text stringlengths 6 4.81k | source stringlengths 10 123 | tokens int64 5 60 |
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Here
ν
1
,
ν
2
{\displaystyle \nu _{1},\nu _{2}}
represents the combined eigenvalues
(
... | Wikipedia - Clebsch–Gordan coefficients for SU(3) | 44 |
If one can put an equation in a factored form E⋅F = 0, then the problem of solving the equation splits into two independent (and generally easier) problems E = 0 and F = 0. | Wikipedia - Factorization | 35 |
To solve this problem, we need to determine the value of x, which represents the number of students who said they liked apples. | MetaMathQA | 26 |
On average, he needs to sell 8 bracelets per day. | MetaMathQA | 13 |
In practice, the extent of the high-level frequency range is not as important as the smoothness of the midrange and treble frequency response. | Wikipedia - Compact Cassette tape types and formulations | 23 |
We are given that the total amount spent is $x, so we can write: $130 + $5y = $x.
Solving for y, we get: $5y = $x - $130. | MetaMathQA | 46 |
In some instances, a high-purity UV grade of fused quartz has been used to make several of the individual uncoated lens elements of special-purpose lenses including the Zeiss 105 mm f/4.3 UV Sonnar, a lens formerly made for the Hasselblad camera, and the Nikon UV-Nikkor 105 mm f/4.5 (presently sold as the Nikon PF10545... | Wikipedia - Fused quartz | 55 |
Artificial Intelligence in Education: AIEd for Personalised Learning Pathways | Semantic Scholar - Artificial Intelligence in Education: AIEd for Per... (2022, 227 cit.) | 9 |
Scientific computing (or computational science) is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems. | Wikipedia - Computer science | 28 |
We argue for the perspective that this transition period will be characterized by a law of diminishing returns in quantum error correction (QEC), where the ability of the architecture to maintain quality operations at scale determines the point of diminishing returns. | Semantic Scholar - Early Fault-Tolerant Quantum Computing... (2023, 34 cit.) | 41 |
So Sandy drinks 500/1000 = 0.5 liters of water every 2 hours. | MetaMathQA | 18 |
The idea of absolute zero was generalised in 1848 by Lord Kelvin. | Wikipedia - History of thermodynamics | 12 |
2\pi r = 80\pi$.
Dividing both sides by $\pi$, we get $r^2 + 2r = | MetaMathQA | 29 |
Wade has an average of 20 points per game, so in 5 games, he will score 20 * 5 = 100 points. | MetaMathQA | 26 |
Observations of the Sunyaev–Zel'dovich effect provide a nearly redshift-independent means of detecting galaxy clusters. Some synchrotron radiation facilities scatter laser light off the stored electron beam. This Compton backscattering produces high energy photons in the MeV to GeV range subsequently used for nuclear p... | Wikipedia - Compton scattering | 45 |
Biological systems are composed of numerous components of which proteins are of particularly high functional significance. Network models are useful abstractions for studying these components in context. Network representations display molecules as nodes and their interactions as edges. | Semantic Scholar - Applications of targeted proteomics in systems bio... (2015, 159 cit.) | 38 |
= \frac{6!}{4!2!} = \frac{6 \cdot 5 \cdot 4 \cdot 3}{4 \cdot 3 \cdot 2} = \frac{6 \cdot 5}{2} = 15$. | MetaMathQA | 55 |
In order to fully realize all of the European Genetics Foundation's aims, the Foundation has identified a permanent site for the ESGM at the Hermitage of Ronzano, a monastery situated in the hills of Bologna, at 3.5 km from the city center and 7 km from the airport. | Wikipedia - European Genetics Foundation | 48 |
Sizes of asteroids range from the large dwarf planet Ceres at ~1000 km diameter down to m-sized objects, below which they are called meteoroids or dust. The size distribution of asteroids smaller than ~100 km in size follows the steady state collisional fragmentation distribution of Dohnanyi. | Wikipedia - Dust astronomy | 46 |
Chromatin functions as a means of packaging very long DNA molecules into highly organized and densely compacted shapes, which prevents the strands from becoming tangled, reinforces the DNA during cell division, helps to prevent DNA damage, and plays an important role in regulating gene expression and DNA replication. | Wikipedia - Glossary of cellular and molecular biology (0–L) | 48 |
analysis). This equation may be solved for the mass flow rate to yield Poiseuille's law. Huntley's recognition of quantity of matter as an independent quantity dimension is evidently successful in the problems where it is applicable, but his definition of quantity of matter is open to interpretation, as it lacks specif... | Wikipedia - Dimensional analysis | 59 |
More than 16.9 million Americans (8.1 million males and 8.8 million females) with a history of cancer were alive on January 1, 2019; this number is projected to reach more than 22.1 million by January 1, 2030 based on the growth and aging of the | Semantic Scholar - Cancer treatment and survivorship statistics, 2019... (2019, 3572 cit.) | 45 |
For example, the usual form of the equation for dehydration of methanol to dimethylether is:
2 CH3OH → CH3OCH3 + H2O
Sometimes an extension is used, where some substances with their stoichiometric coefficients are moved above or below the arrow, preceded by a plus sign or nothing for a reactant, and by a minus sign ... | Wikipedia - Chemical equation | 58 |
An intramolecular [3+2] cycloaddition then spontaneously occurred to afford the target tigliane 66. The formal intramolecular [4+2] cycloaddition of 1,6-enynes of the type 67 mediated by gold catalysis is another example of a transition-metal-catalyzed cascade (Scheme 14). | Wikipedia - Cascade reaction | 37 |
AI literacy or artificial intelligence literacy, is the ability to understand, use, monitor, and critically reflect on AI applications. The term usually refers to teaching skills and knowledge to the general public, particularly those who are not adept in AI. | Wikipedia - AI literacy | 40 |
Bioenvironmental Engineers (BEEs) within the United States Air Force (USAF) blend the understanding of fundamental engineering principles with a broad preventive medicine mission to identify, evaluate and recommend controls for hazards that could harm USAF Airmen, employees, and their families. | Wikipedia - Bioenvironmental Engineering | 40 |
Chemical reactions usually involve the making or breaking of chemical bonds. Oxidation, reduction, dissociation, acid–base neutralization and molecular rearrangement are some examples of common chemical reactions. A chemical reaction can be symbolically depicted through a chemical equation. | Wikipedia - Chemistry | 37 |
serialization
Is the process of translating data structures or object state into a format that can be stored (for example, in a file or memory buffer) or transmitted (for example, across a network connection link) and reconstructed later (possibly in a different computer environment). | Wikipedia - Glossary of computer science | 44 |
Their relationship is given by:
{
j
1
... | Wikipedia - 6-j symbol | 54 |
Dividing both sides by 11.9, we get: x = 40. | MetaMathQA | 17 |
Dave bought 26 T-shirts in all. | MetaMathQA | 9 |
The reverse process, in which electrons are released in redox reactions and chemical energy is converted to electrical energy, is possible and used in batteries. | Wikipedia - Chemical reaction | 25 |
AutoDock Vina, a new program for molecular docking and virtual screening, is presented. | Semantic Scholar - AutoDock Vina: Improving the speed and accuracy of... (2009, 27473 cit.) | 13 |
Because a transit results in a decrease in the net luminosity from the two objects, the transit method can be used to detect extrasolar planets as they pass in front of their host stars. A transit by an object that appears roughly the same size or larger than the body it is transiting is called an occultation or eclips... | Wikipedia - Glossary of astronomy | 59 |
This review provides insights into the current clinical and pre-clinical nanotechnological applications for cancer drug therapy, diagnostics, imaging, and radiation therapy. | Semantic Scholar - Cancer nanotechnology: current status and perspect... (2021, 156 cit.) | 21 |
In quantum mechanics, wave functions that are unchanged by a parity transformation are described as even functions, while those that change sign under a parity transformation are odd functions.fn=A hydrocarbon compound, solid at room temperature. | Wikipedia - Glossary of engineering: M–Z | 35 |
long non-coding RNA (lncRNA)
A class of non-coding RNA consisting of all transcripts of more than 200 nucleotides in length that are not translated. This limit distinguishes lncRNA from the numerous smaller non-coding RNAs such as microRNA. See also long intervening non-coding RNA. lyonization
See X-inactivation. | Wikipedia - Glossary of cellular and molecular biology (0–L) | 46 |
To find the average number of people added each year, we divide the difference by the number of years: 17,000 / 5 = 3,400. | MetaMathQA | 31 |
We also discuss the latest progress in the use of AFM-IR as a super-resolution correlated scanned-probe infrared spectroscopy for the chemical characterization of polymer materials dealing with polymer composites, polymer blends, multilayers, and biopolymers. | Semantic Scholar - Recent Applications of Advanced Atomic Force Micro... (2020, 93 cit.) | 34 |
Samuel has 28 - 14 - 4 = 10 apples left. | MetaMathQA | 13 |
A tether connecting the robot to a power supply would remove the power supply from the robot entirely. This has the advantage of saving weight and space by moving all power generation and storage components elsewhere. However, this design does come with the drawback of constantly having a cable connected to the robot, ... | Wikipedia - Robotics | 59 |
Resilience and sustainability are fundamentally concerned with preserving societal health and well-being within the context of a broader framework of environmental change. There are significant differences in their emphasis and time scales, particularly in the context of urbanization. | Semantic Scholar - Urban Resilience for Urban Sustainability: Concept... (2022, 151 cit.) | 38 |
It is currently 2021, so Kelsey's older sister is 2021 - 1971 = 50 years old. | MetaMathQA | 20 |
Most natural (or biological) materials are complex composites whose mechanical properties are often outstanding, considering the weak constituents from which they are assembled. These complex structures, which have risen from hundreds of million years of evolution, are inspiring the design of novel materials with excep... | Wikipedia - Ceramic engineering | 53 |
In total, Grace earned $378 + $99 + $90 = $567 during September. | MetaMathQA | 20 |
Techniques for regional‐scale hydrological and ecohydrological modelling support ecological risk assessment and identification of priority flow management and river restoration actions. 5. | Semantic Scholar - Recent advances in environmental flows science and... (2018, 145 cit.) | 22 |
The value of the embodiment approach in the context of cognitive science is perhaps best explained by Andy Clark.: 345–351 He makes the claim that the brain alone should not be the single focus for the scientific study of cognition It is increasingly clear that, in a wide variety of cases, the individual brain should n... | Wikipedia - Embodied cognitive science | 60 |
Numerous luxAB bioreporters have been constructed within bacterial, yeast, insect, nematode, plant, and mammalian cell systems. | Wikipedia - Bioreporter | 16 |
Holly needs to take 2 insulin pills each day, so in a week, she takes 2 x 7 = 14 insulin pills. | MetaMathQA | 26 |
Absolute depth: distance along a path (along hole, vertical, etc.) between a reference point (rotary table, ground level, mean sea level, etc.) and a given point downhole (after Ref. 3, §13.2). True Along-Hole (TAH) depth: along-hole depth based on a calibrated and corrected measurement with an associated uncertainty | Wikipedia - Driller's depth | 48 |
Let's assume the amount Leila spent at the supermarket is x dollars. | MetaMathQA | 15 |
m 2 ⟨ J M | j 1 m 1 j 2 m 2 ⟩ ⟨ j 1 m 1 j 2 m 2 | J ′ M ′ ⟩ = ⟨ J M | J ′ M ′ ⟩ = δ J , J ′ δ M , M ′ . | Wikipedia - Clebsch–Gordan coefficients | 52 |
She now has 40kg of dog food, so she must have already had 40 - 25 = 15kg of dog food. | MetaMathQA | 25 |
Increasingly, modern data also reside on networks and other irregular domains whose structure is better captured by a graph. To process and learn from such data, graph filters account for the structure of the underlying data domain. | Semantic Scholar - Graph Filters for Signal Processing and Machine Le... (2022, 67 cit.) | 37 |
Neugebauer and Sachs had, in fact, noted the possibility of using reciprocal pairs in their original work, and rejected it for this reason. Robson, however, argues that known sources and computational methods of the Old Babylonian period can account for all values of x used. | Wikipedia - Plimpton 322 | 45 |
The railroad line south of West Palm Beach was constructed in phases by the Florida East Coast Railway and its predecessor systems. Founder and owner Henry Flagler began his railroad building in 1892. Under Florida's generous land-grant laws passed in 1893, 8,000 acres (3,200 ha) could be claimed from the state for eve... | Wikipedia - Clarence S. Coe | 57 |
Ahmed also has 8 orange trees, so he has a total of 4 + 8 = 12 trees in his orchard. | MetaMathQA | 25 |
bacterial chromosomes, mitochondrial and plastid DNA, as well as many other varieties of extrachromosomal DNA, including plasmids and some viral DNA. Contrast linear DNA. circulating tumor DNA (ctDNA)
Any extracellular DNA fragments derived from tumor cells which are circulating freely in the bloodstream. cis
On the sa... | Wikipedia - Glossary of cellular and molecular biology (0–L) | 57 |
The amount left on his gift card is $100 - $25 = $75. | MetaMathQA | 17 |
We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. | Semantic Scholar - Combined quantum mechanics/molecular mechanics (QM... (2013, 508 cit.) | 32 |
In the thermal neutron spectrum, more Iodine-129 is destroyed than newly created since Iodine-128 is short lived and the isotope ratio is in favor of 129I. | Wikipedia - Fission products (by element) | 26 |
= -2b$.
Expanding, we have $5b-10 = -2b$.
Adding $2b$ to both sides, we have $7b - 10 = 0$.
Adding 10 to both sides, we have $7b = 10$. | MetaMathQA | 56 |
It contains all available matrices for auxiliary sequence prediction as well as new ones for binding sites of the 9G8 and Tra2-β Serine-Arginine proteins and the hnRNP A1 ribonucleoprotein. | Semantic Scholar - Human Splicing Finder: an online bioinformatics to... (2009, 2435 cit.) | 29 |
The inequivalence of these two formulations shows up in the Zeeman effect and the Aharonov–Bohm effect. | Wikipedia - Canonical commutation relation | 16 |
Computer engineering deals with the design of computers and computer systems. This may involve the design of new hardware. Computer engineers may also work on a system's software. However, the design of complex software systems is often the domain of software engineering, which is usually considered a separate discipli... | Wikipedia - Electrical engineering | 49 |
The total distance Kevin ran is the sum of the distances he ran at each speed: 5 + 10 + x * 0.25. | MetaMathQA | 27 |
To solve this problem, we need to determine the value of x, which represents the number of passengers a single train car can carry. | MetaMathQA | 27 |
The Hundred Fowls Problem is a problem first discussed in the fifth century CE Chinese mathematics text Zhang Qiujian suanjing (The Mathematical Classic of Zhang Qiujian), a book of mathematical problems written by Zhang Qiujian. It is one of the best known examples of indeterminate problems in the early history of mat... | Wikipedia - Hundred Fowls Problem | 52 |
Hidden Markov models in computational biology. Applications to protein modeling. | Semantic Scholar - Hidden Markov models in computational biology. App... (1993, 2098 cit.) | 10 |
If the boundary of the convex set is a smooth submanifold, then the coefficients of the Steiner formula are defined by its curvature. | Wikipedia - Herbert Federer | 23 |
Again, the set of loop currents cannot be chosen arbitrarily. To guarantee a set of independent variables the loop currents must be those associated with a certain set of loops. This set of loops consists of those loops formed by replacing a single link of a given tree of the graph of the circuit to be analysed. | Wikipedia - Circuit topology (electrical) | 57 |
Subdwarf B (sdB) stars are in essence the cores of core-helium burning giants who have somehow lost most of their hydrogen envelopes, to the extent that there is no hydrogen-burning shell. They have multiple oscillation periods that range between about 1 and 10 minutes and amplitudes anywhere between 0.001 and 0.3 mag ... | Wikipedia - Asteroseismology | 55 |
n s − k i ≤ 1 {\displaystyle \sum _{i=1}^{n}s^{-k_{i}}\leq 1} where s {\displaystyle s} is the size of the alphabet S {\displaystyle S} . Without loss of generality, let's suppose we may order the
k
i
{\displaystyle k_{i}}
... | Wikipedia - Algorithmic probability | 50 |
The psychology of extinction has been studied for decades. Approximately 10 years ago, however, there began a concerted effort to understand the neural circuits of extinction of fear conditioning, in both animals and humans. | Semantic Scholar - Fear extinction as a model for translational neuro... (2012, 1247 cit.) | 34 |
was little contact between geologists and chemists. Geochemistry emerged as a separate discipline after major laboratories were established, starting with the United States Geological Survey (USGS) in 1884, which began systematic surveys of the chemistry of rocks and minerals. | Wikipedia - Geochemistry | 39 |
In the linear aerospike the spike consists of a tapered wedge-shaped plate, with exhaust exiting on either side at the "thick" end. This design has the advantage of being stackable, allowing several smaller engines to be placed in a row to make one larger engine while augmenting steering performance with the use of ind... | Wikipedia - Aerospike engine | 57 |
He bought an 11-ounce bottle but spilled 2 ounces, so he has 11 - 2 = 9 ounces of wax left. | MetaMathQA | 25 |
The laboratory was practically abandoned after HKU researchers completed their experiments, as no other experiments of a similar nature made further use of the facility. | Wikipedia - Aberdeen Tunnel Underground Laboratory | 25 |
DNA that is synthesized from a single-stranded RNA template (typically mRNA or miRNA) in a reaction catalyzed by the enzyme reverse transcriptase. cDNA is produced both naturally by retroviruses and artificially in certain laboratory techniques, particularly molecular cloning. | Wikipedia - Glossary of cellular and molecular biology (0–L) | 38 |
CACTTUS Education - since 2016 has a number of programs in systems and software engineering offering two year professional vocational Education in ICT
Professional training centers and academies (Cisco, Microsoft, ECDL, Oracle, RedHat etc.)
Universities abroad. | Wikipedia - Information and communications technology in Kosovo | 36 |
On the practical side, the implementation issues of modal regression including the computational algorithm and the tuning parameters selection are discussed. Numerical assessments on modal regression are also conducted to verify our findings empirically. | Semantic Scholar - A Statistical Learning Approach to Modal Regressio... (2017, 78 cit.) | 34 |
Minix 3 does the same, and provides a modern operating system with many newer tools and many Unix applications. Prof. Tanenbaum once said:
Please be aware that MINIX 3 is not your grandfather's MINIX ... MINIX 1 was written as an educational tool ... | Wikipedia - Minix 3 | 44 |
Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations. The arguments centre on the probabilistic nature of quantum mechanics, the difficulties with wavefunction collapse and the related measurement problem, and quantu... | Wikipedia - Quantum mechanics | 58 |
Finally, we outline the open research directions in this promising area. | Semantic Scholar - Blockchain for Internet of Things: A Survey... (2019, 879 cit.) | 11 |
A new graphical user interface to the MOSFLM program has been developed to simplify the processing of macromolecular diffraction data. The interface, iMOSFLM, allows data processing via a series of clearly defined tasks and provides visual feedback on the progress of each stage. | Semantic Scholar - iMOSFLM: a new graphical interface for diffraction... (2011, 2714 cit.) | 43 |
The simulation model must be sufficiently faithful to the original, so that it behaves in practically the same way as the original brain. Whole brain emulation is a type of brain simulation that is discussed in computational neuroscience and neuroinformatics, and for medical research purposes. It has been discussed in ... | Wikipedia - Artificial general intelligence | 59 |
Transcription factors can effectively turn "on" and "off" specific genes in order to make sure they are expressed at the right times and in the right places; for this reason, they are a fundamental and ubiquitous mechanism of gene regulation. transcription start site (TSS)
Also transcription initiation site. | Wikipedia - Glossary of cellular and molecular biology (M–Z) | 48 |
We have conducted two MEG experiments on three subjects: assessment of somatosensory evoked magnetic field (SEF) and auditory evoked magnetic field (AEF) using our OPM-based MEG system and a commercial MEG system based on superconducting quantum interference devices (SQUIDs). | Semantic Scholar - Non-Invasive Functional-Brain-Imaging with an OPM-... (2020, 124 cit.) | 39 |
Moving by six inex (a de la Hire cycle) preserves the latitude fairly well but the longitude change is very variable because of the variation of the solar anomaly. | Wikipedia - Eclipse cycle | 29 |
The numerical value of the acid dissociation constant, Ka, of the acid is known or assumed. The pH is calculated for given values of the concentrations of the acid, HA and of a salt, MA, of its conjugate base, A−; for example, the solution may contain acetic acid and sodium acetate. | Wikipedia - Glossary of engineering: A–L | 51 |
On a spring, the bearing area refers to the amount of area on the top or bottom surface of the spring in contact with the constraining part. The ways of machine tools, such as dovetail slides, box ways, prismatic ways, and other types of machine slides are also bearing surfaces. | Wikipedia - Bearing surface | 50 |
(-1) = 847. | MetaMathQA | 7 |
In 2015, the UK government opposed a ban on lethal autonomous weapons, stating that "international humanitarian law already provides sufficient regulation for this area", but that all weapons employed by UK armed forces would be "under human oversight and control". | Wikipedia - Artificial intelligence arms race | 40 |
Book Reviews: Foundations of Statistical Natural Language Processing | Semantic Scholar - Book Reviews: Foundations of Statistical Natural L... (1999, 5832 cit.) | 8 |
agroforestry - (sustainability) an ecologically based farming system, that, through the integration of trees in farms, increases social, environmental and economic benefits to land users. air pollution - the modification of the natural characteristics of the atmosphere by a chemical, particulate matter, or biological a... | Wikipedia - Glossary of environmental science | 45 |
Short GRBs may also result from the collision of neutron stars. gas giant
A giant planet composed mainly of hydrogen and helium gases rather than heavier elements, e.g. Jupiter and Saturn in the Solar System. geocenter
The geometric center of the Earth, i.e. | Wikipedia - Glossary of astronomy | 43 |
Exploring the Top Five Evolving Threats in Cybersecurity: An In-Depth Overview | Semantic Scholar - Exploring the Top Five Evolving Threats in Cyberse... (2023, 51 cit.) | 11 |
Leading AI-centric companies and start-ups include Baidu, Tencent, Alibaba, SenseTime, 4Paradigm and Yitu Technology. Chinese AI companies iFlytek, SenseTime, Cloudwalk and DJI have received attention for facial recognition, sound recognition and drone technologies. | Wikipedia - Artificial intelligence industry in China | 33 |
Earth's heating/cooling rate can then be analyzed over selected timeframes (Δt) as the net change in energy (ΔE) associated with these attributes:
Δ
E
/
Δ
... | Wikipedia - Earth's energy budget | 60 |
In the first year, Bobby's number of toy cars increases by 50% of 16, which is 16 * 0.50 = 8. | MetaMathQA | 28 |
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