It includes concepts of logarithms including properties and log tables. The methodology to find out values using log tables and anti log tables is also mentioned in a detailed manner. Moreover, questions related to logarithms are mentioned for practice.
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It includes concepts of logarithms including properties and log tables. The methodology to find out values using log tables and anti log tables is also mentioned in a detailed manner. Moreover, questions related to logarithms are mentioned for practice.
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
Benefits:-
# Students can catch up on notes they missed because of an absence.
# Underachievers can find peer developed notes that break down lecture and study material in a way that they can understand
# Students can earn better grades, save time and study effectively
Our Vision & Mission – Simplifying Students Life
Our Belief – “The great breakthrough in your life comes when you realize it, that you can learn anything you need to learn; to accomplish any goal that you have set for yourself. This means there are no limits on what you can be, have or do.”
Like Us - https://www.facebook.com/FellowBuddycom
Had to make this dumb powerpoint for my algebra II class and I put a lot of work into it for some reason... so yeah it's just been sitting on my laptop doing nothing and I thought why not upload this to help other people? So yeah, hope you guys find it useful...
Had to make this dumb powerpoint for my algebra II class and I put a lot of work into it for some reason... so yeah it's just been sitting on my laptop doing nothing and I thought why not upload this to help other people? So yeah, hope you guys find it useful...
This slide show give the details of how to find the domain of a logarithmic function, graph it using the MyLabsPlus graphing software, and then find the x and y intercepts of that logarithmic function.
Lots of students find logarithm complicated and tricky.For them this slide may prove useful.This is the most easy way to learn logarithm.Best of luck!! :)
Daffodil International University is a co-educational private university located in Dhanmondi, Dhaka, Bangladesh. It was established on 24 January 2002 under the Private University Act, 1992
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
This first lecture describes what EMT is. Its history of evolution. Main personalities how discovered theories relating to this theory. Applications of EMT . Scalars and vectors and there algebra. Coordinate systems. Field, Coulombs law and electric field intensity.volume charge distribution, electric flux density, gauss's law and divergence
Lecture 9: Dimensionality Reduction, Singular Value Decomposition (SVD), Principal Component Analysis (PCA). (ppt,pdf)
Appendices A, B from the book “Introduction to Data Mining” by Tan, Steinbach, Kumar.
Logs or Logarithm (Algebra): Theory & Assorted Problems on Logs
If you like the video and approve of it, then share with others and also subscribe to the YouTube channel “Sunil Kishanchandani”. Also check out other videos on different concepts in mathematics.
https://youtu.be/Xb7PpSjizz0
Avionics 738 Adaptive Filtering at Air University PAC Campus by Dr. Bilal A. Siddiqui in Spring 2018. This lecture covers background material for the course.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
The increased availability of biomedical data, particularly in the public domain, offers the opportunity to better understand human health and to develop effective therapeutics for a wide range of unmet medical needs. However, data scientists remain stymied by the fact that data remain hard to find and to productively reuse because data and their metadata i) are wholly inaccessible, ii) are in non-standard or incompatible representations, iii) do not conform to community standards, and iv) have unclear or highly restricted terms and conditions that preclude legitimate reuse. These limitations require a rethink on data can be made machine and AI-ready - the key motivation behind the FAIR Guiding Principles. Concurrently, while recent efforts have explored the use of deep learning to fuse disparate data into predictive models for a wide range of biomedical applications, these models often fail even when the correct answer is already known, and fail to explain individual predictions in terms that data scientists can appreciate. These limitations suggest that new methods to produce practical artificial intelligence are still needed.
In this talk, I will discuss our work in (1) building an integrative knowledge infrastructure to prepare FAIR and "AI-ready" data and services along with (2) neurosymbolic AI methods to improve the quality of predictions and to generate plausible explanations. Attention is given to standards, platforms, and methods to wrangle knowledge into simple, but effective semantic and latent representations, and to make these available into standards-compliant and discoverable interfaces that can be used in model building, validation, and explanation. Our work, and those of others in the field, creates a baseline for building trustworthy and easy to deploy AI models in biomedicine.
Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
2. Example:
the logarithm of 1000 to base 10 is 3,
because 10 to the power 3 is 1000:
1000 = 10 × 10 × 10 = 103
2
More generally, for any two real numbers b
and x where b is positive and b ≠ 1.
y = 𝒃 𝒙 x = 𝒍𝒐𝒈 𝒃(y)
𝟒 𝟑
= 64 3 = 𝒍𝒐𝒈 𝟒(64)
3. Logarithmic identities : 3
1. Product, quotient, power and root:
• The logarithm of a product is the sum of the logarithms of the
numbers being multiplied, the logarithm of the ratio of two numbers
is the difference of the logarithms.
• The logarithm of the p-th power of a number is p times the logarithm
of the number itself; the logarithm of a p-th root is the logarithm of
the number divided by p. The following table lists these identities with
examples.
• Each of the identities can be derived after substitution of the
logarithm definitions 𝒙 = 𝒃𝒍𝒐𝒈 𝒃(𝒙) or y = 𝒃𝒍𝒐𝒈 𝒃(𝒚) in the left hand sides
left hand sides.
5. 5Logarithmic identities :
2. Change of base
• The logarithm 𝒍𝒐𝒈 𝒃(x) can be computed from the logarithms of x
and b with respect to an arbitrary base k using the following formula:
𝑙𝑜𝑔 𝑏(x) =
𝑙𝑜𝑔 𝑘(𝑥)
𝑙𝑜𝑔 𝑘(𝑏)
• Typical scientific calculators calculate the logarithms to bases 10
and e. Logarithms with respect to any base b can be determined
using either of these two logarithms by the previous formula:
𝑙𝑜𝑔 𝑏(x) =
𝑙𝑜𝑔10(𝑥)
𝑙𝑜𝑔10(𝑏)
=
𝑙𝑜𝑔 𝑒(𝑥)
𝑙𝑜𝑔 𝑒(𝑏)
6. 6
• Given a number x and its logarithm 𝑙𝑜𝑔 𝑏(x) to an unknown base b,
the base is given by:
𝑏 = 𝑥
1
𝑙𝑜𝑔 𝑏(𝑥)
7. 7
HistoryLogarithm tables, slide rules, and historical applications
• By simplifying difficult calculations, logarithms contributed to the advance of
science, and especially of astronomy. They were critical to advances in
surveying, celestial navigation, and other domains. Pierre-Simon Laplace
called logarithms.
8. • These tables listed the values of 𝒍𝒐𝒈 𝒃(x) and 𝑏 𝑥
for any number x in a certain
range, at a certain precision, for a certain base b (usually b = 10).
8
• Subsequently, tables with increasing scope and precision were written.
• A key tool that enabled the practical use of logarithms before calculators
and computers was the table of logarithms. The first such table was
compiled by Henry Briggs in 1617, immediately after Napier's invention.
• For example, Briggs' first table contained the common logarithms of all
integers in the range 1–1000, with a precision of 8 digits.
• As the function f(x) = 𝑏^𝑥 is the inverse function of 𝑙𝑜𝑔 𝑏(x), it has been called
the antilogarithm.
9. 9
Applications A nautilus displaying
a logarithmic spiral
• Logarithms have many applications inside and outside mathematics. Some
of these occurrences are related to the notion of scale invariance. For
example, each chamber of the shell of a nautilus is an approximate copy of
the next one, scaled by a constant factor. This gives rise to a logarithmic
spiral.
10. 10Application
1. Logarithmic scale
• Scientific quantities are often expressed as logarithms of other
quantities, using a logarithmic scale. For example, the decibel is a unit
of measurement associated with logarithmic-scale quantities.
• It is based on the common logarithm of ratios—10 times the common logarithm
of a power ratio or 20 times the common logarithm of a voltage ratio.
• It is used to quantify the loss of voltage levels in transmitting electrical signals, to
describe power levels of sounds in acoustics, and the absorbance of light in the
fields of spectrometry and optics.
• The signal-to-noise ratio describing the amount of unwanted noise in relation to
a (meaningful) signal is also measured in decibels.
• In a similar vein the peak signal-to-noise ratio is commonly used to assess the
quality of sound and image compression methods using the logarithm.
11. Application
2. Fractals
11
• Logarithms occur in definitions of the dimension
of fractals are geometric objects that are self-
similar: small parts reproduce, at least roughly,
the entire global structure.
• The Sierpinski triangle (pictured) can be covered by three copies of itself,
each having sides half the original length. This makes the Hausdorff
dimension of this structure log(3)/log(2) ≈ 1.58.
• Another logarithm-based notion of dimension is obtained by counting the
number of boxes needed to cover the fractal in question.