1) The document contains exercises on the completeness property of real numbers from an introduction to real analysis course.
2) It includes problems, solutions, and proofs regarding the infimum and supremum of sets, bounded sets, and the completeness property.
3) Key results proven include if A and B are bounded subsets of the real numbers, then their union A ∪ B is bounded, and if S is a bounded set and S0 is a nonempty subset of S, then the infimum of S0 is greater than or equal to the infimum of S.
Salah satu materi perkuliahan prodi pendidikan matematika mata kuliah teori himpunan dan logika matematika - Kardinalitas, definisi kardinalitas, himpunan kuasa, operasi relasi dua himpunan, himpunan bagian
oleh neneng
Nurwaningsih
(06081281520066)
Nurwaningsih30@gmail.com
PROGRAM STUDI PENDIDIKAN MATEMATIKA
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS SRIWIJAYA
INDRALAYA
2017
semoga bermanfaat
Salah satu materi perkuliahan prodi pendidikan matematika mata kuliah teori himpunan dan logika matematika - Kardinalitas, definisi kardinalitas, himpunan kuasa, operasi relasi dua himpunan, himpunan bagian
oleh neneng
Nurwaningsih
(06081281520066)
Nurwaningsih30@gmail.com
PROGRAM STUDI PENDIDIKAN MATEMATIKA
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS SRIWIJAYA
INDRALAYA
2017
semoga bermanfaat
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
I am Falid B. I am a Mathematical Statistics Assignment Expert at excelhomeworkhelp.com. I hold a Master's in Statistics, from George Town, Malaysia. I have been helping students with their assignments for the past 6 years. I solved an assignment related to Mathematical Statistics.
Visit excelhomeworkhelp.com or email info@excelhomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with Mathematical Statistics Assignment.
The simplest and most common form of mathematical induction infers that a statement involving a natural number n (that is, an integer n ≥ 0 or 1) holds for all values of n. The proof consists of two steps:
The base case (or initial case): prove that the statement holds for 0, or 1.
The induction step (or inductive step, or step case): prove that for every n, if the statement holds for n, then it holds for n + 1. In other words, assume that the statement holds for some arbitrary natural number n, and prove that the statement holds for n + 1
Sentient Arithmetic and Godel's Incompleteness TheoremsKannan Nambiar
For me, there is only one logic that we rational human beings are able to accept and appreciate, and that is the mathematical logic of ZF theory. But in the last century we found that ZF theory is not in a position to provide all that we want, and went in search of a new mode of thinking and got one which we called meta mathematics. My question is: if we can put the unambiguous logic of ZF theory on paper, why can't we do the same with meta mathematics. This paper is my feeble attempt in that direction.
I am Falid B. I am a Mathematical Statistics Assignment Help Expert at statisticshomeworkhelper.com. I hold a Master's in Statistics, from George Town, Malaysia.I have been helping students with their assignment for the past 6 years. I solve assignments related to Mathematical Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.You can also call on +1 678 648 4277 for any assistance with Mathematical Statistics Assignment.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
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.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
The ASGCT Annual Meeting was packed with exciting progress in the field advan...
ANALISIS RIIL 1 2.3 ROBERT G BARTLE
1. INTRODUCTION TO REAL ANALYSIS 1
INDIVIDUAL TASK
EXERCISES 2.3
THE COMPLETENESS PROPERTY OF
By:
Muhammad Nur Chalim
4101414101
MATHEMATICS DEPARTMENT
MATHEMATICS AND NATURAL SCIENCES FACULTY
SEMARANG STATE UNIVERSITY
2016
2. EXERCISES 2.3
Problem
4. Let *
( )
+. Find and .
5. Let be a nonempty subset of that is bounded below.
Prove that * +
8. Let be nonempty. Show that if , then for every number the
number is not an upper bound of , but the number is an upper bound of .
(The converse is also true; see Exercise 2.4.3.)
9. Show that if and are bounded subsets of , then is a bounded set. Show that
( ) * +
10. Let S be bounded set in and let be nonempty subset of .
Show that
Solution
4. Let *
( )
+. Find inf and sup .
Solution:
Choose
( )
( )
,
( )
,
( )
,
( )
,
( )
and etc.
then we conclude that :
a. If we substitute by even number, then value of will be increased with the
minimum value of is as the lower bound.
3. b. If we substitute by odd number, then value of will be decreased with the
maximum value of is as the upper bound.
So, * +
Thus, inf and sup
5. Let be a nonempty subset of that is bounded below.
Prove that * +
Proof :
Given is bounded below, then based on Definition 2.3.2 (b) there exists .
Let * +
is bounded below then is bounded above and Supremum Property implies that there
exists is sup
Let ( ) .
We get
( ) ( ) (multiply both sides by )
( , then )
Based on the definition of infimum, we get
( )
( * +)
Thus, ( * +)
8. Given be nonempty,
It will be shown that number is not an upper bound of but the number is
an upper bound of for every number .
(a) Suppose that is an upper bound.
Based on 2.4.2 definition:
If is an upper bound of S, and let
Then we will obtain
4. ( ) ( ) ( ) ( Add by to both sides)
( ) ( A1 and A4)
( ) (A2)
(A3)
Since , it is not satisfy that equation. It is a contradiction.
We obtain .
Since , then is not an upper bound of S.
(i) Suppose that is not an upper bound.
Based on 2.4.2 definition:
If , is an upper bound of , and let
( ) ( ) ( ) ( Add by to both sides)
( ) ( A1 and A4)
( ) (A2)
(A3)
Since , it is not satisfy that equation. It is a contradiction.
We obtain .
Since , then is an upper bound of S.
9. Given if A and B are bounded subsets of , then is a bounded set
It will be shown that ( ) * +
For , then
( ) * +
( ) * +
5. So, we can conclude that is a bounded set.
Let and * +
and
is an upper bound of , because
if , then , and if , then .
We get .
If z is any upper bound of
then is an upper bound of and , so that
Hence . Therefore, ( ).
Thus, ( ) * +
10. Given be bounded set in and
It will be shown that
Let
To show that we divide this problem into 2 cases:
(i)
Because of , so that
and
From Definition 2.4.1 and 2.4.2 , we can conclude that , for S
is a nonempty subset of R, so we get
(ii)
Because of S0 S, so that
and
From Definition 2.4.1 and 2.4.2 , we can conclude that , for S is
a nonempty subset of R, so we get
Thus, from (i) and (ii), we can conclude that