Numerical methods ppt
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The bisection method is a root-finding algorithm that can be used to find real roots of polynomials. It works by repeatedly bisecting an interval defined by two values with opposite signs of a continuous function, and selecting the subinterval where the function changes sign, narrowing in on the root. Other methods like Descartes' Rule of Signs, Sturm's theorem, and Budan's theorem can help determine if a polynomial has real roots within an interval to make bisection more efficient. The example demonstrates using bisection to find a root of the polynomial f(x)=x^3 - x - 2, converging on the solution of 1.521 after 15 iterations of bisecting intervals.
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Context. The observation of several L-band emission sources in the S cluster has led to a rich discussion of their nature. However, a definitive answer to the classification of the dusty objects requires an explanation for the detection of compact Doppler-shifted Brγ emission. The ionized hydrogen in combination with the observation of mid-infrared L-band continuum emission suggests that most of these sources are embedded in a dusty envelope. These embedded sources are part of the S-cluster, and their relationship to the S-stars is still under debate. To date, the question of the origin of these two populations has been vague, although all explanations favor migration processes for the individual cluster members. Aims. This work revisits the S-cluster and its dusty members orbiting the supermassive black hole SgrA* on bound Keplerian orbits from a kinematic perspective. The aim is to explore the Keplerian parameters for patterns that might imply a nonrandom distribution of the sample. Additionally, various analytical aspects are considered to address the nature of the dusty sources. Methods. Based on the photometric analysis, we estimated the individual H−K and K−L colors for the source sample and compared the results to known cluster members. The classification revealed a noticeable contrast between the S-stars and the dusty sources. To fit the flux-density distribution, we utilized the radiative transfer code HYPERION and implemented a young stellar object Class I model. We obtained the position angle from the Keplerian fit results; additionally, we analyzed the distribution of the inclinations and the longitudes of the ascending node. Results. The colors of the dusty sources suggest a stellar nature consistent with the spectral energy distribution in the near and midinfrared domains. Furthermore, the evaporation timescales of dusty and gaseous clumps in the vicinity of SgrA* are much shorter ( 2yr) than the epochs covered by the observations (≈15yr). In addition to the strong evidence for the stellar classification of the D-sources, we also find a clear disk-like pattern following the arrangements of S-stars proposed in the literature. Furthermore, we find a global intrinsic inclination for all dusty sources of 60 ± 20◦, implying a common formation process. Conclusions. The pattern of the dusty sources manifested in the distribution of the position angles, inclinations, and longitudes of the ascending node strongly suggests two different scenarios: the main-sequence stars and the dusty stellar S-cluster sources share a common formation history or migrated with a similar formation channel in the vicinity of SgrA*. Alternatively, the gravitational influence of SgrA* in combination with a massive perturber, such as a putative intermediate mass black hole in the IRS 13 cluster, forces the dusty objects and S-stars to follow a particular orbital arrangement. Key words. stars: black holes– stars: formation– Galaxy: center– galaxies: star formation
BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptx
Ahota Beel, nestled in Sootea Biswanath Assam , is celebrated for its extraordinary diversity of bird species. This wetland sanctuary supports a myriad of avian residents and migrants alike. Visitors can admire the elegant flights of migratory species such as the Northern Pintail and Eurasian Wigeon, alongside resident birds including the Asian Openbill and Pheasant-tailed Jacana. With its tranquil scenery and varied habitats, Ahota Beel offers a perfect haven for birdwatchers to appreciate and study the vibrant birdlife that thrives in this natural refuge.
Post translation modification by Suyash Garg
overview of PTM helps to the students who wants to clear their basics about it.
Mapping the Growth of Supermassive Black Holes as a Function of Galaxy Stella...
The growth of supermassive black holes is strongly linked to their galaxies. It has been shown that the population
mean black hole accretion rate (BHAR) primarily correlates with the galaxy stellar mass (Må) and redshift for the
general galaxy population. This work aims to provide the best measurements of BHAR as a function of Må and
redshift over ranges of 109.5 < Må < 1012 Me and z < 4. We compile an unprecedentedly large sample with 8000
active galactic nuclei (AGNs) and 1.3 million normal galaxies from nine high-quality survey fields following a
wedding cake design. We further develop a semiparametric Bayesian method that can reasonably estimate BHAR
and the corresponding uncertainties, even for sparsely populated regions in the parameter space. BHAR is
constrained by X-ray surveys sampling the AGN accretion power and UV-to-infrared multiwavelength surveys
sampling the galaxy population. Our results can independently predict the X-ray luminosity function (XLF) from
the galaxy stellar mass function (SMF), and the prediction is consistent with the observed XLF. We also try adding
external constraints from the observed SMF and XLF. We further measure BHAR for star-forming and quiescent
galaxies and show that star-forming BHAR is generally larger than or at least comparable to the quiescent BHAR.
Unified Astronomy Thesaurus concepts: Supermassive black holes (1663); X-ray active galactic nuclei (2035);
Galaxies (573)
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Quality assurance B.pharm 6th semester BP606T UNIT 5
Warehousing
Good warehousing practices
Material management
Methods of grain storage Structures in India.pdf
•Post-harvestlossesaccountforabout10%oftotalfoodgrainsduetounscientificstorage,insects,rodents,micro-organismsetc.,
•Totalfoodgrainproductioninindiais311milliontonnesandstorageis145mt.InIndia,annualstoragelosseshavebeenestimated14mtworthofRs.7,000croreinwhichinsectsaloneaccountfornearlyRs.1,300crores.
•InIndiaoutofthetotalproduction,about30%ismarketablesurplus
•Remaining70%isretainedandstoredbyfarmersforconsumption,seed,feed.Hence,growerneedstoragefacilitytoholdaportionofproducetosellwhenthemarketingpriceisfavourable
•TradersandCo-operativesatmarketcentresneedstoragestructurestoholdgrainswhenthetransportfacilityisinadequate
The Limited Role of the Streaming Instability during Moon and Exomoon Formation
It is generally accepted that the Moon accreted from the disk formed by an impact between the proto-Earth and
impactor, but its details are highly debated. Some models suggest that a Mars-sized impactor formed a silicate
melt-rich (vapor-poor) disk around Earth, whereas other models suggest that a highly energetic impact produced a
silicate vapor-rich disk. Such a vapor-rich disk, however, may not be suitable for the Moon formation, because
moonlets, building blocks of the Moon, of 100 m–100 km in radius may experience strong gas drag and fall onto
Earth on a short timescale, failing to grow further. This problem may be avoided if large moonlets (?100 km)
form very quickly by streaming instability, which is a process to concentrate particles enough to cause gravitational
collapse and rapid formation of planetesimals or moonlets. Here, we investigate the effect of the streaming
instability in the Moon-forming disk for the first time and find that this instability can quickly form ∼100 km-sized
moonlets. However, these moonlets are not large enough to avoid strong drag, and they still fall onto Earth quickly.
This suggests that the vapor-rich disks may not form the large Moon, and therefore the models that produce vaporpoor disks are supported. This result is applicable to general impact-induced moon-forming disks, supporting the
previous suggestion that small planets (<1.6 R⊕) are good candidates to host large moons because their impactinduced disks would likely be vapor-poor. We find a limited role of streaming instability in satellite formation in an
impact-induced disk, whereas it plays a key role during planet formation.
Unified Astronomy Thesaurus concepts: Earth-moon system (436)
Compositions of iron-meteorite parent bodies constrainthe structure of the pr...
Magmatic iron-meteorite parent bodies are the earliest planetesimals in the Solar System,and they preserve information about conditions and planet-forming processes in thesolar nebula. In this study, we include comprehensive elemental compositions andfractional-crystallization modeling for iron meteorites from the cores of five differenti-ated asteroids from the inner Solar System. Together with previous results of metalliccores from the outer Solar System, we conclude that asteroidal cores from the outerSolar System have smaller sizes, elevated siderophile-element abundances, and simplercrystallization processes than those from the inner Solar System. These differences arerelated to the formation locations of the parent asteroids because the solar protoplane-tary disk varied in redox conditions, elemental distributions, and dynamics at differentheliocentric distances. Using highly siderophile-element data from iron meteorites, wereconstruct the distribution of calcium-aluminum-rich inclusions (CAIs) across theprotoplanetary disk within the first million years of Solar-System history. CAIs, the firstsolids to condense in the Solar System, formed close to the Sun. They were, however,concentrated within the outer disk and depleted within the inner disk. Future modelsof the structure and evolution of the protoplanetary disk should account for this dis-tribution pattern of CAIs.
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seed production, Nursery & Gardening.pdf
This presentation offers a general idea of the structure of seed, seed production, management of seeds and its allied technologies. It also offers the concept of gene erosion and the practices used to control it. Nursery and gardening have been widely explored along with their importance in the related domain.
Hariyalikart Case Study of helping farmers in Bihar
Helping farmers all across India through our latest technologies of modern farming like drones for irrigation and best pest control For more visit : https://www.hariyalikart.com/case-study
TOPIC OF DISCUSSION: CENTRIFUGATION SLIDESHARE.pptx
Centrifugation is a powerful technique used in laboratories to separate components of a heterogeneous mixture based on their density. This process utilizes centrifugal force to rapidly spin samples, causing denser particles to migrate outward more quickly than lighter ones. As a result, distinct layers form within the sample tube, allowing for easy isolation and purification of target substances.
Recently uploaded (20)
Candidate young stellar objects in the S-cluster: Kinematic analysis of a sub...
Candidate young stellar objects in the S-cluster: Kinematic analysis of a sub...
BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptx
BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptx
Mapping the Growth of Supermassive Black Holes as a Function of Galaxy Stella...
Mapping the Growth of Supermassive Black Holes as a Function of Galaxy Stella...
Noida Call Girls Number 9999965857 Vip Call Girls Lady Of Your Dream Ready To...
Noida Call Girls Number 9999965857 Vip Call Girls Lady Of Your Dream Ready To...
Quality assurance B.pharm 6th semester BP606T UNIT 5
Quality assurance B.pharm 6th semester BP606T UNIT 5
acanthocytes_causes_etiology_clinical sognificance-future.pptx
acanthocytes_causes_etiology_clinical sognificance-future.pptx
The Limited Role of the Streaming Instability during Moon and Exomoon Formation
The Limited Role of the Streaming Instability during Moon and Exomoon Formation
Compositions of iron-meteorite parent bodies constrainthe structure of the pr...
Compositions of iron-meteorite parent bodies constrainthe structure of the pr...
Hariyalikart Case Study of helping farmers in Bihar
Hariyalikart Case Study of helping farmers in Bihar
TOPIC OF DISCUSSION: CENTRIFUGATION SLIDESHARE.pptx
TOPIC OF DISCUSSION: CENTRIFUGATION SLIDESHARE.pptx
Numerical methods ppt
- 3. DEFINITION The bisection method is a root finding method that applies to any continuous functions for which one knows two values with opposite signs. The method consist of repeatedly bisecting the interval defined by these values and then selecting the subinterval in the function changes sign and therefore must contain the root.
- 4. POLYNOMIALS For polynomials more elaborated method exists for testing the existence of a root in an interval. Descarte’s Rule of Signs Sturm’s theorem Budan’s theorem They allow existing bisection method into efficient algorithms for finding all real roots of a polynomial.
- 5. Example Suppose that the bisection method is used to find a root of the polynomial 𝑓 𝑥 = 𝑥3 − 𝑥 − 2 Put x=1,2,… 𝑓 1 = 13 − 1 − 2 = −2 𝑓 2 = 23 − 2 − 2 = 4 Both had –ve points So the midpoint is 𝑐 = 2=1 2 = 1.5 𝑓 1 = 1.53 − 1.5 − 2 = −0.125
- 6. ITERATION 𝒂 𝒏 𝒃 𝒏 𝒄 𝒏 𝒇(𝒄 𝒏) 1 1 2 1.5 -0.125 2 1.5 2 1.75 1.609 3 1.5 1.75 1.625 1.666 4 1.5 1.625 1.5625 0.252 5 1.5 1.5625 1.5312500 0.059 6 1.5 1.5312500 1.5156250 -0.034 7 1.5156250 1.5312500 1.5234375 0.0122 8 1.5156250 1.5234375 1.5195313 -0.0109 9 1.5195313 1.5214844 1.5205078 0.0006 10 1.5195313 1.5214844 1.5209961 -0.0051 11 1.5205078 1.5214844 1.5212402 -0.0022 12 1.5209961 1.5214844 1.5212402 -0.0008 13 1.5212402 1.5214844 1.5213623 -0.0001 14 1.5213623 1.5214844 1.5214233 0.0002 15 1.5213623 1.5214233 1.5213928 0.00078
- 7. RESULT 1.521 is a Real root of the equation 𝑓 𝑥 = 𝑥3 − 𝑥 − 2
- 8. THANK YOU