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Fresnel Integrals

Среда, 16 Ноября 2011 г. 13:37 + в цитатник

Fresnel Integrals

There are a number of slightly different definitions of the Fresnel integrals. In physics, the Fresnel integrals denoted and are most often defined by

			(1)
			(2)

			(3)
			(4)

These Fresnel integrals are implemented in Mathematica as FresnelC[z] and FresnelS[z].

and are entire functions.

The and integrals are illustrated above in the complex plane.

They have the special values

			(5)
			(6)
			(7)

and

			(8)
			(9)
			(10)

An asymptotic expansion for gives

			(11)
			(12)

Therefore, as , and . The Fresnel integrals are sometimes alternatively defined as

			(13)
			(14)

Letting so , and

			(15)
			(16)

In this form, they have a particularly simple expansion in terms of spherical Bessel functions of the first kind. Using

			(17)
			(18)
			(19)

where is a spherical Bessel function of the second kind

			(20)
			(21)
			(22)
			(23)
			(24)

Related functions , , , and are defined by

			(25)
			(26)
			(27)
			(28)

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). "Fresnel Integrals." §7.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 300-302, 1972.

Leonard, I. E. "More on Fresnel Integrals." Amer. Math. Monthly 95, 431-433, 1988.

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Fresnel Integrals, Cosine and Sine Integrals." §6.79 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 248-252, 1992.

Prudnikov, A. P.; Marichev, O. I.; and Brychkov, Yu. A. "The Generalized Fresnel Integrals and ." §1.3 in Integrals and Series, Vol. 3: More Special Functions. Newark, NJ: Gordon and Breach, p. 24, 1990.

Spanier, J. and Oldham, K. B. "The Fresnel Integrals and ." Ch. 39 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 373-383, 1987.

CITE THIS AS:

Weisstein, Eric W. "Fresnel Integrals." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/FresnelIntegrals.html

Метки: Fresnel Integrals

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New York Statistics Tutor

Пятница, 11 Ноября 2011 г. 17:46 + в цитатник

New York Statistics Tutor.

PhD in Physics and Math.

Phone: 718-223-0228,

email: admin@TutorState.com

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Unsolved Problems in Physics

Четверг, 10 Ноября 2011 г. 18:47 + в цитатник

List of unsolved problems in physics

From Wikipedia, the free encyclopedia

This is a list of some of the major unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to test a proposed theory or investigate a phenomenon in greater detail.

Theoretical problems

The following problems are either fundamental theoretical problems, or theoretical ideas which lack experimental evidence and are in search of one, or both, as most of them are. Some of these problems are strongly interrelated. For example, extra dimensions or supersymmetry may solve the hierarchy problem. It is thought that a full theory of quantum gravity should be capable of answering most of these problems (other than the Island of stability problem).

Quantum gravity, cosmology, and general relativity

Vacuum catastrophe: Why does the predicted mass of the quantum vacuum have little effect on the expansion of the universe?
Quantum gravity: Can quantum mechanics and general relativity be realized as a fully consistent theory (perhaps as a quantum field theory)?^[1] Is spacetime fundamentally continuous or discrete? Would a consistent theory involve a force mediated by a hypothetical graviton, or be a product of a discrete structure of spacetime itself (as in loop quantum gravity)? Are there deviations from the predictions of general relativity at very small or very large scales or in other extreme circumstances that flow from a quantum gravity theory?
Black holes, black hole information paradox, and black hole radiation: Do black holes produce thermal radiation, as expected on theoretical grounds? Does this radiation contain information about their inner structure, as suggested by Gauge-gravity duality, or not, as implied by Hawking's original calculation? If not, and black holes can evaporate away, what happens to the information stored in them (quantum mechanics does not provide for the destruction of information)? Or does the radiation stop at some point leaving black hole remnants? Is there another way to probe their internal structure somehow, if such a structure even exists?
Extra dimensions: Does nature have more than four spacetime dimensions? If so, what is their size? Are dimensions a fundamental property of the universe or an emergent result of other physical laws? Can we experimentally "see" evidence of higher spatial dimensions?
Cosmic inflation: Is the theory of cosmic inflation correct, and if so, what are the details of this epoch? What is the hypothetical inflaton field giving rise to inflation? If inflation happened at one point, is it self-sustaining through inflation of quantum-mechanical fluctuations, and thus ongoing in some impossibly distant place?
Multiverse: Are there physical reasons to expect other universes that are fundamentally non-observable? For instance: Are there quantum mechanical "alternative histories" or "many worlds"? Are there "other" universes with physical laws resulting from alternate ways of breaking the apparent symmetries of physical forces at high energies, possibly incredibly far away due to cosmic inflation? Is the use of the anthropic principle to resolve global cosmological dilemmas justified?
The cosmic censorship hypothesis and the chronology protection conjecture: Can singularities not hidden behind an event horizon, known as "naked singularities", arise from realistic initial conditions, or is it possible to prove some version of the "cosmic censorship hypothesis" of Roger Penrose which proposes that this is impossible?^[2] Similarly, will the closed timelike curves which arise in some solutions to the equations of general relativity (and which imply the possibility of backwards time travel) be ruled out by a theory of quantum gravity which unites general relativity with quantum mechanics, as suggested by the "chronology protection conjecture" of Stephen Hawking?
Arrow of time: What do the phenomena that differ going forward and backwards in time tell us about the nature of time? How does time differ from space? Why are CP violations observed in certain weak force decays, but not elsewhere? Are CP violations somehow a product of the Second Law of Thermodynamics, or are they a separate arrow of time? Are there exceptions to the principle of causality? Is there a single possible past? Is the present moment physically distinct from the past and future or is it merely an emergent property of consciousness? Why do people appear to agree on what the present moment is? (See also Entropy (arrow of time) below)
Locality: Are there non-local phenomena in quantum physics? If they exist, are non-local phenomena limited to the entanglement revealed in the violations of the Bell Inequalities, or can information and conserved quantities also move in a non-local way? Under what circumstances are non-local phenomena observed? What does the existence or absence of non-local phenomena imply about the fundamental structure of spacetime? How does this relate to quantum entanglement? How does this elucidate the proper interpretation of the fundamental nature of quantum physics?
Future of the universe: Is the universe heading towards a Big Freeze, a Big Rip, a Big Crunch or a Big Bounce? Is our universe part of an infinitely recurring cyclic model?

High energy physics/Particle physics

Nuclear physics

Quantum chromodynamics: What are the phases of strongly interacting matter, and what roles do they play in the cosmos? What is the internal landscape of the nucleons? What does QCD predict for the properties of strongly interacting matter? What governs the transition of quarks and gluons into pions and nucleons? What is the role of gluons and gluon self-interactions in nucleons and nuclei? What determines the key features of QCD, and what is their relation to the nature of gravity and spacetime?
Nuclei and Nuclear astrophysics: What is the nature of the nuclear force that binds protons and neutrons into stable nuclei and rare isotopes? What is the origin of simple patterns in complex nuclei? What is the nature of neutron stars and dense nuclear matter? What is the origin of the elements in the cosmos? What are the nuclear reactions that drive stars and stellar explosions?
Island of stability: What is the heaviest possible stable or metastable nucleus?

Empirical phenomena lacking clear scientific explanation

Cosmology

Existence of the Universe: What is the origin of matter, energy, spacetime and the fundamental forces that form the universe / multiverse?
Baryon asymmetry: Why is there far more matter than antimatter in the observable universe?
Cosmological constant problem: Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?

Estimated distribution of dark matter and dark energy in the universe

Dark matter: What is dark matter?^[5] Is it related to supersymmetry? Do the phenomena attributed to dark matter point not to some form of matter but actually to an extension of gravity?

The log-log plot of dark energy density ρ _* and material density ρ_m Vs scale factor a . The two straight lines intersect at current epoch.^[6]

Dark energy: What is the cause of the observed accelerated expansion (deSitter phase) of the Universe? Why is the energy density of the dark energy component of the same magnitude as the density of matter at present when the two evolve quite differently over time; could it be simply that we are observing at exactly the right time? Is dark energy a pure cosmological constant, or are models of quintessence such as phantom energy applicable?
Dark flow: What is the cause of a large swath of galaxy clusters all moving towards one part of the universe?^[7]
Entropy (arrow of time): Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics?^[4]
Horizon problem: Why is the distant universe so homogeneous, when the Big Bang theory seems to predict measurable anisotropies of the night sky larger than those observed? Cosmological inflation is generally accepted as the solution, but there are also other possible explanations such as the variable speed of light hypothesis.
Ecliptic alignment of CMB anisotropy: Some large features of the microwave sky, at distances of over 13 billion light years, appear to be aligned with both the motion and orientation of the Solar System. Is this due to systematic errors in processing, contamination of results by local effects, or an unexplained violation of the Copernican principle?
Shape of the Universe: What is the 3-manifold of comoving space, i.e. of a comoving spatial section of the Universe, informally called the "shape" of the Universe? Neither the curvature nor the topology is presently known, though the curvature is known to be "close" to zero on observable scales. The cosmic inflation hypothesis suggests that the shape of the Universe may be unmeasurable, but since 2003, Jean-Pierre Luminet et al. and other groups have suggested that the shape of the Universe may be the Poincaré dodecahedral space. Is the shape unmeasurable, the Poincaré space, or another 3-manifold?

High energy physics/Particle physics

Electroweak symmetry breaking: What is the mechanism responsible for breaking the electroweak gauge symmetry, giving mass to the W and Z bosons? Is it the simple Higgs mechanism of the Standard Model,^[4] or does nature make use of strong dynamics in breaking electroweak symmetry, as proposed by Technicolor?
Neutrino mass: What is the mechanism responsible for generating neutrino masses? Is the neutrino its own antiparticle? Or could it be an antiparticle that simply cannot join and annihilate with a normal particle because of its irregular state?
OPERA neutrino anomaly: The Oscillation Project with Emulsion-tRacking Apparatus (OPERA) is an experiment to test the phenomenon of neutrino oscillations. In September 2011, CERN and OPERA announced that time of flight measurements made by their collaboration had indicated muon neutrinos traveling at faster than lightspeed. What is the explanation for this anomaly?
Inertial mass/gravitational mass ratio of elementary particles: According to the equivalence principle of general relativity, the ratio of inertial mass to gravitational mass of all elementary particles is unity. However, there is no experimental confirmation for many particles. In particular, we do not know what the weight of a macroscopic lump of antimatter of known mass would be.
Proton spin crisis: As initially measured by the European Muon Collaboration, the three main ("valence") quarks of the proton account for about 12% of its total spin. Can the gluons that bind the quarks together, as well as the "sea" of quark pairs that are continually being created and annihilated, properly account for the rest of it?
Quantum chromodynamics (QCD) in the non-perturbative regime: The equations of QCD remain unsolved at energy scales relevant for describing atomic nuclei, and, among others, mainly numerical approaches seem to begin to give answers at this limit. How does QCD give rise to the physics of nuclei and nuclear constituents?
Confinement: Why has there never been measured a free quark or gluon, but only objects that are built out of them, like mesons and baryons? How does this phenomenon emerge from QCD?^{[citation needed]}
Strong CP problem and axions: Why is the strong nuclear interaction invariant to parity and charge conjugation? Is Peccei-Quinn theory the solution to this problem?
Hypothetical particles: Which of the hypothetical particles predicted by supersymmetric theories and other fairly well known theories actually occur in nature?

Astronomy and astrophysics

Relativistic jet. The environment around the AGN where the relativistic plasma is collimated into jets which escape along the pole of the supermassive black hole

Accretion disc jets: Why do the accretion discs surrounding certain astronomical objects, such as the nuclei of active galaxies, emit relativistic jets along their polar axes? Why are there quasi-periodic oscillations in many accretion discs? Why does the period of these oscillations scale as the inverse of the mass of the central object? Why are there sometimes overtones, and why do these appear at different frequency ratios in different objects?
Coronal heating problem: Why is the Sun's Corona (atmosphere layer) so much hotter than the Sun's surface? Why is the magnetic reconnection effect many orders of magnitude faster than predicted by standard models?
Gamma ray bursts: How do these short-duration high-intensity bursts originate?^[4]
Supermassive black holes: What is the origin of the M-sigma relation between supermassive black hole mass and galaxy velocity dispersion?^[8]
Observational anomalies

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Can the discrepancy between the curves be attributed to dark matter?

Hipparcos anomaly: What is the actual distance to the Pleiades?^{[citation needed]}; Pioneer anomaly^[5]: What causes the small additional sunward acceleration of the Pioneer spacecraft?^[4]^[5]; Flyby anomaly: Why is the observed energy of satellites flying by earth different by a minute amount from the value predicted by theory?; Galaxy rotation problem: Is dark matter responsible for differences in observed and theoretical speed of stars revolving around the center of galaxies, or is it something else?
Supernovae: What is the exact mechanism by which an implosion of a dying star becomes an explosion?
Ultra-high-energy cosmic ray^[5]: Why is it that some cosmic rays appear to possess energies that are impossibly high (the so called OMG particle), given that there are no sufficiently energetic cosmic ray sources near the Earth? Why is it that (apparently) some cosmic rays emitted by distant sources have energies above the Greisen-Zatsepin-Kuzmin limit?^[4]^[5]
Rotation rate of Saturn: Why does the magnetosphere of Saturn exhibit a (slowly changing) periodicity close to that at which the planet's clouds rotate? What is the true rotation rate of Saturn's deep interior? ^[9]

Condensed matter physics

Amorphous solids: What is the nature of the glass transition between a fluid or regular solid and a glassy phase? What are the physical processes giving rise to the general properties of glasses?^[10]^[11]
Cold fusion: What is the explanation for the controversial reports of excess heat, radiation and transmutations?^[5]^[12]^[13]
Cryogenic electron emission: Why does the electron emission in the absence of light increase as the temperature of a photomultiplier is decreased?^[14]^[15]
High-temperature superconductors: What is the mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 50 kelvins?^[4]
Sonoluminescence: What causes the emission of short bursts of light from imploding bubbles in a liquid when excited by sound?^[16]
Turbulence: Is it possible to make a theoretical model to describe the statistics of a turbulent flow (in particular, its internal structures)?^[4] Also, under what conditions do smooth solutions to the Navier-Stokes equations exist?

Biological physics

These fields of research normally belong to biology, and traditionally were not included in physics but are included here because increasingly it is physicists who are researching them using methods and tools more popular in physics research than biology.^[17]^[18]

Synaptic plasticity: It is necessary for computational and physical models of the brain, but what causes it, and what role does it play in higher-order processing outside the hippocampus and visual cortex?
Axon guidance: How do axons branching out from neurons find their targets? This process is crucial to nervous system development, allowing the building up of the brain.
Stochasticity and robustness to noise in gene expression: How do genes govern our body, withstanding different external pressures and internal stochasticity? Certain models exist for genetic processes, but we are far from understanding the whole picture, in particular in development where gene expression must be tightly regulated.
Quantitative study of the immune system: What are the quantitative properties of immune responses? What are the basic building blocks of immune system networks? What roles are played by stochasticity?
Consciousness: What mechanism causes sentience within arrangements of otherwise non-sentient particles (as with the human brain, for example)? Is this mechanism reproducible?

Problems solved in recent decades

Long-duration gamma ray bursts (2003): Long-duration bursts are associated with the deaths of massive stars in a specific kind of supernova-like event commonly referred to as a collapsar. However, there are also long-duration GRBs that show evidence against an associated supernova, such as the Swift event GRB 060614.
Solar neutrino problem (2002): Solved by a new understanding of neutrino physics, requiring a modification of the Standard Model of particle physics—specifically, neutrino oscillation.
Age Crisis (1990s): The estimated age of the universe was around 3 to 8 billion years younger than estimates of the ages of the oldest stars in our galaxy. Better estimates for the distances to the stars, and the recognition of the accelerating expansion of the universe, reconciled the age estimates.
Quasars (1980s): The nature of quasars was not understood for decades.^[19] They are now accepted as a type of active galaxy where the enormous energy output results from matter falling into a massive black hole in the center of the galaxy.^[20]

References

^ Alan Sokal (July 22, 1996), "Don't Pull the String Yet on Superstring Theory", New York Times, http://query.nytimes.com/gst/fullpage.html?res=9D0DE7DB1639F931A15754C0A960958260
^ Joshi, Pankaj S. (January 2009), "Do Naked Singularities Break the Rules of Physics?", Scientific American, http://www.sciam.com/article.cfm?id=naked-singularities
^ Dirac, Paul, "Quantised Singularities in the Electromagnetic Field". Proceedings of the Royal Society A 133, 60 (1931).
^ ^a ^b ^c ^d ^e ^f ^g ^h Baez, John C. (March 2006). "Open Questions in Physics". Usenet Physics FAQ. University of California, Riverside: Department of Mathematics. http://math.ucr.edu/home/baez/physics/General/open_questions.html. Retrieved March 7, 2011.
^ ^a ^b ^c

Метки: unsolved problems in physics physics

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Science Regents Examinations: Physical Setting/Earth Science

Суббота, 05 Ноября 2011 г. 21:02 + в цитатник

Science Regents Examinations: Physical Setting/Earth Science

August 2011
- Examination (1.3 MB)
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June 2011
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- Important Notice
  - Notice to Teachers: Spanish Edition, Only - Question 24 (9 KB)
  - Notice to Teachers: Chinese Edition, Only - Questions 56-59
    - PDF version (60 KB)
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January 2011
- Examination (646 KB)
- Answer Booklet (66 KB)
- Scoring Key and Rating Guide (104 KB)
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August 2010
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June 2010
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January 2010
- Physical Setting/Earth Science Examination (523 KB)
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August 2009
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June 2009
- Physical Setting/Earth Science Examination (517 KB)
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- Important Notice: Spanish edition, only (76 KB)
January 2009
- Physical Setting/Earth Science Examination (789 KB)
- Scoring Key (172 KB)
- Answer Booklet (109KB)
- Conversion Chart (182 KB)
August 2008
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June 2008
- Physical Setting/Earth Science Examination (695 KB)
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January 2008
- Physical Setting/Earth Science Examination (704 KB)
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- Answer Booklet (226 KB)
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August 2007
- Physical Setting/Earth Science Examination (1.23 MB)
- Scoring Key (396 KB)
- Answer Booklet (53 KB)
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June 2007
- Physical Setting/Earth Science Examination (1.11 MB)
- Scoring Key (110 KB)
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January 2007
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- Answer Booklet (92 KB)
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August 2006
- Physical Setting/Earth Science Examination (1.00 MB)
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June 2006
- Physical Setting/Earth Science Examination (1.53 MB)
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Метки: Science Regents Examinations Physical Setting/Earth Science Physical Setting Earth Science Science Regents Examinations Science Regents Examinations

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NYC Regents Test Preparation and Tutoring

Суббота, 05 Ноября 2011 г. 18:59 + в цитатник

NYC Regents Test Preparation and Tutoring

Phone: 718-223-0228, Email: admin@TutorState.com

NYC Regents Test Preparation and Tutoring

Tutoring Service in Math, Physics, Computer Science, Statistics

I will assist your child in the review of academic material, test taking strategies and time management. One-on-One assistance is available at my location on the Bay Ridge, Brooklyn or in your home.

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I serve students from PreK-12th grade, as well as college students. In addition to Test Preparation, tutoring is available in all core subjects – Math, Calculus, Science, Physics, Statistics, Computers, Chemistry, and Special Needs.

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Самый мощный в мире суперкомпьютер преодолел барьер в 10 петафлопс

Четверг, 03 Ноября 2011 г. 21:16 + в цитатник

Computer performance
Name	FLOPS
yottaFLOPS	10²⁴
zettaFLOPS	10²¹
exaFLOPS	10¹⁸
petaFLOPS	10¹⁵
teraFLOPS	10¹²
gigaFLOPS	10⁹
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What is Limit?

Понедельник, 31 Октября 2011 г. 09:44 + в цитатник

Suppose f(x) is a real-valued function and c is a real number. The expression

$\lim_{x \to c}f(x) = L$

means that f(x) can be made to be as close to L as desired by making x sufficiently close to c. In that case, it can be stated that "the limit of f of x, as x approaches c, is L". Note that this statement can be true even if f(c) ≠ L. Indeed, the function f(x) need not even be defined at c. 1320039543_lim (320x240, 15Kb)

Метки: real-valued function real number lim limit

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100 Ways to Pass the Earth Science Regents with Test Tips

Понедельник, 31 Октября 2011 г. 09:04 + в цитатник

The true shape of the Earth is an Oblate Spheroid.

The best model of the Earth at any reasonable scale is a perfect circle.

The altitude of Polaris equals your latitude.

Latitude lines are drawn east-west and measure angular distance north and south.

Longitude lines are drawn north-south, and measure angular distances east and west.

*** Practice these terms while playing some games! Click here to play games and study these terms ***

Longitude is based on observations of the sun.

NOT TO SCALE

The earth rotates from west to east (24 hours).

WEST

EAST

The earth revolves counterclockwise (365.26 days) when viewed from above the North Pole.

click here to restart the animation below

NOT TO SCALE

The sun appears to rise in the east and set in the west.

NOT TO SCALE

The moon has phases because the angle between the earth and moon changes because the moon revolves around us (remember though that half is always lit).

click here to restart the animation below

NOT TO SCALE

We can only see half of the moon at a time and half of the moon is always lit.
The red line shows the half of the moon that we can see in relation to each of its phases.

<1-10> <11-20> <21-30> <31-40> <41-50> <51-60> <61-70> <71-80> < 81-90> <91-100>

Note: To access the practice regent’s questions, your browser must support pop-ups. Teachers: To link to this section of the site simply cut and paste the URL into a link onto your page (http://www.reviewearthscience.com/100ways). Printable black and white copy of just the key terms without the illustrations.

© 2005-2011 Review Earth Science ™| All material published to this site is copyrighted to their respective owner(s).
All materials are to be loaded only from this site and cannot be uploaded and displayed on any other site, including not for profit and/or educational sites.

Метки: Earth Science Earth Science Regents Test Tips

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100 Ways to Pass the Earth Science Regents with Test Tips

Понедельник, 31 Октября 2011 г. 01:55 + в цитатник

If pressure and temperature are constant, density of any substance, regardless of size is the same.

As pressure increases on a solid or gas, density increases.

As temperature of matter increases, its density decreases (in an open system).

Water expands when it freezes.

These are molecules of water; a.k.a., H2O (gray is hydrogen & red is oxygen). The first picture shows a typical structure of liquid water and the second is an ice structure (note the extra open space in the ice). This open space is caused by the expansion of water molecules as it freezes. This lowers the ice’s density, which causes it to float in water.

Many changes are cyclic (an event which repeats itself).

The tidal fluctuations show cyclic changes over the time.

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Water is most dense at 4°C, when it is a liquid.

The closer the isolines are the steeper the slope or gradient.

When calculating percent deviation, the accepted value is the correct answer while the measured value is subject to error.

Dynamic equilibrium means balance.

Earth absorbs short waves (visible light) and radiates long waves (infrared energy).

<1-10> <11-20> <21-30> <31-40> <41-50> <51-60> <61-70> <71-80> < 81-90> <91-100>

Метки: Earth Science Earth Science Regents Regents

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Algebra Tutor in Bay Ridge — Brooklyn

Понедельник, 31 Октября 2011 г. 00:44 + в цитатник

Algebra Tutor in Bay Ridge

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Algebra Tutor in Bay Ridge — Brooklyn

Понедельник, 31 Октября 2011 г. 00:41 + в цитатник

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Без заголовка

Среда, 26 Октября 2011 г. 04:59 + в цитатник

Решение математических задач нестандартными методами.
Задачи для 5 - 8 класса.

С алгеброй и без нее.

Задача 1. Вышел из срока

Чтобы сдать в срок книгу в библиотеку ученик должен был читать ежедневно по 40 страниц.
Однако он читал каждый день на 15 страниц меньше и вернул книгу на 6 дней позже срока.

За сколько дней ученик должен был прочитать книгу?

http://www.math-on-line.com/olympiada-edu/logica-zadacha-algebra-1.html

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"актуальная физика"

Суббота, 16 Июля 2011 г. 17:17 + в цитатник

Так, думаю можно начать дописывать главы учебников физики, сконцентрировавшись на состоянии физики, как науки, сегодня. В связи с этим можно ввести термин, ну например, "актуальная физика", так как естественно напрашивающийся термин "современная физика" просто занят определенными разделами физики. Так чем же занимаются ученые, которые себя называют физиками, если они не работают в направлении разделов физики, называемых "современной физикой"? Скорее всего они изучают явления, которые возникают на стыке, пересечении классических разделов физики. А что это за явления и какие это есть "классические разделы физики"? Тут можно составить таблицу, где по вертикали и горизонтали будут расписаны разделы физики, а в клетках на пересечении - "перекрёстные" явления. Но разделов у физики много..., по-видимому нужно взять просто параграфы школьного учебника физики.

Метки: учебник физики состоянии физики науки актуальная физика

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Links

Суббота, 16 Июля 2011 г. 09:21 + в цитатник

Метки: links

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Храм Василия Блаженного

Четверг, 14 Июля 2011 г. 17:41 + в цитатник

ПУЩАЕВ Юрий

ПОКРОВСКИЙ СОБОР (+ видео)
Чего мы не знаем о «Храме Василия Блаженного»?

Это собор Василия Блаженного? Неправда. Это был главный храм Москвы? Неправда. Иван Грозный ослепил создателей храма? Неправда. Здесь в советское время был только музей? Неправда. А что же правда?

Метки: храм василия блаженного

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Прорыв: датчики, которые могут преобразовывать мысли в речь

Четверг, 14 Июля 2011 г. 17:06 + в цитатник

Это кажется фантастикой, но появилось сообщение, что ученые научились считывать мысли и преобразовывать их в речь. Так ли это, или сообщение не совсем верно еще предстоит выяснить, но в сообщении есть ссылка на конкретного профессора (Bradley Greger) и университет ( Utah University ), где работает эта исследовательская группа

Метки: датчики мысли речь считывать мысли

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Так как же школьникам обьяснить деление на ноль?

Пятница, 01 Июля 2011 г. 02:36 + в цитатник

На школьном этапе обучения все надо как-то объяснить детям, исходя из их естественного опыта. Нельзя (!!!) вводить, например, сложение из аксиом, а надо показывать, что если было два яблока, а затем добавили еще три, то теперь, если пересчитать яблоки, их окажется пять. Так как же школьникам обьяснить деление на ноль? Может так?: Если вы делите на маленкое (положительное) число, которое много меньше единицы, то в результате получается большое число. (1:0.01=100) Если делитель ещё уменьшить, результат ещё станет больше. (1:0.00001=100000) А при делении на самое маленькое число результат получается больше всех чисел, но такого числа, которое больше всех чисел, нет, поэтому мы и говорим, что делить на ноль нельзя. - Как вы думаете, понятно и полезно ли будет детям такое объяснение?

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Сможете выполнить следующие действия?

Четверг, 30 Июня 2011 г. 22:14 + в цитатник

(2²⁰¹¹-2²⁰¹⁰)/2²⁰¹⁰

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Сможете найти, чему равно следующее выражение?

Четверг, 30 Июня 2011 г. 22:06 + в цитатник

(√3−√2) (√3+√2)=?

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Воскресенье, 19 Сентября 2010 г. 18:52 + в цитатник

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