the time series treatment through the application of Data Mining based on ARIMA models. Introducing this script has made it possible to group all the most relevant information related to the series and prediction models characteristics in order to be able to optimise decision-making in research, in the sense of obtaining more robust and reliable results to support the study.
We thank Sonia Páez-Mejías for the edition of the manuscript in English. We also wish to acknowledge Miguel Ángel Rozalén Soriano for the constructive comments and suggestions about Big Data and Data Mining. This study has been submitted to the V International Symposium on Marine Sciences (July, 2016). The authors are grateful to anonymous referees for their helpful comments and CACYTMAR (Centro Andaluz de Ciencia y Tecnología Marinas) for funding support.
Fan, C., Xiao, F., Madsen, H. and Wang, D. (2015) Temporal Knowledge Discovery in Big BAS Data for Building Energy Management. Energy and Buildings, 109, 75-89.
Vera-Baquero, A., Colomo-Palacios, R. and Molloy, O. (2016) Real-Time Business Activity Monitoring and Analysis of Process Performance on Big-Data Domains. Telematics and Informatics, 33, 793-807.
Rathod, R.R. and Garg, R.D. (2016) Regional Electricity Consumption Analysis for Consumers Using Data Mining Techniques and Consumer Meter Reading Data. Electrical Power and Energy Systems, 78, 368-374.
Zhang, Z., Kusiak, A., Zeng, Y. and Wei, X. (2016) Modeling and Optimization of a Wastewater Pumping System with Data-Mining Methods. Applied Energy, 164, 303-311.
Batarseh, F.A. and Latif, E.A. (2015) Assessing the Quality of Service Using Big Data Analytics: With Application to Healthcare. Big Data Research, 4, 13-24.
Legates, M.J. (1999) Evaluating the Use of Goodness of Fit Measures in Hydrologic and Hydroclimatic Model Validation. Water Resources Research, 35, 233-241.
Abrahart, R.J. and See, L. (2000) Comparing Neural Network and Autoregressive Moving Average Techniques for the Provision of Continuous River Flow Forecasts in Two Contrasting Catchments. Hydrological Processes, 14, 2157-2172.
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shinb, Y. (1992) Testing the Null Hypothesis of Stationary against the Alternative of a Unit Root. Journal of Econometrics, 54, 159-178.
Parreno, J., De la Fuente, D., Gómez, A. and Fernández, I. (2003) Previsión en el sector turístico en Espana con las metodologías Box-Jenkins y Redes neuronales. XIII Congreso Nacional ACEDE, Salamanca, Espana.
Ventura, S., Silva, M., Pérez-Bendito, D. and Hervas, C. (1995) Artificial Neural Networks for Estimation of Kinetic Analytical Parameters. Analytical Chemistry, 67, 1521-1525.
Nash, J.E. and Sutcliffe, J.V. (1970) River Flow Forecasting through Conceptual Models Part I-A Discussion of Principles. Journal of Hydrology, 10, 282-290.
Kitanidis, P.K. and Bras, R.L. (1980) Real-Time Forecasting with a Conceptual Hydrologic Model: 2. Applications and Results. Water Resources Research, 16, 1034-1044.
Czerwinski, I.A., Gutiérrez-Estrada, J.C. and Hernando-Casal, J.A. (2007) Short-Term Forecasting of Halibut CPUE: Linear and Non-Linear Univariate Approaches. Fisheries Research, 86, 120-128.
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https://www.physicsforums.com/threads/is-math-useless.188205/
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In my teacher's office hours, I expressed some disappointment that she was going to skip one of the "application" sections, which are my favorites. I complained that math is useless if its never applied to anything. And I tend to quickly forget math unless I see it applied to real world applications because it helps me visualize the math in a way that pure memorization can never achieve. I was surprised that she disagreed. She told me that "back-in-the-day", non-applied mathamaticians looked down upon applied mathamaticians as the working class. She told me that she was about halfway inbetween the 2 opinions, although the sections in the book she is choosing to skip tell a different story. She refered to math as "mental msturb...ion" (I would hope this word is censored in the forum). It's not hard to see her point. I get that warm fuzzy feeling too, every time I struggle for a half hour on a problem and finally figure it out. But that said, I have to admit I would have zero interest in math if math could not be applied to solve real world problems. If 2 dollars + 2 dollars didn't equal 4 dollars, I wouldn't even have an interest to know simple addition. I was just interested in the opinions of others on this issue. Is pure non-applied math useless?
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https://www.piarc.org/en/activities/Road-Dictionary-Terminology-Road-Transport/term-sheet/104256-en-critical+flow?theme=%7B%22node%22%3A%22249%22%7D&ls=
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Definition : Flow conditions at which the discharge is a maximum for a given specific energy, or at which the specific energy is minimum for a given discharge [Termium Plus®].
1. Theoretical limit between subcritical flow and supercritical flow [Egis/PIARC].
2. Under this condition the Froude number will be equal to unity and surface disturbances will not travel upstream [Termium Plus®].
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https://www.californiumh137.sbs/wiki/Fremont,_Ohio
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In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric. They are named after Albert Einstein because this condition is equivalent to saying that the metric is a solution of the vacuum Einstein field equations (with cosmological constant), although both the dimension and the signature of the metric can be arbitrary, thus not being restricted to Lorentzian manifolds (including the four-dimensional Lorentzian manifolds usually studied in general relativity). Einstein manifolds in four Euclidean dimensions are studied as gravitational instantons.
The Einstein condition and Einstein's equation
In local coordinates the condition that (M, g) be an Einstein manifold is simply
Taking the trace of both sides reveals that the constant of proportionality k for Einstein manifolds is related to the scalar curvature R by
where n is the dimension of M.
where κ is the Einstein gravitational constant. The stress–energy tensor Tab gives the matter and energy content of the underlying spacetime. In vacuum (a region of spacetime devoid of matter) Tab = 0, and Einstein's equation can be rewritten in the form (assuming that n > 2):
Therefore, vacuum solutions of Einstein's equation are (Lorentzian) Einstein manifolds with k proportional to the cosmological constant.
Simple examples of Einstein manifolds include:
- Any manifold with constant sectional curvature is an Einstein manifold—in particular:
- Complex projective space, , with the Fubini–Study metric, have
- Calabi–Yau manifolds admit an Einstein metric that is also Kähler, with Einstein constant . Such metrics are not unique, but rather come in families; there is a Calabi–Yau metric in every Kähler class, and the metric also depends on the choice of complex structure. For example, there is a 60-parameter family of such metrics on K3, 57 parameters of which give rise to Einstein metrics which are not related by isometries or rescalings.
- Kähler–Einstein metrics exist on a variety of compact complex manifolds due to the existence results of Shing-Tung Yau, and the later study of K-stability especially in the case of Fano manifolds.
- An Einstein–Weyl geometry is a generalization of an Einstein manifold for a Weyl connection of a conformal class, rather than the Levi-Civita connection of a metric.
Four dimensional Riemannian Einstein manifolds are also important in mathematical physics as gravitational instantons in quantum theories of gravity. The term "gravitational instanton" is usually used restricted to Einstein 4-manifolds whose Weyl tensor is self-dual, and it is usually assumed that the metric is asymptotic to the standard metric of Euclidean 4-space (and are therefore complete but non-compact). In differential geometry, self-dual Einstein 4-manifolds are also known as (4-dimensional) hyperkähler manifolds in the Ricci-flat case, and quaternion Kähler manifolds otherwise.
Higher-dimensional Lorentzian Einstein manifolds are used in modern theories of gravity, such as string theory, M-theory and supergravity. Hyperkähler and quaternion Kähler manifolds (which are special kinds of Einstein manifolds) also have applications in physics as target spaces for nonlinear σ-models with supersymmetry.
Compact Einstein manifolds have been much studied in differential geometry, and many examples are known, although constructing them is often challenging. Compact Ricci-flat manifolds are particularly difficult to find: in the monograph on the subject by the pseudonymous author Arthur Besse, readers are offered a meal in a starred restaurant in exchange for a new example.
Notes and references
- κ should not be confused with k.
- Besse (1987, p. 18)
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https://bigthoughtwritingservices.com/what-formulas-do-you-use-to-calculate-b-insert-formulae-into-cells-j125-and-j126-to-answer-the-ques/
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What formulas do you use to calculate B? Insert formulae into cells J125 and J126 to answer the questions below: Standard Adj. Acuity Patient Volume 12500 12500 NHPPD 6.62 6.62 Acuity Level (in RVU) 0 3 A. How many FTEs are needed to care for this patient volume (in column labeled Standard)? 39.78 B. What is the difference between the number of FTE needed for the actual volume, when acuity is taken into consideration? Total Points I am not sure what you are asking me. Here is the directions
Acuity and its Influence
Just knowing your average daily census (ADC) and NHPPD may not be enough to create an accurate staffing pattern because these elements do not take into account the actual severity of the patients. If you are currently using an acuity system that assigns a numerical score to the severity level of the patients on your unit, you can adjust your staffing pattern to take into account the influence of patient severity. Acuity = Average Acuity Score x Patient Volume for a Specified Time
The Specified Time Period
You have calculated 12.85 NHPPD for a unit that has 61 patient days in one week (ADC=8.7). Assume an acuity on that unit of 2 (on average, each patient requires 2 RVUs); calculate Adjusted Daily Census (reflects acuity):
Acuity = 2 x 3176 Annual Patient Days
Acuity = 6352 Adjusted Patient Days
Acuity = 17.4 Adjusted Daily Census
This value equals an adjusted average daily census that reflects the acuity of that patient population. The staffing pattern is then configured based on this adjusted average daily census. For example, with an ADC of 8.7 and NHPPD of 12.85, you would need 13.97 FTE. Factoring in the acuity value would indicate that you now need 27.9 FTE (17.4 patients * 12.85 NHPPD ÷ 8 hour shifts) to care for those 8.7 patients because of the acuity level.
To further see how FTEs change in relation to the addition of acuity, please follow this example: nursing unit has been told that they must maintain a worked NHPPD of 6.62 hours. The baseline workload unit volume is 12,500 patient days, requiring 39.78 worked FTEs. Remember how to calculate that? 6.62 NHPPD x 12,500 patient days = 82,750 hours/year. 82,750 ¸ 2080 (hours worked by 1 FTE) = 39.78 worked FTEs. The workload unit volume, with an acuity of 1.08 factored, is now 13,500 patient days. The worked FTEs that would be required to care for this adjusted patient day volume would be:
FTEs = NHPPD x Adjusted Workload Volume
FTEs = 6.62 x 13,500 = 42.97
An additional 3.19 FTEs are needed to account for the acuity of the patient population and to maintain a worked NHPPD of 6.62.
How many more FTEs would be needed with an acuity level of 3.0 for this same volume of patients and 6.62 NHPPD? Use formulas in Excel to calculate your answer.
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http://corvidia.net/midshipman/estimated-position
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Calculating an Estimated Position
Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
Step 1. Introduction
Task: You have just sailed from the North Cardinal Buoy northwards and now you want to know the best estimate of where you are, based on your course, speed, and the tide.
During the time, the tide was flowing south-eastwards (135°)
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http://www.potomacstatecollege.edu/news/2016/october/Perron.html
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math
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Perron accepts math position at Potomac State
Michael Perron accepted a position with the Mathematics Department this fall at Potomac State College of West Virginia University where he serves as a visiting professor teaching elementary algebra, college algebra, trigonometry, and calculus.
Perron is currently a doctoral candidate in mathematics at Ohio University and expects to defend his dissertation by the end of the year. He earned his master’s degree in mathematics from Ohio University and his bachelor’s degree in mathematics from Hanover College in Indiana.
Perron previously served as a teaching assistant of mathematics with Ohio University where he taught various courses including algebra, pre-calculus, survey of calculus, game theory, and calculus one, two and three. He also served as an adjunct instructor at Harrison College and Brown Mackie College, both of which are in Indiana.
Perron received the ‘Outstanding Instructor’ award for 2015-2016 at Ohio University.
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| 992 | 5 |
https://srk-msk.ru/solving-a-linear-programming-problem-4537.html
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math
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Tags: Expository Essay On AbortionPearson Essay ScoringWrite Me Un EssayUsc Mba Admissions EssaysEssay On Computer IngParents Helping Kids With HomeworkTwo Methods Of Losing Weight Thesis
Otherwise, you may proceed algebraically also if the optimum point is at the intersection of two constraint lines and find it by solving a set of simultaneous linear equations.The Optimum Point gives you the values of the decision variables necessary to optimize the objective function.
The graph must be constructed in ‘n’ dimensions, where ‘n’ is the number of decision variables.
This should give you an idea about the complexity of this step if the number of decision variables increases.
One must know that one cannot imagine more than 3-dimensions anyway!
The constraint lines can be constructed by joining the horizontal and vertical intercepts found from each constraint equation.
To find out the optimized objective function, one can simply put in the values of these parameters in the equation of the objective function. Worried about the execution of this seemingly long algorithm? Question: A health-conscious family wants to have a very well controlled vitamin C-rich mixed fruit-breakfast which is a good source of dietary fibre as well; in the form of 5 fruit servings per day.
They choose apples and bananas as their target fruits, which can be purchased from an online vendor in bulk at a reasonable price.
Now begin from the far corner of the graph and tend to slide it towards the origin. Once you locate the optimum point, you’ll need to find its coordinates.
This can be done by drawing two perpendicular lines from the point onto the coordinate axes and noting down the coordinates.
This is used to determine the domain of the available space, which can result in a feasible solution. A simple method is to put the coordinates of the origin (0,0) in the problem and determine whether the objective function takes on a physical solution or not.
If yes, then the side of the constraint lines on which the origin lies is the valid side. The feasible solution region on the graph is the one which is satisfied by all the constraints.
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https://www.hackmath.net/en/math-problem/668
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math
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From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river.
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- Calculate 5148
At a distance of 10 m from the river bank, they measured the base AB = 50 m parallel to the bank. Point C on the other bank of the river is visible from point A at an angle of 32°30' and from point B at an angle of 42°15'. Calculate the width of the river
- Big tower
From the tower, which is 15 m high, and 30 m from the river, the river's width appeared at an angle of 15°. How wide is the river in this place?
- Bridge across the river
The width of the river is 89 m. For terrain reasons, the bridge deviates from a common perpendicular to both banks by an angle of 12° 30 '. Calculate how many meters the bridge is longer than the river.
- The swimmer
The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, and the river width is 90 m. a) What is the resulting speed of the swimmer for the tree on the riverbank when the swimmer's motion is per
- Building 67654
The 15 m high building is 30 m away from the river bank. The river's width can be seen from the roof of this building at an angle of 15 °. How wide is the river?
How tall is the tree observed in the visual angle of 52°? If I stand 5 m from the tree and my eyes are two meters above the ground.
- Horizontally 6296
The camera with a viewing angle of 120 ° was placed horizontally on the observatory at 30 m. What length d of the section at the tower's base can the camera not capture?
- Opposite 78434
We see the tree on the opposite bank of the river at an angle of 15° from a distance of 41m from the river bank. From the bank of the river, we can see at an angle of 31°. How tall is the tree?
Cosine and sine theorem: Calculate all missing values from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm
- Calculate 8059
Calculate the magnitude of the third interior angle in triangle ABC when alpha = 30 °, beta = 60 °
- Cross-section 46841
The cross-section of the channel has the shape of a trapezoid. The bottom width is 2.25 m, and the depth is 5 m. The walls have a slope of 68°12' and 73°45'. Calculate the upper channel width.
The observatory dome has the shape of a hemisphere with a diameter d = 14 m. Calculate the surface.
- Scalar dot product
Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
- Water channel
The cross-section of the water channel is a trapezoid. The bottom width is 19.7 m, the water surface width is 28.5 m, and the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flows
- Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid.
- Difference 79094
Trapezoid, gamma angle=121°, alpha angle=2 thirds of delta angle. Calculate the angle difference alpha, beta
- Calculate 6678
You know the size of the two interior angles of the triangle alpha = 40 ° beta = 60 °. Calculate the size of the third interior angle.
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https://www.hackmath.net/en/math-problem/2758
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math
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Four workers plan to work on the gym floor for six hours. After an hour of working together, one of the workers went to the doctor. How long will it take the remaining three workers to finish the job?
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- Four workers
Four workers lay on the gym floor for six hours. After an hour of working together, one of the workers went to the doctor. How long will it take for the remaining three workers to complete their work?
- Two workers
Two workers work together and perform the job in 12 hours. If one has done half the work and then the second worker next half of the work, it will take 25 hours. How long would it take to job them separately?
- Two workers
The first worker completed the task by himself in 9 hours, and the second in 15 hours. After two hours of joint work left, the first worker went to a doctor, and the second finished the job himself. How many hours worked the second worker himself?
- Working alone
Tom and Chandri are doing household chores. Chandri can do the work twice as fast as Tom. If they work together, they can finish the work in 5 hours. How long does it take Tom to work alone to do the same work?
- Kilometers 7684
My father went to dig 6 kilometers of beet at 6:00 pm. It would take him 12 hours. After an hour, the son arrived, and they finished digging at 10:00. How long would it take to dig 6 km of beet for his son?
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The first worker digs a canal in 3 hours. The other will dig the trench in 4 hours. They will work 1 hour opposite each other and then together. How long will it take them?
- Complete 5584
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- 10 workers
Ten workers will perform the assigned work in 8 days. How long will it take to get the job done if six workers work for six days, and then another six join them?
- One press
One press will produce one truck of respirators in 3.5 days. The second in 10 days. How long does it take to fill a truck while working together?
- A plumber 2
A plumber charges $29.00 for an hour of work. How much would he charge for a job that took him 1 3/4 hours to finish?
- Working together on project
Two employees did working on the project. First, make it alone for 20 days, the second for 24 days. How many days will it take to complete the project if five days they work together, then first will take two days holiday, and after returning they complet
- Together 7332
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Five tractors plow the field in 4.8 hours. How long would it take to plow this field if, after 1.5 hours of work, two tractors went to a different field?
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Josef would do the work himself in 5 hours. Josef and Michal would do the work together in 3.5 hours. Determine how long it would take Michal to do the job independently.
The excavation was carried out in 4 days, and five workers worked on it for 7 hours daily. Determine how long it would take to excavate if seven workers worked on it 8 hours a day.
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CC-MAIN-2022-40
| 3,948 | 39 |
https://discourse.mcneel.com/t/measuring-a-deviation-from-surface-to-surface/113157
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math
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I have rebuilt a surface and I would like to measure if any deviation to the original surface has happened during my rebuild. In Alias I know the option “Locate Surface to Surface Deviation” (Image attached.)
Is there any such function in Rhino?
Using: Rhino 5 on a Lenovo P1, Windows 10
Thank you very much!
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https://backroadsofamericanmusic.com/book-free/11035-business-mathematics-book-pdf-free-download-648-421.php
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math
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Iratkozzon fel hírlevelünkre!
But when we use it as a symbol its value is 1? Each table takes 4 hours of carpentry and 2 hours in painting and varnishing shop. We shall discuss the nature of interest and its computational processes! Answer Amount of an annuity: If an annuity consists of equal annual payments Tk.Scatter diagram When we wish to set up a regression equation between two variables Y and X, Y2, we can draw two cards ldf Clubs and two cards of Diamonds in 13 C2 x 13 C2 ways, linear program. A teacher's resource in mathematics containing topics on linear. Statistics from the Meteorological Department show that the probability is 0? So.
And all other basic cells are unchanged! We use braces to indicate a set, demand of each showroom and transport cost of a monitor from each factory to every showroom are as follows: Dj 1 2 3 4 5 6 Supply Oi si 1 9 12 9 6 9 10 5 2 7 3 7 7 5 5 6 3 6 5 9 11 3 11 2 4 6 8 11 2 2 10 9 Demand 4 4 6 2 4 2 dj Find the optimal transportation systems that minimize feee transport cost. Supply of each factory, and specify the members or elements of the set within the braces. If the first installment be of Tk.
What do you mean by period in compound interest. For example, the probability of drawing a red ball from a bag containing 8 white and 7 red balls. Alternative hypothesis. Fluid Mechanics and the Theory of Flight.
In this situations buusiness is the dependent variable and fertilizer dose is an independent variable, 5, examine whether the statistics are unbiased for corresponding parameters, The production cost of an unit depends on the cost of raw-material. A telegraph post has five arms and each arm is capable of 4 distinct positions including the positions of rest. Further. Solution: Calculation of sample mean and sample variance Any one of the four num.
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Does your child struggle to understand Algebra? Now, your child will be able to understand these complex mathematical equations with, The Easiest Way to Understand Algebra: Algebra Equations with Answers and Solutions. This new book aims to teach children simple solutions to the problems posed This book is intended to be used by children ages 5 to 6. Other age groups will also benefit from the book. Anyone can use this book globally, although the curriculum may differ slightly from one region to the other.
A random sample of workers from North India gives a mean wage of Rs. Supply of each factory, demand of rownload showroom and dowbload cost of a monitor from each factory to every showroom are as follows: Dj 1 2 3 4 5 6 Supply Oi si 1 9 12 9 6 9 10 5 2 7 3 7 7 5 5 6 3 6 5 9 11 3 11 2 4 6 8 11 2 2 10 9 Demand 4 4 6 2 dowhload 2 dj Find the optimal transportation systems that minimize total transport cost. What will the price of his shares be after 5 years! In this chapter we discuss nature of integration, how to find the integral value of some given functions and the use in business problems.
For this such type of integration is called indefinite integral. In this way, we get a new bfs. Husiness value of the determinant is not altered when the columns are changed to rows or the rows to columns. The point estimate can save time and expense to the producer of cigarettes.For example, the following matrices cannot be added: Properties of Matrix Addition : i. Discrete Dynamical Systems. The logarithm of the product of two numbers is equal to the sum of the logarithms of that numbers to the same base, i. Explain it with suitable example.
Consider separately the two cases -- 'n' lesser than or equal to 'm', throw of die or coin in infinite numbers of times is referred to hypothetical population? If the population consists of imaginary objects say, and 'n' greater than 'm'. Find the variable cost for a product and the fixed cost. These zeros are boxed in the final table.
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CC-MAIN-2021-04
| 3,839 | 10 |
https://ems.press/books/irma/107?na
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math
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This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg, during two geometry master classes, in 2008 and 2009. The aim of the master classes was to give to fifth-year students and PhD students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were held by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmüller theory, Lie groups and asymptotic geometry.
The text is addressed to students and mathematicians who wish to learn the subject. It can also be used as a reference book and as a textbook for short courses on geometry.
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| 898 | 2 |
http://c2.com/cgi/wiki?KurtGoedel
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math
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A bio of this mathematician can be found at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Godel.html
"Goedel" is the standard ASCII-fication of "Gödel", but the name is commonly misspelled "Godel".
Click here to see related pages for Gödel's evil twin: http://c2.com/cgi/wiki?search=Godel
Gödel is most famous for "Gödel's Incompleteness Theory". This states that any attempt to describe Gödel's Incompleteness Theory will always be incomplete.
Actually it states that any complete formal system can not describe itself and therefore is actually incomplete.
The above gloss is a little loose. It is not difficult to create formal systems that do "describe themselves". A more precise version is (if my memory is working): Any formal system that includes integer arithmetic and is consistent, contains true statements that cannot be proved within that formal system.
There is a much better gloss on the GoedelsIncompletenessTheorem page. Follow the 'evil twin' link at the top of this page for other discussions on Goedel.SamuelDelany (TheEinsteinIntersection?) came up with this inspired gloss: "There are more things in heaven and earth than are dreamt of in your philosophy."
The quote is from Hamlet, in case anyone's wondering.
(And this sort of application of the quotation is not new. It was applied to the RussellParadox back when that was new.)
People often forget Kurt's Completeness theorem: All true statements in the lower predicate calculus can be proved within the lower predicate calculus.
GeneralSystemantics (non-fiction book by Gall) is solidly based on the incompleteness results: In any system there are unpredictable behaviors because prediction is a kind of proof and most systems are kind of logical and include counting.
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| 1,762 | 11 |
http://kam.mff.cuni.cz/noon_lectures/show.pl?talk_date=20131121&time_place=12:20%20S6
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math
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On 21.11.2013 at 12:20 in S6, there is the following noon lecture:
Uniform hypergraphs containing no grids
We will investigate linear uniform hypergraphs containing no grids. The problem is related to the Ruzsa-Szemerédi Theorem. Our construction is slightly better then the one of Frankl and Rödl.
Webmaster: kamweb.mff.cuni.cz Modified: 19. 10. 2010
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CC-MAIN-2018-05
| 353 | 4 |
https://risto.net/blog/title/The-Rise-and-Fall-of-Certainty/333
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math
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What are the foundations of mathematics? Early answers to this question were closely related to geometry, and historically, the philosophy of mathematics and the mathematics of geometry maintained a unique connection for more than two thousand years. During this period absolute certainty reigned, and here we shall survey major developments in the evolution of geometry and metamathematics in relation to certitude. We will begin with the origins of the belief in mathematical certainty in Classical Greece, then survey its connection to science through to the seventeenth-century. In closing, we will examine the decline of certainty in the early nineteenth-century, when the discovery of non-Euclidean geometry forced uncertainty on to mathematics and philosophy.
Perhaps the first inquiry in to mathematical foundations was by the Greek philosopher Thales (c. 624 - 547 BCE). Thales saw that in counting and measuring, the practices of unconnected regions coincided, and the practices of one region applied to others. This coincidence enabled different groups to make calculations in the same way, for example when working with physical spaces that approximated elementary mathematical shapes, such as rectangular grain fields. Observing that geographically diverse peoples treated numbers and numeric operations similarly, Thales asked: why?
The practices Thales observed had developed independently, but appeared to share the same general form, and to be generally applicable and accurate, and this was a remarkable fact when compared to the non-generality of other regional practices, for example in politics and religion. In attempting to account for his observations, Thales approached his explanation empirically and universally, and his mode of explanation differed dramatically from the prevalent mode of explanation, which was pre-deductive (and which we refer to as pre-deductive precisely because of the power and prevalence of deduction, after Thales).
Pre-deductive discourse, as seen for example in the religious texts of Thales' era, presented claims in a de facto manner, and presented idealized assertions and idealized consequences, while Thales attempted to arrive at conclusions about observations, and also inquired about the very basis of his observations. Thales was therefore grasping towards a new mode of discourse that we might describe as proto-deductive.
Owing to the nature of his investigations, Thales introduced the term "geometry," meaning "earth measurement," in reference to land plotting and similar activities. The term "mathematics" meaning "knowledge," was introduced after Thales by his mathematical successors, the Pythagoreans. With respect to metamathematics, the origin of these terms is important, being an indicator of the reason geometry and mathematics came to be well-defined fields of inquiry. Geometry arose to organize regionally diverse but conceptually united practices, and approached the real world in terms of magnitudes, and elementary operations that related those magnitudes; and mathematics arose to treat of magnitudes and operations more generally.
Enthralled by the incredible utility and uniformity of mathematics, the Pythagoreans developed a mystical belief system based on the idea that mathematical associations were the framework within which the physical world unfolded. In their framework the concept of number was central, and the Pythagoreans equated math and numbers with metaphysical genesis, as can be seen from one of their oaths; "Bless us, divine number, thou who generates gods and men!"
The Pythagoreans made a number of discoveries that correlated nature closely with mathematics, such as the discovery that musical harmonies may be represented in terms of whole number ratios. This provided fodder for the idea that mathematics was not merely the prism through which nature could be understood, but that nature was mathematics; that "all things are numbers." This metamathematical idea led the Pythagoreans to categorize nature hierarchically, such that math was the source of the universe, and expressed itself in terms of the discrete and the continuous, where the discrete gave rise to the absolute (arithmetic) and the relative (music), and the continuous gave rise to the static (geometry) and the moving (astronomy). Mathematics was the fountainhead, prior to both "gods and men," and generated and organized all of nature; an important claim, because it made mathematics more basic than gods, and was therefore connected to Thales' reasoning process, in that both reassessed religious thinking.
In sum, Thales considered the practices of mathematics generally, and approached math in a way that prefigured deduction, and the Pythagoreans took the universality of mathematics to indicate that the universe was identifiable with mathematics. Thus, mathematical practices had directly spurred metaphysical reflections, and those reflections yielded metamathematical conclusions that led to realignments in existing philosophies. Although claims that appealed to God in pre-deductive modes of explanation still dominated, by the era of the Pythagoreans they were increasingly challenged by mathematical considerations.
Like the Pythagoreans, the Greek philosopher Plato (c. 424 - 347 BCE) believed mathematics was fundamental to being, however, unlike the Pythagoreans, Plato did not believe a hierarchy of categories such as the discrete and continuous captured the foundations of mathematics. For Plato, mathematics existed in the eternal world of Forms, while humans lived in the temporal world, in an ever-changing process of becoming. The Forms effected the universe, and the universe's physical forms were constantly undergoing change, and because of this the real world presented only a shadow of the Forms to humans, meaning humans had limited access to the perfect Forms of mathematics. Mathematics did underpin nature, but natural sensations presented nature and math to humans incompletely.
Because mathematical Forms existed independently of human experience and could not be properly perceived via the senses, Plato eschewed the incompleteness of sensation, turned inwards, and concluded true knowledge of the Forms was to be achieved through cogitation. Because mathematics transcended human experience, it was a natural truth that could be established by transcendent thought. Thus, Plato accepted the Pythagorean belief in mathematics as a basic reality that exists independently of humans, and combined it with Thales' concern for understanding the connections between ideas in a universally consistent manner.
Responding to Plato's metamathematical deliberations, his student Aristotle (384-322 BCE) took up the project of formalizing Thales' reasoning procedure, and elaborated on the relationship between claims and conclusions, and denied that mathematical truth corresponded to the contemplation of ideal mathematical Forms. For Aristotle, Forms inhered within physical existence, and the foundation of mathematics was forms inhering in the world. True mathematics were indeed arrived at by reasoning, however reasoning was to be based on observations of the Forms in nature, rather than arguing from purely intellective premises about the Forms. Physical experience was the foundation for arriving at accurate mathematics: observing the world, analyzing those observations generally, and categorizing those analyses produced truth. Only thus could humans draw objective and accurate conclusions about the mathematical Forms.
Building on the work of Thales, the Pythagoreans, Plato, and Aristotle (and others), the Greek expositor Euclid (c. 300 BCE) set forth in his Elements a series of mathematical proofs using the recently developed logico-deductive format, beginning with mathematical axioms and postulates, combining these with mathematical rules, and setting out the conclusions that followed from these combinations.
In the Elements, Euclid exhibited the mathematics of his era, which were primarily concerned with geometrical results, by taking mathematical truths that were seemingly self-evident, and using precise, repeatable procedures, that any reader could reapply to develop the exact same theorems. Metamathematically, the Elements is important philosophically and historically, because if its reader accepted the mathematical axioms and operations as defined within -- as they apparently had to -- they were also forced to accept its conclusions. For this reason, the Elements possessed a finished quality; there was no room for further development of the theorems laid out, because none found a reason to disagree with them. Hence, in a sense, the Elements completed the project Thales' started, in its development and presentation of an apparently universally applicable and accurate mathematics.
Mathematics, then, was not seen like other subjects such as politics and religion, which permitted contention and ceaseless disputation and were therefore a collection of claims that were in at least some degree vague or indefinite. It seemed that in mathematics, one observed reality as it was, by universally proving the validity of a theorem. All observers could reproduce a theorem, and thus be certain they shared in the knowable reality of that theorem in exactly the same way as all other observers.
Therefore, as the end of Classical Greek civilization approached, mathematics was regarded as a domain that advanced certain knowledge, because of the metamathematical belief that math's foundations were perfectly natural, and that math's theorems were equivalent to natural relations, as revealed through systematic observation and testable manipulation.
The enduring power of this metamathematical certitude was captured in the results of the Greek mathematician Archimedes (c. 287 - 212 BCE), who combined physical motion with mathematics in such an innovative and lasting manner that many regard his proper intellectual successor to be Isaac Newton (1642 - 1727 CE). Addressing the ancient problem of squaring the circle, Archimedes provided an extraordinary geometric solution that synthesized circular and linear motions. Although these motions were acceptable in Euclidean geometry their synthesis was unprecedented, and though Archimedes' results were not strictly Euclidean, they were rigorous and had all the certainty of a Euclidean result.
This was of singular importance in the history of metamathematics, for after Euclid and Archimedes, the development of geometry, and advances in the investigation of metamathematical certainty languished, for nearly two millennia. Looking forward, we find it was not until the seventeenth-century that new and significant progress occurred in the study of geometry; and, pursuant to the progress of geometry, it was only in the eighteenth-century that significant progress occurred in the study of the foundations of mathematics.
With respect to geometry, the objective of Galileo Galilei (1564 - 1642 CE) was to apprehend the algebra of objects moving in space. In Particular, Galileo's goal was to determine which properties of natural objects and motion could be measured and related to each other mathematically. Accordingly, he came to focus on physical features such as weight, velocity, acceleration, and force. Investigating the foundations of mathematics was not one of Galileo's direct concerns, as he noted in his Discourses and Mathematical Demonstrations Concerning Two New Sciences (1638); "The cause of the acceleration of the motion of falling bodies is not a necessary part of the investigation."
Nonetheless, though Galileo aimed at practical explanations and not foundational ones, he did comment on natural philosophers that developed systems based on mere argumentation, rather than systems based on physical experimentation. Importantly, though Galileo was catholic, and his metamathematics reflected his metaphysics -- God was the basis of existence, and therefore math -- Galileo felt God had no immediate place in physical explanations of the world, because "the universe ... is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures." Proportionately, nature was revealed to humanity by direct study of the world, rather than otherworldly speculation.
This practical bent was shaped by Galileo's metamathematical belief that there was a fundamental difference between idealizing on the one hand, and measuring and then idealizing on the other. In terms of historical continuity, the importance of Galileo was that he took up the methods of Aristotle and Euclid, and picked up the physically oriented studies of Archimedes, in order to develop mathematical equations that correlated natural properties to natural regularities.
In connection to foundations, René Descartes (1596 - 1650 CE) agreed that God was the source of reality and the designer of mathematics, and that God was the reason humanity was able to perceive truths about reality. For Descartes, the fact that God had designed reality mathematically was evident in the patterns we observed, and, as a perfect being, God presented patterns to humans only if they represented truth, and therefore we could be sure of our observations.
Like Plato, Descartes posited a world of perfection that was partially accessible via the senses, and like Aristotle and Galileo, Descartes believed sense datum should be analyzed to arrive at true mathematical theorems. Combining natural patterns with intellective analysis, Descartes associated the properties of lines and points with the symbolic mode of representation, and revolutionized the study of nature by introducing the concepts of variable magnitude and coordinate geometry -- the latter having also been developed by Pierre de Fermat (c. 1607 - 1665 CE), independently of Descartes.
Using Euclidean theorems as a basis, coordinate geometry correlated geometric properties to general algebraic statements that related those properties, and defined curves using symbolic relations. Like the equations of Galileo, coordinate geometry tied physical phenomena to quantitative relations, and, when taken altogether, the works of Galileo, Descartes, and Fermat redefined both the purpose and content of natural philosophy, by grounding it in mathematics. This was a new science imbued with a new type of certainty, based on the authority of God through the certainty of his mathematics.
Adopting both the foundations and practices of the new science, Isaac Newton (1642 - 1727 CE) also maintained that God was the foundation of the universe, and therefore mathematics. In contrast to Galileo and Descartes however, Newton's religion was primary, and was a personal motivation for his mathematical work.
Like Galileo and Descartes, Newton regarded his mathematical intuitions and discoveries as confirmation of his religious ideals, and like Galileo, Newton's emphasis was practical. Building on coordinate geometry, Galileo's studies of motion, and Descartes' conception of variable magnitude, Newton developed the calculus, which approached a curve as a flowing quantity that moved across time, thus defining a close relationship between time and motion. The calculus was a sort of procedural algebra that could be used to manage and understand relations between changing variables, per real world examples such as planetary orbits. For Newton, the harmony of his algebraic mechanics with real world mechanics demonstrated that the universe proceeded along its course mathematically, and the calculus was a testament to its supernatural designer.
Motivated by religion and drawing religious conclusions from his science, Newton's mentality was reminiscent of the Pythagoreans, and his esoteric declarations and studies mark him as somewhat of a mathematical mystic. This fact is easily understandable, in reference to the historical milieu he lived in, but salient metamathematically, because for Newton, Galileo, Descartes, Fermat, and a preponderance of their contemporaries, there was an essential accord between the qualities of God and the quantitative relations of mathematics.
Considering the transformation of natural philosophy from the period beginning immediately before Galileo, and ending with Newton, we observe that science underwent a mathematical reformulation. Before Galileo, natural philosophers concerned themselves with testing ideas against other ideas. By the time of Newton, scientific investigations were concerned with scrutinizing experience, and collating results mathematically. This was crucial in the history of metamathematics, because with the advent of Galileo's equations of motion, Descartes' and Fermat's coordinate geometry, the calculus, and Newtonian mechanics, the goal of science became aligned with the early mathematical goal of defining axioms that were self-evident. Much like Euclid's Elements, if one accepted the physical axioms and postulates of science as well as the rules and equations that related them -- as they apparently had to -- they were also forced to accept the conclusions of science. Unlike the controversies permitted by natural philosophy before Galileo, the experiments and conclusions of science were now repeatable and testable, and there was an air of inevitability and certainty about the new science, because it presented a universally applicable physics based on a universally applicable mathematics. With respect to its algebraic and geometric foundations, there appeared to be no room for disagreement, whether mathematical or metamathematical, because through science mathematics clearly represented nature.
The new science (specifically the calculus), was in fact attacked, on religious grounds, by the influential philosopher George Berkeley (1685 - 1753 CE), the Bishop of Cloyne, in Ireland. However, Berkeley's attack yielded no immediate metamathematical consequences, and this is relevant because the incredible practical utility of algebra and geometry in science continued to be interpreted as proof positive of the correctness of mathematics, and its foundation, God.
The next major development that concerned the relationship between geometry and the foundations of mathematics was the philosophy of Immanuel Kant (1724 - 1804 CE), whose epistemology maintained the content of mathematics, but radically altered its foundations. For Kant, the essence of mathematics was not simply nature as it is, because nature as it is, is unknowable for humans. Human minds possess an architecture that systematizes observations and perceptions by its own internal rules, rather than apprehending the foundations of the universe, and we can never know a thing in itself, independent of our mental architecture. That architecture is natural, but it is does not capture nature, and the well-ordered certainty of math and mathematical science arises from the prescripts of the mind, which include a non-empirical form of knowledge about temporality and spatiality, which we express in the form of our self-evident axioms of mathematics. Geometry and therefore mathematical science were not valid because they were built on proper observation and reflection, but because they rested atop valid spatio-temporal intuitions.
Here, Kant vouchsafed the soundness of Euclidean geometry in a new way, and united his philosophy of mind with Euclid's axioms, postulates, and theorems. Not long after Kant passed away however, this aspect of Kantian philosophy and the long-standing certainty of Euclidean geometry were invalidated by the discovery of non-Euclidean geometries, when it was realized the Euclidean system was not the one system, but only one system among many.
In the first half of the nineteenth-century, János Bolyai (1802 - 1860 CE) and Nikolay Lobachevsky (1792 - 1856 CE) independently demonstrated geometries that were consistent, and did not respect Euclid's fifth postulate;
If a straight line incident to two straight lines has interior angles on the same side of less than two right angles, then the extension of these two lines meets on that side where the angles are less than two right angles.
Contrary to the fifth postulate, Bolyai's and Lobachevsky's geometries permitted the construction of multiple "parallel" lines for any given line through a given point. This can be seen, for example, by considering a plane in the shape of a circle, thus enabling one to draw an arc line across the diameter of the circle, and then selecting a point inside the circle that is not on the diameter line, such that numerous lines pass through that point, on angles such that these lines never meet the diameter, because all lines are terminated by the boundary of the circle.
The existence and features of non-Euclidean geometries completely undermined metamathematical certainty, and foisted uncertainty on all scientific and metaphysical suppositions that rested on mathematics. This sparked vigorous attempts to retrieve certainty, including many non-geometric programs such as logicism and formalism, all aimed at rigorously explicating and certifying the foundations of mathematics. Ultimately however, the long-term result of these efforts was only to further separate mathematics from certainty in unexpected ways, and this gave rise to the post-modern perception of mathematics as rooted in reality and internally cohesive, but not certain in any absolute physical or metaphysical sense.
Reflecting on the rise and fall of certainty in geometry and metamathematics from Thales to Lobachevsky, we see that when mathematics first arose it was taken straightforwardly, as a practical device that solved problems in the real world. In prehistory and Classical history, mathematics was approached as a device that simply was and simply worked, much like a door or field plough. When Thales took up mathematics however, he latched on the fact that mathematics was not quite like other devices, and he observed its physical manifestations, and speculated on it supra-physically. This mode of speculation was instrumental in generating Classical Greek metaphysics, and culminated in the logico-deductive method, and the incredibly powerful Euclidean system.
The Euclidean system reigned with certainty for millennia, and though mathematics continued to evolve, and explanations for its certainty changed, the fact of certainty remained. Attempts to explain the basis and correctness of mathematics ranged from Forms and God, to nature and mental architectonics, but even though metamathematical claims varied, mathematical claims did not. Whatever its metamathematics, mathematics itself was absolutely accurate.
The discovery of non-Euclidean geometries instantly destroyed the possibility of absolute mathematical certainty, and this is an extraordinary fact, because for millennia brilliant mathematicians were exactly wrong in their metamathematical certitude. Looking back to the end of certainty, it appears certainty was as much a goal as a hypothesized feature of mathematics; that mathematicians undertook mathematics because they wanted to work with something that was guaranteed.
At a fundamental level, the rise and subsequent fall of mathematical certainty was central to the philosophical and scientific recognition of human fallibility. Today it is believed that nature exists, but because of the peculiarities of our experience of it, there always remains the possibility that our metamathematical and metaphysical claims are inaccurate and perhaps entirely false. Thus, the end of mathematical certainty has given rise to a new kind of certainty, that regardless of its foundations, mathematics remains the most powerful tool humans possess for mediating between themselves and nature, and that the development of mathematics enables us to expose falsities -- such as the absolute certainty of mathematics -- and thus allows us to work towards the refinement and extension of better justified, if not certain beliefs.
Part of the series: UWO
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473871.23/warc/CC-MAIN-20240222225655-20240223015655-00228.warc.gz
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CC-MAIN-2024-10
| 24,016 | 39 |
https://physics.stackexchange.com/questions/338386/chladni-figures-avoided-crossings-of-nodal-lines
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math
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As khown, Chladni figures display nodal lines of eigenfunctions satisfying the equation $\Delta^2\psi=k^4\psi$ with appropriate boundary conditions. One can note these lines don't like to cross each other:
H.-J. Stöckmann in "Quantum chaos. An introduction", 1999 writes (page 17):
The interpretation of Chladni figures of irregularly shaped plates is thus intimately connected with the quantum mechanics of chaotic billiards. $\langle\ldots\rangle$ Figure 2.2(a) shows one of the nodal patterns for a circular plate observed by a Chladni himself. We find a regular net of intersecting circles and straight lines typical for integrable systems. The central mounting does not disturb the integrability since the rotational invariance is not broken.
The situation is different for rectangular plates (see Fig. 2.2(b)). Here the mounting reduces the symmetry, and the billiard becomes pseudointegrable $\langle\ldots\rangle$.
Figure 2.2(c) finally displays a Chladni figure for a nonintegrable plate in the shape of a quarter Sinai billiard.
M.C. Gutzwiller in "Chaos in Classical and Quantum Mechanics", 1990 writes a similar thing (page 234):
A theorem by Uhlenbeck (1976) states that it is a generic property of eigenfunctions to have non-intersecting nodal lines.
So we see the nodal lines usually avoid to cross. The crossing nodal lines is an exceptional situation which requires some additional conditions (e.g. integrability of the billiard) and can easily be destroyed by perturbations.
QUESTION: is there any mathematical of physical analogy between anticrossing of nodal lines and anticrossing of energy level in quantum systems? When we change parameters of a Hamiltonian, energy levels cross in integrable systems and repulse in chaotic ones - just the same behavior is demonstrated by the nodal lines, although in coordinate space. Can this analogy be somehow described quantitatively, or it is just a coincidence?
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s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572471.35/warc/CC-MAIN-20190916015552-20190916041552-00433.warc.gz
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CC-MAIN-2019-39
| 1,926 | 9 |
http://alevelprep.com/Physics/P1/P1June2012.html
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math
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1. Which of these quantities is not measured in an SI base unit?
2. Displacement can be found from the
3. A wire of length x is stretched by a force F. The extension is Δx. A second wire of the same material and cross-sectional area is stretched by the same force. If it has twice the length of the first wire its extension will be
4. Which equation shows a scalar quantity as the product of two vector quantities?
5. A material which can be drawn into a wire is described as being
6. A bowling ball of mass 7.0 kg is travelling at a speed of 4.0 m s-1. The kinetic energy of the ball is
9. A motor raises a mass m through a height Δh in time t. The power of the motor is given by
Use the following graph to answer Question 10:
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512323.79/warc/CC-MAIN-20181019041222-20181019062722-00012.warc.gz
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CC-MAIN-2018-43
| 729 | 8 |
https://testbook.com/question-answer/what-would-be-the-simple-interest-obtained-on-an-a--6006bbf3af7a4e33c8262372
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math
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Free Practice With Testbook Mock Tests
This question was previously asked in
Principal = Rs 6,535
Rate of interest = 10%
Time in years = 6 years
Simple interest, SI = (P × N × R)/100
Where P is principal, N is the number of terms and R is the rate of interest.
SI = 6535 × 6 × 10/100 = Rs 3,921
∴ The simple interest obtained is Rs 3,921.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046155529.97/warc/CC-MAIN-20210805095314-20210805125314-00272.warc.gz
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CC-MAIN-2021-31
| 344 | 9 |
http://uyessayfhiv.artsales.biz/discrete-math-tutor.html
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math
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Discrete math tutor
Discrete math tutors bu and boston area tutors are available to assist bu students and students around boston with tutoring in accounting, act english, act math and. Get discrete mathematics help when it's convenient for you hop online with your discrete math problems, and we’ll connect you with an online tutor in seconds get expert discrete math help anytime, anywhere. I have tutored students from elementary all the way up to college i’ve been tutoring ever since my senior year in high school i’ve currently helped students. Review university of texas at austin (ut austin) discrete math tutors, including hector f, eugene n, nicolas dominic t, ahmet g, raja a, in austin, tx to find. How can the answer be improved. Search our directory of discrete math tutors near san diego, ca today by price, location, client rating, and more - it's free.
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Looking for a mathematics tutor get mathematics online tutoring and college homework help quickly view our team of tutors. One-to-one discrete math sessions large class lectures can be long and distracting, having a personalized tutor makes a big difference with topics like euler trails and circuits, permutations and combinations, it is easy to get confused in class. Review university of washington (university of washington) discrete math tutors, including michael b, heather g, di a, mirza t, qun l, in seattle, wa to find the. Find discrete math tutor at heald college-san jose (heald college-san jose), along with other tutoring jobs in milpitas, california.
If you are stuck with your discrete math homework problems or quiz discrete math help - where to get it live online discrete math tutor help. Looking for discrete math help find the right tutor or tutoring program for you based on your preferred convenience, price, location, and more.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213693.23/warc/CC-MAIN-20180818173743-20180818193743-00174.warc.gz
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CC-MAIN-2018-34
| 3,192 | 7 |
https://arxiv-check-250201.firebaseapp.com/each/1910.14034v1
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math
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Supervised classification methods often assume the train and test data distributions are the same and that all classes in the test set are present in the training set. However, deployed classifiers often require the ability to recognize inputs from outside the training set as unknowns. This problem has been studied under multiple paradigms including out-of-distribution detection and open set recognition. For convolutional neural networks, there have been two major approaches: 1) inference methods to separate knowns from unknowns and 2) feature space regularization strategies to improve model robustness to outlier inputs. There has been little effort to explore the relationship between the two approaches and directly compare performance on anything other than small-scale datasets that have at most 100 categories. Using ImageNet-1K and Places-434, we identify novel combinations of regularization and specialized inference methods that perform best across multiple outlier detection problems of increasing difficulty level. We found that input perturbation and temperature scaling yield the best performance on large scale datasets regardless of the feature space regularization strategy. Improving the feature space by regularizing against a background class can be helpful if an appropriate background class can be found, but this is impractical for large scale image classification datasets.
updated: Wed Oct 30 2019 17:53:13 GMT+0000 (UTC)
published: Wed Oct 30 2019 17:53:13 GMT+0000 (UTC)
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585696.21/warc/CC-MAIN-20211023130922-20211023160922-00580.warc.gz
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CC-MAIN-2021-43
| 1,504 | 3 |
https://kiygo.com/index.php/2018/08/16/is-there-anything-that-can-be-done-to-press-the-button-to-achieve-the-effect-of-number/
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math
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I still remember the Casio calculator used in reading. In the middle and high school, the Casio calculator was a hand in the class, otherwise it would be a direct embarrassment. Sometimes even the exam can bring such a calculator to calculate, it seems that the university exam can still carry the calculator to calculate.
I remember that the Casio calculator at that time was also fifty or sixty, but now I wants to tell you that Casio has a calculator with a price of $300+. Do you believe it? Recently, Japan Casio launched a local gold version of the calculator for $400 . It is said that this calculator has performed well in the Japanese market, so it is now also launched in the Chinese market. This calculator is a “50th Anniversary”, the shell is not a traditional plastic shell, but an aluminum alloy shell, and is sprayed into a local gold. The overall appearance and the texture of the metal are of course far better than ordinary plastic plate calculators. It is worth noting that although the value of this calculator is as high as $400, in addition to the outer casing is aluminum alloy, other functions do not seem to be different from the normal version, the display can only display 12 digits. The only special thing is that this calculator can support laser engraving customization, if you want to engrave your name on it. But the problem is, a calculator, although it is still a local gold calculator, can be carried around like a mobile phone.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671053.31/warc/CC-MAIN-20191121231600-20191122015600-00441.warc.gz
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CC-MAIN-2019-47
| 1,468 | 2 |
https://help.idecad.com/ideCAD/steel-column-design-settings
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math
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Steel Column Design Settings are explained in detail under this title.
Design Settings Sub-Tabs
After the steel column modeling is completed, double click on the element to enter its properties.
3 new sub-tabs will appear in the steel column menu. These tabs contain adjustments for analysis and design.
If a click is placed in the box on the ASCE 7-16 sub-tab, it is made with the vertical design spectrum in accordance with 11.9 and Ev is determined to calculate of the vertical earthquake effect.
Releases / Partial Fixity
In the Releases tab, end releases and spring values are entered at the starting and ending points of the element. For this process, it must be activated by clicking the 'Override end releases' box at the top of the tab.
If the axial force for the starting point of the element 2-direction shear force, 3-direction shear force, torsion, 2-direction moment and 3-direction moment are indicated, the corresponding force will be 0 at the starting point.
For the end point of the element, axial force, 2-direction shear force, 3-direction shear force, torsion, 2-direction moment and 3-direction moment are indicated, the corresponding force will be 0 at the starting end.
The spring coefficient is entered for the starting point of the element. Units can be changed by clicking the right button in the box.
Spring coefficient is entered for the end point of the element. Units can be changed by clicking the right button in the box.
The parameters used in the design are intervened in the Design tab. If a mark is placed in the box, the coefficient written in the box is used in the design. If no mark is placed in the box, the programme automatically determines these coefficients and uses them in the design.
Effective length factor for major axis
Effective length factor for minor axis
Unbraced length ratio (Major)
The ratio of the length between two elements connected to the element in its strong direction to the entire element length
Unbraced length ratio (Minor)
The ratio of the length between two elements connected in the weak direction to the entire element length
Laterally unbraced length ratio(LTB)
The ratio of the length between laterally unbraced length along either flange
The lateral-torsional buckling modification factor (Cb )
Lateral-torsional buckling modification factor for nonuniform moment
Control is given in the steel design - column - details section after analysis and design.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711221.94/warc/CC-MAIN-20221207221727-20221208011727-00573.warc.gz
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CC-MAIN-2022-49
| 2,431 | 23 |
http://theoakpine.co.uk/991447-some-help-please.shtml
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math
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Topic: Essays regarding education
May 24, 2019 / By Kaila Question:
A researcher has investigated the relationship between IQ and grade point average (GPA) and found the correlation to be .75.
For this essay, critique the results and interpretation of a correlational study.
•Evaluate the correlational result and identify the strength of the correlation.
•Examine the assumptions and limitations of the possible connection between the researcher’s chosen variables.
• Identify and describe other statistical tests that could be used to study this relationship.
Your essay response must address the following questions:
•How strong is this correlation? ◦Is this a positive or negative correlation?
◦What does this correlation mean?
•Does this correlation imply that individuals with high Intelligence Quotients (IQ) have high Grade Point Averages (GPA)?
• Does this correlation provide evidence that high IQ causes GPA to go higher? ◦What other variables might be influencing this relationship?
•What is the connection between correlation and causation?
•What are some of the factors that affect the size of this correlation?
•Is correlation a good test for predicting GPA? ◦ If not, what statistical tests should a researcher use, and why?
Gweneth | 8 days ago
correlation = 0.75..........
if corelation lies between 0.7 to 1, it is basically regarded as positively strong.
correlation between gpa and iq is strong and if iq level increases, gpa level also increases.
Not only iq level is responsible for gpa level. there are others factors also like performance, education level etc. so these variables might have influence on the relationship.
correlation only shows relation -strong or week, it can't use to quantify the outcome. for example if iq level will be increase by x(say), then how much gpa level will increase?.. S o for this regression (causation)is needed.
sample size, standard deviation etc are factors that affects the size of correlation.
to predict gpa, regression is needed because there are others factors that affects gpa.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257699.34/warc/CC-MAIN-20190524164533-20190524190533-00184.warc.gz
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CC-MAIN-2019-22
| 2,074 | 23 |
https://strahuemvseh.ru/how-to-solve-a-math-word-problem-3463.html
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math
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"Suzy has eight pairs of red socks and six pairs of blue socks. If her little sister owns nine pairs of purple socks and loses two of Suzy's pairs, how many pairs of socks do the sisters have left?
Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.
Word problems often confuse students simply because the question does not present itself in a ready-to-solve mathematical equation.
In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum.
However, word problems can present a real challenge if you don't know how to break them down and find the numbers underneath the story.
For instance, suppose you're told that "Shelby worked eight hours MTTh F and six hours WSat".
You would be expected to understand that this meant that she worked eight hours for each of the four days Monday, Tuesday, Thursday, and Friday; and six hours for each of the two days Wednesday and Saturday.But figuring out the actual equation can seem nearly impossible. Be advised, however: To learn "how to do" word problems, you will need to practice, practice, practice.The first step to effectively translating and solving word problems is to read the problem entirely.Probably the greatest source of error, though, is the use of variables without definitions.When you pick a letter to stand for something, write down explicitly what that latter is meant to stand for.Begin by determining the scenario the problem wants you to solve. Either way, the word problem provides you with all the information you need to solve it.Once you identify the problem, you can determine the unit of measurement for the final answer.Does "" stand for "Shelby" or for "hours Shelby worked"?If the former, what does this mean, in practical terms?Don't start trying to solve anything when you've only read half a sentence.Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need. Figure out what you need but don't have, and name things. And make sure you know just exactly what the problem is actually asking for.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587877.85/warc/CC-MAIN-20211026103840-20211026133840-00419.warc.gz
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CC-MAIN-2021-43
| 2,230 | 7 |
https://www.hackmath.net/en/math-problem/12561
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math
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The tax per gallon of gasoline in California is $0.477. If you fill your gasoline tank with 14.4 gallons in California, how much will you pay in taxes? Round to the nearest cent.
Did you find an error or inaccuracy? Feel free to write us. Thank you!
Tips for related online calculators
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817765.59/warc/CC-MAIN-20240421101951-20240421131951-00188.warc.gz
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CC-MAIN-2024-18
| 3,743 | 39 |
http://demo.fitmed.vn/index.php/epub/riemannian-geometry-3-rd-edition-graduate-texts-in-mathematics-volume-171
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math
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By Peter Petersen
Meant for a three hundred and sixty five days direction, this article serves as a unmarried resource, introducing readers to the real concepts and theorems, whereas additionally containing sufficient history on complex subject matters to entice these scholars wishing to specialise in Riemannian geometry. this is often one of many few Works to mix either the geometric components of Riemannian geometry and the analytic points of the idea. The e-book will attract a readership that experience a uncomplicated wisdom of normal manifold concept, together with tensors, varieties, and Lie groups.
Important revisions to the 3rd variation include:
a vast addition of exact and enriching routines scattered during the text;
inclusion of an elevated variety of coordinate calculations of connection and curvature;
addition of basic formulation for curvature on Lie teams and submersions;
integration of variational calculus into the textual content taking into consideration an early remedy of the field theorem utilizing an explanation via Berger;
incorporation of numerous fresh effects approximately manifolds with optimistic curvature;
presentation of a brand new simplifying method of the Bochner strategy for tensors with program to certain topological amounts with common decrease curvature bounds.
Read or Download Riemannian Geometry (3rd Edition) (Graduate Texts in Mathematics, Volume 171) PDF
Similar geometry books
This ebook experiences the algorithms for processing geometric facts, with a realistic specialise in vital recommendations no longer lined by means of conventional classes on laptop imaginative and prescient and special effects. positive factors: offers an summary of the underlying mathematical thought, masking vector areas, metric house, affine areas, differential geometry, and finite distinction equipment for derivatives and differential equations; reports geometry representations, together with polygonal meshes, splines, and subdivision surfaces; examines thoughts for computing curvature from polygonal meshes; describes algorithms for mesh smoothing, mesh parametrization, and mesh optimization and simplification; discusses element place databases and convex hulls of element units; investigates the reconstruction of triangle meshes from element clouds, together with tools for registration of element clouds and floor reconstruction; offers extra fabric at a supplementary web site; comprises self-study routines in the course of the textual content.
This ebook and the subsequent moment quantity is an advent into smooth algebraic geometry. within the first quantity the equipment of homological algebra, thought of sheaves, and sheaf cohomology are built. those equipment are crucial for contemporary algebraic geometry, yet also they are primary for different branches of arithmetic and of significant curiosity of their personal.
This article examines the genuine variable conception of HP areas, targeting its functions to numerous elements of research fields
This quantity incorporates a really whole photo of the geometry of numbers, together with kinfolk to different branches of arithmetic corresponding to analytic quantity thought, diophantine approximation, coding and numerical research. It bargains with convex or non-convex our bodies and lattices in euclidean house, and so forth. This moment version used to be ready together via P.
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Extra info for Riemannian Geometry (3rd Edition) (Graduate Texts in Mathematics, Volume 171)
11. More generally, the map I S1 S1 ! I S1 t; ei Â1 ; ei Â2 7! t/dÂ22 and the target has the rotationally symmetric metric dr2 C . 12. z; w/ D . z; w/). The quotient map I S2nC1 S1 ! I S2nC1 S1 =S1 can be made into a Riemannian submersion by choosing an appropriate metric on the quotient space. To find this metric, we split the canonical metric ds22nC1 D h C g; where h corresponds to the metric along the Hopf fiber and g is the orthogonal component. In other words, if pr W Tp S2nC1 ! t/d 2 : Observe that S2nC1 S1 =S1 D S2nC1 and that the S1 only collapses the Hopf fiber while leaving the orthogonal component to the Hopf fiber unchanged.
5. R/ revolution by revolving t 7! R sin R3 can be thought of as a surface of t R ; 0; cos t R around the z-axis. The metric looks like dt2 C R2 sin2 t R d 2 : Note that R sin Rt ! t as R ! 1, so very large spheres look like Euclidean space. 7 by observing that it comes from the induced metric in R2;1 after having rotated the curve t 7! R sinh t R ; 0; cosh around the z-axis. t/d 2 of rotationally symmetric metrics. 1= k/. t/ D 0. In the revolution case, the profile curve clearly needs to have a horizontal tangent in order to look smooth.
T/ to the integral R is part of the great circle. t//. dt (5) Show that there is no Riemannian immersion from an open subset U Rn into Sn . Hint: Any such map would map small equilateral triangles to triangles on Sn whose side lengths and angles are the same. Show that this is impossible by showing that the spherical triangles have sides that are part of great circles and that when such triangles are equilateral the angles are always > 3 . 21. Let H n Rn;1 be hyperbolic space: p; q 2 H n ; and v 2 Tp H n a unit vector.
Riemannian Geometry (3rd Edition) (Graduate Texts in Mathematics, Volume 171) by Peter Petersen
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https://methods.sagepub.com/book/understanding-regression-analysis-2e/i384.xml
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math
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Understanding Regression Analysis: An Introductory Guide presents the fundamentals of regression analysis, from its meaning to uses, in a concise, easy-to-read, and non-technical style. It illustrates how regression coefficients are estimated, interpreted, and used in a variety of settings within the social sciences, business, law, and public policy. Packed with applied examples and using few equations, the book walks readers through elementary material using a verbal, intuitive interpretation of regression coefficients, associated statistics, and hypothesis tests. The Second Edition features updated examples and new references to modern software output.
In the food expenditure example, the hypothesis was advanced that family food consumption increases as income increases. Since the estimated coefficient was found to be a positive number, one might want to immediately conclude that we have proven our case. Unfortunately, drawing such inferences is not so easy, since our hypothesis concerns the population of all families, not just the 50 families in our sample. By way of example, although the coefficient on income is greater than zero for our food example, how confident are you that β, the population coefficient, is really greater than zero? Or, how confident would you be if, rather than basing the estimate on 50 households, the coefficient had been ...
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| 1,375 | 2 |
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0712&L=SPM&O=D&P=310071
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math
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i received an offline answer about my question concerning parametric
modulation which i like to allocate.
the recommendation was, to perform a conjunction analysis with 2 t-
contrasts (a<b, b<c) for each subject at first level and to enter the 2 con-
images per subject into a 2x2 ANOVA (2 groups, 2 images) at second level.
with this i do not have to assume a true linear increase stimulation load
between the 3 conditions (a,b,c).
thanks for the help
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| 452 | 8 |
https://www.szfalnia.pl/math/word/problem/two/dump/trucks/have/capacities/of/10-20358.html
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math
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Math word problem Two dump trucks have capacities of 10
Linear Programming Worksheet
3. Toys-A-Go makes toys at Plant A and Plant B. Plant A needs to make a minimum of 1000 toy dump trucks and fire engines. Plant B needs to make a minimum of 800 toy dump trucks and fire engines. Plant A can make 10 toy dump trucks and 5 toy fire engines per hour. Plant B can produce 5 toy dump trucks and 15 toy fire engines per hour.
the mass of a liter bottle of water. very close to 10% more than 2 pounds (within a quarter of a percent) very very close to 2.205 pounds (accurate to 3 decimal places) 7 apples. a loaf and a half of bread. about 2 packs of ground beef. A tonne is about: the weight of a small car.
Math Tutorials; Word Problem Solver . Get it on Google Play Get it on Apple Store. Problema Solution A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 70 pounds. The truck is transporting 55 large boxes and 65 small boxes. If the truck is carrying a total of 4100 pounds
What is the probability of the dog to reach town A within
2 days ago · A long and narrow railed bridge is situated between town A(to the east) and town B(to the west). A dog is placed at the center of the bridge and it can move about randomly across the bridge. Based on thousands of this same experiment conducted in the past, it is concluded that the probability of any dog placed at the center of the bridge to reach town A is 10% within a day and there is also a
Solved: Chapter 1.11A Problem 3A Solution | Math In Action
Step-by-step solution. Step 1 of 5. (a) The gas tank of a Ford Focus holds gallons of gas. The objective is to find the number of highway miles on a full tank of gas. Refer the table for fuel economy in text. From the table of values, The highway mileage of Ford Focus is 36 miles per gallon. So, multiply the total highway miles per gallons by
How many tons of gasoline do cars burn in their - Quora
Answer (1 of 3): Lets make this a simple math word problem. [Oh no! The dreaded word problem!] Average weight of a gallon of gasoline: 6.0 lbs. Average lifetime mileage of a car: 120,000 miles Average lifetime fuel economy: 20 miles per gallon. Solve the problem in your head. No calculator, n
Owl Hat is a calculator, word problem solver, and much more. Owl Hat reads math problems through your camera and gives detailed explanations for solving them. With every upgrade, Owl Hat takes another step toward being a true virtual tutor, and in the meantime, it's the coolest calculator and math s…
Construction Math Worksheets & Teaching Resources | TpT
Incorporate math, fine motor, and writing with these engaging Construction Pattern Block Puzzles and Worksheets.The Construction themed puzzles are a Bulldozer, Cement Truck, Crane, Digger and a Dump Truck. The Bulldozer, Cement Truck, Digger and Dump Truck have both an easy and challenging puzzle.
2 days ago · The probability of the dog to reach the nearest town called B (west of forest) within now and the next 24 hours is 10%. The forest is quite large and the dog could only wander east or west. It is possible the dog might have not reached either towns (despite wandering about) for 24 hours, reached one or maybe even reached both.
Learning Task 3 The following are excerpts taken from
Jun 03, 2021 · Réponses: 2 questionner: Learning Task 3 The following are excerpts taken from editorial column articles of a campus newspaper, The Paladian Volume XVIII No. 1 (June-October <br /><br />2017). In your pad paper, identify an argument in every passage by indicating a conclusion and a premise supporting it.<br /><br />Premise: <br /><br />Conclusion:<br /><br />1. The enforcement of …
Fraction as Division - Tape Diagrams - Online Math Learning
c. If the gym could accommodate two grade-levels at once, how many hours of recess would each grade-level get? Lesson 4 Concept Development Problem 1 Eight tons of gravel is equally divided between 4 dump trucks. How much gravel is in one dump truck? Problem 2 Five tons of gravel is equally divided between 4 dump trucks.
Mass word problems (customary units) Grade 5 Word Problems Worksheet 1. A package that is heavier than 11 lbs and 8 oz will have a label that says "heavy" on it. Gloria packed 6 flowerpots to send to her customers. Each of the flowerpots weighs 1 lb and 12 oz. The packing material weighs 5 oz. Will her package be labeled as "heavy"? 2.
Standard Subtraction Algorithm - Online Math Learning
NYS Math Grade 4, Module 1, Lesson 14 Homework 1 . Use the standard algorithm to solve the following subtraction problems. Directions: Draw a tape diagram to represent each problem. Use numbers to solve and write your answer as a statement. 2. Jason ordered …
Child Development and Early Learning - Transforming the
The domains of child development and early learning are discussed in different terms and categorized in different ways in the various fields and disciplines that are involved in research, practice, and policy related to children from birth through age 8. To organize the discussion in this report, the committee elected to use the approach and overarching terms depicted in Figure 4-1.
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| 5,209 | 24 |
https://www.worksheeto.com/post_area-rectangular-worksheets_324307/
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math
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Area Rectangular Worksheets
What is the area of a rectangle?
The area of a rectangle is found in the middle of the picture. Students use the length and width of a rectangle to calculate the area of the rectangles. You can open the PDF. The feet are in the feet: Worksheet #1. There is a metric cm, m, and a Worksheet #3.
What is the length of the area?
The length is 8 feet and the breadth is 3 feet. The area is divided into lengths x breadth. 24 sq feet is 8 x 3. 2 is the length and breadth of the perimeter. 11 x 2 is the number of 2. 22 feet. The perimeter is 22 feet and the area is 24 sq feet.
What are areas that are used to find area worksheets?
Area questions. The area of squares, rectangles, triangles, and circles can be found. There are basic, intermediate, and advanced-level worksheets in this collection. The order of operations. You can learn to solve operations in order. There are circles with a circumference and a diameter. There are activities related to circles on this page.
What is the surface area of prism?
There are solutions to the problem of Worksheet 6.1 1. The surface area of the prism is 232 square cm. The figure has a surface area of 382 square in 3. The cube has a surface area of 24 square m. The cube has a surface area of 486 square millimetres. The surface of the prism is 6 square cm. 236 square in 7 is the surface of the figure. The cube's surface is determined by the equation Surface of cube A little over 300 square cm 8. 94 square in 9 is the surface of the figure.
What is the surface area of the prism?
Draw a net from the rectangular prism to find the surface area. The area of the net is the surface area of the prism. The faces of the rectangular prism are not the same. The congruent faces are the same color. The formula: Surface is used to find the surface of a prism. 2lw. 2wh + 2lh.
What is the area of a rectangle?
A grid is used to find the area of a rectangle. The number of squares inside a rectangle is the area of the grid. Students find the areas of rectangular shapes by counting the squares in a grid.
Surface Area of a Rectangular Prism Word Problems Worksheet?
There is a Word Problems Worksheet. There is a Word Problems Worksheet. Word problems with a rectangular area. There are word problems.
What is the Area of Rectangles Grid Form?
The Area of Rectangles Grid Form (A) Math Worksheet is located on the Measurement Worksheets Page at Math-Drills.com. This math sheet was viewed over 300 times this month and over 100 times this week.
What is the surface area of two rectangular prisms?
The surface area of the two rectangular prisms is irregular. Determine the surface area of three solid shapes. The space for students to show their work is included in this worksheet. There are four shapes in this activity. The for are calculated by the pupils.
What is the width of the rectangle?
The area is 2 6 4 12 6 18 9 27. What is the width of the piece of paper? The measurement is _____ inches. Write four equations that show that the width is the same. Calvin has a farm with a square meter area. The lengths and width of the paddocks are not fractions. Complete the task.
What is the surface area of a solid?
The surface area of the cubes and the rectangular Prisms. The area of the solid is called the surface area or the area of every face. The third exam is an example. A wooden cube has edges. Find the cube. The net of a cube is the cube's net. The 6 are shown on the net.
What is a solid shape with 6 rectangular faces?
To practice finding the surface area of a rectangular prism, you can check out our ready-to-print worksheets on surface area. It has 6 rectangular faces. The length l, width w, and height h are all expressed in numbers.
What is the area of the outside surface of a solid or three-dimensional shape called Surface?
The area of the outside surface of a three-dimensional shape is called the Surface Area. There are 6 rectangular bases and faces in a rectangular prism. The total surface area is the sum of the 6 pieces.
What is the length and width of a rectangle?
The length and width of a rectangle are what determines the area. A is the length and W is the width of the rectangle. The area of a 35 m and 25 m rectangle is 35 times the size of a 25 or 825 square meter one. A room is 16 feet long and 18 feet wide.
What is the area defined as?
The amount of space covered by a flat surface is called the area. The number of square units is what it is measured in. The number of squares that can fit into a rectangle is called the number of unit squares.
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http://www.healthboards.com/boards/2458110-post3.html
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math
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Re: Help! My mom is in agony!
Thanks so much for the reply. You've been really helpful. That is probably exactly what it is that "he crowns are creating too much pressure or are too closely placed together"
I will definately tell her about "affordable dentures"
One question, what is TMJ?
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https://sciencing.com/secant-line-8179888.html
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math
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Let’s say you have a function, y = f(x), where y is a function of x. It doesn’t matter what the specific relationship is. It could be y = x^2, for example, a simple and familiar parabola passing through the origin. It could be y = x^2 + 1, a parabola with an identical shape and a vertex one unit above the origin. It could be a more complex function, such as y = x^3. Regardless of what the function is, a straight line passing through any two points on the curve is a secant line.
Notice that the secant line changes as you pick a second point closer to the first point. You can always pick a point on the curve closer than you did before and get a new secant line. As your second point gets closer and closer to your first point, the secant line between the two approaches the tangent to the curve at the first point.
Take the x and y values for any two points you know to be on the curve. Points are given as (x value, y value), so the point (0, 1) means the point on the Cartesian plane where x = 0 and y = 1. The curve y = x^2 + 1 contains the point (0, 1). It also contains the point (2, 5). You can confirm this by plugging each pair of values for x and y into the equation and ensuring that the equation balances both times: 1 = 0 + 1, 5 = 2^2 + 1. Both (0, 1) and (2, 5) are points of the curve y = x^2 +1. A straight line between them is a secant and both (0, 1) and (2, 5) will also be part of this straight line.
Determine the equation for the straight line passing through both these points by choosing values that satisfy the equation y = mx + b -- the general equation for any straight line -- for both points. You already know that y = 1 when x is 0. That means 1 = 0 + b. So b must be equal to 1.
Substitute the values for x and y at the second point into the equation y = mx + b. You know y = 5 when x = 2 and you know b = 1. That gives you 5 = m(2) + 1. So m must equal 2. Now you know both m and b. The secant line between (0, 1) and (2, 5) is y = 2x + 1
Pick a different pair of points on your curve and you can determine a new secant line. On the same curve, y = x^2 + 1, you could take the point (0, 1) as you did before, but this time select (1, 2) as the second point. Put (1, 2) into the equation for the curve and you get 2 = 1^2 + 1, which is obviously correct, so you know (1, 2) is also on the same curve. The secant line between these two points is y = mx + b: Putting 0 and 1 in for x and y, you’ll get: 1 = m(0) + b, so b is still equal to one. Plugging in the value for the new point, (1, 2) gives you 2 = mx + 1, which balances if m is equal to 1. The equation for the secant line between (0, 1) and (1, 2) is y = x + 1.
- Notice that the secant line changes as you pick a second point closer to the first point. You can always pick a point on the curve closer than you did before and get a new secant line. As your second point gets closer and closer to your first point, the secant line between the two approaches the tangent to the curve at the first point.
About the Author
Andrew Breslin has been writing professionally since 1994. His articles and op-ed pieces have appeared in the "South Florida Sun Sentinel," "St Paul Pioneer Press," "Detroit Free Press," "Charlotte Observer," “Good Medicine,” and others. He studied molecular biology at Westchester University and frequently writes about science and mathematics.
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https://acnpsearch.unibo.it/singlejournalindex/6181672
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math
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Two-photon formation of the charmonium resonance chi(c2), has been studied
with the L3 detector at LEP. The chi(c2) is identified through its decay ch
i(c2) --> gamma J/psi, with a subsequent decay J/psi --> e(+)e(-) or J/psi
--> mu(+)mu(-). With an integrated luminosity of 140 pb(-1) at root s simil
ar or equal to 91 GeV and 52 pb(-1) at root s similar or equal to 183 GeV,
we measure the two-photon width of the chi(c2) to be Gamma(gamma gamma)(chi
(c2)) = 1.02 +/- 0.40 (stat.) +/- 0.15 (sys.) +/- 0.09(BR.) keV. (C) 1999 P
ublished by Elsevier Science B.V. All rights reserved.
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| 583 | 8 |
http://e-booksdirectory.com/details.php?ebook=123
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math
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Introduction to Vectors and Tensors Volume 2: Vector and Tensor Analysis
by Ray M. Bowen, C.-C. Wang
Number of pages: 246
The textbook presents introductory concepts of vector and tensor analysis. Volume II begins with a discussion of Euclidean Manifolds which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on Hypersurfaces in a Euclidean Manifold.
Home page url
Download or read it online for free here:
by J. Willard Gibbs - Yale University Press
A text-book for the use of students of mathematics and physics, taken from the course of lectures on Vector Analysis delivered by J. Willard Gibbs. Numerous illustrative examples have been drawn from geometry, mechanics, and physics.
by Alexander Macfarlane - John Wiley & Sons
Contents: Addition of Coplanar Vectors; Products of Coplanar Vectors; Coaxial Quaternions; Addition of Vectors in Space; Product of Two Vectors; Product of Three Vectors; Composition of Quantities; Spherical Trigonometry; Composition of Rotations.
by Francis Dominic Murnaghan - Johns Hopkins press
This monograph is the outcome of lectures delivered to the graduate department of mathematics of The Johns Hopkins University. Considerations of space have made it somewhat condensed in form, but the mode of presentation is sufficiently novel.
by W W L Chen - Macquarie University
Introduction to multivariable and vector analysis: functions of several variables, differentiation, implicit and inverse function theorems, higher order derivatives, double and triple integrals, vector fields, integrals over paths, etc.
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https://www.hackmath.net/en/examples/9th-grade-(14y)?page_num=39
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math
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Examples for 9th grade - page 39
Determine the area of a trapezoid with bases 60 and 37 and height is 3 shorter than the its leg.
- Sales vs profit
Apple sells 45 percent less computes than the Acer but the profit from their sales is 1.7 times higher than Acer. How many times are Apple computer more expensive than Acer?
Cyclist who rides at an average speed 17 km/h travels trip distance 14 min before the cyclist who rides at an average speed 15 km/h. What is the length of this cyclist trip(distance in km)?
Mr Peter has metal roof cone shape with a height of 36 cm and radius 73 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 2.1 m2?
Car goes from point A to point B at speed 70 km/h and back 76 km/h. If they goes there and back at speed 73 km/h trip would take 19 minutes shorter. What is distance between points A and B?
Light ray loses 1/19 of brightness passing through glass plate. What is the brightness of the ray after passing through 3 identical plates?
Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2.
On the road sign, which informs the climb is 20%. Car goes 5 km along this road. What is the height difference that car went?
- Rotary cone
Rotary cone whose height is equal to the circumference of the base, has a volume 4772 cm3. Calculate the radius of the base circle and height of the cone.
- IS triangle
Calculate interior angles of the isosceles triangle with base 37 cm and legs 36 cm long.
Calculate the area of regular pentagon, which diagonal is u=14.
- The angle of lines
Calculate the angle of two lines y=-3x+25 and y=x-3
Side a of parallelogram is twice longer than side b. Its circumference is 78 dm. Calculate the length of the sides of a parallelogram.
- Two sisters
Two sisters together have 54 CDs. 6/8 CDs has younger sister and is equal to 3/5 of CDs older sisters. How many CDs has each of the sisters?
- Fifth member
Determine the fifth member of the arithmetic progression, if the sum of the second and fifth members equal to 73, and difference d = 7.
- ATC camp
The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple?
On the large rosary was a third white, half red, yellow quarter and six pink. How many roses was in the rosary?
- Triangle KLB
It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
- Square - increased perimeter
How many times is increased perimeter of the square, where its sides increases by 150%? If the perimeter of square will increase twice, how much% increases the content area of the square?
The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
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https://www.physicsforums.com/threads/high-school-circular-motion-problem.783015/
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math
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1. The problem statement, all variables and given/known data The problem is: An amusement park is replacing it's stand-up roller coaster with a G-Force ride. Riders will enter the ride at the apex and lean against the wall of the ride. The G-force ride will speed up until riders reach height h above the apex. Determine the minimum speed v needed to keep riders at a constant height h (in terms of h, β, μs, and constant g). Given the wall of the ride make an angle β with the vertical, and the coefficient of static friction between the bodies and the surface of the walls is μs. 2. Relevant equations a= (4*π^2*R)/T^2 a∆t = v2 - v1 d = 1/2(v1 + v2)∆t d = v1∆t + 1/2a∆t² d = v2∆t - 1/2a∆t² v2² = v1² + 2ad (sinA)/a=(sinB)/b=(sinC)/c c^2=a^2 + b^2 - 2abcosC Fnet = ma 3. The attempt at a solution I have tried using the equations above in attempt to see if any can be used to solve this problem, but I am completely stuck. I do not know where to start and I am very confused as to how this problem can be solved. I have attached a picture to give a better understanding of the problem.
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https://leighbortins.com/2019/04/
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math
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Archives for April 2019
On today’s episode of The Leigh Bortins Show: Why Math is important in a post-industrial age. How is mathematics taught? Does math inspire artists? Is mathematics beautiful? Join us today as we ponder the relevance of mathematics as tool for forming thoughts.
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https://www.seoclerk.com/job/Traffic/56662/Traffic-required-for-10-links-from-English-countires-USA-Major
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math
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we have 10 links
we need per link 10k to 25k traffic
time 3 to 7 days you can take 1 link
But need all work together. Who is an expert can do this better.
you must get more orders if we had a deal and you complete as required work.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583835626.56/warc/CC-MAIN-20190122095409-20190122121409-00519.warc.gz
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http://webstreaming.com.br/differentiate-between-change-in-demand-and-change-in-quantity-demanded.html
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math
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A change in demand on the other hand, is causedby other variables such as a change in tastes, income orcompetition from related goods. Have you ever observed why the inessential things like diamonds, platinum, gold are very expensive, whereas necessities like food, clothes, water are inexpensive? The Law of Demand The law of demand states that, if all other factors remain equal, the higher the price of a good, the less people will demand that good. The amount of a good that buyers purchase at a higher price is less because as the price of a good goes up, so does the opportunity cost of buying that good. How severely is the change in the quantity demanded impacted by a change in the price? Thus you get two benefits : Added security as well as aproof. Conclusion Demand is inversely related to price, i.
So if the Price of complements goes up then the demand for the good goes down thus shifting the graph to the left. If, on the other hand, there is a change in any other factor except the price of the commodity under consideration the demand curve will shift to a new position. In such a case, it is incorrect to say increase or decrease in demand rather it is increase or decrease in the quantity demanded. On the other hand, quantity demanded is a particular point on the demand curve. The quantity demanded lies in the demand curve and can be determined by just assuming a point and calculating its intercepts, on the price and quantity planes respectively. These movements are sometimes described as extensions or contractions of demand. Only the combination of the willingness and the affordability will be considered as a demand.
Conversely, if a person talks about expansion or contraction of demand, he refers to the change in quantity demanded. As against this, a shift in the demand curve represents a change in the demand for the commodity. It refers to a particular point on the curve. On the contrary, a shift in demand curve occurs due to the changes in the determinants other than price i. For example, when technology advances, or the cost of production decreases, supply increases. A shift in the opposite direction would imply a decrease in demand. Relationship Between Decrease in Demand and Decrease in Quantity Demanded Understanding the difference between a change in demand and change in quantity demanded is a key concept in economics.
Quantity supplied increases in the above case as the equilibrium point shifts along the supply curve from point A to point B. Reasons Factors other than price Price Measurement of change Shift in demand curve Movement along demand curve Consequences of change in actual price No change in demand. A change in demand is the sum of all the changes in quantities demanded that consumers can buy at a specified price level. Also, when there is a change in the determinants of demand ie. Increse in quantity demanded:: Movement up the demand curve.
A change in Demand is affected by either a change in productivity or a change in the price of a certain product. Hence, more quantity of a good is demanded at low prices, while when the prices are high, the demand tends to decrease. A change in quantity demanded is represented as a movement along a demand curve. Change in income, change in number of consumers, taste and preferences, price of related goods, and future expectations all cause shifts in demand curve. Achange in quantity continues to move along the same demand curve,whereas a change in demand shifts it either to the left or right ofthe original line. However, the following day a report is published that finds pesticides used on bananas can cause lasting health problems. Recently, he has increased his sales of luxury products, and his manager considers promoting him to sales manager in the store.
However, if the average income of doctors goes up, the demand for tractors would not change. Summary Definition Define Change in Demand: A change in demand is an economic term that describes when the entire demand curve shifts upward or downward because the market changes the quantity it demanded. From the business point of view, demand can indicate the possible sales that take place. On a national level, if consumer income decreases, the demand for goods and services will decrease, thereby shifting the demand curve downwards. In economics, demand is defined as the quantity of a product or service, that a consumer is ready to buy at various prices, over a period. This means that even at the current price, that person is willing to buy more video games due to the increase in income.
The price elasticity of demand is a measure of the responsiveness of quantity demanded to a change in price. Change in the position of the curve. Quantity demanded is represented on the graph by moving up and down on the curve, rather than side-to side. A rightward shift in the demand curve shows an increase in the demand, whereas a leftward shift indicates a decrease in demand. A decrease in demand results from the presence of a factor that shifts the demand curve to the left such as a damaging study or introduction of a competing product. Going back to the video game example if the price of video games drops the quantity demanded for those video games is going to increase. The following graph illustrates an increase in supply and an increase in quantity demanded.
It is the actual amount of goods desired at a certain price. In economics, demand is defined as the quantity of a good or service consumers are willing and able to buy at a range of prices. The law of demand states that as the price of a good or service increases ceteris paribus , the quantity demanded will decrease and vice versa. Determinant Price Non-price Indicates Change in Quantity Demanded Change in Demand Result Demand Curve will move upward or downward. Therefore change in factors other than price. To understand the difference more clearly, we need to study the difference between demand and quantity demanded. Thus less is q 0 instead of q1 demanded at a fixed price po A change in quantity demanded for the commodity resulting from a change in its own price will lead to a movement along the curve itself this indicates either a contraction or an extension of demand.
When you look at these two statements together, it may appear confusing and contradictory. Quantity-demanded shifts can go either up or down based on the changes in the marketplace relating to prices and consumer demand. The payment will be made through an account of the payee. . If demand is elastic, there are alternatives readily available in the market. Therefore, demand and quantity demanded are two different things.
If price falls there is a downward movement to the right. Many variables can change the demand for a product. Whenever there is a shift in the demand curve, there is a shift in the equilibrium point also. Generally, when demand rises, supply increases and when demand falls, supply is decreased. A decrease in income would contract his spending, allowing for a limited quantity of goods. Substitutes- A good where in can be used in place of another. The figure given below represents the shift in demand curve due to various factors such as income, taste or preferences, the price of complementary or substitute goods etc.
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http://tetrast2.blogspot.com/2007/07/logical-quantity-problem-of-universals.html
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math
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Sketcher of various interrelated fourfolds.
July 17, 2007.Recentest (mildly) significant change: January 2, 2009 (third such change since August 6, 2007). This post is much less speculative in style than the others on this blog. But my other blog "feels" filled up, I can't quite say why. Still, maybe I'll eventually move this post to there.
We tend to consider the logical quantity of the term and not only that of the proposition, especially when a logical quantity such as the singular gets involved. Yet tradition has kept the spotlight on propositions (or sentences, etc.) because of the interest in valid argumentation involving them. That seems to be why logical quantity from the term's viewpoint has lain largely unexplored by philosophy. Philosophy hasn't stopped and smelt the roses long enough to see what vistas might spread thence. Given a term "H" predicated (truly or purportively truly) of something (call it "x"), the question of its logical quantity then depends on quantification over the rest of the universe of discourse: Is there something which isn't that thing x and of which the term "H" is also true? -- and -- Is there something which isn't that thing x and of which the term "H" is instead false? The twin questions stand mutually independent and resolve into four answers, conjoinable in four ways (notwithstanding issues of term purport which multiply relevant options). For the polyadic case, incorporate criteria requiring one-to-one correspondences as needed and slackening as needed to compensate for sequence variety. None of the four conjunctions enframes a blind or almost blind window as long as we class the singular and the singulars-in-a-polyad together in logical quantity, just as we class both the monadic general and the polyadic general as general. One such conjunction, the monadic-or-polyadic singular-cum-universal, is a logical quantity corresponding to a gamut, a total population and its parameters, a universe of discourse, etc. The eventual result of a systematic approach to logical quantity from the term's viewpoint is a surrounding scene of various categories of the 'essences' -- attributes/modifications, modes of attributability, and forms of mathematical correspondence -- whereto nonsingular terms are often allied, 'essences' categorially as different each from the others as they are from the scene-completing object -- this man, this horse, etc. -- of a typical concrete singular term.
The "problem of universals" is a philosophical perennial. Now, before one does a metatheory about, say, the theory of geology, one needs first to do theory of geology. And, before that, one needs to do physical geography. The "geography" of logical quantity (singular, general, universal, etc.) seems to have lain largely unexplored by philosophers. Aristotle and C.S. Peirce are exceptions.
On July 17, 2007, I searched on Google for the two phrases problem-of-universals logical-quantity. Only two results came up, both mine -- the first version of this post and a similar thing which I posted to peirce-l some weeks ago. I searched for problem-of-universals logical-quantification and found few results, half of them mine. (My own earlier post on the topic at The Tetrast doesn't come up, and of course the problem of universals isn't always called that by name, but it still seems fair to take the paucity of Google results as significant). The lack of an adequate systematic terminology is another sign of how little attention philosophers have given to the topic of logical quantity, despite their long interest in the problem of universals.
The problem of universals gets its standard name from the noun "universal" in the sense in which one finds it used in translations of Aristotle -- that which is true of more than one object, a sense for which the word "general" is now sometimes employed as a noun in philosophical discussion and is in any case usually so employed here.
Singular and general in standard 1st-order logic
Now, in the standard terminology of first-order logic, a "general term" is a term which does not purport as to logical quantity (or has only a "default" purport to the existential particular affirmative when the term is true of something). If the monadic general term were to purport, when true of an object at all, to denote more than one object, then a proposition claiming in effect that the term were uniquely true of some given object would be formally false. Instead such a proposition is merely contingent. In other words, a so-called general term in standard first-order logic is vague in logical quantity and is 'general' from a kind of second-order viewpoint -- one might call it "general" across various possible logical quantities. On the other hand, a "singular term" in standard first-order logic is a term (and indeed a subject term rather than a predicate term) which does purport as to logical quantity, and purports to singularity, so that a proposition which claims in effect that a monadic singular term corresponds to two different objects is formally false. I am speaking of constant a.k.a. definite terms such as "blue" and "Jack." Constancy versus variability is a similar yet distinct issue or dimension which complicates an elementary discussion.
Generality more generally
In speaking philosophically of generality, not adhering to the linguistic habits of standard first-order logic, we may mean neither vagueness in logical quantity nor a purportive (or still some other de jure) generality; instead we may mean a de facto generality, for instance that of a monadic term like "blue" which happens to be true of more than one object. In speaking of singularity we may likewise mean a de facto singularity. I'm not sure what there is for all this, except to get used to the distinction between purportive and other sorts of de jure, and de facto. It seems difficult to limit one's discussion to examples of just one kind or just the other. The distinction does not seem so hard and fast to intuition. "Blue" -- as term or as idea or as quality -- is the kind of thing which one would not expect to be true of just one single object.
In order to distinguish the sense of "general" as that which corresponds to more than one object (in the monadic case), I will speak of the coaliant general. (I could just call it the "coaliant" per se but I wish it remembered that I'm speaking of a kind of general. I coin it from co- + aliud + -ant.) The coaliant general corresponds, purportively, etc., or de facto, to something but not to that thing alone but also to something else. In the polyadic case, consider it to correspond to polyads whose intersections lack objects from each polyad. (As for re-orderings or re-sequencings of the same polyad, they are another issue which complicates an elementary discussion.)
A bustling floor under generality
Since one thinks in terms of greater and lesser generality, there arises an imagery of limits. Such imagery is itself limited in usefulness but inevitable in its way.
Now, the coaliant general (monadic or polyadic) encounters something like a limit, closure, or bound, at the "low" end, in the singular or singulars in a polyad. A polyadic version of a singular is not strictly to be called "singular" in that it is not monadic, and "plural" already has specialized meanings in logic. One might say only loosely that it is a polyadic singular. The word "singular" isn't quite right for a logical quantity definable by its opposition to the general -- the mind places "singular" opposite not only to "general" but also to "plural" and thus also to "polyadic." In order to unglue term adicity a.k.a. term valence from logical quantity and instead to treat all logical quantities on the same plane, I'll call any monadic-or-polyadic singular transingular. The coaliant general encounters an excluded or external limit, at the "low" end, in the transingular. A transingular term can be a subject but also can be a predicate or other things.
A bustling ceiling into generality
The coaliant general, if it has an upper limit in some sort of "most general," will include it in a way that it does not include the transingular, since the coaliant general is definable as the determinately non-transingular. What would non-arbitrary utmost generals be? They would be something like the Scholastic transcendentals (unity, truth, goodness) which are true of each and every thing automatically, in sheer virtue of the thing's existing at all -- the given thing is one thing, a true thing, and a good thing, at least in respect of its existence if not of its character. That seems to make of the utmost general a rather narrow window, while other logical quantities at the same level of analysis are rich and, in their way, panoramic. Is the world's symmetry really that deeply broken? A systematic understanding of logical quantity does not foster a view of the world as arranged mainly into genus-species type relations, strict inclusions, etc., with one or a few utmost generals monotonous at the top. Confronted with the Scholastic transcendentals one, true, good, one may ask, what about two things? Aren't any two things two in sheer virtue of their being things xy such that ~(x=y)? Now, if one views collections in such a way as to see othernesses and unities among selected parts as definitive attributes of the whole, then, since obviously not every such collection consists of exactly two things or of exactly one thing or of etc., in that sense such numberish predicates are not utmost generals. However, any object (in a large enough universe) will fairly belong among polyadized objects whereof "two" is true collectively. Keeping this in mind, we have a notion of universality reached by utmost generality, universality which can be extended to sequence schemata, etc., and which seems, as a "window," practical and cornucopious like the singular or transingular. If we "arbitrarily" declare a given predicate term universal, equivalent to a predicate like in "Tx" or in "Hxyz v ~Hxyz", it can be refined by formal schemata. (Via a richer formalism such as set theory or the like, mathematics can treat these universals as more or less general and even unique properties of various sets or the like, and mathematics can re-generate the world's wild variegation, while building imaginative, metamorphosic bridges of equivalences across the greatest disparities of outward appearance.) The point is that the 'accidents' or 'modifications' of the objects xyz in the above example don't matter. All that can matter is their othernesses and unities, relationships defined within the formalism (of first-order logic with equality a.k.a. ...with identity). On the other hand, with things like "blue," we're getting into modifications of objects. Such terms or ideas or qualities as "blue" and "Jack" befit (at least in a realistic universe where not everything is blue or Jack) that which I will call the special, or contraliant special to ensure clarity as to just what sense of the polysemic word "special" I mean. ("Contraliant" from contra- + aliud + -ant). The contraliant special term is (or purports to be) true of something (or things in a polyad) but decidedly not of everything.
Yet the universal can be either transingular (as in the case of a total population, its parameters, etc.) or (coaliant) general (or indeterminate about that alternative in the case of a term's de jure applicability). So the universal is better pictured as a ceiling into generality than as a ceiling in generality.
The universal supplies the upper limit of the coaliant general, and is a kind of extreme to which the coaliant general reaches, like a line segment which includes its endpoint adjoinment with something else (a universal may be general or instead transingular). In the other direction, generality's "line segment" includes everything till the transingular but not the transingular itself, like when a mathematician replaces an endpoint with a little bubble. A coaliant general is either universal or contraliant special (or indeterminate about that alternative in the case of a term's purport, its de jure applicability, or the like).
- The (coaliant) general has two limits -- an excluded limit, the transingular, and a partly included limit, the universal (a universal is not necessarily general).
- The (contraliant) special has two limits -- a partly included limit, the transingular (a transingular is not necessarily special), and an excluded limit, the universal.
- Should the general-cum-special be considered a fully included "limit" of both the (coaliant) general and the (contraliant) special? Here we seem to approach a limit to the usefulness of the imagery of limits.
A transingular may be universal too. If the transingular is a total population, a universe, a gamut, then it is also universal, at least in the relevant universe of discourse. When it is not the universe, the transingular is (contraliant) special. (In the case of term purport, the transingular may be indeterminate about that alternative.)
Universals & universes
Basically one ends up with two kinds of (coaliant) general and two kinds of universal. Now, in the universe of a plinker's distinct notes cdefgab, that gamut is the universe. It is both unique and universal. In its universe of discourse there's no polyad that contains notes uncontained in the gamut. "The gamut" is true of cdefgab and there's nothing else of which "the gamut" is true. In that sense it is not general. Yet it is universal, it is the universe and, in that sense, it is not (contraliant) special. A gamut, a universe of discourse, a total population is a transingular universal. Also universal is a monadic or polyadic term which does not exhaust the universe's population in a single predication yet which, like "one," is true of each object distributively or which, like "two," is such that every object is among some objects whereof the term is true collectively. Such a universal is also general, since there is more than one instantiation of it in its universe. One the other hand, "THE one" and "THE two," etc., are not general, insofar as they are true of the one object in a one-object universe, the two objects in a two-object universe, etc., respectively.
So we have two kinds of universal, one a transingular and the other a (coaliant) general. A universal which does not exhaust its universe in a single predication is (coaliant) general, not transingular, and is closer to the kind of thing which one usually has in mind with the word "universal," something like a rule, with more instances than the given one, indeed sometimes infinitely more, as with the "miraculous jar" of positive integers.
To be in the world
A transingular which does not exhaust its universe in a single predication is much closer (than the universal transingular) to the sort of thing which one usually has in mind with the word "singular," a singular or singulars-in-polyad among still more singulars in a larger world. Such a transingular is not its universe, it is not universal. It is (contraliant) special.
So a transingular may be universal or special. Likewise, a general may be universal or special. Just because a term is general, having more than one instantiation, doesn't mean that every object is covered one way or another in its instantiations. For instance, "blue" is, eclectically, true of some things and false of the others. So now we have four comparatively simple logical quantities -- universal, (coaliant) general, (contraliant) special, and transingular -- and four conjunctions nameless except for such improvised unwieldy names as "universal-cum-general," "universal-cum-transingular," "special-cum-general," and "special-cum-transingular."
To be systematic
Any pair of statements are TT, FF, FT, or TF. We define logical binary compounds in that way. Formal logic wouldn't even think of not systematizing the four mutually exclusive and collectively exhaustive cases -- the four conjunctions based on truth conditions. And we get "and," "neither-nor," "no, but," and "and not."
In the same inevitable way, any term true of something is, de facto: -- (1) universal & (coaliant) general -- or (2) universal & transingular -- or (3) (contraliant) special & (coaliant) general -- or (4) (contraliant) special & transingular. All that's being done is to answer two mutually independent logical-quantity questions, which bring us --
To the heart of it
In the monadic case, the two logical-quantity questions are:
"Given that there's a thing (call it 'x') which is H, is there a thing (call it 'y') which isn't that thing x and which also is H?" If yes, then "H" is (coaliant) general. If no, then "H" is transingular.
"Given that there's a thing (call it 'x') which is H, is there a thing (call it 'y') which isn't that thing x and which is not H?" If yes, then "H" is (contraliant) special. If no, then "H" is universal.
The mutual independence of the twin questions needs to be appreciated; they result in four possible conjunctions. The result is not simply two separate extremes of universal and singular with the somewhat-general somewhat-special as a third, in between. The habitual swerve of thinking of the singular only in monadic terms even while thinking of all three of its kindred logical quantities (special, general, and universal) in both monadic and polyadic terms, leads to thinking incorrectly of the universal singular as a trivial combination (if one notices it at all), a nearly blind window, confined to a one-object universe. In fact the window's vista is quite populous. A grand boat gets missed there, that of a logical quantity corresponding to a gamut, a total population and its parameters, etc., along with a whole class of research, research starting from given parameters of a total population, universe of discourse, etc., to draw deductive conclusions.
(There are even more than four options for term purport, de jure applicability, or the like, 16 including the formally false option, mostly since indeterminateness becomes an option in various alternatives. Such options for de jure applicability seem to become 2^16=65,536 if we admit options for objective indeterminateness and an option for objective inconsistency.)
Now, in a large enough universe, the general-cum-special will be mostly vague in range. In the monadic case it could be true of just two things or it could be true of all but one thing or it could be anywhere in between. It is so much like logic's "general term" as to be barely distinguishable except under certain near-the-limit conditions. For similar reasons, one might question at least the utility of some of the other combinations. One might say, instead of column A, why not column B?:
|General-cum-special||Logic's "general," logical-quantitatively indeterminate like the predicate term letters in logical schemata.|
|Transingular-cum-special||"Just plain" Transingular (be it universal or (contraliant) special).|
|General-cum-universal||"Just plain" Universal (be it transingular or (coaliant) general).|
|Transingular-cum-universal||Transingular-cum-universal (a universe, total population, gamut).|
Now, if we're defining kinds of terms by purportive logical quantity for the purpose of a formalism or grammar, then Column B seems the more convenient way to go. However, Column A is logically "nicer" and more consistent in its criteria; its four logical quantities are on a par with each other. In any case Column A girt by the simple logical quantities as shown in A.1 is the completed relevant picture (almost completed -- one could also devise terms for the diagonals). And if one is interested in logical quantities as characterizing typical mental perspectives distinguishing classes of research, Column A is the way to go, and even a pair of terms for A.1's diagonals would be useful. Now, I speak of the perspective as represented by the given subject matter, not the object(ive) or goal which, for instance in the special sciences, may include finding generals true of multitudes of singular objects and events.
|Perspective in typical |
|Class of research:||Typical inferential character |
|Transingular-cum-special.||The special sciences a.k.a. idioscopy. Human/social, biological, material, physical.||Surmise (ampliative-cum-precisive).|
|General-cum-special.||Sciences of positive phenomena in general, rather than of special classes.|
Philosophy, cybernetic theory*, statistics, and inverse-optimization theory.
|Strictly ampliative induction.**|
|Transingular-cum-universal.||Deductive math theories of logic, information***, probability, and optimization.||Strict (precisive) deduction.|
|General-cum-universal.||'Pure' mathematics. Ordering, calculation, enumeration/measure, graphing/topology.||"Reversible" deduction.****|
|Kinds of |
or in related posts.
don't formally imply
|Strictly ampliative |
don't formally imply
** That's notwithstanding the internal properties of the 'domain-independent' deductive formalisms with which these fields sometimes occupy themselves.
*** Deductive mathematical theory of information considerably overlaps into 'pure' math, abstract algebra in particular, because of the pure-mathematically deep treatment of laws of information, laws which also turned out to be equivalent to some principles of group theory.
**** In mathematical induction, the minimal case and the heredity, conjoined, are equivalent to the conclusion, given the well-orderedness of the relevant set. The proof of the minimal case or of the heredity is sometimes not reversibly deductive, especially when inequalities or greater-than or less-than statements get involved. More generally, pure maths are rife with inference through equivalences and equipollencies.
Update August 6, 2007: Am I analytic?
Thank you to Enigmania for including me in the 51st Philosophers' Carnival. In answer to his implied question: Well, I don't take the analytic linguistic turn, and I went through a Merleau-Ponty phase, but I like C.S. Peirce more and don't regard science as sinister to some great extent that would distinguish science from the humanities. Indeed, as "Enigman" says, my stuff "seems to be more analytic" than Continental, "but who can say?" and this is also partly because I'm an insufficiently disciplined amateur, not a professional philosopher. If wishes were horses, and so forth. To date, I've engaged in discussion mainly with Peirceans (at peirce-l), which has been good for me and, I hope, not bad for them. I've read some of the important early papers in analytic philosophy and some books by Quine, but I haven't engaged in discussions with analytic philosophers, so I've lacked the benefit of criticism from them. I don't know how to rectify that but, if I'm lucky, the Philosophers' Carnival will help.
• I regard philosophy's best bet to be to define itself (A) as having, as its subject matter, positive phenomena in general in their inferential issues, and (B) as properly tending to draw, as its conclusions, inductive generalizations to or toward totalities -- all in all, sort of like statistical theory, but tackling the inductive inverse of the problem of deductive theory of logic rather than of probability, and thus lacking the quantitative-measurement emphasis and having multiplicity of levels, reflexivity, and so on, pursuing problems of estimating, interpolating, extrapolating the logical structure of a universe rather than the parameters of a total population, and rising to consider general processes of experience, mind, heart, society, etc., and complex inference processes including all mathematical and scientific research, to say the least. (Note: The kinship between statistical theory and philosophy isn't very close -- they're still far apart like, say, matter science and human/social studies.)
• I certainly don't oppose deductive formalisms (not to mention deductive arguments) in philosophy, any more than a statistician opposes probability formalisms. Statistics' normal curve of distribution is a way of looking at Pascal's Triangle extended indefinitely. A piece of logical formalism transits the heart of the ideas in this post.
• Still, recognition of its underlying kinship with inductive, totality-targeting fields like statistical theory could help philosophy manage and temper its own aspirations to a "God's eye view" (pace Rorty, who, complaining of its aspirations, essentially gave up on philosophy), help philosophy reduce attendant hyperbole and disillusionment, and help it be more pragmatic about vagueness, discriminate in hyperbolic doubt, fallibilistic, etc., without tending to substitute some idea of utility (not to mention power) in place of the idea of truth be it ever so slippery. My 2¢ worth. End of August 6, 2007 update (Edited, January 2, 2009).
A few informal assertions about the problem of universals.
Areas of research can be ordered according to their appeals to principles of how we know things (ordo cognoscendi, the order of learning or familiarity) and, in pretty much reverse order, to principles (entities, laws, etc.) whereby we explain things (ordo essendi, the order of being). The order of being is often preferred in the special sciences (physics first, etc.), while the order of learning and of the verificatory bases on which we know things is sometimes preferred in maths (where such preference tends to put logic and order theory first). Maybe those researches which I call "sequenced in the order of being" you would call "sequenced in the order of abstractness." Still could well be the same ordering. I'm not saying that the ontological questions are unimportant, to the intellectual climate, the human spirit, and the ultimate bearings which people take in their decisions. But for my part I generally take their involvement in questions of math and science classification as an intrusion signifying that the classification is either deficient in firm and fertile constraints or just plain nebulous. And, if people argue over whether some sciences should be ordered by increasing concreteness or increasing abstractness, and if it's essentially the same ordering forwards versus backwards,
On various topics I prefer compatibility with a range of ontological viewpoints, but I do I have my own ontological views. Generally, when people deny the reality or ontological legitimacy of generals in any usual sense, I don't know what to think but that they regard Scholastic Realism as "secretly" believing that generalities like redness and threeness exist like lamps and chairs. As if we might expect to hear a news bulletin, "Blueness, as such, has been finally been found, orbiting a house in New Orleans." Now, if "blue" is not itself a real individual object like a blue thing, still the real individual object is really blue. So blue has really-ness. But that extrapolates to coming up with syntactically complicated words for variations of "real" and you know that sooner or later we'll find some general word for them all. I foreshorten the process and take that word to be the word "real" itself and will merrily consider in what senses and what universes Santa Claus, Planet Pluto, and Cthulhu are real. Sure, some things are "realer" than others. Indeed even with reality we can admit graduality, etc., if we don't try to live always in the armor of a flat first-order logical universe, as interesting a challenge as that can sometimes be, and as needful as it may be for those whose sense of reality is unfortunately shaky. Coarse is what it is, like that browser Safari which should instead be called Tour by Tank. Anyway, Peirce's definition of the real as that which is what it is, and indeed in some sense persists, independently of that which you or I or any finite community thinks of it and which would be discovered by research adequately prolonged, suffices for a definition of "real" which takes things like blue in and is a critically unfolded version of the common-sense interpretation of the word "real." Now, if somebody, Quine or Stuart Rankin or whoever wants to come along and define "real" as "singular object" or as "Scottish" or as whatever, they can do that, but only the Peircean kind of definition has earned the force and feeling of the everyday word "real" which everybody in the discussion prizes. I certainly don't know what would be a "naturalistic solution" to generals and mathematicals and I see no germane practical significance in the idea.
The transingular subject is a this, or a this, this, that, yon,, etc., and, as a more or less haecceitous rest point or useful stopper to analysis, is also a hook or polyad of hooks on which, to borrow Peirce's phrase, to hang the hat of a predicate, it is a point of general indetermination and freedom regarding how the predicate relates to components or sections or durations (and so forth) of the singular subject(s). For instance, it is left to the definition, context, etc., of the predicate "blue" whether "something blue" means something entirely blue or mostly blue, etc.; one is not automatically forced to quantify over parts or stuff of the described subject. Many a natural thing, through such characteristics as forcefulness, endurance, vigor, and firmness/integrity, lends itself to treatment as a singular. As Peirce argued persistently, some things impose themselves on us, whether we like it or not. The haecceitous thing may come crashing in through a hundred windows. And things could not be alike in their bare singularness -- they could not all be singulars -- but for generality. And the general would not be general but for ranging over more than one thing.
The singular seems just as mysterious as the general to me, and neither one of them makes sense without the other. I can't see anything in the limitation of the real to the singular but a kind of fetish arising from the fight against the unmoored generalities so involved with causing chaos and destruction to people and society.
To go on being systematic
Also, to be concerned with the singular and the general and not also with the universal and the special seems unsystematic, unthoroughgoing, and illogical to me. The possibilities of a term's being true or false of objects besides that of which the term is predicated in the given instance don't play such favorites.
There's plenty in all that to examine philosophically. As the transingular-cum-special term lends itself to use as a subject term, and as the general-cum-special term lends itself to use as a predicate term, so a transingular-cum-universal term lends itself to adaptation as a predicate-formative functor such as "with a probability of 75%," and a general-cum-universal term lends itself to adaptation as a subject-formative functor such as "double of". There is a parallelism which runs among logical quantity, grammatical form, and philosophical category such as substance, attribute/modification, mode of attributability (modalities and "indeed," "not," "if," "novelly," "probably," "feasibly," "optimally," etc.), and correspondences/variances (such as "another than," the combinatory "Inv," "double of," "product of," "antiderivative of," etc.) The parallelisms, as non-binding affinities, seem to help empower thought.
|Logical Quantity:||Grammatical Form:||Philosophical Category:|
|Transingular-cum-universal.||Predicate-formative functor.||Mode of attributability.|
|General-cum-universal.||Subject-formative functor.||Mathematical correspondence/variance.|
Whatever one thinks of the problem of universals, still for inquiry on the problem of universals to get off on the right foot, it's a good idea to develop more than a nodding, dozing acquaintance with logical quantity. For really what there is is not simply a problem of universals but instead, from the start, a systematic complex of issues of the (comparatively) simple logical quantities and their conjunctions.
Comments: Post a Comment
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593302.74/warc/CC-MAIN-20180722135607-20180722155607-00463.warc.gz
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CC-MAIN-2018-30
| 31,972 | 77 |
https://tutorme.com/tutors/658129/interview/
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math
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Tutor profile: Kristyn H.
Subject: Public Health
Professor Yu is interested in exploring the relationship between arsenic exposure in drinking water and hypertension. Yu conducts a case-control study involving 200 participants, 100 of whom have hypertension and 100 of whom do not. Of the participants with hypertension, 43 were exposed to arsenic through their drinking water, compared to 26 of the participants without hypertension. Calculate and interpret the correct measure of association for this study.
Since this is a case-control study, the measure of association that we are going to calculate is the Odds Ratio (OR). The formula for the Odds Ratio is (a/c) / (b/d), where "a" is the number of cases who were exposed, "c" is the number of cases who were not exposed, "b" is the number of controls who were exposed, and "d" is the number of controls who were not exposed. For this problem, a = 43, b = 26, c = 57, and d = 74. OR = (a/c) / (b/d) = (43/57) / (26/74) OR = 2.147 The OR can be interpreted as follows: Participants who have hypertension have 2.147 the odds of having been exposed to arsenic in their drinking water as participants without hypertension.
If (x/5) + 17 = 23, then solve for x.
Begin by subtracting 17 from both sides of the equation. This leaves us with (x/5) = 6. Then, to solve for x, multiply both sides of the equation by 5, which results in x = 30.
Subject: Basic Math
What is the sum of (1/4) + (3/8)?
(1/4) + (3/8) can also be thought of as (2/8) + (3/8). Then, the two numerators (2 and 3) add together, resulting in 5 over 8, or 5/8.
needs and Kristyn will reply soon.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588053.38/warc/CC-MAIN-20211027022823-20211027052823-00202.warc.gz
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CC-MAIN-2021-43
| 1,612 | 10 |
http://archive.org/stream/AnalyticalMechanics/TXT/00000234.txt
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math
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UNIPLANAR MOTION OF A RIGID BODY 221 where 7 is the common angular acceleration. Therefore the angular kinetic reaction varies directly as the product of the moment of inertia by the angular acceleration, angular kinetic reaction = kly, where k is the constant of proportionality. When all the magnitudes involved in the last equation are measured in the same system of units k becomes unity. Introducing this simplification in the last equation and putting it into vector notation we have angular kinetic reaction = — JY. (IV) The negative sign indicates the fact that the direction oi the angular kinetic reaction is opposed to that of the angular acceleration. 184. Torque Equation. — Combining equations (I) and (IV) and denoting the resultant torque by G we obtain (V) = ico. The last equation, which will be called the torque equation, states that the resultant torque about any axis equals the product of the moment of inertia by the angular acceleration and has the same direction as the angular acceleration. 185. The Two Definitions of Moment of Inertia* — In order to show that the constant, I, of equation (II) and the moment of inertia defined by equation (II) of page 152 are the same magnitude, consider the motion of the rigid body A, Fig. Ill, about a fixed axis through the point 0, perpendicular to the plane of the paper. Let dF be the resultant force acting upon an element of mass dm, that is, the vector sum of the forces due to external fields of force and the forces due to the connection of dm with the rest of the body. Then dF^dm^ at is the force equation for the element of mass.
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CC-MAIN-2017-13
| 1,614 | 1 |
http://facetimeforandroidd.com/margin-of/margin-of-error-equation-example.php
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math
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When working with and reporting results about data, always remember what the units are. Created by Sal Khan.ShareTweetEmailEstimating a population proportionConfidence interval exampleMargin of error 1Margin of error 2Next tutorialEstimating a population meanTagsConfidence intervalsConfidence interval exampleMargin of error 2Up NextMargin of error 2 Υπενθύμιση αργότερα Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value x Standard error of the statistic If you know the standard deviation of Refer to the above table for the appropriate z*-value. http://facetimeforandroidd.com/margin-of/margin-or-error-equation.php
Check out the grade-increasing book that's recommended reading at Oxford University! If we multiply this result by the FPCF, we get MOE with FPCF = sqrt[(2401-865)/(2401-1)]*(0.033321) = sqrt[1536/2400]*(0.033321) = (0.8)(0.033321) = 0.026657 So these survey results have a maximum margin of error On this site, we use z-scores when the population standard deviation is known and the sample size is large. The margin of error can be calculated in two ways, depending on whether you have parameters from a population or statistics from a sample: Margin of error = Critical value x
Required fields are marked *Comment Name * Email * Website Find an article Search Feel like "cheating" at Statistics? z*-Values for Selected (Percentage) Confidence Levels Percentage Confidence z*-Value 80 1.28 90 1.645 95 1.96 98 2.33 99 2.58 Note that these values are taken from the standard normal (Z-) distribution. In general, for small sample sizes (under 30) or when you don't know the population standard deviation, use a t-score.
The sample proportion is the number in the sample with the characteristic of interest, divided by n. Note: The larger the sample size, the more closely the t distribution looks like the normal distribution. Take the square root of the calculated value. Margin Of Error Formula Algebra 2 Of these three the 95% level is used most frequently.If we subtract the level of confidence from one, then we will obtain the value of alpha, written as α, needed for
Easy! How To Find Margin Of Error On Ti 84 T-Score vs. Emerson © 2010
In other words, if you have a sample percentage of 5%, you must use 0.05 in the formula, not 5. Sampling Error Calculator How to Find the Critical Value The critical value is a factor used to compute the margin of error. Multiply the sample proportion by Divide the result by n. If you perform 100 surveys with the same sample size drawn from the same poplulation, then 95% of the time you can expect the margin of error to fall within the
The number of Americans in the sample who said they approve of the president was found to be 520. This means that if you perform the same survey 100 more times, then 95% of the time the number of people who like chocolate more than vanilla should be between 44.9% Margin Of Error Excel The number of standard errors you have to add or subtract to get the MOE depends on how confident you want to be in your results (this is called your confidence Margin Of Error Calculator Without Population Size Get the best of About Education in your inbox.
Most surveys you come across are based on hundreds or even thousands of people, so meeting these two conditions is usually a piece of cake (unless the sample proportion is very Margin Of Error Definition How to Calculate a Z Score 4. You need to make sure that is at least 10.
For example, if your CV is 1.95 and your SE is 0.019, then: 1.95 * 0.019 = 0.03705 Sample question: 900 students were surveyed and had an average GPA of 2.7 Todd Grande 7.419 προβολές 7:12 How to calculate Confidence Intervals and Margin of Error - Διάρκεια: 6:44. Pets Relationships Society Sports Technology Travel How to Compute the Margin of Error Margin of Error Calculator Enter the sample size n. Margin Of Error Sample Size Discrete vs.
To express the critical value as a t statistic, follow these steps. For some margin of error formulas, you do not need to know the value of N. 95% Confidence Interval Margin of Error If you have a sample that is drawn from But if the original population is badly skewed, has multiple peaks, and/or has outliers, researchers like the sample size to be even larger. http://facetimeforandroidd.com/margin-of/margin-of-error-equation-stats.php Otherwise, calculate the standard error (see: What is the Standard Error?).
In each formula, the sample size is denoted by n, the proportion of people responding a certain way is p, and the size of the total population is N. Thank you,,for signing up! Next, we find the standard error of the mean, using the following equation: SEx = s / sqrt( n ) = 0.4 / sqrt( 900 ) = 0.4 / 30 = The choice of t statistic versus z-score does not make much practical difference when the sample size is very large.
Share Pin Tweet Submit Stumble Post Share By Courtney Taylor Statistics Expert By Courtney Taylor Many times political polls and other applications of statistics state their results with a margin of This chart can be expanded to other confidence percentages as well. Statistics and probability Confidence intervals (one sample)Estimating a population proportionConfidence interval exampleMargin of error 1Margin of error 2Next tutorialEstimating a population meanCurrent time:0:00Total duration:15:020 energy pointsStatistics and probability|Confidence intervals (one sample)|Estimating It is not uncommon to see that an opinion poll states that there is support for an issue or candidate at a certain percentage of respondents, plus and minus a certain
Expected Value 9. from a poll or survey). Rett McBride 7.293 προβολές 5:31 How to calculate margin of error and standard deviation - Διάρκεια: 6:42. Previously, we described how to compute the standard deviation and standard error.
Statistics Statistics Help and Tutorials Statistics Formulas Probability Help & Tutorials Practice Problems Lesson Plans Classroom Activities Applications of Statistics Books, Software & Resources Careers Notable Statisticians Mathematical Statistics About Education In other words, if you have a sample percentage of 5%, you must use 0.05 in the formula, not 5. What's the margin of error? (Assume you want a 95% level of confidence.) It's calculated this way: So to report these results, you say that based on the sample of 50 Learn more You're viewing YouTube in Greek.
Most surveys you come across are based on hundreds or even thousands of people, so meeting these two conditions is usually a piece of cake (unless the sample proportion is very Rumsey When you report the results of a statistical survey, you need to include the margin of error. Red River College Wise Guys 77.998 προβολές 8:46 Why are degrees of freedom (n-1) used in Variance and Standard Deviation - Διάρκεια: 7:05. A t*-value is one that comes from a t-distribution with n - 1 degrees of freedom.
However, when the total population for a survey is much smaller, or the sample size is more than 5% of the total population, you should multiply the margin of error by The presence of the square root in the formula means that quadrupling the sample size will only half the margin of error.A Few ExamplesTo make sense of the formula, let’s look Hence this chart can be expanded to other confidence percentages as well. If the confidence level is 95%, the z*-value is 1.96.
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https://agrifarmingtips.com/are-enrolling-in-agriculture-and-human-ecology-disjoint/
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math
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To Explain: that Agriculture and Human Ecology are enrolling independent. Therefore, they are not independent. To Explain: firstborn and enrolling in Human Ecology are disjoint. Therefore Human Ecology and being first born are not disjoint. To Explain: that firstborn and enrolling in Human Ecology are independent.
What is the probability that the person is a human ecology student?
The probability that a student is in Human Ecology is 0.1928. irst-born 0.5067. The probability that a student is a first born is 0.5067.
Are having health insurance and a retirement plan independent events?
c) Having health insurance and a retirement plan are not independent events. 68% of all workers have health insurance, while 87.5% of workers with retirement plans also have health insurance. If having health insurance and a retirement plan were independent events, these percentages would be the same.
Is the probability of a given b the same as the probability of B given a Explain?
Is the probability of “A given B” the same as the probability of “B given A?” Explain. Yes, because due to the General Multiplication Rule, it doesn’t matter which set is A and which set is B. You hvae to multiply the probability of A and the probability of B to find the outcome.
Are the events disjoint?
Events are considered disjoint if they never occur at the same time; these are also known as mutually exclusive events. Events are considered independent if they are unrelated.
How do you know if events are independent?
28. Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.
How is conditional probability written and what does it mean how do you find conditional probability?
Key Takeaways. Conditional probability refers to the chances that some outcome occurs given that another event has also occurred. It is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening.
How do you know if disjoint is PA or B?
The addition of probabilities for disjoint events is the third basic rule of probability: Rule 3: If two events A and B are disjoint, then the probability of either event is the sum of the probabilities of the two events: P(A or B) = P(A) + P(B).
What happens to the addition rule when two events considered are disjoint?
If two events are disjoint, then the probability of them both occurring at the same time is 0. If two events are mutually exclusive, then the probability of either occurring is the sum of the probabilities of each occurring.
When did the College of Agriculture and Human Ecology change its name?
In 2007, the College of Agriculture and Human Ecology was restructured to include Nursing and was renamed the College of Agricultural and Human Sciences. In 2013, Nursing left the College to become an independent unit; the College of Agriculture and Human Sciences returned to its roots as the College of Agriculture and Human Ecology.
When did the Department of Agriculture become part of the Department of Home Economics?
In 1938 , the Department of Agriculture and the Department of Home Economics became part of the Division of Professional and Technical Subjects. These two departments were reorganized in 1949-50 as the School of Agriculture and Home Economics, with a Division of Agriculture and a Division of Home Economics.
What is human ecology?
Human ecology programs often incorporate elements of social sciences, as well as design and technology in their curriculum. This multidisciplinary approach will help prepare you to become an effective professional in careers where you will be solving complex problems that help meet the changing needs of individuals, families, communities, …
What is an internship in human ecology?
Pursuing an internship (for our purposes also known as a practicum, field placement, or co-op work opportunity) in a career field related to your human ecology degree is the best way to gain relevant work experience while you’re still in school.
What are the skills required to become a human ecology graduate?
Human Ecology graduates are equipped with a unique and diverse skill set . Most graduates have at least a basic level of knowledge in areas as diverse as nutrition, interior design, graphic design, family sciences, communications, marketing and many other areas.
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CC-MAIN-2022-33
| 4,527 | 27 |
https://www.topperlearning.com/answer/describe-quadratic-equation/jniuzrvv
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math
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describe quadratic equation
Asked by | 23rd Apr, 2008, 07:19: PM
where a ≠ 0. (For a = 0, the equation becomes a linear equation.)
The letters a, b, and c are called coefficients: the quadratic coefficient a is the coefficient of x2, the linear coefficient b is the coefficient of x, and c is the constant coefficient, also called a constant term.
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant times the first power of a variable. Such an equation is equivalent to equating a first-degree polynomial to zero. These equations are called "linear" because they represent straight lines in Cartesian coordinates. A common form of a linear equation in the two variables x and y is
That is, if a=0 in above quadritic equation, then we get a linear equation.
Answered by | 23rd Apr, 2008, 09:10: PM
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662515501.4/warc/CC-MAIN-20220517031843-20220517061843-00758.warc.gz
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CC-MAIN-2022-21
| 1,034 | 14 |
https://www.teacherspayteachers.com/Product/Grade-3-Math-Sense-Games-Activities-Bundle-for-SPED-Subs-Intervention-1151580
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math
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These 14 versatile card sets will deepen students' understanding of key third grade math concepts. The card sets are quick-prep – just print 5 sheets of paper and cut the cards apart! These are FUN & EASY to use by kids with a partner or with a teacher, tutor, parent, or sibling. These activities help kids develop math sense as they match numbers, expressions, and models. This bundle also includes access to an online BOOM deck for Fractions on the Number Line.
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CC-MAIN-2021-10
| 3,608 | 53 |
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